38.Fundamentals of Soil Behaviour 3nd Edition (James K.mitchell&Kenichi Soga

Fundamentals ofSoil Behavior

Third Edition

James K. MitchellKenichi Soga

JOHN WILEY & SONS, INC.

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Copyright © 2005 John Wiley & Sons Retrieved from: www.knovel.com

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Library of Congress Cataloging-in-Publication Data:Mitchell, James Kenneth, 1930–

Fundamentals of soil behavior / James K. Mitchell, KenichiSoga.—3rd ed.

p. cm.ISBN-13: 978-0-471-46302-7 (cloth : alk. paper)ISBN-10: 0-471-46302-7 (cloth : alk. paper)

1. Soil mechanics. I. Soga, Kenichi. II. Title.TA710.M577 2005624.1�5136—dc22

2004025690

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

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v

CONTENTS

Preface xi

CHAPTER 1 INTRODUCTION 1

1.1 Soil Behavior in Civil and Environmental Engineering 11.2 Scope and Organization 31.3 Getting Started 3

CHAPTER 2 SOIL FORMATION 5

2.1 Introduction 52.2 The Earth’s Crust 52.3 Geologic Cycle and Geological Time 62.4 Rock and Mineral Stability 72.5 Weathering 82.6 Origin of Clay Minerals and Clay Genesis 152.7 Soil Profiles and Their Development 162.8 Sediment Erosion, Transport, and Deposition 182.9 Postdepositional Changes in Sediments 252.10 Concluding Comments 32

Questions and Problems 33

CHAPTER 3 SOIL MINERALOGY 35

3.1 Importance of Soil Mineralogy in GeotechnicalEngineering 35

3.2 Atomic Structure 383.3 Interatomic Bonding 383.4 Secondary Bonds 393.5 Crystals and Their Properties 403.6 Crystal Notation 423.7 Factors Controlling Crystal Structures 443.8 Silicate Crystals 453.9 Surfaces 453.10 Gravel, Sand, and Silt Particles 483.11 Soil Minerals and Materials Formed by Biogenic and

Geochemical Processes 493.12 Summary of Nonclay Mineral Characteristics 493.13 Structural Units of the Layer Silicates 493.14 Synthesis Pattern and Classification of the Clay Minerals 523.15 Intersheet and Interlayer Bonding in the Clay Minerals 553.16 The 1�1 Minerals 563.17 Smectite Minerals 593.18 Micalike Clay Minerals 623.19 Other Clay Minerals 64

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vi CONTENTS

3.20 Summary of Clay Mineral Characteristics 653.21 Determination of Soil Composition 653.22 X-ray Diffraction Analysis 703.23 Other Methods for Compositional Analysis 743.24 Quantitative Estimation of Soil Components 793.25 Concluding Comments 80


CHAPTER 4 SOIL COMPOSITION AND ENGINEERING PROPERTIES 83

4.1 Introduction 834.2 Approaches to the Study of Composition and Property

Interrelationships 854.3 Engineering Properties of Granular Soils 854.4 Dominating Influence of the Clay Phase 944.5 Atterberg Limits 954.6 Activity 974.7 Influences of Exchangeable Cations and pH 974.8 Engineering Properties of Clay Minerals 984.9 Effects of Organic Matter 1044.10 Concluding Comments 105


CHAPTER 5 SOIL FABRIC AND ITS MEASUREMENT 109

5.1 Introduction 1095.2 Definitions of Fabrics and Fabric Elements 1105.3 Single-Grain Fabrics 1125.4 Contact Force Characterization Using Photoelasticity 1195.5 Multigrain Fabrics 1215.6 Voids and Their Distribution 1225.7 Sample Acquisition and Preparation for Fabric Analysis 1235.8 Methods for Fabric Study 1275.9 Pore Size Distribution Analysis 1355.10 Indirect Methods for Fabric Characterization 1375.11 Concluding Comments 140


CHAPTER 6 SOIL–WATER–CHEMICAL INTERACTIONS 143

6.1 Introduction 1436.2 Nature of Ice and Water 1446.3 Influence of Dissolved Ions on Water 1456.4 Mechanisms of Soil–Water Interaction 1466.5 Structure and Properties of Adsorbed Water 1466.6 Clay–Water–Electrolyte System 1536.7 Ion Distributions in Clay–Water Systems 1536.8 Elements of Double-Layer Theory 1546.9 Influences of System Variables on the Double Layer 1576.10 Limitations of the Gouy–Chapman Diffuse

Double Layer Model 1596.11 Energy and Force of Repulsion 1636.12 Long-Range Attraction 1646.13 Net Energy of Interaction 1646.14 Cation Exchange—General Considerations 1656.15 Theories for Ion Exchange 1676.16 Soil–Inorganic Chemical Interactions 1676.17 Clay–Organic Chemical Interactions 168

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CONTENTS vii

6.18 Concluding Comments 169Questions and Problems 169

CHAPTER 7 EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS 173

7.1 Introduction 1737.2 Principle of Effective Stress 1737.3 Force Distributions in a Particulate System 1747.4 Interparticle Forces 1747.5 Intergranular Pressure 1787.6 Water Pressures and Potentials 1807.7 Water Pressure Equilibrium in Soil 1817.8 Measurement of Pore Pressures in Soils 1837.9 Effective and Intergranular Pressure 1847.10 Assessment of Terzaghi’s Equation 1857.11 Water–Air Interactions in Soils 1887.12 Effective Stress in Unsaturated Soils 1907.13 Concluding Comments 193


CHAPTER 8 SOIL DEPOSITS—THEIR FORMATION, STRUCTURE,GEOTECHNICAL PROPERTIES, AND STABILITY 195

8.1 Introduction 1958.2 Structure Development 1958.3 Residual Soils 2008.4 Surficial Residual Soils and Taxonomy 2058.5 Terrestrial Deposits 2068.6 Mixed Continental and Marine Deposits 2098.7 Marine Deposits 2098.8 Chemical and Biological Deposits 2128.9 Fabric, Structure, and Property Relationships: General

Considerations 2138.10 Soil Fabric and Property Anisotropy 2178.11 Sand Fabric and Liquefaction 2238.12 Sensitivity and Its Causes 2268.13 Property Interrelationships in Sensitive Clays 2358.14 Dispersive Clays 2398.15 Slaking 2438.16 Collapsing Soils and Swelling Soils 2438.17 Hard Soils and Soft Rocks 2458.18 Concluding Comments 245


CHAPTER 9 CONDUCTION PHENOMENA 251

9.1 Introduction 2519.2 Flow Laws and Interrelationships 2519.3 Hydraulic Conductivity 2529.4 Flows Through Unsaturated Soils 2629.5 Thermal Conductivity 2659.6 Electrical Conductivity 2679.7 Diffusion 2729.8 Typical Ranges of Flow Parameters 2749.9 Simultaneous Flows of Water, Current, and Salts

Through Soil-Coupled Flows 2749.10 Quantification of Coupled Flows 277

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viii CONTENTS

9.11 Simultaneous Flows of Water, Current, and Chemicals 2799.12 Electrokinetic Phenomena 2829.13 Transport Coefficients and the Importance of Coupled

Flows 2849.14 Compatibility—Effects of Chemical Flows on Properties 2889.15 Electroosmosis 2919.16 Electroosmosis Efficiency 2949.17 Consolidation by Electroosmosis 2989.18 Electrochemical Effects 3039.19 Electrokinetic Remediation 3059.20 Self-Potentials 3059.21 Thermally Driven Moisture Flows 3079.22 Ground Freezing 3109.23 Concluding Comments 319


CHAPTER 10 VOLUME CHANGE BEHAVIOR 325

10.1 Introduction 32510.2 General Volume Change Behavior of Soils 32510.3 Preconsolidation Pressure 32710.4 Factors Controlling Resistance to Volume Change 33010.5 Physical Interactions in Volume Change 33110.6 Fabric, Structure, and Volume Change 33510.7 Osmotic Pressure and Water Adsorption Influences on

Compression and Swelling 33910.8 Influences of Mineralogical Detail in Soil Expansion 34510.9 Consolidation 34810.10 Secondary Compression 35310.11 In Situ Horizontal Stress (K0) 35510.12 Temperature–Volume Relationships 35910.13 Concluding Comments 365


CHAPTER 11 STRENGTH AND DEFORMATION BEHAVIOR 369

11.1 Introduction 36911.2 General Characteristics of Strength and Deformation 37011.3 Fabric, Structure, and Strength 37911.4 Friction Between Solid Surfaces 38311.5 Frictional Behavior of Minerals 38911.6 Physical Interactions Among Particles 39311.7 Critical State: A Useful Reference Condition 40011.8 Strength Parameters for Sands 40411.9 Strength Parameters for Clays 41111.10 Behavior After Peak and Strain Localization 41511.11 Residual State and Residual Strength 41711.12 Intermediate Stress Effects and Anisotropy 42211.13 Resistance to Cyclic Loading and Liquefaction 42511.14 Strength of Mixed Soils 43211.15 Cohesion 43611.16 Fracturing of Soils 43811.17 Deformation Characteristics 44411.18 Linear Elastic Stiffness 44711.19 Transition from Elastic to Plastic States 45211.20 Plastic Deformation 45611.21 Temperature Effects 460

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CONTENTS ix

11.22 Concluding Comments 462Questions and Problems 462

CHAPTER 12 TIME EFFECTS ON STRENGTH AND DEFORMATION 465

12.1 Introduction 46512.2 General Characteristics 46612.3 Time-Dependent Deformation–Structure Interaction 47012.4 Soil Deformation as a Rate Process 47812.5 Bonding, Effective Stresses, and Strength 48112.6 Shearing Resistance as a Rate Process 48812.7 Creep and Stress Relaxation 48912.8 Rate Effects on Stress–Strain Relationships 49712.9 Modeling of Stress–Strain–Time Behavior 50312.10 Creep Rupture 50812.11 Sand Aging Effects and Their Significance 51112.12 Mechanical Processes of Aging 51612.13 Chemical Processes of Aging 51712.14 Concluding Comments 520


List of Symbols 523

References 531

Index 559

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xi

PREFACE

According to the National Research Council (1989, 2005), sound geoengineering is key inmeeting seven critical societal needs. They are waste management and environmental protec-tion, infrastructure development and rehabilitation, construction efficiency and innovation, se-curity, resource discovery and recovery, mitigation of natural hazards, and the exploration anddevelopment of new frontiers. Solution of problems and satisfactory completion of projects ineach of these areas cannot be accomplished without a solid understanding of the composition,structure, and behavior of soils because virtually all of humankind’s structures and facilitiesare built on, in, or with the Earth. Thus, the purpose of this book remains the same as for theprior two editions; namely, the development of an understanding of the factors determiningand controlling the engineering properties and behavior of soils under different conditions,with an emphasis on why they are what they are. We believe that this understanding and itsprudent application can be a valuable asset in meeting these societal needs.

In the 12 years since publication of the second edition, environmental problems requiringgeotechnical inputs have remained very important; dealing with natural hazards and disasterssuch as earthquakes, floods, and landslides has demanded increased attention; risk assessmentand mitigation applied to existing structures and earthworks has become a major challenge;and the roles of soil stabilization, ground improvement, and soil as a construction materialhave expanded enormously. These developments, as well as the introduction of new compu-tational, geophysical, and sensing methods, new emphasis on micromechanical analysis andbehavior, and, perhaps regrettably, the reduced emphasis on laboratory measurement of soilproperties have required looking at soil behavior in new ways. More and more it is becomingappreciated that geochemical and microbiological phenomena and processes play an essentialrole in many types of geotechnical problems. Some of these considerations have been incor-porated into this new edition.

Although the format of the book has remained much the same as in the first two editions,the contents have been reviewed and revised in detail, with deletion of some material nolonger considered to be essential and introduction of substantial new material to incorporateimportant recent developments. We have reorganized the material among chapters to improvethe flow of topics and logic of presentation. Time effects on soil strength and deformationbehavior have been separated into a new Chapter 12. Additional soil property correlationshave been incorporated. The addition of sets of questions and problems at the end of eachchapter provide a feature not present in the first two editions. Many of these questions andproblems are open ended and without single, clearly defined answers, but they are designedto stimulate broad thinking and the realization that judgment and incorporation of conceptsand methods from a range of disciplines is often needed to provide satisfactory solutions tomany geoengineering problems.

We are indebted to innumerable students and professional colleagues whose inquiring mindsand perceptive insights have helped us clarify issues and find new and better explanations forobserved processes and behavior. J. Carlos Santamarina and David Smith provided helpfulsuggestions on the overall content and organization. Charles J. Shackelford reviewed andprovided valuable suggestions for the sections of Chapter 9 on chemical osmosis and advectiveand diffusive chemical flows. Other important contributions to this third edition in the form

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xii PREFACE

of valuable comments, photos, resources, and proof checking were made by Hendrikus Al-lersma, Khalid Alshibli, John Atkinson, Bob Behringer, Malcolm Bolton, Lis Bowman, JimBuckman, Pierre Delage, Antonio Gens, Henry Ji, Assaf Klar, Hideo Komine, Jean-MarieKonrad, Ning Liu, Yukio Nakata, Albert Ng, Masanobu Oda, Kenneth Sutherland, ColinThornton, Yoichi Watabe, Siam Yimsiri, and Guoping Zhang.

KS thanks his wife, Mikiko, for her encouragement and special support.We dedicate this book to the memory of Virginia (‘‘Bunny’’) Mitchell, whose continuing

love, support, encouragement, and patience over more than 50 years, made this and the priortwo editions possible.

JAMES K. MITCHELLUniversity Distinguished Professor, EmeritusVirginia Tech, Blacksburg, Virginia

KENICHI SOGAReader in GeomechanicsUniversity of Cambridge, Cambridge, England

March 2005

ReferencesNational Research Council. 1989. Geotechnology—Its Impact on Economic Growth, the En-vironment, and National Security. National Academy Press, Washington, DC.National Research Council. 2005. Geological and Geotechnical Engineering in the New Mil-lennium, National Academy Press, Washington, DC.

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1

CHAPTER 1

Introduction

1.1 SOIL BEHAVIOR IN CIVIL ANDENVIRONMENTAL ENGINEERING

Civil and environmental engineering includes the con-ception, analysis, design, construction, operation, andmaintenance of a diversity of structures, facilities, andsystems. All are built on, in, or with soil or rock. Theproperties and behavior of these materials have majorinfluences on the success, economy, and safety of thework. Geoengineers play a vital role in these projectsand are also concerned with virtually all aspects ofenvironmental control, including water resources, wa-ter pollution control, waste disposal and containment,and the mitigation of such natural disasters as floods,earthquakes, landslides, and volcanoes. Soils and theirinteractions with the environment are major consider-ations. Furthermore, detailed understanding of the be-havior of earth materials is essential for mining, forenergy resources development and recovery, and forscientific studies in virtually all the geosciences.

To deal properly with the earth materials associatedwith any problem and project requires knowledge,understanding, and appreciation of the importanceof geology, materials science, materials testing, andmechanics. Geotechnical engineering is concernedwith all of these. Environmental concerns—especiallythose related to groundwater, the safe disposal and con-tainment of wastes, and the cleanup of contaminatedsites—has spawned yet another area of specialization;namely, environmental geotechnics, wherein chemistryand biological science are important. Geochemical andmicrobiological phenomena impact the composition,properties, and stability of soils and rocks to degreesonly recently beginning to be appreciated.

Students in civil engineering are often quite sur-prised, and sometimes quite confused, by their firstcourse in engineering with soils. After studying statics,

mechanics, and structural analysis and design, whereinproblems are usually quite clear-cut and well defined,they are suddenly confronted with situations where thisis no longer the case. A first course in soil mechanicsmay not, at least for the first half to two-thirds of thecourse, be mechanics at all. The reason for this is sim-ple: Analyses and designs are useless if the boundaryconditions and material properties are improperly de-fined.

Acquisition of the data needed for analysis and de-sign on, in, and with soils and rocks can be far moredifficult and uncertain than when dealing with otherengineering materials and aboveground construction.There are at least three important reasons for this.

1. No Clearly Defined Boundaries. An embank-ment resting on a soil foundation is shown in Fig.1.1a, and a cantilever beam fixed at one end isshown in Fig. 1.1b. The free body of the canti-lever beam, Fig. 1.1c, is readily analyzed for re-actions, shears, moments, and deflections usingstandard methods of structural analysis. However,what are the boundary conditions, and what is thefree body for the embankment foundation?

2. Variable and Unknown Material Properties.The properties of most construction materials(e.g., steel, plastics, concrete, aluminum, andwood) are ordinarily known within rather narrowlimits and usually can be specified to meet certainneeds. Although this may be the case in construc-tion using earth and rock fills, at least part ofevery geotechnical problem involves interactionswith in situ soil and rock. No matter how exten-sive (and expensive) any boring and samplingprogram, only a very small percentage of the sub-surface material is available for observation andtesting. In most cases, more than one stratum is

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2 1 INTRODUCTION

Figure 1.1 The problem of boundary conditions in geo-technical problems: (a) embankment on soil foundation, (b)cantilever beam, and (c) free body diagram for analysis ofpropped cantilever beam.

present, and conditions are nonhomogeneous andanisotropic.

3. Stress and Time-Dependent Material Proper-ties. Soils, and also some rocks, have mechan-ical properties that depend on both the stresshistory and the present stress state. This is be-cause the volume change, stress–strain, andstrength properties depend on stress transmissionbetween particles and particle groups. Thesestresses are, for the most part, generated by bodyforces and boundary stresses and not by internalforces of cohesion, as is the case for many othermaterials. In addition, the properties of most soilschange with time after placement, exposure, andloading. Because of these stress and time de-pendencies, any given geotechnical problem mayinvolve not just one or two but an almost infinitenumber of different materials.

Add to the above three factors the facts that soil androck properties may be susceptible to influences fromchanges in temperature, pressure, water availability,and chemical and biological environment, and onemight conclude that successful application of mechan-ics to earth materials is an almost hopeless proposition.It has been amply demonstrated, of course, that such

is not the case; in fact, it is for these very reasons thatgeotechnical engineering offers such a great challengefor imaginative and creative work.

Modern theories of soil mechanics, the capabilitiesof modern computers and numerical analysis methods,and our improved knowledge of soil physics and chem-istry make possible the solution of a great diversity ofstatic and dynamic problems of stress deformation andstability, the transient and steady-state flow of fluidsthrough the ground, and the long-term performance ofearth systems. Nonetheless, our ability to analyze andcompute often exceeds considerably our ability to un-derstand, measure, and characterize a problem orprocess. Thus, understanding and the ability to con-ceptualize soil and rock behavior become all the moreimportant.

The objectives of this book are to provide a basisfor the understanding of the engineering properties andbehavior of soils and the factors controlling changeswith time and to indicate why this knowledge is im-portant and how it is used in the solution of geotech-nical and geoenvironmental problems.

It is easier to state what this book is not, rather thanwhat it is. It is not a book on soil or rock mechanics;it is not a book on soil exploration or testing; it is nota book that teaches analysis or design; and it is not abook on geotechnical engineering practice. Excellentbooks and references dealing with each of these im-portant areas are available. It is a book on the com-position, structure, and behavior of soils as engineeringmaterials. It is intended for students, researchers, andpracticing engineers who seek a more in-depth knowl-edge of the nature and behavior of soils than is pro-vided by classical and conventional treatments of soilmechanics and geotechnical engineering.

Here are some examples of the types of questionsthat are addressed in this book:

• What are soils composed of? Why?• How does geological history influence soil prop-

erties?• How are engineering properties and behavior re-

lated to composition?• What is clay?• Why are clays plastic?• What are friction and cohesion?• What is effective stress? Why is it important?• Why do soils creep and exhibit stress relaxation?• Why do some soils swell while others do not?• Why does stability failure sometimes occur at

stresses less than the measured strength?• Why and how are soil properties changed by dis-

turbance?

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GETTING STARTED 3

• How do changes in environmental conditionschange properties?

• What are some practical consequences of the pro-longed exposure of clay containment barriers towaste chemicals?

• What controls the rate of flow of water, heat,chemicals, and electricity through soils?

• How are the different types of flows through soilinterrelated?

• Why is the residual strength of a soil often muchless than its peak strength?

• How do soil properties change with time after dep-osition or densification and why?

• How do temperature changes influence the me-chanical properties of soils?

• What is soil liquefaction, and why is it important?• What causes frost heave, and how can it be pre-

vented?• What clay types are best suited for sealing waste

repositories?• What biological processes can occur in soils and

why are they important in engineering problems?

Developing answers to questions such as these re-quires application of concepts from chemistry, geol-ogy, biology, materials science, and physics. Principlesfrom these disciplines are introduced as necessary todevelop background for the phenomena under study. Itis assumed that the reader has a basic knowledge ofapplied mechanics and soil mechanics, as well as ageneral familiarity with the commonly used engineer-ing properties of soils and their determination.

1.2 SCOPE AND ORGANIZATION

The topics covered in this book begin with consider-ation of soil formation in Chapter 2 and soil mineral-ogy and compositional analysis of soil in Chapter 3.Relationships between soil composition and engineer-ing properties are developed in Chapter 4. Soil com-position by itself is insufficient for quantification ofsoil properties for specific situations, because the soilfabric, that is, the arrangements of particles, particlegroups, and pores, may play an equally important role.This topic is covered in Chapter 5.

Water may make up more than half the volume ofa soil mass, it is attracted to soil particles, and theinteractions between water and the soil surfaces influ-ence the behavior. In addition, owing to the colloidal

nature of clay particles, the types and concentrationsof chemicals in a soil can influence significantly itsbehavior in a variety of ways. Soil water and the clay–water–electrolyte system are then analyzed in Chapter6. An analysis of interparticle forces and total and ef-fective stresses, with a discussion of why they are im-portant, is given in Chapter 7.

The remaining chapters draw on the preceding de-velopments for explanations of phenomena and soilproperties of interest in geotechnical and geoenviron-mental engineering. The formation of soil deposits,their resulting structures and relationships to geotech-nical properties and stability are covered in Chapter 8.The next three chapters deal with those soil propertiesthat are of primary importance to the solution of mostgeoengineering problems: the flows of fluids, chemi-cals, electricity, and heat and their consequences inChapter 9; volume change behavior in Chapter 10; anddeformation and strength and deformation behavior inChapter 11. Finally, Chapter 12 on time effects onstrength and deformation recognizes that soils are notinert, static materials, but rather how a given soil re-sponds under different rates of loading or at some timein the future may be quite different than how it re-sponds today.

1.3 GETTING STARTED

Find an article about a problem, a project, or issue thatinvolves some aspect of geotechnical soil behavior asan important component. The article can be from thepopular press, from a technical journal or magazine,such as the Journal of Geotechnical and Geoenviron-mental Engineering of the American Society of CivilEngineers, Geotechnique, The Canadian GeotechnicalJournal, Soils and Foundations, ENR, or elsewhere.

1. Read the article and prepare a one-page infor-mative abstract. (An informative abstract sum-marizes the important ideas and conclusions. Adescriptive abstract, on the other hand, simplystates the article contents.)

2. Summarize the important geotechnical issues thatare found in the article and write down what youbelieve you should know about to understandthem well enough to solve the problem, resolvethe issue, advise a client, and the like. In otherwords, what is in the article that you believe thesubject matter in this book should prepare you todeal with? Do not exceed two pages.

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5

CHAPTER 2

Soil Formation

2.1 INTRODUCTION

The variety of geomaterials encountered in engineeringproblems is almost limitless, ranging from hard, dense,large pieces of rock, through gravel, sand, silt, and clayto organic deposits of soft, compressible peat. All thesematerials may exist over a wide range of densities andwater contents. A number of different soil types maybe present at any site, and the composition may varyover intervals as small as a few millimeters.

It is not surprising, therefore, that much of thegeoengineer’s effort is directed at the identification ofsoils and the evaluation of the appropriate propertiesfor use in a particular analysis or design. Perhaps whatis surprising is that the application of the principles ofmechanics to a material as diverse as soil meets withas much success as it does.

To understand and appreciate the characteristics ofany soil deposit require an understanding of what thematerial is and how it reached its present state. Thisrequires consideration of rock and soil weathering, theerosion and transportation of soil materials, deposi-tional processes, and postdepositional changes in sed-iments. Some important aspects of these processes andtheir effects are presented in this chapter and in Chap-ter 8. Each has been the subject of numerous booksand articles, and the amount of available informationis enormous. Thus, it is possible only to summarize thesubject and to encourage consultation of the referencesfor more detail.

2.2 THE EARTH’S CRUST

The continental crust covers 29 percent of Earth’s sur-face. Seismic measurements indicate that the continen-tal crust is about 30 to 40 km thick, which is 6 to 8times thicker than the crust beneath the ocean. Granitic

(acid) rocks predominate beneath the continents, andbasaltic (basic) rocks predominate beneath the oceans.Because of these lithologic differences, the continentalcrust average density of 2.7 is slightly less than theoceanic crust average density of 2.8. The elementalcompositions of the whole Earth and the crust are in-dicated in Fig. 2.1. There are more than 100 elements,but 90 percent of Earth consists of iron, oxygen, sili-con, and magnesium. Less iron is found in the crustthan in the core because its higher density causes it tosink. Silicon, aluminum, calcium, potassium, and so-dium are more abundant in the crust than in the corebecause they are lighter elements. Oxygen is the onlyanion that has an abundance of more than 1 percentby weight; however, it is very abundant by volume.Silicon, aluminum, magnesium, and oxygen are themost commonly observed elements in soils.

Within depths up to 2 km, the rocks are 75 percentsecondary (sedimentary and metamorphic) and 25 per-cent igneous. From depths of 2 to 15 km, the rocks areabout 95 percent igneous and 5 percent secondary.Soils may extend from the ground surface to depths ofseveral hundred meters. In many cases the distinctionbetween soil and rock is difficult, as the boundary be-tween soft rock and hard soil is not precisely defined.Earth materials that fall in this range are sometimesdifficult to deal with in engineering and construction,as it is not always clear whether they should be treatedas soils or rocks.

A temperature gradient of about 1�C per 30 m existsbetween the bottom of Earth’s crust at 1200�C and thesurface.1 The rate of cooling as molten rock magma

1 In some localized areas, usually within regions of recent crustalmovement (e.g., fault lines, volcanic zones) the gradient may exceed20�C per 100 m. Such regions are of interest both because of theirpotential as geologic hazards and because of their possible value assources of geothermal energy.

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6 2 SOIL FORMATION

Oxygen 46%

Oxygen 30%

Silicon 28%

Silicon 15%

Aluminum 8%

Aluminum 1.1%

Iron 6%

Iron 35%

Magnesium 4%Magnesium 13%

Calcium 2.4% Calcium 1.1%Potassium 2.3%Sodium 2.1%

Nickel 2.4%Sulfur 1.9%Other <1%Other <1%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Earth's Crust Whole Earth

Figure 2.1 Elemental composition of the whole Earth andthe crust (percent by weight) (data from Press and Siever,1994).

Figure 2.2 Geologic cycle.

Figure 2.3 Simplified version of the rock cycle.

moves from the interior of Earth toward the surfacehas a significant influence on the characteristics of theresulting rock. The more rapid the cooling, the smallerare the crystals that form because of the reduced timefor atoms to attain minimum energy configurations.Cooling may be so rapid in a volcanic eruption that nocrystalline structure develops before solidification, andan amorphous material such as obsidian (volcanicglass) is formed.

2.3 GEOLOGIC CYCLE AND GEOLOGICALTIME

The surface of Earth is acted on by four basic proc-esses that proceed in a never-ending cycle, as indi-cated in Fig. 2.2. Denudation includes all of those pro-cesses that act to wear down land masses. These in-clude landslides, debris flows, avalanche transport,wind abrasion, and overland flows such as rivers andstreams. Weathering includes all of the destructive me-chanical and chemical processes that break downexisting rock masses in situ. Erosion initiates thetransportation of weathering products by variousagents from one region to another—generally fromhigh areas to low. Weathering and erosion convertrocks into sediment and form soil. Deposition involvesthe accumulation of sediments transported previously

from some other area. Sediment formation pertains toprocesses by which accumulated sediments are densi-fied, altered in composition, and converted into rock.

Crustal movement involves both gradual rising ofunloaded areas and slow subsidence of depositional ba-sins (epirogenic movements) and abrupt movements(tectonic movements) such as those associated withfaulting and earthquakes. Crustal movements may alsoresult in the formation of new rock masses throughigneous or plutonic activity. The interrelationships ofthese processes are shown in Fig. 2.3.

More than one process acts simultaneously in na-ture. For example, both weathering and erosion takeplace at the surface during periods of uplift, or oro-genic activity (mountain building), and deposition, sed-iment formation, and regional subsidence are generallycontemporaneous. This accounts in part for the widevariety of topographic and soil conditions in any area.

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ROCK AND MINERAL STABILITY 7

Holocene

PleistocenePliocene

MioceneOligocene

Eocene

Paleocene

Epoch

Quaternary

Neogene

Paleogene

Period

Cretaceous

Jurassic

Triassic

Permian

Pennsylvanian

Mississippian

Devonian

Silurian

Ordovician

Cambrian

Era

Cenozoic

Mesozoic

Paleozoic

Eon

Phanerozoic

Proterozoic

Archean

0.01

1.6

5

23

35

57

65146

208

245

290

323

363

409

439

510

570

2500 Precambrian

Ter

tiary

Figure 2.4 Stratigraphic timescale column. Numbers repre-sent millions of years before the present.

The stratigraphic timescale column shown in Fig.2.4 gives the sequence of rocks formed during geolog-ical time. Rocks are grouped by age into eons, eras,periods, and epochs. Each time period of the columnis represented by its appropriate system of rocks ob-served on Earth’s surface along with radioactive agedating. Among various periods, the Quaternary period(from 1.6 million years ago to the present) deservesspecial attention since the top few tens of meters ofEarth’s surface, which geotechnical engineers oftenwork in, were developed during this period. The Qua-ternary period is subdivided into the Holocene (the10,000 years after the last glacial period) and the Pleis-tocene. The deposits during this period are controlledmainly by the change in climate, as it was too short atime for any major tectonic changes to occur in thepositions of land masses and seas. There were as manyas 20 glacial and interglacial periods during the Qua-ternary. At one time, ice sheets covered more thanthree times their present extent. Worldwide sea leveloscillations due to glacial and interglacial cycles affectsoil formation (weathering, erosion, and sedimenta-tion) as well as postdepositional changes such as con-solidation and leaching.

2.4 ROCK AND MINERAL STABILITY

Rocks are heterogeneous assemblages of smaller com-ponents. The smallest and chemically purest of thesecomponents are elements, which combine to form in-organic compounds of fixed composition known asminerals. Hence, rocks are composed of minerals oraggregates of minerals. Rocks are sometimes glassy(volcanic glass, obsidian, e.g.), but usually consist ofminerals that crystallized together or in sequence(metamorphic and igneous rocks), or of aggregatesof detrital components (most sedimentary rocks).Sometimes, rocks are composed entirely of one typeof mineral (say flint or rock salt), but generally theycontain many different minerals, and often the rock isa collection or aggregation of small particles that arethemselves pieces of rocks. Books on petrography maylist more than 1000 species of rock types. Fortunately,however, many of them fall into groups with similarengineering attributes, so that only about 40 rocknames will suffice for most geotechnical engineeringpurposes.

Minerals have a definite chemical composition andan ordered arrangement of components (a crystal lat-tice); a few minerals are disordered and without defin-able crystal structure (amorphous). Crystal size andstructure have an important influence on the resistanceof different rocks to weathering. Factors controlling thestability of different crystal structures are consideredin Chapter 3. The greatest electrochemical stability ofa crystal is reached at its crystallization temperature.As temperature falls below the crystallization temper-ature, the structural stability decreases. For example,olivine crystallizes from igneous rock magma at hightemperature, and it is one of the most unstable igneous-rock-forming minerals. On the other hand, quartz doesnot assume its final crystal structure until the temper-ature drops below 573�C. Because of its high stability,quartz is the most abundant nonclay mineral in soils,although it comprises only about 12 percent of igneousrocks.

As magma cools, minerals may form and remain, orthey may react progressively to form other minerals atlower temperatures. Bowen’s reaction series, shown inFig. 2.5, indicates the crystallization sequence ofthe silicate minerals as temperature decreases from1200�C. This reaction series closely parallels variousweathering stability series as shown later in Table 2.2.For example, in an intermediate granitic rock, horn-blende and plagioclase feldspar would be expected tochemically weather before orthoclase feldspar, whichwould chemically weather before muscovite mica, andso on.

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8 2 SOIL FORMATION

Figure 2.5 Bowen’s reaction series of mineral stability. Eachmineral is more stable than the one above it on the list.

Mineralogy textbooks commonly list determinativeproperties for about 200 minerals. The list of the mostcommon rock- or soil-forming minerals is rather short,however. Common minerals found in soils are listed inTable 2.1. The top six silicates originate from rocks byphysical weathering processes, whereas the other min-erals are formed by chemical weathering processes.Further description of important minerals found insoils is given in Chapter 3.

2.5 WEATHERING

Weathering of rocks and soils is a destructive processwhereby debris of various sizes, compositions, andshapes is formed.2 The new compositions are usuallymore stable than the old and involve a decrease in theinternal energy of the materials. As erosion moves theground surface downward, pressures and temperaturesin the rocks are decreased, so they then possess aninternal energy above that for equilibrium in the newenvironment. This, in conjunction with exposure to theatmosphere, water, and various chemical and biologicalagents, results in processes of alteration.

A variety of physical, chemical, and biological proc-esses act to break down rock masses. Physical proc-esses reduce particle size, increase surface area, andincrease bulk volume. Chemical and biological proc-esses can cause complete changes in both physical andchemical properties.

2 A general definition of weathering (Reiche, 1945; Keller, 1957) is:the response of materials within the lithosphere to conditions at ornear its contact with the atmosphere, the hydrosphere, and perhapsmore importantly, the biosphere. The biosphere is the entire spaceoccupied by living organisms; the hydrosphere is the aqueous enve-lope of Earth; and the lithosphere is the solid part of Earth.

Physical Processes of Weathering

Physical weathering processes cause in situ breakdownwithout chemical change. Five processes are impor-tant:

1. Unloading Cracks and joints may form todepths of hundreds of meters below the groundsurface when the effective confining pressure isreduced. Reduction in confining pressure may re-sult from uplift, erosion, or changes in fluid pres-sure. Exfoliation is the spalling or peeling off ofsurface layers of rocks. Exfoliation may occurduring rock excavation and tunneling. The termpopping rock is used to describe the sudden spall-ing of rock slabs as a result of stress release.

2. Thermal Expansion and Contraction The ef-fects of thermal expansion and contraction rangefrom creation of planes of weakness from strainsalready present in a rock to complete fracture.Repeated frost and insolation (daytime heating)may be important in some desert areas. Fires cancause very rapid temperature increase and rockweathering.

3. Crystal Growth, Including Frost Action Thecrystallization pressures of salts and the pressureassociated with the freezing of water in saturatedrocks may cause significant disintegration. Manytalus deposits have been formed by frost action.However, the role of freeze–thaw in physicalweathering has been debated (Birkeland, 1984).The rapid rates and high amplitude of tempera-ture change required to produce necessary pres-sure have not been confirmed in the field. Instead,some researchers favor the process in which thinfilms of adsorbed water is the agent that promotesweathering. These films can be adsorbed sotightly that they cannot freeze. However, the wa-ter is attracted to a freezing front and pressuresexerted during the migration of these films canbreak the rock apart.

4. Colloid Plucking The shrinkage of colloidalmaterials on drying can exert a tensile stress onsurfaces with which they are in contact.3

5. Organic Activity The growth of plant roots inexisting fractures in rocks is an important weath-ering process. In addition, the activities ofworms, rodents, and humans may cause consid-erable mixing in the zone of weathering.

3 To appreciate this phenomenon, smear a film of highly plastic claypaste on the back of your hand and let it dry.

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WEATHERING 9

Table 2.1 Common Soil Minerals

Name Chemical Formula Characteristics

Quartz SiO2 Abundant in sand and siltFeldspar (Na,K)AlO2[SiO2]3

CaAl2O4[SiO2]2

Abundant in soil that is not leached extensively

Mica K2Al2O5[Si2O5]3Al4(OH)4

K2Al2O5[Si2O5]3(Mg,Fe)6(OH)4

Source of K in most temperate-zone soils

Amphibole (Ca,Na,K)2,3(Mg,Fe,Al)5(OH)2[(Si,Al)4O11]2 Easily weathered to clay minerals and oxidesPyroxene (Ca,Mg,Fe,Ti,Al)(Si.Al)O3 Easily weatheredOlivine (Mg,Fe)2SiO4 Easily weatheredEpidoteTourmalineZirconRutileKaolinite

Ca2(Al,Fe)3(OH)Si3O12

NaMg3Al6B3Si6O27(OH,F)4

ZrSiO4

TiO2

Si4Al4O10(OH)8

Highly resistant to chemical weathering; usedas ‘‘index mineral’’ in pedologic studies

Smectite,vermiculite,chlorite

Mx(Si,Al)8(Al,Fe,Mg)4O20(OH)4,where M � interlayer cation

Abundant in clays as products of weathering;source of exchangeable cations in soils

Allophane Si3Al4O12 � nH2O Abundant in soils derived from volcanic ashdeposits

Imogolite Si2Al4O10 � 5H2OGibbsite Al(OH)3 Abundant in leached soilsGoethite FeO(OH) Most abundant Fe oxideHematite Fe2O3 Abundant in warm regionFerrihydrate Fe10O15 � 9H2O Abundant in organic horizonsBirnessite (Na,Ca)Mn7O14 � 2.8H2O Most abundant Mn oxideCalcite CaCO3 Most abundant carbonateGypsum CaSO4 � 2H2O Abundant in arid regions

Adapted from Sposito (1989).

Physical weathering processes are generally theforerunners of chemical weathering. Their main con-tributions are to loosen rock masses, reduce particlesizes, and increase the available surface area for chem-ical attack.

Chemical Processes of Weathering

Chemical weathering transforms one mineral to an-other or completely dissolves the mineral. Practicallyall chemical weathering processes depend on the pres-ence of water. Hydration, that is, the surface adsorptionof water, is the forerunner of all the more complexchemical reactions, many of which proceed simulta-neously. Some important chemical processes are listedbelow.

1. Hydrolysis, probably the most important chemi-cal process, is the reaction between the mineraland H� and (OH)� of water. The small size of

the ion enables it to enter the lattice of mineralsand replace existing cations. For feldspar,Orthoclase feldspar:

� �K silicate � H OH� �→ H silicate � K OH (alkaline)

Anorthite:

� �Ca silicate � 2H OH

→ H silicate � Ca(OH) (basic)2

As water is absorbed into feldspar, kaolinite isoften produced. In a similar way, other clay min-erals and zeolites (microporous aluminosilicates)may form by weathering of silicate minerals asthe associated ions such as silica, sodium, potas-sium, calcium, and magnesium are lost into so-

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10 2 SOIL FORMATION

Figure 2.6 Solubility of alumina and amorphous silica inwater (Keller, 1964b).

lution.Hydrolysis will not continue in the presence of

static water. Continued driving of the reaction tothe right requires removal of soluble materials byleaching, complexing, adsorption, and precipita-tion, as well as the continued introduction of H�

ions.Carbonic acid (H2CO3) speeds chemical

weathering. This weak acid is formed by the so-lution in rainwater of a small amount of carbondioxide gas from the atmosphere. Additional car-bonic acid and other acids are produced by theroots of plants, by insects that live in the soil,and by the bacteria that degrade plant and animalremains.

The pH of the system is important because itinfluences the amount of available H�, the solu-bility of SiO2 and Al2O3, and the type of claymineral that may form. The solubility of silicaand alumina as a function of pH is shown in Fig.2.6.

2. Chelation involves the complexing and removalof metal ions. It helps to drive hydrolysis reac-tions. For example,Muscovite:

K [Si Al ]Al O (OH) � 6C O H � 8H O2 6 2 4 20 4 2 4 2 2

� � 0 �→ 2K � 6C O Al � 6Si(OH) � 8OH2 4 4

Oxalic acid (C2O4H2), the chelating agent, re-leases C2O4

2�, which forms a soluble complexwith Al3� to enhance dissolution of muscovite.Ring-structured organic compounds derived fromhumus can act as chelating agents by holdingmetal ions within the rings by covalent bonding.

3. Cation exchange is important in chemical weath-ering in at least three ways:a. It may cause replacement of hydrogen on

hydrogen bearing colloids. This reduces theability of the colloids to bring H� to unweath-ered surfaces.

b. The ions held by Al2O3 and SiO2 colloids in-fluence the types of clay minerals that form.

c. Physical properties of the system such as thepermeability may depend on the adsorbed ionconcentrations and types.

4. Oxidation is the loss of electrons by cations, andreduction is the gain of electrons. Both are im-portant in chemical weathering. Most importantoxidation products depend on dissolved oxygenin the water. The oxidation of pyrite is typical ofmany oxidation reactions during weathering(Keller, 1957):

2FeS � 2H O � 7O → 2FeSO � 2H SO2 2 2 4 2 4

FeSO � 2H O → Fe(OH) � H SO4 2 2 2 4

(hydrolysis)

Oxidation of Fe(OH)2 gives

4Fe(OH) � O � 2H O → 4Fe(OH)2 2 2 3

2Fe(OH) → Fe O � nH O (limonite)3 2 3 2

The H2SO4 formed in these reactions rejuvenatesthe process. It may also drive the hydrolysis ofsilicates and weather limestone to produce gyp-sum and carbonic acid. During the constructionof the Carsington Dam in England in the early1980s, soil in the reservoir area that containedpyrite was uncovered during construction follow-ing the excavation and exposure of air and waterof the Namurian shale used in the embankment.The sulfuric acid that was released as a result ofthe pyrite oxidation reacted with limestone toform gypsum and CO2. Accumulation of CO2 inconstruction shafts led to the asphyxiation ofworkers who were unaware of its presence. It isbelieved that the oxidation process was mediatedby bacteria (Cripps et al., 1993), as discussed fur-

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WEATHERING 11

Figure 2.7 Microogranisms attached to soil particle sur-faces: (a) bacteria attached to sand particle (from Robertsonet al. 1993 in Chenu and Stotzky, 2002), (b) bacterial mi-croaggregate [from Robert and Chenu (1992) in Chenu andStotzky (2002)], and (c) biofilm on soil surface (from Chenuand Stotzky (2002).

ther in the next section.Many iron minerals weather to iron oxide

(Fe2O3, hematite). The red soils of warm, humidregions are colored by iron oxides. Oxides canact as cementing agents between soil particles.

Reduction reactions, which are of importancerelative to the influences of bacterial action andplants on weathering, store energy that may beused in later stages of weathering.

5. Carbonation is the combination of carbonate orbicarbonate ions with earth materials. Atmos-pheric CO2 is the source of the ions. Limestonemade of calcite and dolomite is one of the rocksthat weather most quickly especially in humidregions. The carbonation of dolomitic limestoneproceeds as follows:

CaMg(CO ) � 2CO � 2H O3 2 2 2

→ Ca(HCO ) � Mg(HCO )3 2 3 2

The dissolved components can be carried off inwater solution. They may also be precipitated atlocations away from the original formation.

Microbiological Effects

Several types of microorganisms are found in soils;there are cellular microorganisms (bacteria, archea, al-gae, fungi, protozoa, and slime molds) and noncellularmicroorganisms (viruses). They may be nearly round,rodlike, or spiral and range in size from less than 1 to100 �m, which is equivalent to coarse clay size to finesand size. Figure 2.7a shows bacteria adhering toquartz sand grains, and Fig. 2.7b shows clay mineralscoating around the cell envelope, forming what arecalled bacterial microaggregates.4 A few billion to 3trillion microorganisms exist in a kilogram of soil nearthe ground surface and bacteria are dominant. Micro-organisms can reproduce very rapidly. The replicationrate is controlled by factors such as temperature, pH,ionic concentrations, nutrients, and water availability.Under ideal conditions, the ‘‘generation time’’ for bac-terial fission can be as short as 10 min; however, anhour scale is typical. These high-speed generationrates, mutation, and natural selection lead to very fastadaptation and extraordinary biodiversity.

Autotrophic photosynthetic bacteria, that is, photo-autotrophs, played a crucial role in the geological de-

4 Further details of how microorganisms adhere to soil surfaces aregiven in Chenu and Stotzky (2002).

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12 2 SOIL FORMATION

velopment of Earth (Hattori, 1973; McCarty, 2004).Photosynthetic bacteria, cyanobacteria, or ‘‘blue-greenbacteria’’ evolved about 3.5 billion years ago (Proter-ozoic era—Precambrian), and they are the oldestknown fossils. Cyanobacteria use energy from the sunto reduce the carbon in CO2 to cellular carbon and toobtain the needed electrons for oxidizing the oxygenin water to molecular oxygen. During the Archaeanperiod (2.5 billion years ago), cyanobacteria convertedthe atmosphere from reducing to oxidizing andchanged the mineral nature of Earth.

Eukaryotic algae evolved later, followed by the mul-ticellular eukaryotes including plants. Photosynthesisis the primary producer of the organic particulate mat-ter in shale, sand, silt, and clay, as well as in coal,petroleum, and methane deposits. Furthermore, cyano-bacteria and algae increase the water pH when theyconsume CO2 dissolved in water, resulting in carbonateformation and precipitation of magnesium and calciumcarbonates, leading to Earth’s major carbonate forma-tions.

Aerobic bacteria live in the presence of dissolvedoxygen. Anaerobic bacteria survive only in the absenceof oxygen. Facultative bacteria can live with or withoutoxygen. Some bacteria may resort to fermentation tosustain their metabolism under anaerobic conditions(Purves et al., 1997). For example, in the case of an-aerobic conditions, fermenting bacteria oxidize carbo-hydrates to produce simple organic acids and H2 thatare used to reduction of ferric (Fe3�) iron, sulfate re-duction, and the generation of methane (Chapelle,2001). Microbial energy metabolism involves electrontransfers, and the electron sources and acceptors canbe both organic and inorganic compounds (Horn andMeike, 1995). Most soil bacteria derive their carbonand energy directly from organic matter and its oxi-dation. Some other bacteria derive their energy fromoxidation of inorganic substances such as ammonium,sulfur, and iron and most of their carbon from carbondioxide. Therefore, biological activity mediates geo-chemical reactions, causing them to proceed at ratesthat are sometimes orders of magnitude more rapidthan would be predicted solely on the basis of the ther-mochemical reactions involved.

Bacteria tend to adhere to mineral surfaces and formmicrocolonies known as biofilms as shown in Fig. 2.7c.Some biofilms are made of single-type bacteria, whileothers involve symbiotic communities where two ormore bacteria types coexist and complement eachother. For example, biofilms involved in rock weath-ering may involve an upper aerobic layer, followed byan intermediate facultative layer that rests on top of theaerobic layer that produces the weathering agents

(e.g., acids) directly on the rock surface (Ehrlich,1998). Biofilms bind cations in the pore fluid and fa-cilitate nucleation and crystal growth even at low ionicconcentrations in the pore fluid (Konhauser and Urru-tia, 1999). After nucleation is initiated, further mineralgrowth or precipitation can occur abiotically, includingthe precipitation of amorphous iron–aluminum sili-cates and poorly crystallized claylike minerals, such asallophone, imogolite, and smectite (Urrutia and Bev-eridge, 1995; Ehrlich, 1999; Barton et al., 2001).

In the case of the Carsington Dam construction,Cripps et al. (1993) hypothesized that autotrophic bac-teria greatly accelerated the oxidation rate of the pyrite,so that it occurred within months during construction.The resulting sulfuric acid reacted with the drainageblanket constructed of carboniferous limestone, whichthen resulted in precipitation of gypsum and iron hy-droxide, clogging of drains and generation of carbondioxide.

Weathering Products

The products of weathering, several of which will gen-erally coexist at one time, include:

1. Unaltered minerals that are either highly resistantor freshly exposed

2. Newly formed, more stable minerals having thesame structure as the original mineral

3. Newly formed minerals having a form similar tothe original, but a changed internal structure

4. Products of disrupted minerals, either at or trans-ported from the site. Such minerals might includea. Colloidal gels of Al2O3 and SiO2

b. Clay mineralsc. Zeolitesd. Cations and anions in solutione. Mineral precipitates

5. Unused guest reactants

The relationship between minerals and differentweathering stages is given in Table 2.2. The similaritybetween the order of representative minerals for thedifferent weathering stages and Bowen’s reaction se-ries given earlier (Fig. 2.5) may be noted.

Contrasts in compositions between terrestrial and lu-nar soils can be accounted for largely in terms of dif-ferences in chemical weathering. Soils on Earth arecomposed mainly of quartz and clay minerals becausethe minerals of lower stability, such as feldspar, oli-vine, hornblende, and glasses, are rapidly removed bychemical weathering. On the Moon, however, the ab-sence of water and free oxygen prevent chemicalweathering. Hence, lunar soils are made up mainly offragmented parent rock and rapidly crystallized

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WEATHERING 13

Table 2.2 Representative Minerals and SoilsAssociated with Weathering Stages

Weath-eringStage

RepresentativeMinerals Typical Soil Groups

Early Weathering Stages

1

2

3

4

5

Gypsum (also halite,sodium nitrate)

Calcite (also dolomiteapatite)

Olivine-hornblende(also pyroxenes)

Biotite (also glauco-nite, nontronite)

Albite (also anorthitemicrocline, ortho-clase)

Soils dominated bythese minerals in thefine silt and clay frac-tions are the youthfulsoils all over theworld, but mainlysoils of the desertregions where limitedwater keeps chemicalweathering to a mini-mum.

Intermediate Weathering Stages

678

QuartzMuscovite (also illite)2�1 layer silicates (in-

cluding vermiculite,expanded hydrousmica)

Montmorillonite

Soils dominated bythese minerals in thefine silt and clay frac-tions are mainly thoseof temperate regionsdeveloped under grassor trees. Includes themajor soils of thewheat and corn beltsof the world.

Advanced weathering stages

101112

13

KaoliniteGibbsiteHematite (also geothite,

limonite)Anatase (also rutile,

zircon)

Many intensely weath-ered soils of the warmand humid equatorialregions have clayfractions dominatedby these minerals.They are frequentlycharacterized by theirinfertility.

From Jackson and Sherman (1953).

glasses. Mineral fragments in lunar soils include pla-gioclase feldspar, pyroxene, ilmenite, olivine, and po-tassium feldspar. Quartz is extremely rare because it isnot abundant in the source rocks. Carrier et al. (1991)present an excellent compilation of information aboutthe composition and properties of lunar soil.

Effects of Climate, Topography, Parent Material,Time, and Biotic Factors

The rate at which weathering can proceed is controlledby parent material and climate. Topography, apart fromits influence on climate, determines primarily the rateof erosion, and this controls the depth of soil accu-mulation and the time available for weathering prior toremoval of material from the site. In areas of steeptopography, rapid mechanical weathering followed byrapid down-slope movement of the debris results information of talus slopes (piles of relatively unweath-ered coarse rock fragments).

Climate determines the amount of water present, thetemperature, and the character of the vegetative cover,and these, in turn, affect the biologic complex. Somegeneral influences of climate are:

1. For a given amount of rainfall, chemical weath-ering proceeds more rapidly in warm than in coolclimates. At normal temperatures, reaction ratesapproximately double for each 10�C rise in tem-perature.

2. At a given temperature, weathering proceedsmore rapidly in a wet climate than in a dry cli-mate provided there is good drainage.

3. The depth to the water table influences weather-ing by determining the depth to which air isavailable as a gas or in solution and by its effecton the type of biotic activity.

4. Type of rainfall is important: short, intense rainserode and run off, whereas light-intensity, long-duration rains soak in and aid in leaching.

Table 2.3 summarizes geomorphologic processes indifferent morphoclimatic zones. The nature and rate ofthese geomorphologic processes control landform as-semblages.

During the early stages of weathering and soil for-mation, the parent material is much more importantthan it is after intense weathering for long periods oftime. Climate ultimately becomes a more dominantfactor in residual soil formation than parent material.

Of the igneous rock-forming minerals, only quartzand, to a much lesser extent, feldspar, have sufficientchemical durability to persist over long periods ofweathering. Quartz is most abundant in coarse-grainedgranular rocks such as granite, granodiorite, andgneiss, where it typically occurs in grains in the mil-limeter size range. Consequently, granitic rocks are themain source of sand.

In addition to the microbiological activities dis-cussed previously, biological factors of importance in-clude the influences of vegetation on erosion rate andthe cycling of elements between plants and soils. Mi-

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14 2 SOIL FORMATION

Table 2.3 Morphoclimatic Zones and the Associated Geomorphologic Processes

MorphoclimaticZone

MeanAnnual

Temperature(�C)

MeanAnnual

Precipitation(mm) Relative Importance of Geomorphologic Processes

Glacial �0 0–1000 Mechanical weathering rates (especially frost action)high; chemical weathering rates low, massmovement rates low except locally; fluvial actionconfined to seasonal melt; glacial action at amaximum; wind action significant

Periglacial �1 to 2 100–1000 Mechanical weathering very active with frost action ata maximum; chemical weathering rates low tomoderate; mass movement very active; fluvialprocesses seasonally active; wind action rateslocally high. Effects of the repeated formation anddecay of permafrost.

Wet midlatitude 0–20 400–1800 Chemical weathering rates moderate, increasing tohigh at lower latitudes; mechanical weatheringactivity moderate with frost action important athigher latitudes; mass movement activity moderateto high; moderate rates of fluvial processes; windaction confined to coasts.

Dry continental 0–10 100–400 Chemical weathering rates low to moderate;mechanical weathering, especially frost action,seasonally active; mass movement moderate andepisodic; fluvial processes active in wet season;wind action locally moderate.

Hot dry (aridtropical)

10–30 0–300 Mechanical weathering rates high (especially saltweathering), chemical weathering minimum, massmovement minimal; rates of fluvial activitygenerally very low but sporadically high; windaction at maximum.

Hot semidry(semiaridtropical)

10–30 300–600 Chemical weathering rates moderate to low;mechanical weathering locally active especially ondrier and cooler margins; mass movement locallyactive but sporadic; fluvial action rates high butepisodic; wind action moderate to high.

Hot wet–dry(humid–aridtropical)

20–30 600–1500 Chemical weathering active during wet season; ratesof mechanical weathering low to moderate; massmovement fairly active; fluvial action high duringwet season with overland and channel flow; windaction generally minimum but locally moderate indry season.

Hot wet(humidtropical)

20–30 �1500 High potential rates of chemical weathering;mechanical weathering limited; active, highlyepisodic mass movement; moderate to low rates ofstream corrosion but locally high rates of dissolvedand suspended load transport.

AzonalMountainzone

Highlyvariable

Highlyvariable

Rates of all processes vary significantly with altitude;mechanical and glacial action becomes significant athigh elevations.

From Fookes et al. (2000).

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ORIGIN OF CLAY MINERALS AND CLAY GENESIS 15

crobial decomposition of the heavy layers of organicmatter in top soils formed through photosynthesis re-sults in oxygen depletion and carbon oxidation back toCO2, which is leached by rainwater that penetrates intothe subsurface. The high CO2 concentration, loweredpH, and anaerobic nature of these penetrating waterscause reduction and solutioning of iron and manganeseminerals, the reduction of sulfates, and dissolution ofcarbonate rocks. If the moving waters become co-mingled with oxygenated water in the ground, or asgroundwater emerges into rivers and streams, iron,manganese, and sulfide oxidation results, and carbon-ate precipitation can occur (McCarty, 2004).

The time needed to weather different materials var-ies greatly. The more unconsolidated and permeablethe parent material, and the warmer and more humidthe climate, the shorter the time needed to achievesome given amount of soil formation. The rates ofweathering and soil development decrease with in-creasing time.

The time for soil formation from hard rock parentmaterials may be very great; however, young soils candevelop in less than 100 years from loessial, glacial,and volcanic parent material (Millar et al., 1965). Py-rite bearing rocks are known to break apart and un-dergo chemical and mineral transformations in only afew years.

2.6 ORIGIN OF CLAY MINERALS AND CLAYGENESIS

There are three general mechanisms of clay formationby weathering (Eberl, 1984): (1) inheritance, (2) neo-formation, and (3) transformation. Inheritance meansthat a clay mineral originated from reactions that oc-curred in another area during a previous stage in therock cycle and that the clay is stable enough to remainin its present environment. Origin by neoformationmeans that the clay has precipitated from solution orformed from reactions of amorphous materials. Trans-formation genesis requires that the clay has kept someof its inherited structure while undergoing chemicalreactions. These reactions are typically characterizedby ion exchange with the surrounding environmentand/or layer transformation in which the structure ofoctahedral, tetrahedral, or fixed interlayer cations ismodified.

The behavior of nonclay colloids such as silica andalumina during crystallization is important in deter-mining the specific clay minerals that form. Certaingeneral principles apply.5

5 The considerations in Chapter 6 provide a basis for these statements.

1. Alkaline earths (Ca2�, Mg2�) flocculate silica.2. Alkalis (K�, Na�, Li�) disperse silica.3. Low pH flocculates colloids.4. High electrolyte content flocculates colloids.5. Aluminous suspensions are more easily floccu-

lated than siliceous suspensions.6. Dispersed phases are more easily removed by

groundwater than flocculated phases.

Factors important in determining the formation ofspecific clay minerals are discussed below. The struc-ture and detailed characterization of these minerals arecovered in Chapter 3.

Kaolinite Minerals

Kaolinite formation is favored when alumina is abun-dant and silica is scarce because of the 1�1 sil-ica�alumina structure, as opposed to the 2�1 silica toalumina structure of the three-layer minerals. Condi-tions leading to kaolinite formation usually include lowelectrolyte content, low pH, and the removal of ionsthat tend to flocculate silica (Mg, Ca, Fe) by leaching.Most kaolinite is formed from feldspars and micas byacid leaching of acidic (SiO2-rich) granitic rocks. Ka-olinite forms in areas where precipitation is relativelyhigh, and there is good drainage to ensure leaching ofcations and iron.

Halloysite forms as a result of the leaching of feld-spar by H2SO4, which is often produced by the oxi-dation of pyrite, as shown earlier. The combination ofconditions that results in halloysite formation is oftenfound in high-rain volcanic areas such as Hawaii andthe Cascade Mountains of the Pacific Northwest in theUnited States.

Smectite Minerals

Smectites, because of their 2�1 silica�alumina struc-ture, form where silica is abundant, as is the casewhere both silica and alumina are flocculated. Condi-tions favoring this are high pH, high electrolyte con-tent, and the presence of more Mg2� and Ca2� thanNa� and K�. Rocks that are high in alkaline earths,such as the basic and intermediate igneous rocks, vol-canic ash, and their derivatives containing ferromag-nesian minerals and calcic plagioclase, are usual parentmaterials. Climatic conditions where evaporation ex-ceeds precipitation and where there is poor leachingand drainage, such as in arid and semiarid areas, favorthe formation of smectite.

Illite (Hydrous Mica) and Vermiculite

Hydrous mica minerals form under conditions similarto those leading to the formation of smectites. In ad-dition, the presence of potassium is essential; so ig-

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16 2 SOIL FORMATION

neous or metamorphic rocks and their derivatives arethe usual parent rocks. Weathering of feldspar in coolclimates often leads to the development of illite. Al-teration of muscovite to illite and biotite to vermiculiteduring weathering is also a significant source of theseminerals. Interstratifications of vermiculite with micaand chlorite are common. The high stability of illite isresponsible for its abundance and persistence in soilsand sediments.

Chlorite Minerals

Chlorites can form by alteration of smectite throughintroduction of sufficient Mg2� to cause formation ofa brucitelike layer that replaces the interlayer water.Biotite from igneous and metamorphic rocks may alterto trioctahedral chlorites and mixed-layer chlorite–vermiculite. Chlorites also occur in low- to medium-grade metamorphic rocks and in soils derived fromsuch rocks.

Discussion

The above considerations are greatly simplified, andthere are numerous ramifications, alterations, and var-iations in the processes. One clay type may transformto another by cation exchange and weathering undernew conditions. Entire structures may change, for ex-ample, from 2�1 to 1�1, so that montmorillonite formswhen magnesium-rich rocks weather under humid,moderately drained conditions, but then alters to kao-linite as leaching continues. Kaolinite does not form inthe presence of significant concentrations of calcium.

The relative proportions of potassium and magne-sium determine how much montmorillonite and illiteform. Some montmorillonites alter to illite in a marineenvironment due to the high K� concentration. Mixed-layer clays often form by partial leaching of K orMg(OH)2 from between illite and chlorite layers andby incomplete adsorption of K or Mg(OH)2 in mont-morillonite or vermiculite.

Further details of the clay minerals are given inChapter 3. More detailed discussions of clay mineralformation are given by Keller (1957, 1964a & b), Wea-ver and Pollard (1973), Eberl (1984), and Velde(1995), among others.

2.7 SOIL PROFILES AND THEIRDEVELOPMENT

In situ weathering processes lead to a sequence of ho-rizons within a soil, provided erosion does not rapidlyremove soil from the site. The horizons may gradeabruptly from one to the next or be difficult to distin-

guish. Their thickness may range from a few milli-meters to several meters. The horizons may differ inany or all of the following ways:

1. Degree of breakdown of parent material2. Content and character of organic material3. Kind and amount of secondary minerals4. pH5. Particle size distribution

All the horizons considered together, including theunderlying parent material, form the soil profile.6 Thepart of the profile above the parent material is termedthe solum. Eluviation is the movement of soil materialfrom one place to another within the soil, either insolution or in suspension as a result of excess precip-itation over evaporation. Eluvial horizons have lost ma-terial; illuvial horizons have gained material.

Master horizons are designated by the capital lettersO, A, B, C, and R (Table 2.4). Subordinate symbolsare used as suffixes after the master horizon designa-tions to indicate dominant features of different kindsof horizons, as indicated in the table. The O horizonsare generally present at the soil surface under nativevegetation, but they may also be buried by sedimen-tation of alluvium, loess, or ash fall. The A horizon isthe zone of eluviation where humified organic matteraccumulates with the mineral fraction. The amount oforganic matters (fibers to humic/fulvic acids) variesfrom 0.1 percent in desert soils to 5 percent or morein organic soils and affects many engineering proper-ties including compressibility, shrinkage, strength andchemical sorption. The B horizon is the zone of illu-viation where clay, iron compounds, some resistantminerals, cations, and humus accumulate. The R ho-rizon is the consolidated rock, and the C horizon con-sists of the altered material from which A and Bhorizons are formed.

Soil profiles developed by weathering can be cate-gorized into three groups on the basis of their miner-alogy and chemical composition as shown in Fig. 2.8(Press and Siever, 1994). Pedalfers, which are formedin moist climate, are soils rich in aluminum and ironoxides and silicates such as quartz and clay minerals.All soluble minerals such as calcium carbonate isleached away. They have a thick A horizon and can befound in much of the areas of moderate to high rainfallin the eastern United States, Canada, and Europe. Ped-ocals, which are formed in dry climate, are soils rich

6 Residual soil profiles should not be confused with soil profiles re-sulting from successive deposition of strata of different soil types inalluvial, lake, or marine environments.

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SOIL PROFILES AND THEIR DEVELOPMENT 17

Table 2.4 Designations of Master Horizons and Subordinate Symbols forHorizons of Soil Profiles

Master Horizons

O1 Organic undecomposed horizonO2 Organic decomposed horizonA1 Organic accumulation in mineral soil horizonA2 Leached bleached horizon (eluviated)A3 Transition horizon to BAB Transition horizon between A and B—more like A in upper part

A and B A2 with less than 50% of horizon occupied by spots of BAC Transition horizon, not dominated by either A or C

B and A B with less than 50% of horizon occupied by spots of A2B Horizon with accumulation of clay, iron, cations, humus; residual

concentration of clay; coatings; or alterations of originalmaterial forming clay and structure

B1 Transition horizon more like B than AB2 Maximum expression of B horizonB3 Transitional horizon to C or R

C Altered material from which A and B horizons are presumed to beformed

R Consolidated bedrock

Subordinate Symbols

b Buried horizonca Calcium in horizoncs Gypsum in horizoncn Concretions in horizon

f Frozen horizong Gleyed horizonh Humus in horizonir Iron accumulation in horizonm Cemented horizonp Plowed horizon

sa Salt accumulation in horizonsi Silica cemented horizont Clay accumulation in horizonx Fragipan horizon

II, III, IV Lithologic discontinuitiesA�2, B�2 Second sequence in bisequal soil

Adapted from Soil Survey Staff (1975).

in calcium from the calcium carbonates and other sol-uble minerals originated from sedimentary bedrock.Soil water is drawn up near the surface by evaporation,leaving calcium carbonate pellets and nodules. Theycan be found in the southwest United States. Laterite,which is formed in a wet, tropical climate, is rich inaluminum and iron oxides, iron-rich clays, and alu-minum hydroxides. Silica and calcium carbonates areleached away from the soil. It has a very thin A ho-

rizon because most of the organic matter is recycledfrom the surface to the vegetation.

Lithologic discontinuities may be common in land-scapes where erosion is severe, and these discontinui-ties are often marked by stone layers from previouserosion cycles. In some places, soils have developedseveral sequences of A and B horizons, which are su-perimposed over each other. Superimposed soil se-quences are likely the result of climate changes acting

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18 2 SOIL FORMATION

(a) (b) (c)

C

B

A

Humus andleached soil(quartz andclay mineralspresent)

Some iron andaluminium oxidesprecipitated; allsoluble materials,such ascarbonates,leached away

Granitebedrock C

B

A

Sandstone,shale, andlimestonebedrock

Calciumcarbonatepellets andnodulesprecipitated

Humus andleached soil

Thin or absenthumus

Thick masses ofinsoluble iron andaluminum oxides;occasional quartz

Iron-rich clays andaluminumhydroxides

Thin leached zone

Mafic igneousbedrock

Figure 2.8 Major soil types: (a) Pedalfer soil profile developed on granite, (b) Pedocal soilprofile developed on sedimentary bedrock, and (c) Laterite soil profile developed on maficigneous rock (from Press and Siever, 1994).

on uniform geologic materials, or are the remnants offormer soil profiles (paleosoils) that have been buriedunder younger soils (Olson, 1981).

2.8 SEDIMENT EROSION, TRANSPORT, ANDDEPOSITION

Streams, ocean currents, waves, wind, groundwater,glaciers, and gravity continually erode and transportsoils and rock debris away from the zone of weather-ing. Each of these transporting agents may causemarked physical changes in the sediment it carries. Al-though detailed treatment of erosion, transportation,and depositional processes is outside the scope of thisbook, a brief outline of their principles and their effectson the transported soil is helpful in understanding theproperties of the transported material.

Erosion

Erosion includes all processes of denudation that in-volve the wearing away of the land surface by me-

chanical action. The transporting agents, for example,water, wind, and ice, are by themselves capable onlyof limited wearing action on rocks, but the process isreinforced when these agents contain particles of thetransported material.

Transportation of sediment requires first that it bepicked up by the eroding agent. Greater average flowvelocities in the transporting medium may be requiredto erode than to transport particles. Particles are erodedwhen the drag and lift of the fluid exceed the gravi-tational, cohesive, and frictional forces acting to holdthem in place. The stream velocity required to erodedoes not decrease indefinitely with decreasing particlesize because small particles remain within the bound-ary layer adjacent to the stream bed where the actualstream velocity is much less than the average velocity.Relationships between particle size and average streamvelocity required to erode and transport particles bywind and water are shown in Fig. 2.9.

Ice has the greatest competency for sediment move-ment of all the transportation agents. There is no limitto the size of particles that may be carried. Ice pushes

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SEDIMENT EROSION, TRANSPORT, AND DEPOSITION 19

Figure 2.9 Comparison of erosion and transport curves forair and running water. The air is a slightly more effectiveerosional agent than streams for very small particles but isineffective for those larger than sand (from Garrels, 1951).

Figure 2.10 Characteristics of glaciers (from Selmer-Olsen,1964).

material along in front and erodes the bottom and sidesof the valleys through which it flows. In an active gla-cier (Fig. 2.10), there is continuous erosion and trans-port of material from the region of ice accumulationto the region of melting. A dead glacier has been cutoff from a feeding ice field.

Transportation

The different agents of sediment transport are com-pared in Table 2.5. The relative effect listed in the lastcolumn of this table denotes the importance of theagent on a geological scale with respect to the overallamount of sediment moved, with one representing thegreatest amount.

Movement of sediment in suspension by wind andwater depends on the settling velocity of the particlesand the laws of fluid motion. Under laminar flow con-ditions, the settling velocity of small particles is pro-portional to the square of the particle diameter. Forlarger particles and turbulent fluid flow, the settling ve-locity is proportional to the square root of the particlediameter. Particles stay in suspension once they havebeen set in motion as long as the turbulence of thestream is greater than the settling velocity.

The largest particles that can be transported by waterare carried by traction, which consists of rolling anddragging along the boundary between the transportingagent and the ground surface. Particles intermediate insize between the suspended load and the traction loadmay be carried by saltation, in which they move by aseries of leaps and bounds. Soluble materials are car-ried in solution and may precipitate as a result ofchanged conditions. The combined effects mean thatthe concentration of sediment is not constant throughthe depth of the transporting agent but is much greaternear the stream bed than near the top. Fine particlesmay be fairly evenly distributed from top to bottom;however, coarser particles are distributed mainly withinshort distances from the bottom, as shown in Fig. 2.11,which applies to a river following a straight course.

The major effects of transportation processes on thephysical properties of sediments are sorting and ab-rasion. Sorting may be both longitudinal, which pro-duces a progressive decrease in particle size withdistance from the source as the slope flattens, and lo-cal, which produces layers or lenses with differentgrain size distributions. Reliable prediction of the sort-ing at any point along a sediment transport system iscomplicated by the fact that flow rates vary from pointto point and usually with the seasons. Consequently,very complex sequences of materials may be found inand adjacent to stream beds.

Particle size and shape may be mechanically modi-fied by abrasive processes such as grinding, impact,and crushing during transportation. The abrading ef-fects of wind are typically hundreds of times greaterthan those of water (Kuenen, 1959). In general, abra-sion changes the shape and size of gravel size particlesbut only modifies the shapes of sand and smaller sizeparticles. Water-working of sands causes rounding and

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Table 2.5 Comparison of Sediment Transport Agents

AgentType of

Flow

ApproximateAverageVelocity

MaximumSize

Eroded byAverageVelocity Areas Affected

Max Loadper m3

Type ofTransport

RelativeEffect

Streams Turbulent A few km/h Sand All land A few tens ofkilograms

Bed load,suspendedload,solution

1

Waves Turbulent A few km/h Sand Coastlines A few tens ofkilograms

Same asstreams

2

Wind Turbulent 15 km/h Sand Arid, semiarid,beaches,plowed fields

A kilogram Bed load,suspendedload

3

Glaciers Laminar A few m/yr Largeboulders

High latitudesand altitudes

Hundreds ofkilograms

Bed load,suspendedload,surfaceload

2

Groundwater Laminar A few m/yr Colloids Soluble materialand colloids

A kilogram Solution 3

Gravity cm/yr to afew m/s

Boulders Steep slopes,sensitiveclays,saturatedcohesionlesssoils,unconsolidatedrock

2000 kg Bed load 3

Adapted from Garrels (1951).

polishing of grains, and wind-driven impact can causefrosting of grains. The shape and surface character ofparticles influences a soil’s stress–deformation andstrength properties owing to their effects on packing,volume change during shear, and interparticle friction.

Basic minerals, such as the pyroxenes, amphiboles,and some feldspars, are rapidly broken down chemi-cally during transport. Quartz, which is quite stablebecause of its resistant internal structure, may be mod-ified by mechanical action, but only at a slow rate.Quartz sand grains may survive a number of successivesedimentation cycles with no more than a percent ortwo of weight loss due to abrasion.

The surface textures of quartz sand particles reflecttheir origin, as shown by the examples in Fig. 2.12 fordifferent sands, each shown to three or four magnifi-cations. The mechanical and chemical actions, associ-

ated with a beach environment, produce a relativelysmooth, pitted surface texture. Aeolian sands exhibit arougher surface texture, particularly over small dis-tances. Some, but not all, river sands may have a verysmooth particle surface that reflects the influence ofchemical action. Sand that has undergone change afterdeposition and burial is termed diagenetic sand. Itssurface texture may reflect a long and stable period ofinteraction with the groundwater. In some cases, veryrough surface textures can develop. Ottawa sand, a ma-terial that has been used for numerous geotechnicalresearch investigations, is such a material.

Some effects of transportation on sediment proper-ties are summarized in Table 2.6. The gradationalcharacteristics of sedimentary materials reflect theirtransportation mode as indicated in Fig. 2.13. Sedi-ments of different origins lie within specific zones of

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Figure 2.11 Schematic diagram of sediment concentration with depth in a transportingstream.

the figure, which are defined by the logarithm of theratio of 75 percent particle size to 25 percent particlesize and the median (50 percent) grain size.

Deposition

Deposition of sediments from air and water is con-trolled by the same laws as their transportation. If thestream velocity and turbulence fall below the valuesneeded to keep particles in suspension or moving withthe bed load, then the particles will settle. When icemelts, the sediments may be deposited in place or car-ried away by meltwater. Materials in solution canprecipitate when exposed to conditions of changedtemperature or chemical composition, or as a result ofevaporation of water. Sediments may be divided intothose formed primarily by chemical and biologicalmeans and those composed primarily of mineral androck fragments. The latter are sometimes referred to asdetrital or clastic deposits.

The deposition of sediments into most areas is cy-clical. Some causes of cyclic deposition are:

1. Periodic earth movements2. Climatic cycles of various lengths, most notably

the annual rhythm3. Cyclic shifting of tributaries on a delta4. Periodic volcanism

The thickness of deposits formed during any onecycle may vary from less than a millimeter to hundredsof meters. The period may range from months tothousands of years, and only one or many types ofsediments may be involved.

One of the best known sediments formed by cyclicaldeposition is varved clay. Varved clays formed in gla-cial lakes during the ice retreat stage. Each layer con-sists of a lighter-colored, summer-deposited clayey siltgrading into a darker winter-deposited silty clay.Spring and summer thaws contributed clay and silt-laden meltwater to the lake. The coarsest particles set-tled first to form the summer layer. Because of themuch slower settling velocity of the clay particles,most did not settle out until the quiet winter period. Aphotograph of a vertical section through a varved clayis shown in Fig. 2.14. The alternating coarser-grained,light-colored layers and finer-grained, darker layers areclearly visible. The shear resistance along horizontalvarves is much less than that across the varves. Also,the hydraulic conductivity is much greater in the hor-izontal direction than in the vertical direction. Exten-sive deposits of varved clays are found in the northeastand north central United States and eastern Canada.Detailed description of the geology and engineeringproperties of Connecticut Valley varved clay is givenby DeGroot and Lutenegger (2003).

Complex soil deposition processes occur alongcoastlines, estuaries, and shallow shelves in relation to

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22 2 SOIL FORMATION

Figure 2.12 Surface textures of four sands of differing origins: (a) river sand, (b) beachsand, (c) aeolian sand and (d) diagenetic sand (courtesy of Norris, 1975).

the location of the shoreline. Soil deposits include fore-shore sand and gravels, which are sorted by wave ac-tions, organic deposits, and clays preserved in lagoons,offshore fine sands, and muds. River channels may beoverdeepened, and soft sediments then accumulate toform buried valleys. Most coastlines and estuaries ofthe world were subject to sea level changes in the Qua-ternary period. In particular, the post glacial rise of sealevel, which ended about 6000 years ago, has had aworldwide influence on the present-day coastal forms.Figure 2.15 shows alternating layers of marine (Ma)and fluvial (Diluvial-D) sediments in the geotechnicalprofile down to 400 m depth below sea level at OsakaBay, Japan (Tanaka and Locat, 1999). The observedvariation corresponds well to the local relative sea levelduring its geological history up to 1 million years ago.

Chemical and biochemical sediments may consist ofone or two kinds of materials. For example, calciumcarbonate sediments are made of calcite, which origi-nates from the shells of organisms in the deep sea (Fig.2.16a). Some clays contain significant amounts of mi-crofossils due to the depositional environment asshown in Fig. 2.16b; such clays include Mexico Cityclay (Diaz-Rodriguez et al., 1998), Ariake clay (Oht-subo et al., 1995), and Osaka Bay clay (Tanaka andLocat, 1999). The microfossils include diatoms (sili-ceous skeleton of eukarya cells in either freshwater ormarine environments), radiolaria (found in marine en-vironments and consisting mostly of silica), and for-manifera (calcium carbonate shell secreted by marineeukarya). The presence of microfossils can have a pro-found effect on the behavior of the soil mass, confer-

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Figure 2.12 (Continued )

ring unusual geotechnical properties that deviate fromgeneral property expectations, including high porosity,high liquid limit, unusual compressibility, and uniquelyhigh friction angle. For examples, see Tanaka and Lo-cat (1999) and Locat and Tanaka (2001).

While streams and rivers produce deposits accordingto grain size, a glacier transports the finest dust andlarge boulders side by side at the same rate of move-ment. If the material remains unsorted after deposition,it is called till. A mixture of all grain sizes from boul-ders to clays is known as boulder clay, which is adifficult material to work with because large bouldersmay damage excavation equipment.

Loess, which is a nonstratified aeolian deposit, isprobably the single most abundant Quaternary depositon land. It consists of silt with some small fraction ofclay, sand, and carbonate. It originated during the Qua-

ternary period from glacial out wash and deglaciatedtill areas. The deposits are spread widely and blanketpreexisting landforms. The deposits are up to 30 mthick in the Missouri and Rhine River Valleys, morethan 180 m thick in Tajikistan, and up to 330 m thickin northern China.

Depositional Environment

The environment of deposition determines the complexof physical, chemical, and biological conditions underwhich sediments accumulate and consolidate. Thethree general geographical depositional environmentsare continental, mixed continental and marine, and ma-rine. Continental deposits are located above the tidalreach and include terrestrial, paludal (swamp), andlacustrine (lake) sediments. Mixed continental and

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24 2 SOIL FORMATION

Table 2.6 Effects of Transportation on Sediments

Water Air Ice Gravity

Size Reduction through solution, littleabrasion in suspended load, someabrasion and impact in tractionload

Considerablereduction

Considerablegrinding andimpact

Considerableimpact

Shape androundness

Rounding of sand and gravel High degree ofrounding

Angular, soledparticles

Angular, non-spherical

Surface texture Sand: smooth, polished, shinySilt: little effect

Impact producesfrostedsurfaces

Striated surfaces Striated surfaces

Sorting Considerable sorting Very considerablesorting(progressive)

Very little sorting No sorting

Adapted from Lambe and Whitman (1969).

Figure 2.13 Influence of geologic history on sorting of particle sizes (adapted from Selmer-Olsen, 1964).

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POSTDEPOSITIONAL CHANGES IN SEDIMENTS 25

Figure 2.14 Vertical section through varved clay from theNew Jersey meadowlands (courtesy of S. Saxena).

Figure 2.15 Soil profile of Osaka Bay showing alternatingmarine (Ma) and fluvial (Diluvial-D) layers (modified fromTanaka and Locat, 1999).

Figure 2.16 Biochemical sediments: (a) Dogs Bay calciumcarbonate sand (courtesy of E. T. Bowman) and (b) diatomsobserved in Osaka Bay clay (courtesy of Y. Watabe).

marine deposits include littoral (between the tides),deltaic, and estuarine sediments. Marine deposits arelocated below the tidal reach and consist of continentalshelf (neritic), continental slope and rise (bathyal), anddeep ocean (abyssal) sediments. Table 2.7 summarizesmain soil deposits that are formed in various types of

environments (Locat et al., 2003). Characteristic soiltypes and properties associated with these depositionalenvironments are described in Chapter 8.

2.9 POSTDEPOSITIONAL CHANGES INSEDIMENTS

Between the time a sediment is first laid down and thetime it is encountered in connection with some humanactivity, it may have been altered as a result of theaction of any one or more of several postdepositionalprocesses. These processes can be physical, chemical,and/or biological. They occur because the young sed-iment is not necessarily stable in its new environment

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Table 2.7 Depositional Environment of Various Soil Deposits

Deposits Environment Type Texture

Transported Air Aeolian sand SandWaterShallow river Fluvial (glacio-) Sand and gravel

Alluvial (glacio-) Silt and sandShallow lake Littoral Sand and gravel

Muskeg Peat—organicDeep lake Lacustrine (glacio-) Silt and clay

Flow deposits Clay to gravelMarls Silt (fossils)

Shallow ocean Estuarine Silt and clayLittoral Silt and sandShelf Silt and clay

Deep ocean Pelagic Silt and clayOozes—calcareous Silt and clayOozes—siliceous Silt and clayFlow Clay to gravel

Glacier Subglacial till Clay to bouldersSupraglacial till Sand to boulders

Residual Land Tropical soils Clay to sandSaprolite Clay to bouldersDecomposed granite Clay to bouldersColluvial soils Clay to boulders

Chemical and biochemical Lake Evaporites (sakkas)Sea Evaporites

LimestoneGas hydrates

Adapted from Locat et al. (2003).

where the material is exposed to new conditions oftemperature, pressure, and chemistry. An understand-ing of postdepositional changes is essential for under-standing of properties, interpreting soil profile data,and in reconstructing geologic history. A brief outlineof the processes is presented here; their effects on en-gineering properties are described in more detail inChapter 8.

Desiccation

The drying of fine-grained sediments is usually accom-panied by shrinkage and cracking. Precompression ofthe upper portions of clay layers by drying is fre-quently observed. The effects of desiccation on thestrength and water content variations with depth inLondon clay from the Thames estuary are shown inFig. 2.17. Care must be exercised in interpreting pro-files of this type because drying is only one of severalpossible causes of apparent overconsolidation (precon-

solidation pressure greater than present overburden ef-fective pressure) at shallow depths. Other importantmechanisms include partial consolidation under in-creased overburden and the effects of weathering.

Weathering

Weathering and soil-forming processes are initiated innew sedimentary deposits after exposure to the atmo-sphere, just as they are on freshly exposed rock. Insome instances, weathering can result in improvementin properties or protection of underlying material. Forexample, the weathering of uplifted marine clays canlead to the replacement of sodium by potassium as thedominant exchange cation (Moum and Rosenqvist,1957). This increases both the undisturbed and re-molded strength. Water content and strength data for aNorwegian marine clay profile are shown in Fig. 2.18.It may be seen that the upper 5 m of clay, which havebeen weathered, have water content and strength var-

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27

Figure 2.17 Properties of Thames estuary clay. The overconsolidation in the upper 10 ftwas caused by surface drying (Skempton and Henkel, 1953).

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Figure 2.18 Clay characteristics at Manglerud in Oslo, Norway (Bjerrum, 1954).

iation characteristics similar to those of the Thamesestuary clay (see Fig. 2.17). In the case of the Nor-wegian clay, however, the plasticity values have alsochanged in the upper 5 m, providing evidence ofchanged composition. Weathering of the surface ofsome loess deposits has resulted in the formation of arelatively impervious loam that protects the underlyingmetastable loess structure from the deleterious effectsof water.

Consolidation and Densification

Consolidation (termed compaction in geology) of fine-grained sediments occurs from increased overburden,drying, or changes in the groundwater level so that theeffective stress on the material is increased. Depositsof granular material may be affected to some extent inthe same way. More significant densification of cohe-sionless soil occurs, however, as a result of dynamicloading such as induced by earthquakes or the activi-

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ties of humans. The usual effects of consolidation areto increase strength, decrease compressibility, increaseswell potential, and decrease permeability.

Even under constant effective stress conditions,structural readjustments and small compressions maycontinue for long periods owing to the viscous natureof soil structures. This ‘‘secondary compression’’ pro-vides an additional source of increased strength withtime.

Unloading

Erosion of overlying sediments due to glacial processleads to mechanical overconsolidation. A typical ex-ample of this is London clay, a marine clay depositedduring the Eocene period. The erosion took place inlate Tertiary and Pleistocene times and the amount oferosion is estimated to be about 150 m in Essex(Skempton, 1961) to 300 m in the Wraybury district(Bishop et al., 1965). After the unloading, small re-loading occurred by new deposition of gravels in thelate Quaternary period. Within the London clay, fivemajor transgressive–regressive cycles are recognizedduring its deposition. The postdepositional processesare site specific; that is, the degree of weathering anddesiccation and the amount of erosion vary dependingon location. This variation in depositional and post-depositional processes results in complex mechanicalbehavior (Hight et al., 2003).

Authigenesis, Diagenesis, Cementation, andRecrystallization

Authigenesis is the formation of new minerals in placeafter deposition. Authigenesis can make grains moreangular, lower the void ratio, and decrease the per-meability. Small crystals and rock fragments may growinto aggregates of coarser particles.

Diagenesis refers to such phenomena as changes inparticle surface texture, the conversion of mineralsfrom one type to another, and the formation of inter-particle bonds as a result of increased temperature,pressure, and time. Many diagenetic changes are con-trolled by the pH and redox potential of the deposi-tional environment. With increasing depth of burial ina sedimentary basin, clayey sediments may undergosubstantial transformation. Expansive clay mineralscan transform to a nonexpansive form, for example,montmorillonite to mixed layer to illite, as a result ofthe progressive removal of water layers under pressure(Burst, 1969). Burial depths of 1000 to 5000 m maybe required, and the transformation process appearsthermally activated as a result of the increased tem-perature at these depths. Chlorite can form in mud andshale during deep burial (Weaver and Pollard, 1973).

The long-term stability of different clay minerals underconditions of elevated temperature and pressure and indifferent chemical environments is important relativeto the use of clays as containment barriers for nuclearand toxic wastes. Diagenesis studies of locked sandsshow crystal overgrowths caused by pressure solutionand compaction (Barton, 1993; Richards and Burton,1999).

Cementation has important effects on the propertiesand stability of many soil materials. Cementation is notalways easily identified, nor are its effects always read-ily determined quantitatively. It is known to contributeto clay sensitivity, and it may be responsible for anapparent preconsolidation pressure. Removal of ironcompounds from a very sensitive clay from Labrador,Canada, by leaching led to a 30-ton/m2 decrease inapparent preconsolidation pressure (Kenney et al.,1967). Coop and Airey (2003) show for carbonate soilsthat cementation develops soon after deposition andenables the soil to maintain a loose structure.

Failure to recognize cementation has resulted in con-struction disputes. For example, a soil on a major proj-ect was marked on the contract drawings as glacialtill. It proved to be so hard that it had to be blasted.The contractor claimed the soil was cemented becauseduring digging failure took place through pebbles aswell as the clay matrix. The owner concluded that thishappened because the pebbles were weathered. Properevaluation of the material before the award of the con-tract could have avoided the problem.

Clay particles adhere to the surfaces of larger siltand sand particles, a process called clay bounding.Eventually the larger grains become embedded into aclay matrix and their influence on the geotechnical be-havior becomes limited. The clay bounding providesarching of interparticle forces, maintaining a large voidratio even at high effective stresses.

Time Effects

Even freshly deposited or densified sands can developsignificant increases in strength and stiffness over rel-atively short time periods, that is, by a factor of 2 ormore within a few months (Mitchell and Solymar,1984). Time effects and the aging of both cohesiveand cohesionless soils are analyzed and reviewedby Schmertmann (1991). Uncertainty remains as towhether the mechanisms for the observed increases inapparent preconsolidation pressure, strength, and stiff-ness are chemical, physical, or both. Research is con-tinuing on this important aspect of soil behavior so thatit will be possible to predict both the amount and therate of property changes for use in the analysis of geo-technical problems. The aging process is of particular

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30 2 SOIL FORMATION

interest in connection with hydraulic fills and groundimprovement projects, more details are given in Chap-ter 12.

Leaching, Ion Exchange, and Differential Solution

Postdepositional changes in pore fluid chemistry canresult from the percolation of different fluids througha deposit. This may change the forces between col-loidal particles. For example, the uplift of marine clayabove sea level followed by freshwater leaching canlead to both ion exchange and the removal of dissolvedsalts. This process is important in the formation ofhighly sensitive, quick clays, as discussed in more de-tail in Chapter 8.

Materials can be removed from sediments by differ-ential solution and subsequent leaching. Calcareousand gypsiferous sediments are particularly susceptibleto solution, resulting in the formation of channels, sinkholes, and cavities.

Jointing and Fissuring of Clay Soils

Some normally consolidated clays, almost all flood-plain clays, and many preconsolidated clays are weak-ened by joints and fissures. Joints in floodplain claysresult from deposition followed by cyclic expansionand contraction from wetting and drying. Joints andfissures in preconsolidated clays result from unloadingor from shrinkage cracks during drying. Closelyspaced joints in these types of clays may contribute toslides some years after excavation of cuts. The unload-ing enables joints to open, water to enter, and the clayto soften.

Fissures have been found in normally consolidatedclays at high water contents that could not have beencaused by drying or unloading (Skempton and Northey,1952), and increased brittleness has been observed insoft clay chunks that have been stored for some time.These effects may be caused by syneresis, which is themutual attraction of clay particles to form closely knitaggregates with fissures between them. Similar behav-ior is many times observed in gelatin after aging.Weathering and the release of potassium may also re-sult in fissuring.

Vegetation, especially large trees, can cause shrink-age and fissuring of clays (Barber, 1958; Holtz, 1983).The root systems suck up water, causing large capillaryshrinkage pressures. When rain falls on crusted surfacelayers of dried-up saline lakes, it is rapidly absorbedby capillarity. The air may become so compressed thatit causes tension cracking or blowouts in a form similarin appearance to root holes. These sediments may alsoundergo severe cracking, apparently as a result of

shock. Cracks up to 2 ft wide, of unknown depth, andspaced several meters apart have caused damage tobuildings and highways.

Biological Effects

Biological activity affects soil particles by modifyingtheir arrangement, aggregating them, weathering min-eral surfaces, mediating oxidation–reduction reactions,contributing to precipitation and dissolution of miner-als, and degrading organic particles. The survival andactivity of microorganisms are controlled partly bypore geometry and local physicochemical conditions.Therefore, apart from its impact on life itself, biolog-ical activity has influenced the evolution of the earthsurface, impacted mineral, sediment, and rock forma-tion, accelerated the rate of rock weathering and al-tered its products, influenced the composition ofgroundwater, and participated in the formation of gasand petroleum hydrocarbons.

Bioturbance refers to the action of organisms livingon or in sediments. By organic cementation, they mod-ify grain size, density, or cohesion (Richardson et al.,1985; Locat et al., 2003). The aggregation activity ofvarious worms densifies deposits by changing the grainsize of the sediment. Tubes that form can provide localdrainage and decrease the bulk density. The active zoneof bioturbance is usually to depths less than 30 cm.Sticky organic mucus or polymer bridging binds to-gether clay–silt particles, producing clusters.

Chemical transformation processes are mediated byorganisms. Some notable processes are summarized asfollows (Mitchell and Santamarina, 2005):

1. Sulfur Cycle Elemental sulfur (S0) and sulfides(S2�) are the stable forms of sulfur under anaer-obic conditions, whereas sulfates (SO4

2�) are thestable forms of sulfur under aerobic conditions.Sulfides form under anaerobic conditions fromsulfates already present in seawater and sedi-ments or introduced by diffusion and ground-water flow. The sulfate ion is not reduced tosulfide at Earth surface temperature and pressureunless biologically mediated. Sulfate-reducingbacteria are anaerobic and grow best at neutralpH but are known to exist over a broad range ofpH and salt content. When exposed to aerobicconditions, reduced sulfur compounds, hydrogensulfides (H2S), and elemental sulfur are used asan energy source by sulfide-oxidizing bacteriaand converted to sulfates.

2. Iron Cycle Iron in the subsurface exists pre-dominantly in the reduced or ferrous (Fe2�) state

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or the oxidized ferric (Fe3�) state. Several micro-organisms such as the genus Thiobacillus medi-ate the iron oxidation reaction. Chapelle (2001)notes that bacteria are able to derive only relativelittle energy from oxidizing Fe2�; therefore, theymust process large amounts of Fe2� and producelarge amounts of Fe3� to obtain sufficient energyto sustain their growth.

One important consequence of the rapid oxidationof iron sulfide in the presence of oxygen is the for-mation of acid rock drainage. Although Fe(OH)3 haslow solubility, the formation of H2SO4 provides asource of important reactions in the solid and pore wa-ter phases. The total dissolved solids increases owingto the dissolution of carbonates in the soil. Gypsumcan form, with an associated volume increase, at theexpense of carbonate minerals. The precipitated ferrichydroxide is thermodynamically unstable and rapidlytransforms to yellow goethite, FeO–OH. Geothite,while stable under wet conditions, will slowly dehy-drate to red hematite, Fe2O3, under dry conditions.

Microorganisms have a limited effect on the for-mation of coarse grains. However, bioactivity can af-fect diagenetic evolution, promote the precipitation ofcementing agents, cause internal weathering, and alterfines migration, filter performance, and drainage insilts and sands.

Severely water-limited environments distress micro-organisms and hinder biological activity. Nonetheless,there is great bacterial activity in the unsaturated or-ganic surface layer of a soil where plant roots arefound. Fierer et al. (2002) observed that bacterial ac-tivity decreases by 1 or 2 orders of magnitude by 2 mof depth. Horn and Meike (1995) conclude that micro-bial activity requires 60 to 80 percent saturation.Hence, there is less reduction in bacterial count withdepth in saturated sediments. Hindered biological ac-tivities in unsaturated soils may reflect lack of nutrientsin isolated water at menisci, slow nutrient flow in per-colating water paths, and increased ionic concentrationin the pore fluid as water evaporates and dissolved saltsapproach ion saturation conditions.

The physical scales over which the physicochemical,bioorganic, and burial diagenetic processes act rangefrom atomic dimensions to kilometers, and the time-scales range from microseconds to years. Table 2.8summarizes the processes, fabric characteristics, andscales associated with different mechanisms.

Human Effects

The global human population has grown from approx-imately 600 million at the beginning of the eighteenth

century to close to 6 billion today. Human activitiesare now at such a scale as to rival forces of nature intheir influence on soil changes. The activities includerapid changes in land use and the associated landforms,soil erosion related to forest removal, and soil contam-ination by urbanization, mining, and agricultural activ-ities. Ten to 15 percent of Earth’s land surface isoccupied by industrial areas and agriculture, and an-other 6 to 8 percent is pasture land (Vitousek et al.,1997).

Mine wastes are the largest waste volumes producedby humankind. On October 21, 1966, 144 people, 116of them children, were killed when a tip of coal wasteslid onto the village of Aberfan in South Wales, UnitedKingdom. The collapse was caused by tipping of coalwaste over a natural underground spring, and the coalslag slowly turned into a liquid slurry. The tragedy wascaused by two days of continual heavy rain looseningthe coal slag. As a result of the disaster at Aberfan,the Mines and Quarries Tips Act of 1969 was intro-duced. This act was passed in order to prevent disusedtips from becoming a danger to members of the public.

Over 8000 million tons of ore have been mined inthe South African deep-level underground gold miningindustry (Blight et al., 2000). Considerations for dis-posing these wastes into tailings ponds and dams in-clude the physicochemical nature of the extractedminerals as well as the topography and climate of thedisposal sites. Tailings dams have failed, resulting indestructive mudflows (Blight, 1997). One reported casewas the failure of the Merriespruit ring-dyke gold tail-ings dam in South Africa in 1994, which killed 17people in a village nearby. Overtopping of the tailingsdyke occurred after a significant rainfall event, and ap-proximately 500,000 m3 of tailings flowed through thisbreach. The liquefied tailings flowed for a distance ofabout 2 km. A large volume of tailings was in a me-tastable state in situ, and overtopping and erosion ofthe impoundment wall exposed this material, resultingin static liquefaction of the tailings and a consequentflow failure (Fourie et al., 2001).

The urban underground in major cities is congestedby utility lines, tunnels, and building foundations.Much may be more than 100 years old; for example,more than 50 percent of the water supply pipes in Lon-don were built using cast-iron during Victorian time.Aging infrastructure changes the in situ stress condi-tion, as well as groundwater chemistry, and this canlead to changes in the stress–strain–time behavior ofthe subsoil. Underground openings are sources or sinksof different environments; tunnels can act as a ground-water drain as well as source for air into the ground.

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32 2 SOIL FORMATION

Table 2.8 Summary of Processes and of the Fabric Signature and Temporal Scales Associated with VariousMechanisms

Processes Mechanisms

FabricSignaturesa

(predominant) ScalesPhysical

Time Remarks

Physicochemical Electromechanical EF Atomic andmolecular to� 4 �m

�s to ms Two particles may rotateFF

Thermomechanical FF(some EF)

Molecular to �

0.2 mmms to min Initial contacts EF then

rotations to FF:common in selectiveenvironments

Interface dynamics FF and EF �m to �� 0.5mm

s Some large compoundparticles may bepossible at highconcentrations

Bioorganic Biomechanical EF � 0.5 mm to� 2.0 mm

s to min Some FF possibleduring bioturbation

Biophysical EE and FF �m to mm s to min Some very large clayorganic complexespossible

Biochemical Nonunique(unknown)

�m to mm h to yr New chemicals formed,some altered

Burialdiagenesis

Mass gravity FF localizedswirl

cm to km � yr Can operate over largephysical scales

Diagenesis-cementation

Nonunique(unknown)

Molecular � yr New minerals formed,some altered, changesin morphology

aEF, edge-to-face; EE, edge-to-edge; FF, face-to-face.Adapted from Mitchell and Santamarina (2005) and Bennett et al. (1991).

Detailed studies of the geotechnical impacts of suchproblems have, so far, been limited (e.g., Gourvenecet al., 2005), and further studies of the impacts of agingon existing infrastructure are needed.

2.10 CONCLUDING COMMENTS

Knowledge of geologic and soil-forming processesaids in anticipating and understanding the probablecomposition, structure, properties, and behavior of asoil. Along with site investigation data, characteri-zation of the landforms, that is, understanding of theformer and current geomorphological processes asso-ciated with the past and present climatic conditions,often helps to define ground conditions for designinggeotechnical structures and anticipating the long-termperformance. For example, the knowledge can be used

to infer clay mineral types, to detect the presence oforganic and high clay content layers, to locate borrowmaterials for construction, and to estimate the depth tounaltered parent material. Pedological data can be usedto surmise compositions and soil physical properties.

Transported soils are sorted, abraded, and have par-ticle surface textures that reflect the transporting me-dium. Conditions of sedimentation and the depositionalenvironment influence the grain size, size distribution,and grain arrangement. Thus, knowledge of the trans-portation and deposition history provides insight intogeotechnical engineering properties.

In short, the soil and its properties with which wedeal today are a direct and predictable consequence ofthe parent material of many years ago and of all thethings that have happened to it since. The better ourknowledge of what that parent material was and whatthe intervening events have been, the better our ability

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QUESTIONS AND PROBLEMS 33

to deal with the soil as an engineering material. Severalexamples are given in this chapter and more are givenin Chapter 8.

QUESTIONS AND PROBLEMS

1. At what depth below the ground surface does quartzstart to crystallize?

2. What are some likely consequences of the differentphysical and chemical weathering processes on themechanical and flow properties of the rocks andsoils on which they act?

3. Describe the chemical reactions of pyrite oxidationand explain how bacteria can mediate the chemicalprocesses.

4. Discuss what types of clay minerals are likely to beproduced under each morphoclimatic zone listed inTable 2.3.

5. Using Stokes’s law, derive the sedimentation speedsof spherical particles with different sizes in fresh-water under hydrostatic condition. Would theychange in saltwater? Compare the results to the datagiven in Fig. 2.9 and discuss the comparison.

6. List and discuss human activities that may poten-tially change the properties of soils.

7. Compare and contrast soil-forming processes onEarth and on the Moon in terms of the compositionand engineering properties of the soils. Explainsimilarities and differences. What is the relative im-portance of physical, chemical, and biological soil-forming processes on the Moon and on Earth?Why?

8. Considering rock and mineral stability, the typesand characteristics of weathering processes, and theimpacts of weathering on properties, what types ofearth materials would you consider most suitablefor use as chemical, radioactive, and mixed (chem-ical and radioactive) waste containment barriers?Why?

9. Prepare diagrams showing your estimates as a func-tion of elevation of the following soil characteristicsthat you would expect to encounter between thebottom and the top of Mount Kilimanjaro in Tan-zania. Give a brief explanation for each.a. Soil plasticityb. Soil gradation and mean particle sizec. Angularity–roundness of sand and gravel parti-

clesd. Iron contente. Cementation between particlesf. Organic matter contentg. Water content

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35

CHAPTER 3

Soil Mineralogy

Figure 3.1 Particle size ranges in soils.

3.1 IMPORTANCE OF SOIL MINERALOGY INGEOTECHNICAL ENGINEERING

Soil is composed of solid particles, liquid, and gas andranges from very soft, organic deposits through lesscompressible clays and sands to soft rock. The solidparticles vary in size from large boulders to minuteparticles that are visible only with the aid of the elec-tron microscope. Particle shapes range from nearlyspherical, bulky grains to thin, flat plates and long,slender needles. Some organic material and noncrys-talline inorganic components are found in most naturalfine-grained soils. A soil may contain virtually any el-ement contained in Earth’s crust; however, by far themost abundant are oxygen, silicon, hydrogen, and alu-minum. These elements, along with calcium, sodium,potassium, magnesium, and carbon, comprise over 99percent of the solid mass of soils worldwide. Atomsof these elements are organized into various crystallineforms to yield the common minerals found in soil.Crystalline minerals comprise the greatest proportionof most soils encountered in engineering practice, andthe amount of nonclay material usually exceeds theamount of clay. Nonetheless, clay and organic matterin a soil usually influence properties in a manner fargreater than their abundance.

Mineralogy is the primary factor controlling the size,shape, and properties of soil particles. These same fac-tors determine the possible ranges of physical andchemical properties of any given soil; therefore, apriori knowledge of what minerals are in a soil pro-vides intuitive insight as to its behavior. Commonlydefined particle size ranges are shown in Fig. 3.1. Thedivisions between gravel, sand, silt, and clay sizes arearbitrary but convenient. Particles smaller than about200 mesh sieve size (0.074 mm), which is the bound-ary between sand and silt sizes, cannot be seen by the

naked eye. Clay can refer both to a size and to a classof minerals. As a size term, it refers to all constituentsof a soil smaller than a particular size, usually 0.002mm (2 �m) in engineering classifications. As a mineralterm, it refers to specific clay minerals that are distin-guished by (1) small particle size, (2) a net negativeelectrical charge, (3) plasticity when mixed with water,and (4) high weathering resistance. Clay minerals areprimarily hydrous aluminum silicates. Not all clay par-ticles are smaller than 2 �m, and not all nonclay par-ticles are coarser than 2 �m; however, the amount ofclay mineral in a soil is often closely approximated bythe amount of material finer than 2 �m. Thus, it isuseful to use the terms clay size and clay mineral con-tent to avoid confusion. A further important differencebetween clay and nonclay minerals is that the nonclaysare composed primarily of bulky particles; whereas,the particles of most of the clay minerals are platy, andin a few cases they are needle shaped or tubular.

The great range in soil particle sizes in relation toother particulate materials, electromagnetic wavelengths, and other size-dependent factors can be seenin Fig. 3.2. The liquid phase of most soil systems iscomposed of water containing various types andamounts of dissolved electrolytes. Organic compounds,both soluble and immiscible, are found in soils at sites

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36

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37

Figure 3.2 Characteristics of particles and particle dispersoids (adapted from Stanford Re-search Institute Journal, Third Quarter, 1961).

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38 3 SOIL MINERALOGY

Figure 3.3 Simplified representation of an atom.

that have been affected by chemical spills, leakingwastes, and contaminated groundwater. The gas phase,in partially saturated soils, is usually air, although or-ganic gases may be present in zones of high biologicalactivity or in chemically contaminated soils.

The mechanical properties of soils depend directlyon interactions of these phases with each other andwith applied potentials (e.g., stress, hydraulic head,electrical potential, and temperature). Because of theseinteractions, we cannot understand soil behavior interms of the solid particles alone. Nonetheless, thestructure of these particles tells us a great deal abouttheir surface characteristics and their potential inter-actions with adjacent phases.

Interatomic and intermolecular bonding forces holdmatter together. Unbalanced forces exist at phaseboundaries. The nature and magnitude of these forcesinfluence the formation of soil minerals, the structure,size, and shape of soil particles, and the physicochem-ical phenomena that determine engineering propertiesand behavior. In this chapter some aspects of atomicand intermolecular forces, crystal structure, structurestability, and characteristics of surfaces that are perti-nent to the understanding of soil behavior are sum-marized simply and briefly. This is followed by asomewhat more detailed treatment of soil minerals andtheir characteristics.

3.2 ATOMIC STRUCTURE

Current concepts of atomic structure and interparticlebonding forces are based on quantum mechanics. Anelectron can have only certain values of energy. Elec-

tronic energy can jump to a higher level by the ab-sorption of radiant energy or drop to a lower level bythe emission of radiant energy. No more than two elec-trons in an atom can have the same energy level, andthe spins of these two electrons must be in oppositedirections. Different bonding characteristics for differ-ent elements exist because of the combined effects ofelectronic energy quantization and the limitation on thenumber of electrons at each energy level.

An atom may be represented in simplified form bya small nucleus surrounded by diffuse concentric‘‘clouds’’ of electrons (Fig. 3.3). The maximum num-ber of electrons that may be located in each diffuseshell is determined by quantum theory. The numberand arrangement of electrons in the outermost shell areof prime importance for the development of differenttypes of interatomic bonding and crystal structure.

Interatomic bonds form when electrons in adjacentatoms interact in such a way that their energy levelsare lowered. If the energy reduction is large, then astrong, primary bond develops. The way in which thebonding electrons are localized in space determineswhether or not the bonds are directional. The strengthand directionality of interatomic bonds, together withthe relative sizes of the bonded atoms, determine thetype of crystal structure assumed by a given compo-sition.

3.3 INTERATOMIC BONDING

Primary Bonds

Only the outer shell or valence electrons participate inthe formation of primary interatomic bonds. There are

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SECONDARY BONDS 39

three limiting types: covalent, ionic, and metallic. Theydiffer because of how the bonding electrons are local-ized in space. The energy of these bonds per mole ofbonded atoms is from 60 � 103 to more than 400 �103 joules (J; 15 to 100 kcal). As there are 6.023 �1023 molecules per mole, it might be argued that suchbonds are weak; however, relative to the weight of anatom they are very large.

Covalent Bonds In the covalent bond, one or morebonding electrons are shared by two atomic nuclei tocomplete the outer shell for each atom. Covalent bondsare common in gases. If outer shell electrons are rep-resented by dots, then examples for (1) hydrogen gas,(2) methane, and (3) chlorine gas are:

1. H � � �H � H:H

H2.

��C � � 4H � � H:C:H��

H

3.� � � �

:Cl � � �Cl: � :Cl:Cl:� � � �

In the solid state, covalent bonds form primarily be-tween nonmetallic atoms such as oxygen, chlorine,nitrogen, and fluorine. Since only certain electronsparticipate in the bonding, covalent bonds are direc-tional. As a result, atoms bonded covalently pack insuch a way that there are fixed bond angles.

Ionic Bonds Ionic bonds form between positivelyand negatively charged free ions that acquire theircharge through gain or loss of electrons. Cations (pos-itively charged atoms that are attracted by the cathodein an electric field) form by atoms giving up one ormore loosely held electrons that lie outside a com-pleted electron shell and have a high energy level. Met-als, alkalies (e.g., sodium, potassium), and alkalineearths (e.g., calcium, magnesium) form cations. Anions(negatively charged atoms that are attracted to the an-ode) are those atoms requiring only a few electrons tocomplete their outer shell. Because the outer shells ofions are complete, structures cannot form by electronsharing as in the case of the covalent bond. Since ionsare electrically charged, however, strong electrical at-tractions (and repulsions) can develop between them.

The ionic bond is nondirectional. Each cation at-tracts all neighboring anions. In sodium chloride,which is one of the best examples of ionic bonding, asodium cation attracts as many chlorine anions as willfit around it. Geometric considerations and electricalneutrality determine the actual arrangement of ioni-cally bonded atoms.

As ionic bonding causes a separation between thecenters of positive and negative charge in a molecule,the molecule will orient in an electrical field forminga dipole. The strength of this dipole is expressed in

terms of the dipole moment �. If two electrical chargesof magnitude ��e, where e is the electronic charge,are separated by a distance d, then

� � d � �e (3.1)

Covalently bonded atoms may also produce dipolarmolecules.

Metallic Bonds Metals contain loosely held val-ence electrons that hold the positive metal ions to-gether but are free to travel through the solid material.Metallic bonds are nondirectional and can exist onlyamong a large group of atoms. It is the large group ofelectrons and their freedom to move that make metalssuch good conductors of electricity and heat. The me-tallic bond is of little importance in most soils.

Bonding in Soil Minerals

A combination of ionic and covalent bonding is typicalin most nonmetallic solids. Purely ionic or covalentbonding is a limiting condition that is the exceptionrather than the rule in most cases. Silicate minerals arethe most abundant constituents of most soils. The in-teratomic bond in silica (SiO2) is about half covalentand half ionic.

3.4 SECONDARY BONDS

Secondary bonds that are weak relative to ionic andcovalent bonds also form between units of matter. Theymay be strong enough to determine the final arrange-ments of atoms in solids, and they may be sources ofattraction between very small particles and betweenliquids and solid particles.

The Hydrogen Bond

If a hydrogen ion forms the positive end of a dipole,then its attraction to the negative end of an adjacentmolecule is termed a hydrogen bond. Hydrogen bondsform only between strongly electronegative atoms suchas oxygen and fluorine because these atoms producethe strongest dipoles. When the electron is detachedfrom a hydrogen atom, such as when it combines withoxygen to form water, only a proton remains. As theelectrons shared between the oxygen and hydrogen at-oms spend most of their time between the atoms, theoxygens act as the negative ends of dipoles, and thehydrogen protons act as the positive ends. The positiveand negative ends of adjacent water molecules tie themtogether forming water and ice.

The strength of the hydrogen bond is much greaterthan that of other secondary bonds because of the smallsize of the hydrogen ion. Hydrogen bonds are impor-

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Figure 3.4 Examples of some common crystals. (hkl) arecleavage plane indices. From Dana’s Manual of Mineralogy,by C. S. Hurlbut, 16th Edition. Copyright � 1957 by JohnWiley & Sons. Reprinted with permission from John Wiley& Sons.

tant in determining some of the characteristics of theclay minerals and in the interaction between soil par-ticle surfaces and water.

van der Waals Bonds

Permanent dipole bonds such as the hydrogen bond aredirectional. Fluctuating dipole bonds, commonlytermed van der Waals bonds, also exist because at anyone time there may be more electrons on one side ofthe atomic nucleus than on the other. This creates weakinstantaneous dipoles whose oppositely charged endsattract each other.

Although individual van der Waals bonds are weak,typically an order of magnitude weaker than a hydro-gen bond, they are nondirectional and additive betweenatoms. Consequently, they decrease less rapidly withdistance than primary valence and hydrogen bondswhen there are large groups of atoms. They are strongenough to determine the final arrangements of groupsof atoms in some solids (e.g., many polymers), andthey may be responsible for small cohesions in fine-grained soils. Van der Waals forces are described fur-ther in Chapter 7.

3.5 CRYSTALS AND THEIR PROPERTIES

Particles composed of mineral crystals form thegreatest proportion of the solid phase of a soil. A crys-tal is a homogeneous body bounded by smooth planesurfaces that are the external expression of an orderlyinternal atomic arrangement. A solid without internalatomic order is termed amorphous.

Crystal Formation

Crystals may form in three ways:

1. From Solution Ions combine as they separatefrom solution and gradually build up a solid ofdefinite structure and shape. Halite (sodium chlo-ride) and other evaporites are examples.

2. By Fusion Crystals form directly from a liquidas a result of cooling. Examples are igneous rockminerals solidified from molten rock magma andice from water.

3. From Vapor Although not of particular impor-tance in the formation of soil minerals, crystalscan form directly from cooling vapors. Examplesinclude snowflakes and flowers of sulfur.

Examples of some common crystals are shown inFig. 3.4.

Characteristics of Crystals

Certain crystal characteristics are used to distinguishdifferent classes or groups of minerals. Variations inthese characteristics result in different properties.

1. Structure The atoms in a crystal are arrangedin a definite orderly manner to form a three-dimensional network termed a lattice. Positionswithin the lattice where atoms or atomic groups

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CRYSTALS AND THEIR PROPERTIES 41

Figure 3.5 Unit cells of the 14 Bravais space lattices. The capital letters refer to the typeof cell: P, primitive cell; C, cell with a lattice point in the center of two parallel faces; F,cell with a lattice point in the center of each face; I, cell with a lattice point in the centerof the interior; R, rhombohedral primitive cell. All points indicated are lattice points. Thereis no general agreement on the unit cell to use for the hexagonal Bravais lattice; some preferthe P cell shown with solid lines, and others prefer the C cell shown in dashed lines (modifiedfrom Moffatt et al., 1965).

are located are termed lattice points. Only 14 dif-ferent arrangements of lattice points in space arepossible. These are the Bravais space lattices,and they are illustrated in Fig. 3.5.

The smallest subdivision of a crystal that stillpossesses the characteristic composition and spa-tial arrangement of atoms in the crystal is the unit

cell. The unit cell is the basic repeating unit ofthe space lattice.

2. Cleavage and Outward Form The angles be-tween corresponding faces on crystals of thesame substance are constant. Crystals breakalong smooth cleavage planes. Cleavage planeslie between planes in which the atoms are most

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Figure 3.6 The six crystal systems.

densely packed. This is because the center-to-center distance between atoms on opposite sidesof the plane is greater than along other planesthrough the crystal. As a result, the strength alongcleavage planes is less than in other directions.

3. Optical Properties The specific atomic arrange-ments within crystals allow light diffraction andpolarization. These properties are useful for iden-tification and classification. Identification of rockminerals by optical means is common. Opticalstudies in soil are less useful because of the smallsizes of most soil particles.

4. X-ray and Electron Diffraction The orderlyatomic arrangements in crystals cause them tobehave with respect to X-ray and electron beamsin much the same way as does a diffraction grat-ing with respect to visible light. Different crystalsyield different diffraction patterns. This makes X-ray diffraction a powerful tool for the study andidentification of very small particles, such as claythat cannot be seen using optical means.

5. Symmetry There are 32 distinct crystal classesbased on symmetry considerations involving thearrangement and orientation of crystal faces.These 32 classes may be grouped into 6 crystalsystems with the classes within each system bear-ing close relationships to each other.

The six crystal systems are illustrated in Fig. 3.6.Crystallographic axes parallel to the intersection edgesof prominent crystal faces are established for each ofthe six crystal systems. In most crystals, these axes willalso be symmetry axes or axes normal to symmetryplanes. In five of the six systems, the crystals are re-ferred to three crystallographic axes. In the sixth (thehexagonal system), four axes are used. The axes aredenoted by a, b, c (a1, a2, a3, and c in the hexagonalsystem) and the angles between the axes by �, �,and .

Isometric or Cubic System There are three mutu-ally perpendicular axes of equal length. Mineralexamples are galena, halite, magnetite, and pyrite.

Hexagonal System Three equal horizontal axes ly-ing in the same plane intersect at 60� with a fourthaxis perpendicular to the other three and of dif-ferent length. Examples are quartz, brucite, cal-cite, and beryl.

Tetragonal System There are three mutually per-pendicular axes, with two horizontal of equallength, but different than that of the vertical axis.Zircon is an example.

Orthorhombic System There are three mutuallyperpendicular axes, each of different length. Ex-amples include sulfur, anhydrite, barite, diaspore,and topaz.

Monoclinic System There are three unequal axes,two inclined to each other at an oblique angle,with the third perpendicular to the other two. Ex-amples are orthoclase feldspar, gypsum, musco-vite, biotite, gibbsite, and chlorite.

Triclinic System Three unequal axes intersect atoblique angles. Examples are plagioclase feldspar,kaolinite, albite, microcline, and turquoise.

3.6 CRYSTAL NOTATION

Miller indices are used to describe plane orientationsand directions in a crystal. This information, alongwith the distances that separate parallel planes is im-portant for the identification and classification of dif-ferent minerals. All lengths are expressed in terms ofunit cell lengths. Any plane through a crystal may bedescribed by intercepts, in terms of unit cell lengths,on the three or four crystallographic axes for the sys-tem in which the crystal falls. The reciprocals of theseintercepts are used to index the plane. Reciprocals areused to avoid fractions and to account for planes par-allel to an axis (an intercept of infinity equals an indexvalue of 0).

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CRYSTAL NOTATION 43

Figure 3.7 Miller indices: (a) Unit cell of muscovite, (b) (002) plane for muscovite, (c)(014) plane for muscovite, and (d) plane for muscovite.(623)

An example illustrates the determination and mean-ing of Miller indices. Consider the mineral muscovite,a member of the monoclinic system. It has unit celldimensions of a � 0.52 nanometers (nm), b � 0.90nm, c � 2.0 nm, and � � 95� 30�. Both the compo-sition and crystal structure of muscovite are similar tothose of some of the important clay minerals.

The muscovite unit cell dimensions and interceptsare shown in Fig. 3.7a. The intercepts for any plane ofinterest are first determined in terms of unit cell

lengths. Take plane mnp in Fig. 3.7a as an example.The intercepts of this plane are a � 1, b � 1, andc � 1. The Miller indices of this plane are found bytaking the reciprocals of these intercepts and clearingof fractions. Thus,

Reciprocals are 1/1, 1/1, 1/1Miller indices are (111)

The indices are always enclosed within parenthesesand indicated in the order abc without commas. Paren-

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Table 3.1 Atomic Packing, Structure, and StructuralStability

RadiusRatioa Nb Geometry Example Stability

0–0.155 2 Line — —0.155–

0.2253 Triangle (CO3)2� Very high

0.225–0.414

4 Tetrahedron (SiO4)4� Moderatelyhigh

0.414–0.732

6 Octahedron [Al(OH)6]3� High

0.732–1.0

8 Body-cen-tered cube

Iron Low

1.0 12 Sheet K–O bondin mica

Very low

aRange of cation to anion diameter ratios over whichstable coordination is expected.

bCoordination number.

Table 3.2 Relative Stabilities of Some Soil MineralStructural Units

Structural Unit

ApproximateRelative Bond

Strength(Valence/N)

Silicon tetrahedron, (SiO4)4� 4/4 � 1Aluminum tetrahedron, [Al(OH)4]1� 3/4Aluminum octahedron, [Al(OH)6]3� 3/6 � 1/2Magnesium octahedron, [Mg(OH)6]4� 2/6 � 1/3K–O12

�23 1/12

theses are always used to indicate crystallographicplanes, whereas brackets are used to indicate direc-tions. For example, [111] designates line oq in Fig.3.7a. Additional examples of Miller indices for planesthrough the muscovite crystal are shown in Figs. 3.7b,3.7c, and 3.7d. A plane that cuts a negative axis isdesignated by placing a bar over the index that pertainsto the negative intercept (Fig. 3.7d). The general index(hkl) is used to refer to any plane that cuts all threeaxes. Similarly (h00) designates a plane cutting onlythe a axis, (h0l) designates a plane parallel to the baxis, and so on. For crystals in the hexagonal system,the Miller index contains four numbers. The (001)planes of soil minerals are of particular interest be-cause they are indicative of specific clay mineral types.

3.7 FACTORS CONTROLLING CRYSTALSTRUCTURES

Organized crystal structures do not develop by chance.The most stable arrangement of atoms in a crystal isthat which minimizes the energy per unit volume. Thisis achieved by preserving electrical neutrality, satisfy-ing bond directionality, minimizing strong ion repul-sions, and packing atoms closely together.

If the interatomic bonding is nondirectional, then therelative atomic sizes have a controlling influence onpacking. The closest possible packing will maximizethe number of bonds per unit volume and minimize thebonding energy. If interatomic bonds are directional,as is the case for covalent bonds, then both bond anglesand atomic size are important.

Anions are usually larger than cations because ofelectron transfer from cations to anions. The numberof nearest neighbor anions that a cation possesses in astructure is termed the coordination number (N) or li-gancy. Possible values of coordination number in solidstructures are 1 (trivial), 2, 3, 4, 6, 8, and 12. Therelationships between atomic sizes, expressed as theratio of cationic to anionic radii, coordination number,and the geometry formed by the anions are indicatedin Table 3.1.

Most solids do not have bonds that are completelynondirectional, and the second nearest neighbors mayinfluence packing as well as the nearest neighbors.Even so, the predicted and observed coordination num-bers are in quite good agreement for many materials.The valence of the cation divided by the number ofcoordinated anions is an approximate indication of therelative bond strength, which, in turn, is related to thestructural stability of the unit. Some of the structuralunits common in soil minerals and their relative bondstrengths are listed in Table 3.2.

The basic coordination polyhedra are seldom elec-trically neutral. In crystals formed by ionic bonded pol-yhedra, the packing maintains electrical neutrality andminimizes strong repulsions between ions with likecharge. In such cases, the valence of the central cationequals the total charge of the coordinated anions, andthe unit is really a molecule. Units of this type are heldtogether by weaker, secondary bonds. An example isbrucite, a mineral that has the composition Mg(OH)2.The Mg2� ions are in octahedral coordination with six(OH)� ions forming a sheet structure in such a waythat each (OH)� is shared by 3Mg2�. In a sheet con-taining N Mg2� ions, therefore, there must be 6N/3 �2N (OH)� ions. Thus, electrical neutrality results, andthe sheet is in reality a large molecule. Successive oc-

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SURFACES 45

tahedral sheets are loosely bonded by van der Waalsforces. Because of this, brucite has perfect basal cleav-age parallel to the sheets.

Cations concentrate their charge in a smaller volumethan do anions, so the repulsion between cations isgreater than between anions. Cationic repulsions areminimized when the anions are located at the centersof coordination polyhedra. If the cations have a lowvalence, then the anion polyhedra pack as closely aspossible to minimize energy per unit volume. If, on theother hand, the cations are small and highly charged,then the units arrange in a variety of ways in responseto the repulsions. The silicon cation is in this category.

3.8 SILICATE CRYSTALS

Small cations form structures with coordination num-bers of 3 and 4 (Table 3.1). These cations are oftenhighly charged and generate strong repulsions betweenadjacent triangles or tetrahedra. As a result, such struc-tures share only corners and possibly edges, but neverfaces, since to do so would bring the cations too closetogether. The radius of silicon is only 0.039 nm,whereas that of oxygen is 0.132 nm. Thus silicon andoxygen combine in tetrahedral coordination, with thesilicon occupying the space at the center of the tetra-hedron formed by the four oxygens. The tetrahedralarrangement satisfies both the directionality of thebonds (the Si–O bond is about half covalent and halfionic) and the geometry imposed by the radius ratio.Silicon is very abundant in Earth’s crust, amounting toabout 25 percent by weight, but only 0.8 percent byvolume. Almost half of igneous rock by weight and91.8 percent by volume is oxygen.

Silica tetrahedra join only at their corners, andsometimes not at all. Thus many crystal structures arepossible, and there is a large number of silicate min-erals. Silicate minerals are classified according to howthe silica tetrahedra (SiO4)

4� associate with each other,as shown in Fig. 3.8. The tetrahedral combinations in-crease in complexity from the beginning to the end ofthe figure. The structural stability increases in the samedirection.

Island (independent) silicates are those in which thetetrahedra are not joined to each other. Instead, the fourexcess oxygen electrons are bonded to other positiveions in the crystal structure. In the olivine group, theminerals have the composition R2

2� � SiO44�. Garnets

contain cations of different valences and coordinationnumbers R3

2� � R23�(SiO4)3. The negative charge of the

SiO4 group in zircon is all balanced by the single Zr4�.Ring and chain silicates are formed when corners of

tetrahedra are shared. The formulas for these structures

contain (SiO3)2�. The pyroxene minerals are in this

class. Enstatite, MgSiO3, is a simple member of thisgroup. Some of the positions normally occupied bySi4� in single-chain structures may be filled by Al3�.

Substitution of ions of one kind by ions of anothertype, having either the same or different valence, butthe same crystal structure, is termed isomorphous sub-stitution. The term substitution implies a replacementwhereby a cation in the structure is replaced at sometime by a cation of another type. In reality, however,the replaced cations were never there, and the mineralwas formed with its present proportions of the differentcations in the structure.

Double chains of indefinite length may form with(Si4O11)

6� as part of the structure. The amphiboles fallinto this group (Fig. 3.8). Hornblendes have the samebasic structure, but some of the Si4� positions are filledby Al3�. The cations Na� and K� can be incorporatedinto the structure to satisfy electrical neutrality; Al3�,Fe3�, Fe2�, and Mn2� can replace part of the Mg2� insixfold coordination, and the (OH)� group can be re-placed by F�.

In sheet silicates three of the four oxygens of eachtetrahedron are shared to give structures containing(Si2O5)

2�. The micas, chlorites, and many of the clayminerals contain silica in a sheet structure. Frameworksilicates result when all four of the oxygens are sharedwith other tetrahedra. The most common example isquartz. In quartz, the silica tetrahedra are grouped toform spirals. The feldspars also have three-dimensionalframework structures. Some of the silicon positions arefilled by aluminum, and the excess negative chargethus created is balanced by cations of high coordina-tion such as potassium, calcium, sodium, and barium.Differences in the amounts of this isomorphous sub-stitution are responsible for the different members ofthe feldspar family.

3.9 SURFACES

All liquids and solids terminate at a surface, or phaseboundary, on the other side of which is matter of adifferent composition or state. In solids, atoms arebonded into a three-dimensional structure, and the ter-mination of this structure at a surface, or phase bound-ary, produces unsatisfied force fields. In a fine-grainedparticulate material such as clay soil the surface areamay be very large relative to the mass of the material,and, as is emphasized throughout this book, the influ-ences of the surface forces on properties and behaviormay be very large.

Unsatisfied forces at solid surfaces may be balancedin any of the following ways:

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Figure 3.8 Silica tetrahedral arrangements in different silicate mineral structures. ReprintedGillott (1968) with permission from Elsevier Science Publishers BV.

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SURFACES 47


1. Attraction and adsorption of molecules from theadjacent phase

2. Cohesion with the surface of another mass of thesame substance

3. Solid-state adjustments of the structure beneaththe surface.

Each unsatisfied bond force is significant relative tothe weight of atoms and molecules. The actual mag-nitude of 10�11 N or less, however, is infinitesimalcompared to the weight of a piece of gravel or a grainof sand. On the other hand, consider the effect of re-ducing particle size. A cube 10 mm on an edge has a

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surface area of 6.0 � 10�4 m2. If it is cut in half inthe three directions, eight cubes result, each 5 mm onan edge. The surface area now is 12.0 � 10�4 m2. Ifthe cubes are further divided to 1 �m on an edge, thesurface becomes 6.0 m2 for the same 1000 mm3 ofmaterial. Thus, as a solid is subdivided into smallerand smaller units, the proportion of surface area toweight becomes larger and larger. For a given particleshape, the ratio of surface area to volume is inverselyproportional to some effective particle diameter.

For many materials when particle size is reduced to1 or 2 �m or less the surface forces begin to exert adistinct influence on the behavior. Study of the behav-ior of particles of this size and less requires consider-ations of colloidal and surface chemistry. Most clayparticles behave as colloids, both because of theirsmall size and because they have unbalanced surfaceelectrical forces as a result of isomorphous substitu-tions within their structure.

Montmorillonite, which is one of the members ofthe smectite clay mineral group (see Section 3.17),may break down into particles that are only 1 unit cellthick (1.0 nm) when in a dispersed state and have aspecific surface area of 800 m2/g. If all particles con-tained in about 10 g of this clay could be spread outside by side, they would cover a football field.

3.10 GRAVEL, SAND, AND SILT PARTICLES

The physical characteristics of cohesionless soils, thatis, gravel, sand, and nonplastic silts, are determinedprimarily by particle size, shape, surface texture, andsize distribution. The mineral composition determineshardness, cleavage, and resistance to physical andchemical breakdown. Some carbonate and sulfate min-erals, such as calcite and gypsum, are sufficiently sol-uble that their decomposition may be significant withinthe time frame of many projects. In many cases, how-ever, the nonclay particles may be treated as relativelyinert, with interactions that are predominantly physicalin nature. Evidence of this is provided by the soils onthe Moon. Lunar soils have a silty, fine sand gradation;however, their compositions are totally different thanthose of terrestrial soils of the same gradation. Theengineering properties of the two materials are sur-prisingly similar, however.

The gravel, sand, and most of the silt fraction in asoil are composed of bulky, nonclay particles. As mostsoils are the products of the breakdown of preexistingrocks and soils, they are weathering products. Thus,the predominant mineral constituents of any soil arethose that are one or more of the following:

1. Very abundant in the source material2. Highly resistant to weathering, abrasion, and im-

pact3. Weathering products

The nonclays are predominantly rock fragments ormineral grains of the common rock-forming minerals.In igneous rocks, which are the original source mate-rial for many soils, the most prevalent minerals are thefeldspars (about 60 percent) and the pyroxenes andamphiboles (about 17 percent). Quartz accounts forabout 12 percent of these rocks, micas for 4 percent,and other minerals for about 8 percent.

However, in most soils, quartz is by far the mostabundant mineral, with small amounts of feldspar andmica also present. Pyroxenes and amphiboles are sel-dom found in significant amounts. Carbonate minerals,mainly calcite and dolomite, are also found in somesoils and can occur as bulky particles, shells, precipi-tates, or in solution. Carbonates dominate the compo-sition of some deep-sea sediments. Sulfates, in variousforms, are found primarily in soils of semiarid and aridregions, with gypsum (CaSO4 � 2H2O) being the mostcommon. Iron and aluminum oxides are abundant inresidual soils of tropical regions.

Quartz is composed of silica tetrahedra grouped toform spirals, with all tetrahedral oxygens bonded tosilicon. The tetrahedral structure has a high stability.In addition, the spiral grouping of tetrahedra producesa structure without cleavage planes, quartz is alreadyan oxide, there are no weakly bonded ions in the struc-ture, and the mineral has high hardness. Collectively,these factors account for the high persistence of quartzin soils.

Feldspars are silicate minerals with a three-dimensional framework structure in which part of thesilicon is replaced by aluminum. The excess negativecharge resulting from this replacement is balanced bycations such as potassium, calcium, sodium, strontium,and barium. As these cations are relatively large, theircoordination number is also large. This results in anopen structure with low bond strengths between units.Consequently, there are cleavage planes, the hardnessis only moderate, and feldspars are relatively easilybroken down. This accounts for their lack of abun-dance in soils compared to their abundance in igneousrocks.

Mica has a sheet structure composed of tetrahedraland octahedral units. Sheets are stacked one on theother and held together primarily by potassium ions in12-fold coordination that provide an electrostatic bondof moderate strength. In comparison with the intralayerbonds, however, this bond is weak, which accounts forthe perfect basal cleavage of mica. As a result of the

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STRUCTURAL UNITS OF THE LAYER SILICATES 49

Figure 3.9 Swelling index as a function of mica content forcoarse-grained mixtures (data from Terzaghi, 1931).

thin-plate morphology of mica flakes, sand and siltscontaining only a few percent mica may exhibit highcompressibility when loaded and large swelling whenunloaded, as may be seen in Fig. 3.9. The amphiboles,pyroxenes, and olivine have crystal structures that arerapidly broken down by weathering; hence they areabsent from most soils.

Some examples of silt and sand particles from dif-ferent soils are shown in Fig. 3.10. Angularity androundness can be used to describe particle shapes, asshown in Fig. 3.11. Elongated and platy particles candevelop preferred orientations, which can be respon-sible for anisotropic properties within a soil mass. Thesurface texture of the grains influences the stress–deformation and strength properties.

3.11 SOIL MINERALS AND MATERIALSFORMED BY BIOGENIC AND GEOCHEMICALPROCESSES

Evaporite deposits formed by precipitation of saltsfrom salt lakes and seas as a result of the evaporationof water are sometimes found in layers that are severalmeters thick. The major constituents of seawater andtheir relative proportions are listed in Table 3.3. Alsolisted are some of the more important evaporite de-

posits. In some areas alternating layers of evaporite andclay or other fine-grained sediments are formed duringcyclic wet and dry periods.

Many limestones, as well as coral, have been formedby precipitation or from the remains of various organ-isms. Because of the much greater solubility of lime-stone than most other rock types, it may be the sourceof special problems caused by solution channels andcavities under foundations.

Chemical sediments and rocks in freshwater lakes,ponds, swamps, and bays are occasionally encounteredin civil engineering projects. Biochemical processesform marl, which ranges from relatively pure calciumcarbonate to mixtures with mud and organic matter.Iron oxide is formed in some lakes. Diatomite or dia-tomaceous earth is essentially pure silica formed fromthe skeletal remains of small (up to a few tenths of amillimeter) freshwater and saltwater organisms. Owingto their solubility limestone, calcite, gypsum, and othersalts may cause special geotechnical problems.

Oxidation and reduction of pyrite-bearing earth ma-terials, that is, soils and rocks containing FeS2, can bethe source of many types of geotechnical problems,including ground heave, high swell pressures, forma-tion of acid drainage, damage to concrete, and corro-sion of steel (Bryant et al., 2003). The chemical andbiological processes and consequences of pyritic re-actions are covered in Sections 8.3, 8.11, and 8.16.

More than 12 percent of Canada is covered by apeaty material, termed muskeg, composed almost en-tirely of decaying vegetation. Peat and muskeg mayhave water contents of 1000 percent or more; they arevery compressible, and they have low strength. Thespecial properties of these materials and methods foranalysis of geotechnical problems associated withthem are given by MacFarlane (1969), Dhowian andEdil (1980), and Edil and Mochtar (1984).

3.12 SUMMARY OF NONCLAY MINERALCHARACTERISTICS

Important compositional, structural, and morphologicalcharacteristics of the important nonclay minerals foundin soils are summarized in Table 3.4. Of these miner-als, quartz is by far the most common, both in termsof the number of soils in which it is found and itsabundance in a typical soil. Feldspar and mica are fre-quently present in small percentages.

3.13 STRUCTURAL UNITS OF THE LAYERSILICATES

Clay minerals in soils belong to the mineral familytermed phyllosilicates, which also contains other layer

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Figure 3.10 Photomicrographs of sand and silt particles from several soils: (a) Ottawa stan-dard sand, (b) Monterey sand, (c) Sacramento River sand, (d) Eliot sand, and (e) lunar soilmineral grains (photo courtesy Johnson Space Center). Squares in background area are 1�1mm. (ƒ) Recrystallized breccia particles from lunar soil (photo courtesy of NASA JohnsonSpace Center). Squares in background grid are 1�1 mm.

silicates such as serpentine, pyrophyllite, talc, mica,and chlorite. Clay minerals occur in small particlesizes, and their unit cells ordinarily have a residualnegative charge that is balanced by the adsorption ofcations from solution.

The structures of the common layer silicates aremade up of combinations of two simple structuralunits, the silicon tetrahedron (Fig. 3.12) and the alu-minum or magnesium octahedron (Fig. 3.13). Differentclay mineral groups are characterized by the stackingarrangements of sheets1 (sometimes chains) of these

1 In conformity with the nomenclature of the Clay Minerals Society(Bailey et al., 1971), the following terms are used: a plane of atoms,a sheet of basic structural units, and a layer of unit cells composedof two, three, or four sheets.

units and the manner in which two successive two- orthree-sheet layers are held together.

Differences among minerals within clay mineralgroups result primarily from differences in the type andamount of isomorphous substitution within the crystalstructure. Possible substitutions are nearly endless innumber, and the crystal structure arrangement mayrange from very poor to nearly perfect. Fortunately forengineering purposes, knowledge of the structural andcompositional characteristics of each group, withoutdetailed study of the subtleties of each specific mineral,is adequate.

Silica Sheet

In most clay mineral structures, the silica tetrahedraare interconnected in a sheet structure. Three of the

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STRUCTURAL UNITS OF THE LAYER SILICATES 51


Figure 3.11 Sand and silt size particle shapes as seen insilhouette.

four oxygens in each tetrahedron are shared to form ahexagonal net, as shown in Figs. 3.12b and 3.14. Thebases of the tetrahedra are all in the same plane, andthe tips all point in the same direction. The structurehas the composition (Si4O10)

4� and can repeat indefi-nitely. Electrical neutrality can be obtained by replace-ment of four oxygens by hydroxyls or by union witha sheet of different composition that is positivelycharged. The oxygen-to-oxygen distance is 2.55 ang-stroms (A),2 the space available for the silicon ion is0.55 A, and the thickness of the sheet in clay mineralstructures is 4.63 A (Grim, 1968).

2 In conformity with the SI system of units, lengths should be givenin nanometers. For convenience, however, the angstrom unit is re-tained for atomic dimensions, where 1 A � 0.1 nm.

Silica Chains

In some of the less common clay minerals, silica tet-rahedra are arranged in bands made of double chainsof composition (Si4O11)

6�. Electrical neutrality isachieved and the bands are bound together by alumi-num and/or magnesium ions. A diagrammatic sketchof this structure is shown in Fig. 3.8. Minerals in thisgroup resemble the amphiboles in structure.

Octahedral Sheet

This sheet structure is composed of magnesium or alu-minum in octahedral coordination with oxygens or hy-droxyls. In some cases, other cations are present inplace of Al3� and Mg2�, such as Fe2�, Fe3�, Mn2�,Ti4�, Ni2�, Cr3�, and Li�. Figure 3.13b is a schematicdiagram of such a sheet structure. The oxygen-to-oxygen distance is 2.60 A, and the space available forthe octahedrally coordinated cation is 0.61 A. Thethickness of the sheet is 5.05 A in clays (Grim, 1968).

If the cation is trivalent, then normally only two-thirds of the possible cationic spaces are filled, and thestructure is termed dioctahedral. In the case of alu-minum, the composition is Al2(OH)6. This compositionand structure form the mineral gibbsite. When com-bined with silica sheets, as is the case in clay mineral

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Table 3.3 Major Constituents of Seawater and Evaporite Deposits

Ion Grams per LiterPercent by Weight

of Total Solids Important Evaporite Deposits

Sodium, Na� 10.56 30.61 Anhydrite CaSO4

Magnesium, Mg2� 1.27 3.69 Barite BaSO4

Calcium, Ca2� 0.40 1.16 Celesite SrSO4

Potassium, K� 0.38 1.10 Kieserite MgSO4 � H2OStrontium, Sr2� 0.013 0.04 Gypsum CaSO4 � 2H2OChloride, Cl� 18.98 55.04 Polyhalite Ca2K2Mg(SO4) � 2H2OSulfate, SO4

2� 2.65 7.68 Bloedite Ma2Mg(SO4)2 � 4H2OBicarbonate, HCO3

� 0.14 0.41 Hexahydrite MgSO4 � 6H2OBromide, Br� 0.065 0.19 Epsomite MgSO4 � 7H2OFluoride, F� 0.001 — Kainite K4Mg4(Cl/SO4) � 1 1H2OBoric Acid, H3BO3 0.026 0.08 Halite NaCl

34.485 100.00 Sylvite KClFlourite CaF2

Bischofite MgCl2 � 6H2OCarnallite KMgCl3 � 6H2O

Adapted from data by Degens (1965).

structures, an aluminum octahedral sheet is referred toas a gibbsite sheet.

If the octahedrally coordinated cation is divalent,then normally all possible cation sites are occupied andthe structure is trioctahedral. In the case of magne-sium, the composition is Mg3(OH)6, giving the mineralbrucite. In clay mineral structures, a sheet of magne-sium octahedra is termed a brucite sheet.

Schematic representations of the sheets are usefulfor simplified diagrams of the structures of the differ-ent clay minerals:

Silica sheet or

Octahedral sheet (Various cations in octahedral coordination)

Gibbsite sheet (Octahedral sheet cations are mainly aluminum)

Brucite sheet (Octahedral sheet cations are mainly magnesium)

Water layers are found in some structures and maybe represented by �� for each molecular layer.Atoms of a specific type, for example, potassium, arerepresented thus: .�K

The diagrams are indicative of the clay mineral layerstructure. They do not indicate the correct width-to-length ratios for the actual particles. The structuresshown are idealized; in actual minerals, irregular sub-stitutions and interlayering or mixed-layer structuresare common. Furthermore, direct assembly of the basic

units does not necessarily form the naturally occurringminerals. The ‘‘building block’’ approach is useful,however, for the development of conceptual models.

3.14 SYNTHESIS PATTERN ANDCLASSIFICATION OF THE CLAY MINERALS

The manner in which atoms are assembled into tetra-hedral and octahedral units, followed by the formation

of sheets and their stacking to form layers that combineto produce the different clay mineral groups is illus-trated in Fig. 3.15. The basic structures shown in thebottom row of Fig. 3.15 comprise the great prepon-derance of the clay mineral types that are found insoils.

Grouping the clay minerals according to crystalstructure and stacking sequence of the layers is con-venient since members of the same group have gen-

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SYNTHESIS PATTERN AND CLASSIFICATION OF THE CLAY MINERALS 53

Table 3.4 Properties and Characteristics of Nonclay Minerals in Soils

Mineral FormulaCrystalSystem Cleavage

ParticleShape

SpecificGravity Hardness

Occurrencein Soils of

EngineeringInterest

Quartz SiO2 Hexagonal None Bulky 2.65 7 Veryabundant

Orthoclasefeldspar

KalSi3O8 Monoclinic 2 planes Elongate 2.57 6 Common

Plagioclasefeldspar

NaAlSi3O8

CaAl2Si3O8 (variable)Triclinic 2 planes Bulky—

elongate2.62–2.76 6 Common

Muscovitemica

Kal3Si3O10(OH)2 Monoclinic Perfect basal Thin plates 2.76–3.1 2–21⁄2 Common

Biotite mica K(Mg,FE)3AlSi3O10(OH)2 Monoclinic Perfect basal Thin plates 2.8–3.2 21⁄2–3 CommonHornblende Na,Ca,Mg,Fe,Al silicate Monoclinic Perfect

prismaticPrismatic 3.2 5–6 Uncommon

Augite(pyroxene)

Ca(Mg,Fe,Al)(Al,Si)2O6 Monoclinic Good prismatic Prismatic 3.2–3.4 5–6 Uncommon

Olivine (Mg,Fe)2SiO4 Orthorhombic Conchoidalfracture

Bulky 3.27–3.37 61⁄2–7 Uncommon

Calcite CaCO3 Hexagonal Perfect Bulky 2.72 21⁄2–3 May beabundantlocally

Dolomite CaMg(CO3)2 Hexagonal Perfectrhombohedral

Bulky 2.85 31⁄2–4 May beabundantlocally

Gypsum CaSO4 � 2H2O Monoclinic 4 planes Elongate 2.32 2 May beabundantlocally

Pyrite FeS2 Isometric Cubical Bulky cubic 5.02 6–61⁄2

Data from Hurlbut (1957).

Figure 3.12 Silicon tetrahedron and silica tetrahedra arranged in a hexagonal network.

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Figure 3.13 Octahedral unit and sheet structure of octahedral units.

Figure 3.14 Silica sheet in plan view.

erally similar engineering properties. The mineralshave unit cells consisting of two, three, or four sheets.The two-sheet minerals are made up of a silica sheetand an octahedral sheet. The unit layer of the three-sheet minerals is composed of either a dioctahedral ortrioctahedral sheet sandwiched between two silicasheets. Unit layers may be stacked closely together orwater layers may intervene. The four-sheet structure ofchlorite is composed of a 2�1 layer plus an interlayerhydroxide sheet. In some soils, inorganic, claylike ma-terial is found that has no clearly identifiable crystal

structure. Such material is referred to as allophane ornoncrystalline clay.

The bottom row of Fig. 3.15 shows that the 2�1minerals differ from each other mainly in the type andamount of ‘‘glue’’ that holds the successive layers to-gether. For example, smectite has loosely held cationsbetween the layers, illite contains firmly fixed potas-sium ions, and vermiculite has somewhat organizedlayers of water and cations. The chlorite group repre-sents an end member that has 2�1 layers bonded by anorganized hydroxide sheet. The charge per formula

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INTERSHEET AND INTERLAYER BONDING IN THE CLAY MINERALS 55

Figure 3.15 Synthesis pattern for the clay minerals.

unit is variable both within and among groups, andreflects the fact that the range of compositions is greatowing to varying amounts of isomorphous substitution.Accordingly, the boundaries between groups are some-what arbitrary.

Isomorphous Substitution

The concept of isomorphous substitution was intro-duced in Section 3.13 in connection with some of thesilicate crystals. It is very important in the structureand properties of the clay minerals. In an ideal gibbsitesheet, only two-thirds of the octahedral positions arefilled, and all of the cations are aluminum. In an idealbrucite sheet, all the octahedral spaces are filled bymagnesium. In an ideal silica sheet, silicons occupy alltetrahedral spaces. In clay minerals, however, some ofthe tetrahedral and octahedral spaces are occupied bycations other than those in the ideal structure. Commonexamples are aluminum in place of silicon, magnesiuminstead of aluminum, and ferrous iron (Fe2�) for mag-nesium. This presence in an octahedral or tetrahedralposition of a cation other than that normally found,without change in crystal structure, is isomorphoussubstitution. The actual tetrahedral and octahedral cat-ion distributions may develop during initial formationor subsequent alteration of the mineral.

3.15 INTERSHEET AND INTERLAYERBONDING IN THE CLAY MINERALS

A single plane of atoms that are common to both thetetrahedral and octahedral sheets forms a part of the

clay mineral layers. Bonding between these sheets isof the primary valence type and is very strong. How-ever, the bonds holding the unit layers together maybe of several types, and they may be sufficiently weakthat the physical and chemical behavior of the clay isinfluenced by the response of these bonds to changesin environmental conditions.

Isomorphous substitution in all of the clay minerals,with the possible exception of those in the kaolinitegroup, gives clay particles a net negative charge. Topreserve electrical neutrality, cations are attracted andheld between the layers and on the surfaces and edgesof the particles. Many of these cations are exchange-able cations because they may be replaced by cationsof another type. The quantity of exchangeable cationsis termed the cation exchange capacity (cec) and isusually expressed as milliequivalents (meq)3 per 100 gof dry clay.

Five types of interlayer bonding are possible in thelayer silicates (Marshall, 1964).

1. Neutral parallel layers are held by van der Waalsforces. Bonding is weak; however, stable crystalsof appreciable thickness such as the nonclay min-

3 Equivalent weight � combining weight of an element � (atomicweight /valence). Number of equivalents � (weight of element /atomic weight) � valence. The number of ions in an equivalent �Avogardro’s number /valence. Avogadro’s number � 6.02 � 1023. Anequivalent contains 6.02 � 1023 electron charges or 96,500 coulombs,which is 1 faraday.

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erals of pyrophyllite and talc may form. Theseminerals cleave parallel to the layers.

2. In some minerals (e.g., kaolinite, brucite, gibb-site), there are opposing layers of oxygens andhydroxyls or hydroxyls and hydroxyls. Hydrogenbonding then develops between the layers as wellas van der Waals bonding. Hydrogen bonds re-main stable in the presence of water.

3. Neutral silicate layers that are separated byhighly polar water molecules may be held to-gether by hydrogen bonds.

4. Cations needed for electrical neutrality may be inpositions that control interlayer bonding. In mi-cas, some of the silicon is replaced by aluminumin the silica sheets. The resulting charge defi-ciency is partly balanced by potassium ions be-tween the unit cell layers. The potassium ion justfits into the holes formed by the bases of thesilica tetrahedra (Fig. 3.12). As a result, it gen-erates a strong bond between the layers. In thechlorites, the charge deficiencies from substitu-tions in the octahedral sheet of the 2�1 sandwichare balanced by excess charge on the single-sheetlayer interleaved between the three-sheet layers.This provides a strongly bonded structure thatwhile exhibiting cleavage will not separate in thepresence of water or other polar liquids.

5. When the surface charge density is moderate, asin smectite and vermiculite, the silicate layersreadily adsorb polar molecules, and also the ad-sorbed cations may hydrate, resulting in layerseparation and expansion. The strength of the in-terlayer bond is low and is a strong function ofcharge distribution, ion hydration energy, surfaceion configuration, and structure of the polar mol-ecule.

Smectite and vermiculite particles adsorb water be-tween the unit layers and swell, whereas particles ofthe nonclay minerals, pyrophyllite and talc, which havecomparable structures, do not. There are two possiblereasons (van Olphen, 1977):

1. The interlayer cations in smectite hydrate, andthe hydration energy overcomes the attractiveforces between the unit layers. There are no in-terlayer cations in pyrophyllite; hence, no swell-ing.

2. Water does not hydrate the cations but is ad-sorbed on oxygen surfaces by hydrogen bonds.There is no swelling in pyrophyllite and talc be-cause the surface hydration energy is too smallto overcome the van der Waals forces between

layers, which are greater in these minerals be-cause of a smaller interlayer distance.

Whatever the reason, the smectite minerals are thedominant source of swelling in the expansive soils thatare so prevalent throughout the world.

3.16 THE 1�1 MINERALS

The kaolinite–serpentine minerals are composed of al-ternating silica and octahedral sheets as shown sche-matically in Fig. 3.16. The tips of the silica tetrahedraand one of the planes of atoms in the octahedral sheetare common. The tips of the tetrahedra all point in thesame direction, toward the center of the unit layer. Inthe plane of atoms common to both sheets, two-thirdsof the atoms are oxygens and are shared by both sili-con and the octahedral cations. The remaining atomsin this plane are (OH) located so that each is directlybelow the hole in the hexagonal net formed by thebases of the silica tetrahedra. If the octahedral layer isbrucite, then a mineral of the serpentine subgroup re-sults, whereas dioctahedral gibbsite layers give clayminerals in the kaolinite subgroup. Trioctahedral 1�1minerals are relatively rare, usually occur mixed withkaolinite or illite, and are hard to identify. A diagram-matic sketch of the kaolinite structure is shown in Fig.3.17. The structural formula is (OH)8Si4Al4O10, and thecharge distribution is indicated in Fig. 3.18.

Mineral particles of the kaolinite subgroup consistof the basic units stacked in the c direction. The bond-ing between successive layers is by both van der Waalsforces and hydrogen bonds. The bonding is sufficientlystrong that there is no interlayer swelling in the pres-ence of water.

Because of slight differences in the oxygen-to-oxygen distances in the tetrahedral and octahedral lay-ers, there is some distortion of the ideal tetrahedralnetwork. As a result, kaolinite, which is the most abun-dant member of the subgroup and a common soil min-eral, is triclinic instead of monoclinic. The unit celldimensions are a � 5.16 A, b � 8.94 A, c � 7.37 A,� � 91.8�, � � 104.5�, and � 90�.

Variations in stacking of layers above each other,and possibly in the position of aluminum ions withinthe available sites in the octahedral sheet, produce dif-ferent members of the kaolinite subgroup. The dickiteunit cell is made up of two unit layers, and the nacriteunit cell contains six. Both appear to be formed byhydrothermal processes. Dickite is fairly common assecondary clay in the pores of sandstone and in coalbeds. Neither dickite nor nacrite is common in soils.

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THE 1�1 MINERALS 57

Figure 3.16 Schematic diagrams of the structures of kaolinite and serpentine: (a) kaoliniteand (b) serpentine.

Figure 3.17 Diagrammatic sketch of the kaolinite structure.

Figure 3.18 Charge distribution on kaolinite.

Halloysite

Halloysite is a particularly interesting mineral of thekaolinite subgroup. Two distinct endpoint forms of thismineral exist, as shown in Fig. 3.19; one, a hydratedform consisting of unit kaolinite layers separated fromeach other by a single layer of water molecules andhaving the composition (OH)8Si4Al4O10 � 4H2O, andthe other, a nonhydrated form having the same unitlayer structure and chemical composition as kaolinite.The basal spacing in the c direction d(001) for the non-hydrated form is about 7.2 A, as for kaolinite. Becauseof the interleaved water layer, d(001) for hydrated hal-loysite is about 10.1 A. The difference between these

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Figure 3.19 Schematic diagrams of the structure of halloysite: (a) halloysite (10 A) and (b)halloysite (7 A).

Figure 3.20 Electron photomicrograph of well-crystallizedkaolinite from St. Austell, Cornwall, England. Picture widthis 17 �m (Tovey, 1971).

values, 2.9 A, is the approximate thickness of a singlelayer of water molecules.

The recommended terms for the two forms of hal-loysite are halloysite (7 A) and halloysite (10 A).Transformation from halloysite (10 A) to halloysite (7A) by dehydration can occur at relatively low temper-atures and is irreversible. Halloysite is often found insoils formed from volcanic parent materials in wet en-vironments. It can be responsible for special propertiesand problems in earthwork construction, as discussedlater in this book.

Isomorphous Substitution and Exchange Capacity

Whether or not measurable isomorphous substitutionexists within the structure of the kaolinite minerals isuncertain. Nevertheless, values of cation exchange ca-pacity in the range of 3 to 15 meq/100 g for kaoliniteand from 5 to 40 meq/100 g for halloysite have beenmeasured. Thus, kaolinite particles possess a net neg-ative charge. Possible sources are:

1. Substitution of Al3� for Si4� in the silica sheet ora divalent ion for Al3� in the octahedral sheet.Replacement of only 1 Si in every 400 would beadequate to account for the exchange capacity.

2. The hydrogen of exposed hydroxyls may be re-placed by exchangeable cations. According toGrim (1968), however, this mechanism is notlikely because the hydrogen would probably notbe replaceable under the conditions of mostexchange reactions.

3. Broken bonds around particle edges may give un-satisfied charges that are balanced by adsorbedcations.

Kaolinite particles are charged positively on theiredges when in a low pH (acid) environment, but neg-atively charged in a high pH (basic) environment. Lowexchange capacities are measured under low pH con-ditions and high exchange capacities are obtained for

determinations at high pH. This suggests that brokenbonds are at least a partial source of exchange capacity.That a positive cation exchange capacity is measuredunder low pH conditions when edges are positivelycharged indicates that some isomorphous substitutionmust exist also.

As interlayer separation does not occur in kaolinite,balancing cations must adsorb on the exterior surfacesand edges of the particles.

Morphology and Surface Area

Well-crystallized particles of kaolinite (Fig. 3.20), na-crite, and dickite occur as well-formed six-sided plates.The lateral dimensions of these plates range fromabout 0.1 to 4 �m, and their thicknesses are from about0.05 to 2 �m. Poorly crystallized kaolinite generallyoccurs as less distinct hexagonal plates, and the parti-cle size is usually smaller than for the well-crystallizedvarieties.

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SMECTITE MINERALS 59

Figure 3.21 Electron photomicrograph of halloysite fromBedford, Indiana. Picture width is 2 �m (Tovey, 1971).

Halloysite (10 A) occurs as cylindrical tubes ofoverlapping sheets of the kaolinite type (Fig. 3.21).The c axis at any point nearly coincides with the tuberadius. The formation of tubes has been attributed to amisfit in the b direction of the silica and gibbsite sheets(Bates et al., 1950). The b dimension in kaolinite is8.93 A; in gibbsite it is only 8.62 A. This means thatthe (OH) spacing in gibbsite sheets is stretched in orderto obtain a fit with the silica sheet. Evidently, in hal-loysite (10 A), the reduced interlayer bond, caused bythe intervening layer of water molecules, enables the(OH) layer to revert to 8.62 A, resulting in a curvaturewith the hydroxyls on the inside and the bases of thesilica tetrahedra on the outside. The outside diametersof the tubular particles range from about 0.05 to 0.20�m, with a median value of 0.07 �m. The wall thick-ness is about 0.02 �m. The tubes range in length froma fraction of a micrometer to several micrometers. Dry-ing of halloysite (10 A) may result in splitting or un-rolling of the tubes. The specific surface area ofkaolinite is about 10 to 20 m2/g of dry clay; that ofhalloysite (10 A) is 35 to 70 m2/g.

3.17 SMECTITE MINERALS

Structure

The minerals of the smectite group have a prototypestructure similar to that of pyrophyllite, consisting ofan octahedral sheet sandwiched between two silicasheets, as shown schematically in Fig. 3.22 and dia-grammatically in three dimensions in Fig. 3.23. All thetips of the tetrahedra point toward the center of theunit cell. The oxygens forming the tips of the tetra-hedra are common to the octahedral sheet as well. Theanions in the octahedral sheet that fall directly above

and below the hexagonal holes formed by the bases ofthe silica tetrahedra are hydroxyls.

The layers formed in this way are continuous in thea and b directions and stacked one above the other inthe c direction. Bonding between successive layers isby van der Waals forces and by cations that balancecharge deficiencies in the structure. These bonds areweak and easily separated by cleavage or adsorptionof water or other polar liquids. The basal spacing inthe c direction, d(001), is variable, ranging from about9.6 A to complete separation.

The theoretical composition in the absence ofisomorphous substitutions is (OH)4Si8Al4O20 �n(interlayer)H2O. The structural configuration and cor-responding charge distribution are shown in Fig. 3.24.The structure shown is electrically neutral, and theatomic configuration is essentially the same as that inthe nonclay mineral pyrophyllite.

Isomorphous Substitution in the Smectite Minerals

Smectite minerals differ from pyrophyllite in that thereis extensive isomorphous substitution for silicon andaluminum by other cations. Aluminum in the octahe-dral sheet may be replaced by magnesium, iron, zinc,nickel, lithium, or other cations. Aluminum may re-place up to 15 percent of the silicon ions in the tetra-hedral sheet. Possibly some of the silicon positions canbe occupied by phosphorous (Grim, 1968).

Substitutions for aluminum in the octahedral sheetmay be one-for-one or three-for-two (aluminum oc-cupies only two-thirds of the available octahedral sites)in any combination from a few to complete replace-ment. The resulting structure, however, is either almostexactly dioctahedral (montmorillonite subgroup) ortrioctahedral (saponite subgroup). The charge defi-ciency resulting from these substitutions ranges from0.5 to 1.2 per unit cell. Usually, it is close to 0.66 perunit cell. A charge deficiency of this amount wouldresult from replacement of every sixth aluminum by amagnesium ion. Montmorillonite, the most commonmineral of the group, has this composition. Charge de-ficiencies that result from isomorphous substitution arebalanced by exchangeable cations located between theunit cell layers and on the surfaces of particles.

Some minerals of the smectite group and their com-positions are listed in Table 3.5. An arrow indicates thesource of the charge deficiency, which has been as-sumed to be 0.66 per unit cell in each case. Sodium isindicated as the balancing cation. The formulas shouldbe considered indicative of the general character of themineral, but not as absolute, because a variety of com-positions can exist within the same basic crystal struc-ture. Because of the large amount of unbalanced

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Figure 3.22 Schematic diagrams of the structures of the smectite minerals: (a) montmoril-lonite and (b) saponite.

Figure 3.23 Diagrammatic sketch of the montmorillonitestructure.

Figure 3.24 Charge distribution in pyrophyllite (type struc-ture for montmorillonite).

substitution in the smectite minerals, they have highcation exchange capacities, generally in the range of80 to 150 meq/100 g.


Montmorillonite may occur as equidimensional flakesthat are so thin as to appear more like films, as shown

in Fig. 3.25. Particles range in thickness from 1-nmunit layers upward to about 1/100 of the width. Thelong axis of the particle is usually less than 1 or 2 �m.When there is a large amount of substitution of ironand/or magnesium for aluminum, the particles may belath or needle shaped because the larger Mg2� and Fe3�

ions cause a directional strain in the structure.The specific surface area of smectite can be very

large. The primary surface area, that is, the surface areaexclusive of interlayer zones, ranges from 50 to 120m2/g. The secondary specific surface that is exposed

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SMECTITE MINERALS 61

Table 3.5 Some Minerals of the Smectite Group

MineralTetrahedral Sheet

SubstitutionsOctahedral Sheet

Substitutions Formula/Unit Cella

Dioctahedral, Smectites orMontmorillonites

Montmorillonite None 1Mg2� for every sixth Al3� (OH)4Si8(Al3.34Mg0.66) O20

↓Na0.66

Beidellite Al for Si None (OH)4(Si6.34Al1.66) Al4.34O20

↓Na0.66

Nontronite Al for Si Fe3� for Al (OH)4(Si7.34Al0.66) Fe43�O20

↓Na0.66

Trioctahedral, Smectites,or Saponites

Hectorite None Li for Mg (OH)4Si8(Mg5.34Li0.66) O20

↓Na0.66

Saponite Al for Si Fe3� for Mg (OH)4(Si7.34Al0.66) Mg6O20

↓Na0.66

Sauconite Al for Si Zn for Mg (OH)4(Si8�yAly)(Zn6�xMgx) O20

↓Na0.66

aTwo formula units are needed to give one unit cell.After Ross and Hendricks (1945); Marshall (1964); and Warshaw and Roy (1961).

Figure 3.25 Electron photomicrograph of montmorillonite(bentonite) from Clay Spur, Wyoming. Picture width is 7.5�m (Tovey, 1971).

by expanding the lattice so that polar molecules canpenetrate between layers can be up to 840 m2/g.

Bentonite

A very highly plastic, swelling clay material known asbentonite is very widely used for a variety of purposes,ranging from drilling mud and slurry walls to clarifi-cation of beer and wine. The bentonite familiar to mostgeoengineers is a highly colloidal, expansive alterationproduct of volcanic ash. It has a liquid limit of 500percent or more. It is widely used as a backfill duringthe construction of slurry trench walls, as a soil ad-mixture for construction of seepage barriers, as a groutmaterial, as a sealant for piezometer installations, andfor other special applications.

When present as a major constituent in soft shale oras a seam in rock formations, bentonite may be a causeof continuing slope stability problems. Slide problemsat Portuguese Bend along the Pacific Ocean in southernCalifornia, in the Bearpaw shale in Saskatchewan, andin the Pierre shale in South Dakota are in large mea-

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Figure 3.26 Schematic diagram of the structures of muscovite, illite, and vermiculite: (a)muscovite and illite and (b) vermiculite.

sure due to the high content of bentonite. Stabilityproblems in underground construction may be causedby the presence of montmorillonite in joints and faults(Brekke and Selmer-Olsen, 1965).

3.18 MICALIKE CLAY MINERALS

Illite is the most commonly found clay mineral in soilsencountered in engineering practice. Its structure isquite similar to that of muscovite mica, and it is some-times referred to as hydrous mica. Vermiculite is alsooften found as a clay phase constituent of soils. Itsstructure is related to that of biotite mica.

Structure

The basic structural unit for the muscovite (white mica)is shown schematically in Fig. 3.26a. It is the three-layer silica–gibbsite–silica sandwich that forms pyro-phyllite, with the tips of all the tetrahedra pointingtoward the center and common with octahedral sheetions. Muscovite differs from pyrophyllite, however, inthat about one-fourth of the silicon positions are filledby aluminum, and the resulting charge deficiency isbalanced by potassium between the layers. The layersare continuous in the a and b directions and stacked inthe c direction. The radius of the potassium ion, 1.33A, is such that it fits snugly in the 1.32 A radius holeformed by the bases of the silica tetrahedra. It is in 12-fold coordination with the 6 oxygens in each layer.

A diagrammatic three-dimensional sketch of themuscovite structure is shown in Fig. 3.27. The struc-tural configuration and charge distribution are shown

in Fig. 3.28. The unit cell is electrically neutral andhas the formula (OH)4K2(Si6Al2)Al4O20. Muscovite isthe dioctahedral end member of the micas and containsonly Al3� in the octahedral layer. Phlogopite (brownmica) is the trioctahedral end member, with the octa-hedral positions filled entirely by magnesium. It hasthe formula (OH)4K2(Si6Al2)Mg6O20. Biotite (blackmica) is trioctahedral, with the octahedral positionsfilled mostly by magnesium and iron. It has the generalformula (OH)4K2(Si6Al2)(MgFe)6O20. The relative pro-portions of magnesium and iron may vary widely.

Illite differs from mica in the following ways (Grim,1968):

1. Fewer of the Si4� positions are filled by Al3� inillite.

2. There is some randomness in the stacking of lay-ers in illite.

3. There is less potassium in illite. Well-organizedillite contains 9 to 10 percent K2O (Weaver andPollard, 1973).

4. Illite particles are much smaller than mica parti-cles.

Some illite may contain magnesium and iron in theoctahedral sheet as well as aluminum (Marshall, 1964).Iron-rich illite, usually occurring as earthy green pel-lets, is termed glauconite.

The vermiculite structure consists of regular inter-stratification of biotite mica layers and double molec-ular layers of water, as shown schematically in Fig.3.26b. The actual thickness of the water layer dependson the cations that balance the charge deficiencies in

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MICALIKE CLAY MINERALS 63

Figure 3.27 Diagrammatic sketch of the structure of muscovite.

Figure 3.28 Charge distribution in muscovite.

the biotitelike layers. With magnesium or calciumpresent, which is the usual case in nature, there aretwo water layers, giving a basal spacing of 14 A. Ageneral formula for vermiculite is

(OH)4(MgCa)x(Si8xAlx)(MgFe)6O20yH2O

x � 1 to 1.4 y � 8

Isomorphous Substitution and Exchange Capacity

There is extensive isomorphous substitution in illiteand vermiculite. The charge deficiency in illite is 1.3to 1.5 per unit cell. It is located primarily in the silicasheets and is balanced partly by the nonexchangeablepotassium between layers. Thus, the cation exchangecapacity of illite is less than that of smectite, amount-ing to 10 to 40 meq/100 g. Values greater than 10 to15 meq/100 g may be indicative of some expandinglayers (Weaver and Pollard, 1973). In the absence offixed potassium the exchange capacity would be about150 meq/100 g. Interlayer bonding by potassium is sostrong that the basal spacing of illite remains fixed at10 A in the presence of polar liquids.

The charge deficiency in vermiculite is 1 to 1.4 perunit cell. Since the interlayer cations are exchangeable,the exchange capacity of vermiculite is high, amount-

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Figure 3.30 Schematic diagram of the structure of chlorite.

Figure 3.29 Electron photomicrograph of illite from Morris,Illinois. Picture width is 7.5 �m (Tovey, 1971).

ing to 100 to 150 meq/100 g. The basal spacing, d(001),is influenced by both the type of cation and the hy-dration state. With potassium or ammonium in theexchange positions, the basal spacing is only 10.5 to11 A. Lithium gives 12.2 A. Interlayer water can bedriven off by heating to temperatures above 100�C.This dehydration is accompanied by a reduction inbasal spacing to about 10 A. The mineral quickly re-hydrates and expands again to 14 A when exposed tomoist air at room temperature.


Illite usually occurs as very small, flaky particlesmixed with other clay and nonclay materials. High-purity deposits of illite are uncommon. The flaky par-ticles may have a hexagonal outline if well crystallized.The long axis dimension ranges from 0.1 �m or lessto several micrometers, and the plate thickness may beas small as 3 nm. An electron photomicrograph of illiteis shown in Fig. 3.29. Vermiculite may occur in natureas large crystalline masses having a sheet structuresomewhat similar in appearance to mica. In soils, ver-miculite occurs as small particles mixed with otherclay minerals.

The specific surface area of illite is about 65 to 100m2/g. The primary surface of vermiculites is 40 to 80m2/g, and the secondary (interlayer) surface may be ashigh as 870 m2/g.

3.19 OTHER CLAY MINERALS

Chlorite Minerals

Structure The chlorite structure consists of alter-nating micalike and brucitelike layers as shown sche-matically in Fig. 3.30. The structure is similar to that

of vermiculite, except that an organized octahedralsheet replaces the double water layer between micalayers. The layers are continuous in the a and b direc-tions and stacked in the c direction. The basal spacingis fixed at 14 A.

Isomorphous Substitution The central sheet of themica layer is trioctahedral, with magnesium as the pre-dominant cation. There is often partial replacement ofMg2� by Al3�, Fe2� and Fe3�. There is substitution ofAl3� for Mg2� in the brucitelike layer. The variousmembers of the chlorite group differ in the kind andamounts of substitution and in the stacking of succes-sive layers. The cation exchange capacity of chloritesis in the range of 10 to 40 meq/100 g.

Morphology Chlorite minerals occur as micro-scopic grains of platy morphology and poorly definedcrystal edges in altered igneous and metamorphic rocksand their derived soils. In soils, chlorites always appearto occur in mixtures with other clay minerals.

Chain Structure Clay Minerals

A few clay minerals are formed from bands (doublechains) of silica tetrahedra. These include attapulgiteand imogolite. They have lathlike or fine threadlikemorphologies, with particle diameters of 5 to 10 nmand lengths up to 4 to 5 �m. An electron photomicro-graph of bundles of attapulgite particles is shown inFig. 3.31.

Although these minerals are not frequently encoun-tered, attapulgite is commercially mined and is used asa drilling mud in saline and other special environmentsbecause of its high stability in suspensions.

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DETERMINATION OF SOIL COMPOSITION 65

Figure 3.31 Electron photomicrograph of attapulgite fromAttapulgis, Georgia. Picture width is 4.7 �m (Tovey, 1971).

Mixed-Layer Clays

More than one type of clay mineral is usually foundin most soils. Because of the great similarity in crystalstructure among the different minerals, interstratifica-tion of two or more layer types often occurs within asingle particle. Interstratification may be regular, witha definite repetition of the different layers in sequence,or it may be random. According to Weaver and Pollard(1973), randomly interstratified clay minerals are sec-ond only to illite in abundance.

The most abundant mixed-layer material is com-posed of expanded water-bearing layers and contractednon-water-bearing layers. Montmorillonite–illite ismost common, and chlorite–vermiculite and chlorite–montmorillonite are often found. Rectorite is an inter-stratified clay with high charge, micalike layers withfixed interlayer cations alternating in a regular mannerwith low-charge montmorillonite-like layers containingexchangeable cations capable of hydration.

Noncrystalline Clay Materials

Allophane Clay materials that are so poorly crys-talline that a definite structure cannot be determinedare termed allophane. Such material is amorphous toX-rays because there is insufficient long-range order ofthe octahedral and tetrahedral units to produce sharpdiffraction effects, although in some cases there maybe diffraction bands. Allophane has no definite com-position or shape and may exhibit a wide range ofphysical properties. Some noncrystalline clay materialis probably contained in all fine-grained soils. It iscommon in volcanic soils because of the abundance ofglass particles.

Oxides All soils probably contain some amount ofcolloidal oxides and hydrous oxides (Marshall, 1964).The oxides and hydroxides of aluminum, silicon, andiron are most frequently found. These materials mayoccur as gels or precipitates and coat mineral particles,or they may cement particles together. They may alsooccur as distinct crystalline units; for example, gibb-site, boehmite, hematite, and magnetite. Limonite andbauxite, which are noncrystalline mixtures of iron andaluminum hydroxides, are also sometimes found.

Oxides are particularly common in soils formedfrom volcanic ash and in tropical residual soils. Somesoils rich in allophane and oxides may exhibit signif-icant irreversible decreases in plasticity and increasesin strength when dried. Many are susceptible to break-down and strength loss when subjected to traffic ormanipulation during earthwork construction (Mitchelland Sitar, 1982; Mitchell and Coutinho, 1991).

3.20 SUMMARY OF CLAY MINERALCHARACTERISTICS

The important structural, compositional, and morpho-logical characteristics of the important clay mineralsare summarized in Table 3.6. Data on the structuralcharacteristics of the tetrahedral and octahedral sheetstructures are included.

3.21 DETERMINATION OF SOILCOMPOSITION

Introduction

Identification of the fine-grained minerals in a soil isusually done by X-ray diffraction. Simple chemicaltests can be used to indicate the presence of organicmatter and other constituents. The microscope may beused to identify the constituents of the nonclay frac-tion. Accurate determination of the proportions of dif-ferent mineral, organic, and amorphous solid materialin a soil, while probably possible with the expenditureof great time and at great cost, is unlikely to be worth-while owing to our inability to make exact quantitativelinks from composition to properties. Accordingly,from knowledge of grain size distribution, the relativeintensities of different X-ray diffraction peaks, and afew other simple tests a semiquantitative analysis maybe made that is usually adequate for most purposes.

A general approach is given in this section for thedetermination of soil composition, some of the tech-niques are described briefly, and criteria for identifi-cation of important soil constituents are stated.

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Table 3.6 Summary of Clay Mineral Characteristics

Structural1. Silica Tetrahedron: Si atom at center. Tetrahedron units form hexagonal network � Si4O8(OH)4

2. Gibbsite Sheet: Aluminum in octahedral coordination. Two-thirds of possible positions filled. Al2(OH)—O—O � 2.60 A.3. Brucite Sheet: Magnesium in octahedral coordination. All possible positions filled. Mg2(OH)—O—O � 2.60 A.

TypeSubgroup and

Schematic Structure Mineral Complete Formula / Unit CellaOctahedral Layer

CationsTetrahedral Layer

Cations

Structure

Isomorphous Substitution Interlayer Bond

Allophane Allophanes Amorphous — —

Kaolinite Kaolinite (OH)8Si4Al4O11 Al4 Si4 Little O—OHHydrogen Strong

1�1

Dickite

Nacrite

Halloysite(dehydrated)

Halloysite(hydrated)

(OH)8Si4Al4O10

(OH)8Si4Al4O10

(OH)8Si4Al4O10

(OH)8Si4Al4O10 � 4H2O

Al4

Al4

Al4

Al4

Si4

Si4

Si4

Si4

Little

Little

Little

Little

O—OHHydrogen Strong

O—OHHydrogen StrongO—OHHydrogen StrongO—OHHydrogen Strong

Montmorillonite(OH)4Si8Al4O20 � NH2O(Theoretical

Unsubsitituted)

Montmorillonite (OH)4Si8(Al3.34Mg.66O20nH2O↓ *Na.66

Al3.34Mg.66 Si8 Mg for Al, Net chargealways � 0.66- / unitcell

O—OVery weak

expanding lattice

Beidellite

Nontronite

(OH)4(Si7.34Al66)(Al4)O20nH2O↓

Na.66

(OH)4(Si7.34Al.66)Fe43�O20nH2O

↓Na.66

Al4

Fe4

Si7.34Al.66

Si7.34Al.66

Al for Si, Net chargealways � 0.66- / forunit cell

Fe for Al, Al for Si, Netcharge always � 0.66-/ for unit cell

O—OVery weak

expanding latticeO—OVery weak

expanding lattice

2�1 Saponite Hectorite

Saponite

Sauconite

(OH)4Si8(Mg5.34Li.66)P20nH2O↓

Na.66

(OH)4(Si7.34Al.66)Mg6O20nH2O↓Na.66

(Si6.94Al1.06)Al.66Fe.34Mg.36Zn4.80O20(OH)4

↓ � nH2ONa.66

Mg5.34Li.66

Mg, Fe3�

Al.44Fe.34Mg.36Zn4.80

Si8

Si7.34Al.66

Si6.94Al1.06

Mg, Li for Al, Netcharge always � 0.66-/ unit cell

Mg for Al, Al for Si,Net charge always �0.66- / for unit cell

Zn for Al

O—OVery weak



expanding lattice

Hydrous Mica (Illite) Illites (K, H2O)2(Si)8(Al,Mg,Fe)4,6O20(OH)4 (Al,Mg,Fe)4-6 (Al,Si)8 Some Si always replacedby Al, Balanced by Kbetween layers.

K ions; strong

Vermiculite Vermiculite (OH)4(Mg,Ca)x(Si8�xAlx)(Mg.Fe)6O20.yH2Ox � 1 to 1.4, y � 8

(Mg,Fe)6 (Si,Al)8 Al for Si not charge of 1to 1.4 / unit cell

Weak

2�1�1 Chlorite Chlorite(Several varieties

known)

(OH)4(SiAl)8(Mg.Fe)6O20 (2�1 layer)(MgAl)6(OH)12 interlayer

(Mg,Fe)6(2�1 layer)(Mg,Al)6 interlayer

(Si,Al)8 Al for Si in 2�1 layerAl for Mg in interlayer

ChainStructure

Sepiolite

Attapulgite

Si4O11(Mg.H2)3H2O2(H2O)

(OH2)4(OH)2Mg5Si8O20.4H2O

Fe or Al for Mg

Some for Al for Si Weak � chainslinked by 0

a Arrows indicate source of charge deficiency. Equivalent Na listed as balancing cation. Two formula units (Table 3.4) are required per unit cell.b Electron microscope data.

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Table 3.6 (Continued )

UnitsAll bases in same plane. O—O � 2.55 A—Space for Si � 0.55 A—Thickness8 4.93 A. C—C height � 2.1 A.OH—OH � 2.94 A. Space for ion � 0.61 A. Thickness of unit � 5.05 A. Dioctahedral.OH—OH � 2.94 A. Space for ion � 0.61 A. Thickness of unit � 5.05 A. Trioctahedral.

Structure

Crystal Structure Basal Spacing Shape SizebCation ExchangeCap.(meq / 100 g)

SpecificGravity

Specific Surfacem2 / g

Occurrence in Soilsof Engineering

Interest

Irregular, some-what rounded

0.05–1 �Common

Triclinica � 5.14, b � 8.93, c � 7.37� � 91.6�, � � 104.8�, � 89.9�

7.2 A 6-sided flakes 0.1–4 � �single�0.05–2 �

to 3000 � 4000(stacks)

3–15 2.60–2.68 10–20 Very common

Monoclinica � 5.15, b � 8.95, c � 14.42� � 96�48�

14.4 A Unit cellcontains 2unit layers

6-sided flakes 0.07–300 � 2.5–1000 �

1–30 Rare

Almost Orthorhombica � 5.15, b � 8.96, c � 43� � 90�20�a � 5.14 in O Planea � 5.06 in OH Planeb � 8.93 in O Planeb � 8.62 in OH Plane� layers curve

43 A

7.2 A

10.1 A

Unit cellcontains 6unit layers

Randomstacking ofunit cells

Water layerbetween unitcells

Rounded flakes

Tubes

Tubes

1 � � 0.025–0.15 �

0.07 � O.D.0.04 � I.D.1 � long.

5–10

5–40

2.55–2.56

2.0–2.2 35–70

Rare

Occasional

Occasional

9.6A—Completeseparation

Dioctahedral Flakes (equi-dimensional)

�10 A � up to10 �

80–150 2.35–2.7 50–120 Primary700–840 Secondary

Very common


Dioctahedral Rare


Dioctahedral Laths Breadth � 1 / 5length toseveral � �unit cell

110–150 2.2–2.7 Rare


Trioctahedral To 1 � � unitcell breadth �0.02 � 0.1�

17.5 Rare

Trioctahedral Similar tomont.

Similar to mont. 70–90 2.24–2.30 Rare

Trioctahedral Brand laths 50 A Thick Rare

10 A Bothdioctrahedralandtrioctahedral

Flakes 0.003–0.1 � �up to 10 �

10–40 2.6–3.0 65–100 Very common

a � 5.34, b � 9.20c � 28.91, � � 93�15�

10.5–14 A AlternatingMica anddouble H2Olayers

Similar to illite 100–150 40–80 Primary870 Secondary

Fairly common

Monoclinic (Mainly)a � 5.3, b � 9.3c � 28.52, � � 97�8�

14 A Similar to illite 1 � 10–40 2.6–2.96 Common

Monoclinica � 2 � 11.6, b � 2 � 7.86c � 5.33a0 Sin � � 12.9 b0 � 18c0 � 5.2

Chain

Double silicachains

Flakes or fibers

Laths Max, 4–5 � �50–100 A

Width � 2t

20–30

20–30

2.08 Rare

Occasional

From Grim, R. E. (1968) Clay Mineralogy, 2d edition, McGraw-Hill, New York. Brown, G. (editor) (1961) The X-ray Identification and Crystal Structure of Clay Materials, MineralogicalSociety (Clay Minerals Group), London.

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Methods for Compositional Analysis

Methods and techniques that may be employed for de-termination of soil composition and study of soil grainsinclude:

1. Particle size analysis and separation2. Various pretreatments prior to mineralogical

analysis3. Chemical analyses for free oxides, hydroxides,

amorphous constituents, and organic matter4. Petrographic microscope study of silt and sand

grains5. Electron microscope study6. X-ray diffraction for identification of crystalline

minerals7. Thermal analysis8. Determination of specific surface area9. Chemical analysis for layer charge, cation

exchange capacity, exchangeable cations, pH,and soluble salts

10. Staining tests for identification of clays

Procedures for determination of soil composition aredescribed in detail in publications of the American So-ciety of Agronomy. Part 1—Physical and Mineralog-ical Methods provides a set of procedures formineralogical analyses for use by soil scientists andengineers. Part 2—Microbiological and BiochemicalProperties, published in 1994, is useful for determi-nations needed for bioremediation and other geoen-vironmental purposes. Part 3—Chemical Methods,published in 1996 contains methods for characterizingsoil chemical properties as well as several methods forcharacterizing soil chemical processes. Part 4—Physical Methods, published in 2002, is an updatedversion of the physical methods covered in Part 1. Foreach method, principles are presented as well as thedetails of the method. In addition, the interpretation ofresults is discussed, and extensive bibliographies aregiven.

Accuracy of Compositional Analysis

Techniques for chemical analysis are generally of ahigh order of accuracy. However, this accuracy doesnot extend to the overall compositional analysis of asoil in terms of components of interest in understand-ing and quantifying behavior. This is because knowl-edge of the chemical composition of a soil is of limitedvalue by itself. Chemical analysis of the solid phase ofa soil does not indicate the organization of the ele-ments into crystalline and noncrystalline components.

For quantitative mineralogical analysis of the clayfraction, it is usually necessary to assume that the

properties of the mineral in the soil are the same asthose of a reference mineral. However, different sam-ples of any given clay mineral may exhibit significantdifferences in composition, surface area, particle sizeand shape, and cation exchange capacity. Thus, selec-tion of ‘‘standard’’ minerals for reference is arbitrary.Quantitative clay mineral determinations cannot bemade to an accuracy of more than about plus or minusa few percent without exhaustive chemical and min-eralogical tests.

General Scheme for Compositional Analysis

A general scheme for determination of the componentsof a soil is given in Fig. 3.32. Techniques of the mostvalue for qualitative and semiquantitative analysis areindicated by a double asterisk, and those of particularuse for explaining unusual properties are indicated bya single asterisk. The scheme shown is by no meansthe only one that could be used; a feedback approachis desirable wherein the results of each test are used toplan subsequent tests. Brief discussions of the varioustechniques listed in Fig. 3.32 are given below. X-raydiffraction analysis is treated in more detail in the nextsection because of its particular usefulness for theidentification of fine-grained soil minerals.

Grain Size Analysis Determination of particle sizeand size distribution is usually done using sieve anal-ysis for the coarse fraction [sizes greater than 74 �m(i.e., 200 mesh sieve)] and by sedimentation methodsfor the fine fraction. Details of these methods are pre-sented in standard soil mechanics texts and in the stan-dards of the American Society for Testing andMaterials (ASTM). Determination of sizes by sedi-mentation is based on the application of Stokes’s lawfor the settling velocity of spherical particles:

� s w 2v � D (3.2)18�

where s � unit weight of particle, w � unit weightof liquid, � � viscosity of liquid, and D � diameterof sphere. Sizes determined by Stoke’s law are not ac-tual particle diameters but, rather, equivalent sphericaldiameters. Gravity sedimentation is limited to particlesizes in the range of about 0.2 mm to 0.2 �m, theupper bound reflecting the size limit where flow aroundthe particles is no longer laminar, and the lower boundrepresenting a size where Brownian motion keeps par-ticles in suspension indefinitely.

The times for particles of 2, 5, and 20 �m equivalentspherical diameter to fall through water a distance of10 cm are about 8 h, 1.25 h, and 5 min, respectively,at 20�C. At 30�C the required times are about 6.5 h, 1

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Figure 3.32 Flow sheet for compositional analysis of soils (adapted from Lambe and Martin,1954).

h, and 4 min. A centrifuge can be used for acceleratingthe settlement of small particles and is the most prac-tical means for extracting particles smaller than abouta micrometer in size.

Sedimentation methods call for treatment of a soil–water suspension with a dispersing agent and thoroughmixing prior to the start of the test. This causes break-down of aggregates of soil particles, and the degree ofbreakdown may vary greatly with the method of prep-aration. For example, the ASTM standard method oftest permits the use of either an air dispersion cup ora blender-type mixer. The amount of material less than2 �m equivalent spherical diameter may vary by asmuch as a factor of 2 by the two techniques. The re-lationship between the size distribution that results

from laboratory preparation of the sample to that ofthe particles and aggregates in the natural soil is un-known.

Optical and electron microscopes are sometimesused to study particle sizes and size distributions andto provide information on particle shape, aggregation,angularity, weathering, and surface texture.

Pore Fluid Electrolyte The total concentration ofsoluble salts may be determined from the electricalconductivity of extracted pore fluid. Chemical or pho-tometric techniques may be used to determine the el-emental constituents of the extract (Rhoades, 1982).Removal of excess soluble salts by washing the samplewith water or alcohol may be necessary before pro-ceeding with subsequent analysis. If they are not re-

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moved, the soil may be difficult to disperse, it may bedifficult to remove organic matter, reliable cationexchange capacity determinations will be impossible,and mineralogical analyses will be complicated (Kunzeand Dixon, 1986).

pH Determination of the acidity or alkalinity of asoil in terms of the pH is a relatively simple measure-ment that can be made using a pH meter or specialindicators (American Society for Testing and Materi-als, 1970; McLean, 1982). The value obtained dependson the ratio of soil to water, so it is usual to standardizethe measurement using a 1�1 ratio of soil to water byweight. For highly plastic soils a lower soil-to-waterratio may be required to produce a suspension suitablefor pH measurement. The pH decreases with increas-ing concentration of neutral salts in solution and withincreasing amounts of dissolved CO2.

Carbonates Carbonates, in the form of calcite(CaCO3), dolomite [CaMg(CO3)2], marl, and shells arefrequently found in soils, and they can be readily de-tected by effervescence when the soil is treated withdilute HCl. Many methods for determining inorganiccarbonates, calcite, and dolomite in soils are available(Nelson, 1982). These include dissolution in acid, dif-ferential thermal analysis, X-ray diffraction, and chem-ical analyses.

Gypsum Gypsum (CaSO4 � 2H2O) can be deter-mined by a simple heating test. Visible grains will turnwhite when heated on a metal plate as a result of de-hydration to form ‘‘dead-burnt gypsum’’ (Shearman,1979). Quantitative determinations can be made usingprocedures described by Nelson (1982).

Organic Matter Organic matter can be readily de-tected by treatment of the soil with a 15 percent hy-drogen peroxide solution. H2O2 reacts with organicmatter to give vigorous effervescence. As organic mat-ter has an aggregating effect, and because its presencemay interfere with other mineralogical analyses, it isdesirable to remove most of it by digestion with H2O2

(Kunze and Dixon, 1986). Quantitative analysis meth-ods for soil organic matter are given by the AmericanSociety for Testing and Materials (1970), Nelson andSommers (1982), and Schnitzer (1982).

Oxides and Hydroxides Free oxides and hydrox-ides that may be present in soils include crystalline andnoncrystalline (amorphous) compounds of silicon, alu-minum, and iron. These materials may occur as dis-crete particles, as coatings on particles, and ascementing agents between particles. They may makesoil dispersion difficult, and they may interfere withother analysis procedures. Methods for oxide and hy-droxide detection, quantitative analysis, and removalare given by Jackson et al. (1986).

Exchange Complex Determination of the cationexchange capacity (expressed in milliequivalents perhundred grams of dry soil) is made after first freeingthe soil of excess soluble salts. The adsorbed cationsare then replaced by a known cation species, and theamount of the known cation needed to saturate theexchange sites is determined analytically (Rhoades,1982). The composition of the original cation complexcan be determined by chemical analysis of the originalextract (Thomas, 1982).

Potash The hydrous mica minerals (illites) are theonly minerals commonly found in the clay size fractionof soils that contain potassium in their crystal structure.Thus, knowledge of the K2O content is useful for quan-titative determination of their abundance. A method forpotassium determination is given by Knudsen et al.(1986). Well-organized 10-A illite layers contain 9 to10 percent K2O (Weaver and Pollard, 1973).

Specific Surface Area Ethylene glycol and glyceroladsorb on clay surfaces. As different clay mineralshave different values of specific surface, the amount ofglycol or glycerol retained under controlled conditionscan be used to aid in the quantitative determinationsof clay minerals and for estimation of specific surfacearea (Martin, 1955; Diamond and Kinter, 1956; andAmerican Society for Testing and Materials, 1970).

Use of ethylene glycol monoethyl ether (EGME) asthe polar molecule for determining surface area offersthe advantages of the attainment of adsorption equilib-rium more rapidly and with greater precision (Carteret al., 1982). A monomolecular layer of EGME is as-sumed to form in vacuum on a predried clay sample.The weight of EGME adsorbed after equilibrium isreached is converted to specific surface using a factorof 0.000286 g EGME per square meter of surface.

3.22 X-RAY DIFFRACTION ANALYSIS

X-Rays and Their Generation

X-ray diffraction is the most widely used method foridentification of fine-grained soil minerals and thestudy of their crystal structure. X-rays are one of sev-eral types of waves in the electromagnetic spectrum(Fig. 3.2). X-rays have wavelengths in the range of0.01 to 100 A. When high-speed electrons impinge ona target material, one of two phenomena may occur:

1. The high-speed electron strikes and displaces anelectron from an inner shell of one of the atomsof the target material. An electron from one ofthe outer shells then falls into the vacancy tolower the energy state of the atom. An X-rayphoton of wavelength and intensity characteristic

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X-RAY DIFFRACTION ANALYSIS 71

Figure 3.35 Composite relationship for X-ray intensity as afunction of wavelength.

Figure 3.34 X-ray generation by deceleration of electronsin an electric field.

Figure 3.33 X-ray generation by electron displacement. Let-ters designate shells in which electron transfer takes place.

of the target atom and of the particular electronicpositions is emitted. Because electronic transfersmay take place in several shells and each has acharacteristic frequency, the result is a relation-ship between radiation intensity and wavelengthas shown in Fig. 3.33.

2. The high-speed electron does not strike an elec-tron in the target material but slows down in theintense electric fields near atomic nuclei. The de-crease in energy is converted to heat and to X-ray photons. X-rays produced in this way areindependent of the nature of the bombarded at-oms and appear as a band of continuously vary-ing wavelength as shown in Fig. 3.34.

The resulting output of X-rays from these two ef-fects acting together is shown in Fig. 3.35. X-rays aregenerated using a tube in which electrons stream froma filament to a target material across a voltage drop of20 to 50 kV. Curved crystal monochrometers can beused to give X-rays of a single wavelength. Alterna-tively, certain materials are able to absorb X-rays ofdifferent wavelengths, so it is possible to filter the out-put of an X-ray tube to give rays of only one wave-

length. The wavelengths of monochromatic radiation(usually K�, Fig. 3.33) produced from commonly usedtarget materials range from 0.71 A for molybdenum to2.29 A for chromium. Copper radiation, which is mostfrequently used for mineral identification, has a wave-length of 1.54 A.

Diffraction of X-rays

Because wavelengths of about 1 A are of the sameorder as the spacing of atomic planes in crystallinematerials, X-rays are useful for analysis of crystalstructures. When X-rays strike a crystal, they penetrateto a depth of several million layers before being ab-sorbed. At each atomic plane a minute portion of thebeam is absorbed by individual atoms that then oscil-late as dipoles and radiate waves in all directions. Ra-diated waves in certain directions will be in phase andcan be interpreted in simplistic fashion as a wave re-sulting from a reflection of the incident beam. In-phaseradiations emerge as a coherent beam that can be de-tected on film or by a radiation counting device. Theorientation of parallel atomic planes, relative to the di-rection of the incident beam, at which radiations are inphase depends on the wave length of the X-rays andthe spacing between atomic planes.

Figure 3.36 shows a parallel beam of X-rays ofwavelength � striking a crystal at an angle � to parallelatomic planes spaced at distance d. If the reflectedwave from C is to reinforce the wave reflected fromA, then the path length difference between the twowaves must be an integral number of wave lengths n�.From Fig. 3.36, this difference is distance BC � CD.Thus,

BC � CD � n�

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Figure 3.36 Geometrical conditions for X-ray diffraction according to Bragg’s law.

From symmetry, BC � CD, and by trigonometry,CD � d sin �. Thus the necessary condition is givenby

n� � 2d sin � (3.3)

This is Bragg’s law. It forms the basis for identificationof crystals using X-ray diffraction. Since no two min-erals have the same spacings of interatomic planes inthree dimensions, the angles at which diffractions oc-cur (and the atomic spacings calculated from them) canbe used for identification. X-ray diffraction is partic-ularly well suited for identification of clay mineralsbecause the (001) spacing is characteristic for eachclay mineral group. The basal planes generally give themost intense reflections of any planes in the crystalsbecause of the close packing of atoms in these planes.The common nonclay minerals occurring in soils arealso detectable by X-ray diffraction.

Detection of Diffracted X-rays

Because the small size of most soil particles preventsthe study of single crystals, use is made of the powdermethod and of oriented aggregates of particles. In thepowder method, a small sample containing particles atall possible orientations is placed in a collimated beamof parallel X-rays, and diffracted beams of various in-tensities are scanned by a Geiger, proportional, or scin-tillation tube and recorded automatically to produce achart showing the intensity of diffracted beam as afunction of angle 2�. As an example, the diffractionpattern for quartz is shown in Fig. 3.37. The powdermethod works because the very large number of par-ticles in a sample ensures that some will always beproperly oriented to produce a reflection.

All prominent atomic planes in a crystal will pro-duce a reflection if properly positioned with respect to

the X-ray beam. Thus, each mineral will produce acharacteristic set of reflections at values of � corre-sponding to the interatomic spacings between theprominent planes. The intensities of the different re-flections vary according to the density of atomic pack-ing and other factors.

When the oriented aggregate method is used, platyclay particles are precipitated onto a glass slide, usu-ally by drying from a deflocculated suspension or sep-arated from a suspension on a porous ceramic plate.With most particles oriented parallel to the slide, the(001) reflections are intensified, whereas reflectionsfrom (hk0) planes are minimized.

In the Bragg equation, n may be any whole number.The reflection corresponding to n � 1 is termed thefirst-order reflection. If the first-order reflection for amineral gives d(001) � 10 A, then for n � 2 there canbe a reflection at 5 A, for n � 3 there can be a reflec-tion at 3.33 A, and so on. It is common to refer tothese as higher-order reflections due to the (002) plane,the (003) plane, and so on, even though atomic planesdo not exist at these spacings. They are, in reality, val-ues of d /n � � / (2 sin �) for integer values of n � 1.

Analysis of X-ray Patterns

A complete X-ray diffraction pattern consists of a se-ries of reflections of different intensities at differentvalues of 2�. Each reflection must be assigned to somecomponent of the sample. The first step in the analysisis to determine all values of d/n for the particular typeof radiation (which determines �) using Eq. (3.3). Thetest pattern may be compared directly with patterns forknown materials. The American Society for Testingand Materials maintains a file of patterns for manymaterials indexed on the basis of the strongest lines inthe pattern. X-ray diffraction data for the clay mineralsand other common soil minerals are given in Grim

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X-RAY DIFFRACTION ANALYSIS 73

Figure 3.37 X-ray diffractometer chart for quartz. Peaks occur at specific 2� angles, whichcan be converted to d spacings by Bragg’s law. Numbers in parentheses are the Miller indicesfor the crystal planes responsible for the indicated peak.

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(1968), Carroll (1970), Brindley and Brown (1980),Whittig and Allardice (1986), and Moore and Reyn-olds (1997). The most intense reflections for mineralscommonly found in powder samples of soils are listedin Table 3.7. Basal spacings for different clay mineralsassociated with different pretreatments are listed in Ta-ble 3.8 and shown pictorially in Fig. 3.38.

Criteria for Clay Minerals

The different clay minerals are characterized by first-order basal reflections at 7, 10, or 14 A. Positive iden-tification of specific mineral groups ordinarily requiresspecific pretreatments. Separation of size fractions re-quires thorough dispersion of the sample. As cement-ing compounds may both inhibit dispersion andadversely affect the quality of the diffraction patterns,their removal may be necessary. To ensure uniform ex-pansion due to hydration for all crystals of a particularmineral, the clay should be made homoionic. Magne-sium and potassium are most frequently used for sat-uration of the exchange sites. Detailed procedures forpretreatments useful in X-ray diffraction analysis ofclay soils are given by Whittig and Allardice (1986)and Moore and Reynolds (1997).

Kaolinite Minerals The kaolinite basal spacing ofabout 7.2 A is insensitive to drying or moderate heat-ing. Heating to 500�C destroys kaolinite minerals, butnot the other clay minerals. Hydrated halloysite has abasal spacing of 10 A, which collapses irreversibly to7 A on drying at 110�C. Organic chemical treatmentsare sometimes used to distinguish dehydrated halloy-site from kaolinite (MacEwan and Wilson, 1980). Theelectron microscope can also be used to distinguishdehydrated halloysite with its tubular morphology fromkaolinite.

Hydrous Mica (Illite) Minerals Illite is character-ized by d(001) of about 10 A, which remains fixed bothin the presence of polar liquids and after drying.

Smectite (Montmorillonite) Minerals The expan-sive character of this group of minerals provides thebasis for their positive identification. When air dried,these minerals may have basal spacings of 12 to 15 A.After treatment with ethylene glycol or glycerol, thesmectites expand to a d(001) value of 17 to 18 A. Whenoven dried, d(001) drops to about 10 A as a result of theremoval of interlayer water.

Vermiculite Although an expansive mineral, thegreater interlayer ordering in vermiculite results in lessvariability in basal spacing than occurs in the smectiteminerals. When Mg saturated, the hydration states ofvermiculite yield a discrete set of basal spacings, re-sulting from a changing but ordered arrangement ofMg cations and water in the interlayer complex. Whenfully saturated, the d spacing is 14.8 A, which reduces

to 11.6 A when heated at 70�C. All interlayer watercan be expelled at 500�C, but rehydration is rapid oncooling. Permanent dehydration and collapse to 9.02A can be achieved by heating to 700�C.

Chlorite Minerals The basal spacing of chloriteminerals is fixed at 14 A because of the strong orderingof the interlayer complex. Chlorites often have a clearsequence of four or five basal reflections. The third-order reflection at 4.7 A is often strong. Iron-rich chlo-rites have a weak first-order reflection but strongsecond-order reflections and, thus, may be confusedwith kaolinite. The facts that chlorite is destroyedwhen treated with 1 N HCl at 60�C while kaolinite isunaffected, and that kaolinite is destroyed but chloritemay not be affected on heating to 600�C, are usefulfor distinguishing the two clay mineral types.

Criteria for Nonclay Minerals

Strong X-ray diffraction reflections for some of thenonclay minerals are listed in Table 3.7. These includefeldspar, quartz, and carbonates. More detailed listingsof X-ray powder data for specific iron oxide minerals,silica minerals, feldspars, carbonates, and calcium sul-fate minerals are given in Brindley and Brown (1980)as well as in standard reference files.

Quantitative Analysis by X-ray Diffraction

Quantitative determination of the amounts of differentminerals in a soil on the basis of simple comparisonof diffraction peak heights or areas are uncertainbecause of differences in mass absorption coefficientsof different minerals, particle orientations, sampleweights, surface texture of the sample, mineral crys-tallinity, hydration, and other factors. Estimates basedon X-ray data alone are usually at best semiquantita-tive; however, in some cases techniques that accountfor differences in mass absorption characteristics andutilize comparisons with known mixtures or internalstandards may give good results. Soils containing onlytwo or three well-crystallized mineral components aremore easily analyzed than those with multimineralcompositions and mixed layering. For more detailedtreatment of X-ray diffraction theory, identification cri-teria, and techniques, particularly as related to thestudy of clays, see Klug and Alexander (1974), Carroll(1970), Brindley and Brown (1980), Whittig and Al-lardice (1986), and especially Moore and Reynolds(1997).

3.23 OTHER METHODS FOR COMPOSITIONALANALYSIS

Thermal Analysis

Principle Differential thermal analysis (DTA) con-sists of simultaneously heating a test sample and athermally inert substance at constant rate (usually

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OTHER METHODS FOR COMPOSITIONAL ANALYSIS 75

Table 3.7 X-ray Diffraction Data for Clay Minerals and Common Nonclay Minerals

d (A) Minerala d (A) Minerala

14 Mont. (VS) Chl. Verm. (VS)b 2.93–3.00 Felds.12 Sepiolite, heated corrensite 2.89–2.90 Carb.10 Illite, Mica (S), Halloysite 2.86 Felds.

9.23 Heated Verm. 2.84 Carb. Chl.7 Kaol. (S). Chl. 2.84–2.87 Chl.

6.90 Chl. 2.73 Carb.6.44 Attapulgite 2.61 Attapulgite6.39 Felds. 2.60 Verm., Sepiol.

4.90–5.00 Illite, Mica, Halloysite 2.56 Illite (VS), Kaol.4.70–4.79 Chlor. (S) 2.53–2.56 Chlor., Felds., Mont.

4.60 Verm. (S) 2.49 Kaol. (VS)4.45–4.50 Illite (VS), Sepiolite 2.46 Quartz, heated Verm.

4.46 Kaol. 2.43–2.46 Chlorite4.36 Kaol. 2.39 Verm., Illite4.26 Quartz (S) 2.38 Kaol.4.18 Kaol. 2.34 Kaol. (VS)

4.02–4.04 Felds. (S) 2.29 Kaol. (VS)3.85–3.90 Felds. 2.28 Quartz, Sepiol.

3.82 Sepiol. 2.23 Illite, Chl.3.78 Felds. 2.13 Quartz, Mica3.67 Felds. 2.05–2.06 Kaol. (WK)3.58 Carbonate, Chl. 1.99–2.00 Mica, Illite (S), Kaol. Chl.3.57 Kaol. (VS), Chl. 1.90 Kaol.

3.54–3.56 Verm. 1.83 Carb.3.50 Felds., Chlor. 1.82 Quartz3.40 Carb. 1.79 Kaol.3.34 Quartz (VS) 1.68 Quartz

3.32–3.35 Illite (VS) 1.66 Kaolin3.30 Carb. 1.62 Kaolin3.23 Attapulgite 1.54B Verm. (S), Quartz3.21 Felds. 1.55 Quartz3.20 Mica 1.58 Chl.3.19 Felds. (VS) 1.53 Verm., Illite3.05 Mont. 1.50 Ill. (S), Kaol.3.04 Carb. (VS) 1.48–1.50 Kaol. (VS), Mont.3.02 Felds. 1.45B Kaol.3.00 Heated Verm. 1.38 Quartz, Chl.2.98 Mica (S) 1.31, 1.34, 1.36 Kaol. (B)

a(B) � broad; (S) � strong; (VS) � very strong; (WK) � weak; Mont. � montmorillonite; Ch1. � chlorite; Verm. �vermiculite; Kaol. � kaolinite; Carb. � carbonate; Felds. � feldspar; Sepiol. � sepiolite.

b Italics indicates (001) spacing.

about 10�C/min) to over 1000�C and continuouslymeasuring differences in temperature between the sam-ple and the inert material. Differences in temperaturebetween the sample and the inert substance reflect re-actions in the sample brought about by the heating.Thermogravimetric analyses, based on changes inweight caused by loss of water or CO2 or gain in ox-

ygen, are also used to some extent. Thermal analysistechniques are described in detail by Tan et al. (1986).

The results of differential thermal analysis are pre-sented as a plot of the difference in temperaturebetween sample and inert material ( T) versus tem-perature (T) as indicated in Fig. 3.39. Endothermic re-actions are those wherein the sample takes up heat,

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Table 3.8 X-ray Identification of the Principal Clay Minerals (� 2 �m) in an Oriented Mount of a ClayFraction Separated from Sedimentary Material

Mineral Basal d Spacings (001)Glycolation Effect

(1 h, 60�C) Heating Effect (1 h)

Kaolinite 7.15 A (001); 3.75 A (002) No change Becomes amorphous 550–600�C

Kaolinite, disordered 7.15 A (001) broad; 3.75 Abroad

No change Becomes amorphous at lowertemperatures than kaolinite

Halloysite, 4H2O(hydrated)

10 A (001) broad No change Dehydrates to 2H2O at 110�C

Halloysite, 2H2O(dehydrated)

7.2 A (001) broad No change Dehydrates at 125–150�C;becomes amorphous 560–590�C

Mica 10 A (002); 5 A (004)generally referred to as(001) and (002)

No change (001) becomes more intense onheating but structure ismaintained to 700�C

Illite 10 A (002), broad, otherbasal spacings presentbut small

No change (001) noticeably more intenseon heating as water layersare removed; at highertemperatures like mica

Montmorillonite group 15 A (001) and integralseries of basal spacings

(001) expands to 17A with rationalsequence ofhigher orders

At 300�C (001) becomes 9 A

Vermiculite 14 A (001) and integralseries of basal spacings

No change Dehydrates in steps

Chlorite, Mg-form 14 A (001) and integralseries of basal spacings

No change (001) increases in intensity;�800�C shows weight lossbut no structural change

Chlorite, Fe-form 14 A (001) less intensethan in Mg-form;integral series of basalspacings

No change (001) scarcely increases;structure collapses below800�C

Mixed-layer minerals Regular, one (001) andintegral series of basalspacings

No change unlessan expandablecomponent ispresent

Various, see descriptions ofindividual minerals

Random, (001) is additionof individual mineralsand depends on amountof those present

Expands ifmontmorillonite isa constituent

Depends on minerals present ininterlayered mineral

Attapulgite(palygorskite)

High intensity d reflectionsat 10.5, 4.5, 3.23, and2.62 A

No change Dehydrates stepwise (seedescription)

Sepiolite High intensity reflections at12.6, 4.31, and 2.61 A

No change Dehydrates stepwise (seedescription)

Amorphous clay,allophane

No d reflections No change Dehydrates and loses weight

Compiled by Carroll (1970).

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OTHER METHODS FOR COMPOSITIONAL ANALYSIS 77

Figure 3.38 Pictorial representation of response of phyllosilicates to differentiating treat-ments. Approximate spacings in nm (1 nm � 10 A) (from Whittig and Allardice, 1986).Reproduced with permission from The American Society of Agronomy, Inc., Madison, WI.

and in exothermic reactions, heat is liberated. Analysisof test results consists of comparing the sample curvewith those for known materials so that each deflectioncan be accounted for.

Apparatus Apparatus for DTA consists of a sampleholder, usually ceramic, nickel, or platinum; a furnace;a temperature controller to provide a constant rate ofheating; thermocouples for measurement of tempera-ture and the difference in temperature between thesample and inert reference material; and a recorder forthe thermocouple output. The amount of sample re-

quired is about 1 g. Although the temperatures atwhich thermal reactions take place are a function onlyof the sample, the size and shape of the reaction peaksdepend also on the thermal characteristics of the ap-paratus and the heating rate.

Reactions Producing Thermal Peaks The impor-tant thermal reactions that generate peaks on the ther-mogram are:

1. Dehydration Water in a soil may be present inthree forms in addition to free pore water: (1)

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Figure 3.39 Thermogram of a sandy clay soil.

adsorbed water or water of hydration, which isdriven off at 100 to 300�C, (2) interlayer watersuch as in halloysite and expanded smectite, and(3) crystal lattice water in the form of (OH) ions,the removal of which is termed dehydroxylation.Dehydroxylation destroys mineral structures. Thetemperature at which the major amount of crystallattice water is lost is the most indicative propertyfor identification of minerals. Dehydration reac-tions are endothermic and occur in the range of500 to 1000�C.

2. Crystallization New crystals form from amor-phous materials or from old crystals destroyed ata lower temperature. Crystallization reactionsusually are accompanied by an energy loss and,thus, are exothermic, occurring between 800 and1000�C.

3. Phase Changes Some crystal structures changefrom one form to another at a specific tempera-ture, and the energy of transformation shows upas a peak on the thermogram. For example,quartz changes from the � to � form reversiblyat 573�C. The peak for the quartz phase changeis sharp, and its amplitude is nearly in direct pro-portion to the amount of quartz present. Thequartz peak is frequently masked within the peakfor some other reacting material, but may bereadily identified by determining the thermogramduring cooling of the sample or by letting it coolfirst and then rerunning it. The other minerals aredestroyed during the initial run while the quartzreaction is reversible.

4. Oxidation Exothermic oxidation reactions in-clude the combustion of organic matter and theoxidation of Fe2� to Fe3�. Organic matter oxi-dizes in the 250 to 450�C temperature range.

Beside quartz, the only common nonclay mineralsin soils that give thermal reactions with large peaks arecarbonates and free oxides such as gibbsite, brucite,and goethite. The carbonates give very large endother-mic peaks between about 800 and 1000�C, and the ox-ides have an endothermic peak between about 250 and450�C. Thermograms for many clay and nonclay min-erals are presented by Lambe (1952).

Quantitative Analysis Theoretically, the area of thereaction peak is a measure of the amount of mineralpresent in the sample. For sharp, large amplitude peakssuch as the quartz inversion at 573�C and the kaoliniteendotherm at 650�C, the amplitude can be used forquantitative analysis. In either case, calibration of theapparatus is necessary, and the overall accuracy is ofthe order of plus or minus 5 percent.

Optical Microscope

Both binocular and petrographic microscopes can beused to study the identity, size, shape, texture, and con-dition of single grains and aggregates in the silt andsand size range; for study in the thin section of thefabric, that is, the spatial distribution and interrelation-ships of the constituents; and for study of the orien-tations of groups of clay particles. Because the in-focusdepth of field decreases sharply as magnification in-creases, study of soil thin sections is impractical atmagnifications greater than a few hundred. Thus, in-dividual clay particles cannot usually be distinguishedusing an optical microscope.

Useful information about the shape, texture, size,and size distribution of silt and sand grains may beobtained directly without formal previous training inpetrographic techniques. Some background is neededto identify the various minerals; however, relativelysimple diagnostic criteria that can be used for identi-fication of over 80 percent of the coarse grains in mostsoils are given by Cady et al. (1986). These criteriaare based on such factors as color, refractive index,birefringence, cleavage, and particle morphology. Thenature of surface textures, the presence of coatings,layers of decomposition, and so on are useful both forinterpretation of the history of a soil and as a guide tothe soundness and durability of the particles.

Electron Microscope

With modern electron microscopes it is possible to re-solve distances to less than 100 A, thus making studyof small clay particles feasible. Electron diffractionstudy of single particles may also be useful. Electrondiffraction is similar to X-ray diffraction except anelectron beam instead of an X-ray beam is used.

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QUANTITATIVE ESTIMATION OF SOIL COMPONENTS 79

Magnetic lenses that refract an electron beam formthe basis of the transmission electron microscope(TEM) optical system. An electron beam is focused onthe specimen, which is usually a replica of the surfacestructure of the material under study. Some of the elec-trons are scattered from the specimen, and differentparts of the specimen appear light or dark in proportionto the amount of scattering. After passing through aseries of lenses, the image is displayed on a fluorescentscreen for viewing. Probably the most critical aspectof successful transmission electron microscopy is spec-imen preparation.

In the scanning electron microscope (SEM), second-ary electrons emitted from a sample surface form whatappear to be three-dimensional images. The SEM hasa �20 to �150,000 magnification range and a depthof field some 300 times greater than that of the lightmicroscope. These characteristics, coupled with thefact that clay particles themselves and fracture surfacesthrough soil masses may be viewed directly, have ledto extensive use of the SEM for study of clays. Ex-amples of electron photomicrographs of clays and soilsare given earlier in this chapter and in Chapter 5. Prin-ciples of electron microscopy techniques and addi-tional examples are presented in McCrone and Delly(1973) and Sudo et al. (1981).

3.24 QUANTITATIVE ESTIMATION OF SOILCOMPONENTS

Qualitative X-ray diffraction and a few simple testswill generally indicate the minerals present in a soil.More data are needed, however, for more precise quan-titative estimates. As a rule, the number of differentanalyses needed is equal to the number of mineral spe-cies present. The results of glycol adsorption, cationexchange capacity, X-ray diffraction, differential ther-mal analysis, and chemical tests all give data that maybe used for quantitative estimations. Some pertinentidentification criteria and reference values for the clayminerals are given in Table 3.9.

After the quantities of organic matter, carbonates,free oxides, and nonclay minerals have been deter-mined, the percentages of clay minerals are estimatedusing the appropriate glycol adsorption, cation ex-change capacity, K2O, and DTA data. The nonclayscan be identified, and their abundance determined, us-ing the microscope, grain size distribution analysis, X-ray diffraction, and DTA. The amount of illite isestimated from the K2O content since this is the onlyclay mineral containing potassium. The amount of ka-olinite is most reliably determined from the 600�C

DTA endotherm amplitude. If X-ray has indicatedmontmorillonite, chlorite, and/or vermiculite, thenquantitative estimates are made based on the glycoladsorption and exchange capacity data. The totalexchange capacity and glycol retention are ascribed tothe clay minerals, and the measured values must beaccounted for in terms of proportionate contributionsby the different clay minerals present.

As a simple example, assume that quartz, illite, andsmectite are identified in the �2 �m fraction of a soil.Additional data indicate 4.0 percent K2O, ethylene gly-col retention of 100 mg/g, and a cation exchange ca-pacity of 35 meq/100 g. Then, assuming 9 percent asan average value of for pure illite (Table 3.9), the con-tent of illite is estimated at 4.0/9.0, or 44 percent. Be-cause only the illite and smectite will contribute to theglycol adsorption, the amount of smectite may be es-timated:

0.44 � 60 � S � 300 � 100

100 � 26.4� S � � 25%

300

The remaining 31 percent can be ascribed to quartzand other nonclay components. For this clay mineralcomposition, the theoretical cation exchange capacityshould be, based on the reference values in Table 3.9:

0.44 � 25 � 0.25 � 85 � 11 � 21 � 33 meq/100 g

This compares favorably with the measured quantityof 35 meq/100 g. Thus, the composition of the claysize fraction is

Illite 44%Smectite 25%Quartz and other nonclays 31%

The main difficulty in this method for quantitative min-eralogical analysis is the uncertainty in the referencevalues for the different clay minerals.

A semiquantitative analysis is sufficient for most ap-plications. This may be done as follows. The silt andsand fraction can be examined by microscope and theapproximate proportion of nonclay minerals deter-mined. The amount of clay size material �2 �m canbe estimated by grain size distribution analysis. As afirst approximation, it may be assumed that the amountof clay mineral equals at least the amount of clay size.This assumption is justified for the following reasons.Nonclay minerals, principally quartz, are found in theclay size fraction. On the other hand, for most soils,

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Table 3.9 Summary of Clay Mineral Identification Criteria—Reference Data for Clay Mineral Identification(�2-�m fraction)

ClayX-rayd(001)

Glycol(mg/g)

CEC(meq/100 g)

K2O(%) DTAa

Kaolinite 7 16 3 0 End. 500–660� � Sharpb

Exo. 900–975� SharpDehydrated halloysite 7 35 12 0 Same as kaolinite but 600 peak

slope ratio � 2.5Hydrated halloysite 10 60 12 0 Same as kaolinite but 600� peak

slope ratio � 2.5Illite 10 60 25 8–10 End. 500–650� Broad

End. 800–900� BroadExo. 950�

Vermiculite 10–14 200 150 0Smectite 10–18 300 85 End. 600–750�

End. 900�

Exo. 950�

Chlorite 14c 30 40 0 End. 610 � 10� or 720 � 20�

aFor clays prepared at same relative humidity the size of the 100–300�C endotherm (adsorbed water removal) increasesin the order kaolinite–illite–smectite.

bFor samples started at 50% RH the amplitude of 600� peak/amplitude of adsorbed water peak ��1.cHeat treatment will accentuate 14 A line and weaken 7 A line.

the amount of clay mineral exceeds the amount of claysize. This most probably results from cementation ofsmall clay particles into aggregates larger than 2 �min diameter. Approximate proportions of the differentclay minerals in the clay fraction can be estimatedfrom the relative intensities of the X-ray diffractionreflections for each mineral. The presence of organicmatter and carbonates can be easily detected using thetests listed in Section 3.21.


The sizes, shapes, and surface characteristics of theparticles in a soil are determined in large measure bytheir mineralogy. Mineralogy also determines interac-tions with fluid phases. Together, these factors deter-mine plasticity, swelling, compression, strength, andfluid conductivity behavior. Thus, mineralogy is fun-damental to the understanding of geotechnical prop-erties, even though mineralogical determinations arenot made for many geotechnical investigations. In-stead, other characteristics that reflect both composi-tion and engineering properties, such as Atterberglimits and grain size distribution, are determined.

Interatomic bonding, crystal structure, and surfacecharacteristics determine the size, shape, and stabilityof soil particles and the interactions of soil particleswith liquids and gases. The structural stability of thedifferent minerals controls their resistance to weath-ering and hence accounts in part for the relative abun-dance of different minerals in different soils.

Because interatomic bonds in soil particles arestrong, primary valence bonds, whereas usual interpar-ticle bonds are of the secondary valence or hydrogenbond type, individual particles are strong compared togroups of particles. Thus, most soil masses behave asassemblages of particles in which deformation proc-esses are dominated by displacements between parti-cles and not by deformations of particles themselves,although grain crushing becomes important in coarse-grained soils such as sands and gravels when they areunder very high stresses.

The type of bonding between the unit layers of theclay minerals, coupled with the adsorption propertiesof the particle surfaces, controls soil swelling. Ad-sorption and desorption processes are important ininteractions between chemicals and soils. These inter-actions in turn determine the flow and attenuation ofvarious substances through soil. Changes in surface

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forces owing to changes in chemical environment mayalter the structural state of a soil.

Mineralogy is related to soil properties in much thesame way as the composition and structure of cementand aggregates are to concrete, or as the compositionand crystal structure of steel relate to its strength anddeformability. With these engineering materials—soil,concrete, and steel—mechanical properties can bemeasured directly; however, they cannot be explainedwithout consideration of the composition and structureof their components.

Since about 1980, environmental problems, espe-cially those related to the safe disposal and contain-ment of municipal, hazardous, and nuclear waste andto the clean up of contaminated sites and the protectionof groundwater, have assumed a major role in geo-technical engineering practice. This has required agreatly increased focus on the compositional charac-teristics of soils and their relation to the long-termphysical and chemical properties that control soil be-havior under changed and extreme environmental con-ditions.


1. A montmorillonite has a cation exchange capacityof 130 meq/100 g and a total external and internalsurface area of 800 m2/g.a. How many calcium ions will there be on a par-

ticle that is 0.4 �m � 0.2 �m � one unit cellin thickness?

b. What percentage of the dry weight of the clayis composed of calcium?

2. An orthorhombic crystal has axial ratios of 0.6,0.3, and 1.0. The (500) plane is 2.0 A horizontallyfrom the origin. This crystal is irradiated withCuK� X-rays (wave length of 1.54 A). At whatvalue of � does the second-order (010) reflectionoccur?

3. Sketch the following planes relative to crystallo-graphic axes: (001), (243), (hk0), (hkl), (111),(060), (010).

4. Consider an orthorhombic crystal of dimensionsa � 6A, b � 12 A, c � 8 A. With the aid ofsketches determine the angle of intersection be-tween the planes of each pair indicated below. Ifthe planes do not intersect, then so indicate.a. (002) and (020)b. (001) and (002)c. (111) and (222)

d. (111) and ( )111e. (112) and (001)

5. A clay has a surface density of charge of onecharge per 150 A2. Its cation exchange capacity is10 meq/100 g. Determine the specific surfacearea.

6. Why are soils containing smectite often expansive,whereas soils containing illite and/or kaolinite arenot?

7. As the geotechnical engineer on a project, you findan inorganic soil containing 15 percent by weightof particles finer than 100 �m, as measured byhydrometer analysis. What soil components doyou expect? Why?How could you confirm this expectation? Be spe-cific in terms of tests and diagnostic criteria.

8. What is the smallest interplanar spacing that canbe measured by X-ray diffraction using copper K�

radiation?

9. You suspect that a fine-grained soil sample con-tains kaolinite, illite, and smectite minerals. De-scribe in logical sequence the tests you would doto verify that these clay minerals are present. In-dicate the reasons why you choose these tests andthe criteria for distinguishing among the minerals.

10. An inorganic clay has a liquid limit of 350 percent.a. What is the most probable predominant clay

mineral in this soil?b. Explain the high liquid limit in terms of the

crystal structure of this mineral.c. Would you recommend founding light struc-

tures on shallow footings above this soil? Why?

11. A soil sample has a cation exchange capacity of30 meq/100 g and a specific surface area of 50m2/g. You wish to determine the type of clay min-eral in this soil. Based on your general knowledgeof the area from which it came, including the ge-ology, you suspect the possibility of hydrated hal-loysite, illite, and smectite. State specifically howyou would determine which mineral is present.

12. An X-ray diffraction pattern for a soil sample froma site where light structures (houses, a shoppingcenter) are to be located shows peaks at 2� � 5�,10�, 12.2�, 20.8�, 24.7�, and 26.7�. Copper K� ra-diation was used.a. What minerals are present in the sample?b. If the measure cation capacity is 40 meq/100

g, what is the approximate minimum amount of

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Figure 3.40 Gradation curve for a sandy clay soil.

clay mineral in the sample by weight percent-age?

c. What concerns would you have about this soilas a foundation material?

d. How could you minimize any problems iden-tified in part (c)?

13. In general the average clay particle size as repre-sented by some effective diameter D, for smectiteparticles (S) is less than that of hydrous mica (il-lite) (HM) particles, which, in turn, is less thanthat of kaolinite (K) particles. In addition, the av-erage particle thicknesses are in the order

tS � tHM � tK

and values of the thickness-to-diameter ratio (t /D)are in the order

(t /D)S � (t /D)HM � (t /D)K

What are some implications of these relationshipswith respect to the relative values of plasticity, hy-draulic conductivity, compression–swell behavior,and strength characteristics of three soils: one con-taining a large amount of smectite, one containinga large amount of hydrous mica (illite), and onecontaining a large amount of kaolinite?

14. The gradation curve for a sandy clay soil is shownin Fig. 3.40.a. What are the percentages by weight of sand,

silt, and clay size material?b. Consider a 100-g sample of the soil and assume

that all sand particles are of a size equal to theaverage particle size in the sand size range, thesilt particles are of a size equal to the averageparticle size in the silt size range, and all clayparticles are of a size equal to the average par-ticle size in the clay size range. Base your de-termination of average particle size in eachrange on equal weights of particles coarser andfiner than the average for each size range.

Estimate the number of sand, silt, and clayparticle in the sample. For purposes of thisestimate, the sand and silt particles can beassumed to be spherical. Assume the clayparticles to be flat disks having a diameter-to-thickness ratio of 10. Assume the average sizeof clay particles on the gradation curve to rep-resent the disk diameter.

c. Estimate the specific surface area of this soil insquare meters per gram. Determine the per-centages of this total that are contributed by thesand, silt, and clay fractions.

d. Are the estimates of the numbers of particlesand specific surface area made in this way toohigh, too low, or correct? Why?

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83

CHAPTER 4

Soil Composition andEngineering Properties

4.1 INTRODUCTION

The engineering properties of a soil depend on thecomposite effects of several interacting factors. Thesefactors may be divided into two groups: compositionalfactors and environmental factors. Compositional fac-tors determine the potential range of values for anyproperty. They include:

1. Types of minerals2. Amount of each mineral3. Types of adsorbed cations4. Shapes and size distribution of particles5. Pore water composition6. Type and amount of other constituents, such as

organic matter, silica, alumina, and iron oxide

The influences of compositional factors on engineeringproperties can be studied using disturbed samples.

Environmental factors determine the actual value ofany property. They include:

1. Water content2. Density3. Confining pressure4. Temperature5. Fabric6. Availability of water

Undisturbed samples, or in situ measurements, are re-quired for the study of the effects of environmentalfactors on properties.

Soils are classified as coarse grained, granular, andcohesionless if the amount of gravel and sand exceeds50 percent by weight or fine grained and cohesive ifthe amount of fines (silt and clay-size material) ex-

ceeds 50 percent.1 The engineering properties of co-hesionless soil are often determined by appliedconfining pressure and looseness or denseness as in-dicated by the relation of the current void ratio to thelowest and highest possible values of void ratio for thesoil. The engineering properties of cohesive soil areoften characterized by stiffness and strength and byrelating the current water content and past consolida-tion history to the compositional characterization pro-vided by the plasticity index. Some engineeringcharacteristics of coarse-grained and fine-grained soilsare listed and compared in Fig. 4.1. Detailed discussionof the combined effects of compositional and environ-mental factors on the three most important propertyclasses for engineering problems, that is, conductivity,volume change, and deformation and strength, is givenin Chapters 9, 10, and 11.

Quantitative determination of soil behavior com-pletely in terms of compositional and environmentalfactors is impractical for several reasons:

1. Most natural soil compositions are complex, anddetermination of soil composition is difficult.

2. Physical and chemical interactions occur betweendifferent phases and constituents.

3. The determination and expression of soil fabricin quantitatively useful ways is difficult.

4. Past geologic history and present in situ environ-ment are difficult to simulate in the laboratory.

5. Physicochemical and mechanical theories for re-lating composition and environment to propertiesquantitatively are inadequate.

1 The terms cohesionless and cohesive must be used with care, aseven a few percent of clay mineral in a coarse-grained soil can impartplastic characteristics.

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84 4 SOIL COMPOSITION AND ENGINEERING PROPERTIES

Gravel Sand Silt Clay

“Granular Soils” “Fines”

75 mm3 in.

5 mm0.2 in.

0.07 mm0.003 in.

0.002 mm0.00008 in.

Apples toEnglish peas

English peasto baking flour

Finer thanbaking flour

Much finer thanbaking flour

Particles visible without magnificationGrain size measurable with sieves

Particles not visible without magnificationGrain size not measurable with sievesGrain size measured by sedimentation rate

Grains do not form a coherent masseven when wet – cohesionless

Grains stick together when mixed with water dueto pore water suction and physicochemical porefluid-mineral interaction – cohesive

Nonplastic – there is no range of watercontent where the soil can be deformedwithout cracking or crumbling.

Plastic – deforms without cracking over a rangeof water content between the liquid limit and theplastic limit

Liquid (pancake batter)

Plastic (modeling clay)

Semisolid (chocolate bar)

Solid (chalk)

Liquid Limit (LL)

Plastic Limit (PL)

Shrinkage Limit

Permeability is moderate to high (10-6 to 10-1 m/s).Water flows easily through the voids.

Permeability is low to very low (<10-7 m/s).Water flows slowly through the voids.Drainage takes weeks to tens of years.

Drainage occurs rapidly except under dynamicloading; e.g., earthquakes.Only “drained” strength is important for conditionsother than earthquake loading or rapid landslides.

Both “drained” and “undrained” strengths are important.“Undrained” strength is low when preconsolidationpressure is low.

Most important indicators of mechanical behaviorare relative density, Dr, and applied confiningpressure

Dr = 0 to 20% Very looseDr = 20 to 40% LooseDr = 40 to 60% Med. denseDr = 60 to 80% DenseDr = 80 to 100% Very dense

Very loose _ CompressibleLiquefiable during earthquakesφ ~30°

Very dense _ Very low compressibilityStable during earthquakesφ ~45°

Behavior of siltsvaries from “sand-like” to “clay-like” asgrain size decreases

Most important mechanicalbehavior is “preconsolidationpressure pp” and appliedconfining pressure

Very soft – Very highly compressibleUndrained shear strength <12.5 kPa

Very dense _ Low compressibilityUndrained shear strength >100 kPa

pp = 0 to 50 kPa Very softpp = 50 to 100 kPa Softpp = 100 to 200 kPa Firmpp = 200 to 400 kPa Stiffpp = 400 to 800 kPa Very stiffpp = 0.8 to 1.6 MPa Hard

Figure 4.1 Compositional and environmental factors contributing to engineering properties(adapted from course notes by J. M. Duncan, 1994).

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ENGINEERING PROPERTIES OF GRANULAR SOILS 85

Nonetheless, compositional data are valuable for de-velopment of an understanding of properties and forestablishment of qualitative to semiquantitative guide-lines for how real soils behave. Accordingly, somerelationships between compositional factors and engi-neering properties are summarized in this chapter.

4.2 APPROACHES TO THE STUDY OFCOMPOSITION AND PROPERTYINTERRELATIONSHIPS

Study of soil composition in relation to soil propertiesmay be approached in two ways. In the first, naturalsoils are used, the composition and engineering prop-erties are determined, and correlations are made. Thismethod has the advantage that measured properties arethose of naturally occurring soils. Disadvantages, how-ever, are that compositional analyses are difficult andtime consuming, and that in soils containing severalminerals or other constituents such as organic matter,silica, alumina, and iron oxide the influence of any oneconstituent may be difficult to isolate.

In the second approach, the engineering propertiesof synthetic soils are determined. Soils of known com-position are prepared by blending different commer-cially available clay minerals of relatively high puritywith each other and with silts and sands. Although thisapproach is much easier, it has the disadvantages thatthe properties of the pure minerals may not be thesame as those of the minerals in the natural soil, andimportant interactions among constituents may bemissed. Whether the influences of constituents such asorganic matter, oxides and cementation, and otherchemical effects can be studied successfully using thisapproach is uncertain.

Regardless of the approach used, there are at leasttwo difficulties. One is that often the variability in bothcomposition and properties in any one soil deposit maybe great, making the selection of representative sam-ples difficult. Variations in composition and texture oc-cur in sediments within distances as small as a fewcentimeters. Residual soils, in particular, are likely tobe very nonhomogeneous.

A second difficulty is that the different constituentsof a soil may not influence properties in direct or evenpredictable proportion to the quantity present becauseof physical and physicochemical interactions. As anexample of physical interactions, blending of equalproportions of uniform sand and clay, each having acompacted unit weight of 17 kN/m3, would not nec-essarily yield a mixture also having a unit weight of17 kN/m3 after compaction. The resulting unit weightmight be as high as 20 kN/m3 because the clay canfill void spaces between sand particles.

Physicochemical interaction between clay mineralsis shown in Fig. 4.2. Mixtures of bentonite (sodiummontmorillonite) and kaolinite and of bentonite and acommercial illite containing about 40 percent illite claymineral, with the rest mostly silt-sized nonclay, wereprepared, and the liquid limits were determined. Thedashed line in Fig. 4.2 shows the liquid limit values tobe expected if each mineral contributed in proportionto the amount present. The data points and solid linesshow the actual measured values. Although the ben-tonite–kaolinite mixtures gave values close to theoret-ical, the liquid limit values for the bentonite–illitemixtures were much less than predicted. This resultedfrom excess salt in the illite that, when mixed with thebentonite, prevented full interlayer expansion of themontmorillonite particles in the presence of water.

4.3 ENGINEERING PROPERTIES OFGRANULAR SOILS

The mechanical behavior of granular materials is gov-erned primarily by their structure and the applied ef-fective stresses. Structure depends on the arrangementof particles, density, and anisotropy. Particle sizes,shapes, and distributions, along with the arrangementof grains and grain contacts comprise the soil fabric.The packing characteristics of granular materials arediscussed further in Chapter 5.

Particle Size and Distribution

Figure 4.3 illustrates the tremendous range in particlesizes that may be found in a soil, where different sizesare shown to the same scale. The largest size shownrepresents fine sand. It may be recalled that particlesfiner than about 0.06 mm cannot be seen by the nakedeye. The orders of magnitude difference in particlesizes found in any one soil is often better appreciatedfrom a representation such as that in Fig. 4.3 than bythe usual size distribution (or grading) curve whereparticle diameters are shown to a logarithmic scale.

The origin of a cohesionless soil can be reflected byits grading. Alluvial terrace deposits and aeolian de-posits tend to be poorly graded or sorted. Glacial de-posits such as Boulder clays and tills are often wellgraded, containing a wide variety of particle sizes.Small particles in a well-graded soil fit into the voidsbetween larger particles. Well-graded cohesionlesssoils are relatively easy to compact to a high densityby vibration. The loss of fine fraction by internal ero-sion can lead to large changes in engineering proper-ties. Uniformly graded soils are usually used forcontrolled drainage applications because they are notsusceptible to loss of fines by internal erosion and their

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Figure 4.2 Interactions between clay minerals as indicated by liquid limit (data from Seedet al., 1964).

hydraulic conductivity can be maintained within defin-able and narrow limits.

The slope of the grain size distribution curve is char-acterized by the coefficient of uniformity Cu:

d60C � (4.1)u d10

where d60 and d10 correspond to the sieve sizes that 60and 10 percent of the particles by weight pass through.A soil with Cu � 5 to 10 is considered well-graded.

The possible range of packing of soil particles isoften related to the maximum and minimum void ratios(or minimum and maximum densities) reflecting theloosest and densest states, respectively. Uniformlygraded soils tend to have a narrower range of possibledensities compared to well-graded soils. Soils contain-ing angular particles tend to be less dense than soilswith rounded particles, as discussed later in this sec-tion. However, angular and weak materials may crushsignificantly more during compression, compaction, ordeformation. Figure 4.4 shows how the maximum and

minimum void ratios change by mixing sand and siltin different proportions. At low silt contents, silt par-ticles fit into the voids between larger sand particles,so the void ratio of sand–silt mixtures decreases withincrease in silt content. However, at a certain silt con-tent, the silt fully occupies the voids, and the increasein silt content results in sand particles floating insidethe silt matrix. Then, the void ratios increase with fur-ther increase in silt content.

The relative density, DR, a measure of the currentvoid ratio in relation to the maximum and minimumvoid ratios, and applied effective stresses controls themechanical behavior of cohesionless soils. Relativedensity is defined by

e � emaxD � � 100% (4.2)R e � emax min

in which emax, emin, and e are the maximum, minimum,and actual void ratios.

The relative density correlates well with other prop-erties of granular soils. As different standard test meth-

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Figure 4.3 Different grain sizes in soil.

0 10 20 30 40 50 60 70 80 90 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Silt content (%)

Maximum void ratio

Minimum void ratio

Voi

d ra

tio

Figure 4.4 Maximum and minimum void ratios of Montereysand–silt mixtures (from Polito and Martin, 2001).

Morphology (large scale) Roundness Texture(intermediate scale)

Surface Texture(small scale)

Roundness Texture(intermediate scale)

Figure 4.5 Scale-dependent particle shape characterization.The solid line gives the particle outline. Morphology de-scribes overall shape of the particle as given by the heavydotted line. Texture reflects the smaller scale local featuresof the particles as identified by light dotted circles. The ex-amples are surface smoothness, roundness of edges and cor-ners, and asperities.

ods can give different limiting void ratios, the use ofthe relative density is sometimes criticized, especiallywhen considered in relation to the random in situ var-iations of the density of most sand and gravel deposits.Nonetheless, if properly interpreted, relative densitycan provide a very useful measure of cohesionless soilproperties.

Particle Shape

Particle shape is an inherent soil characteristic thatplays a major role in mechanical behavior of soils.Characterization of particle shape is scale dependent,as shown in Fig. 4.5. At larger scales, that is, that ofthe particle itself, the particle morphology might bedescribed as spherical, rounded, blocky, bulky, platy,

elliptical, elongated, and so forth. At smaller scales,the texture, which reflects the local roughness featuressuch as surface smoothness, roundness of edges andcorners, and asperities, is important.

With the exception of mica, most nonclay mineralsin soils occur as bulky particles.2 Most particles are

2 Quartz particles become flatter with decreasing size and may havea platy morphology when subdivided to a fineness approaching claysize (Krinsley and Smalley, 1973).

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Figure 4.6 Grain shape distribution of Monterey No. 0 sand. Results are based on study of277 particles, d50 � 0.43 mm, Cu � 1.4 (Mahmood, 1973).

not equidimensional, however, and are at least slightlyelongate or tabular. A frequency histogram of particlelength-to-width ratio (L /W) for Monterey No. 0 sandis shown in Fig. 4.6. This well-sorted beach sand iscomposed mainly of quartz with some feldspar. Themean of all the particle measurements is an L /W ratioof 1.39. This distribution is typical of that for manysands and silty sands.

Particle morphology in soil mechanics has histori-cally been described using standard charts againstwhich individual grains may be compared. A typicalchart and some examples are shown in Fig. 4.7 (Krum-bein, 1941; Krumbein and Sloss, 1963; Powers, 1953).Sphericity is defined as the ratio of the diameter of asphere of equal volume to the particle to the diameterof the circumscribing sphere. Roundness is defined asthe ratio of the average radius of curvature of the cor-ners and edges of the particle to the radius of the max-imum sphere that can be inscribed (Wadell, 1932).Sphericity and roundness are measures of two very dif-ferent morphological properties. Sphericity is most de-pendent on elongation, whereas roundness is largelydependent on the sharpness of angular protrusionsfrom the particle. Different definitions of sphericityand roundness are available, as shown in Table 4.1.Due to the variety of definitions available, the quanti-fication of particle shape requires accurate specifica-tion of their definition.

In recent years, techniques for computer analysis ofshape data by digital imaging have improved greatly,and standard software applications include determina-

tion of aspect ratio and roundness. A convenient wayto characterize particle shapes in more detail is by aFourier mathematical technique. For instance, the (R,�) Fourier method is in the following form:

N

R(�) � a � (a cos n� � b sin n�) (4.3)�0 n nn�1

where R(�) is the radius at angle �, N is the total num-ber of harmonics, n is the harmonic number, and a andb are coefficients giving the magnitude and phase foreach harmonic. The lower harmonic numbers give theoverall shape; for instance, the sphericity is expressedby the first and second harmonics. The coefficient val-ues for higher-order descriptors generally decay withincreasing descriptor or harmonic number, which ex-presses smaller features (i.e., texture) (Meloy, 1977).Other mathematical methods to curve-fit particleshapes are listed in Table 4.1. Further discussion onparticle shape characterization is given by Barrett(1980), Hawkins (1993), Santamarina et al. (2001), andBowman et al. (2001).

In an assembly of uniform size spherical particles,the loosest stable arrangement is the simple cubicpacking giving a void ratio of 0.91. The densest pack-ing is the tetrahedral arrangement giving a void ratioof 0.34. Particle shape affects minimum and maximumvoid ratios as shown in Fig. 4.8 (Youd, 1973). Thevalues increase as particles become more angular orthe roundness (defined as roundness 1 in Table 4.1)

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VeryAngular

Angular Rounded WellRounded

(b)

Roundness

(a)

Sph

eric

ity

High Sphericity

Low Sphericity

Subangular Subrounded

0.9

0.7

0.5

0.3

0.90.70.50.30.1

Figure 4.7 Particle shape characterization: (a) Chart for visual estimation of roundness andsphericity (from Krumbein and Sloss, 1963). (b) Examples of particle shape characterization(from Powers, 1953).

decreases. When R � 1, the particle is a sphere. Asparticles become more angular, R decreases to zero.Void ratios are also a function of particle size distri-bution; the values decrease as the range of particlesizes increases (increase in the coefficient of unifor-mity Cu).

The friction angle increases with increase in particleangularity, possibly as a result of an increase in coor-dination number. For example, values of the angle ofrepose3 are plotted against roundness in Fig. 4.9 and

3 Angle of repose can be determined by pouring soil in a graduatedcylinder filled with water. Tilt the cylinder more than 60� and bringit back slowly to the vertical position. The angle of the residual sandslope is the angle of repose. Further details of the method can befound in Santamarina and Cho (2004).

the following linear fit to the relationship is proposed(Santamarina and Cho, 2004);

� � 42 � 17R (4.4)repose

where R is the coefficient of roundness defined asroundness 1 in Table 4.1. Similar data relating frictionangle from drained triaxial tests and particle shape ispresented by Sukumaran and Ashmawy (2001).

Particle Stiffness

Soil mass deformation at very small strains originatesfrom the elastic deformations at points of contact be-tween particles. Contact mechanics shows that the elas-tic properties of particles control the deformations atparticle contacts (Johnson, 1985), and these deforma-

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Table 4.1 Methods for Particle Shape Characterization

Method Definition

Morphology—Sphere

Sphericity 1 Diameter of a sphere of equal volumeDiameter of circumscribing sphere

Sphericity 2 Particle volumeVolume of circumscribing sphere

Sphericity 3

Projection sphericity Area of particle outlineArea of a circle with diameter equal to the longest length of outline

Inscribed circle sphericity Diameter of the largest inscribed circleDiameter of the smallest inscribed circle

Morphology—Ellipse

Eccentricity �p /Rap, where the ellipse is characterized by Rp � �p cos 2� in polar coordinates

Elongation Smallest diameterDiameter perpendicular to the smallest diameter

Slenderness Maximum dimensionMinimum dimension

Texture—Roundness

Roundness 1 Average of radius of curvature of surface features, (�r ) /Ni

Radius of the maximum sphere that can be inscribed, rmax

Roundness 2 Radius of curvature of the most convex part0.5 (longest diameter through the most convex part)

Roundness 3 Radius of curveture of the most convex partMean radius

Morphology—Texture

Fourier method Eq. (4.3), first and second harmonics, characterize sphericity, whereas higher harmonics(around 10th) characterizes roundness. Surface texture is characterized by muchhigher harmonics.

Fourier descriptormethod

More flexible than the Fourier method by using the complex plane (Bowman et al.,2001). Lower harmonics give shape characteristics such as elongation, triangularity,squareness, and asymmetry. Higher harmonics (larger than 8th) give textural features.

Fractal analysis Use as a measure of texture (Vallejo, 1995; Santamarina, et al. 2001).

From Hawkins (1993), Santamarina et al. (2001), and Bowman et al. (2001).

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0.6

0.6

0.4

0.2

0.8

0.8

1.0

1.2

1.4

1 2 3 4 10 156

SubroundedRounded

Coefficient of Uniformity, Cu

0.350.490.70

0.300.25

0.20

R = 0.17

Subangular

Subangular

Angular

R = 0.20

Angular

R = 0.20

Angular

SubroundedRounded

0.70

0.49

0.35

0.30

0.25

0.20

Max

imum

Voi

d ra

tio, e

max

Min

imum

Voi

d R

atio

, em

in

Figure 4.8 Maximum and minimum void ratios of sands asa function of roundness and the coefficient of uniformity(from Youd, 1973).

50

40

30

20

100.0 0.2 0.4 0.6 0.8 1.0

Roundness R

φrepose = 42 – 17RAng

le o

f rep

ose

φ rep

ose

Figure 4.9 Angle of repose as a function of roundness (fromSantamarina and Cho, 2004).

Table 4.2 Elastic Properties of Geomaterials atRoom Temperature

MaterialYoung’s

Modulus (GPa)Shear Modulus

(GPa)Poisson’s

Ratio

Quartz 76 29 0.31Limestone 2–97 1.6–38 0.01–0.32Basalt 25–183 3–27 0.09–0.35Granite 10–86 7–70 0.00–0.30Hematite 67–200 27–78 —Magnetite 31 19 —Shale 0.4–68 5–30 0.01–0.34

After Santamarina et al. (2001).

tions in turn influence the stiffness of particle assem-blages. Elastic properties of different minerals androcks are listed in Table 4.2. The modulus of a singlegrain, which determines the particle contact stiffness,is at least an order of magnitude greater than that ofthe particle assembly. Further details on the relationbetween particle stiffness and particle assemblage stiff-ness are given in Chapter 11.

Particle Strength

The crushability of soil particles has large effects onthe mechanical behavior of granular materials. At highstresses, the compressibility of sand becomes large asa result of particle crushing, and the shape of an e–logp compression curve becomes similar to that of nor-mally consolidated clay (Miura et al., 1984; Coop,1990; Yasufuku et al., 1991). Under constant states ofstress, the amount of particle breakage increases withtime, contributing to creep of the soil (Lade et al.,1996). The amount of crushing in a soil mass dependsboth on the stiffness and strength of the individualgrains and how applied stresses are transmitted throughthe assemblage of soil particles.

Particle strength or hardness is characterized bycrushing at contacts or particle tensile splitting. Thereis a statistical variation in grain strength for particlesof a specified material and of a given size (Moroto andIshii, 1990; McDowell, 2001). Random variation ingrain strengths leads to distributions of particle sizeswhen large stress is applied to a soil assembly. Table4.3 lists the characteristic tensile strengths of some soilparticles. The values are smaller than the yield strengthof the material itself. The strength also depends on theparticle shape. For example, Hagerty et al. (1993) showthat angular glass beads were more susceptible tobreakage than round glass beads.

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Table 4.3 Strength of Soil Particles

Sand Name Size (mm)37% Tensilea

Strength (MPa)Mean Strengthb

(MPa) Reference

QuartzLeighton Buzzard silica sand 1.18 — 29.8 Lee (1992)

2.0 — 24.73.36 — 20.5

Toyoura sand 0.2 147.4 136.6 Nakata et al. (2001)Aio quartz sand 0.85 51.2 52.1 Nakata et al. (1999)

1.0 47.7 46.61.18 37.9 35.61.4 46.7 42.41.7 39.6 38.5

Silica sand 0.5 147.4 132.5 McDowell (2001)1 66.7 59.02 41.7 37.3

Silica sand 0.28 110.9 147.3 Nakata et al. (2001)0.66 72.9 73.11.55 31.0 29.7

FeldsparAio feldspar sand 0.85 20.9 24.6 Nakata et al. (1999)

1.0 24.3 22.81.18 18.1 18.21.4 23.1 21.41.7 18.9 18.3

Calcareous SandOolitic limestone particle 5 — 2.4 Lee (1992)

8 — 2.112 — 1.820 — 1.530 — 1.340 — 1.250 — 1.1

Carboniferous limestone 5 — 14.9particle 8 — 12.2 Lee (1992)

12 — 10.320 — 8.330 — 7.040 — 6.250 — 5.7

Quiou sand 1 109.3 96.19 McDowell and Amon (2000)2 41.4 36.204 4.2 3.878 0.73 0.63

16 0.61 0.54

OthersMasado decomposed granite

soil 1.55 24.2 22.1 Nakata et al. (2001)Glass beads 0.93 365.8 339.6 Nakata et al. (2001)Angular glass 0.93 62.1 60.0 Nakata et al. (2001)

aStress below which 37% of the particles do not fracture.bForce/d 2 at which particle of size d is crushed.

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Grain size (mm)

100

80

60

40

20

00.01 0.1 1.0

20.7 MPa41.4 MPa62.1 MPa103 MPa345 MPa517 MPa689 MPa

Maximum stress

UncrushedPer

cent

Fin

er b

y W

eigh

t

Figure 4.11 Evolution of particle size distribution curveupon crushing (from Hagerty et al., 1993).

1 5 10 50 1000.2

1.0

0.5

5.0

10

50

Average Particle Size (mm)

Leighton Buzzard Sand

Carboniferous Limestone

Angular River Gravel

Rounded River Gravel

Oolitic Limestone

Par

ticle

Str

engt

h (M

Pa)

Figure 4.10 Relationship between tensile strength and particle size (from Lee, 1992).

The breakage potential of a single soil particle in-creases with its size as illustrated in Table 4.3. This isbecause larger particles tend to contain more and largerinternal flaws and hence have lower tensile strength.Fig. 4.10 shows that oolitic limestone, carboniferouslimestone, and quartz sand exhibit near linear declinesin strength with increasing particle size on a log–logplot (Lee, 1992).

The amount of particle crushing in an assemblageof particles depends not only on particle strength, butalso on the distribution of contact forces and arrange-ment of different size particles. It can be argued thatlarger size particles are more likely to break becausethe normal contact forces in a soil element increasewith particle size and the probability of a defect in agiven particle increases with its size as shown in Fig4.10 (Hardin, 1985). However, if a larger particle hascontacts with neighboring particles (i.e., larger coor-dination number), the load on it is distributed, and theprobability of facture is less than for a condition withfewer contacts. Experimental evidences suggest thatfines increase as particles break by increase in appliedpressure. For example, the evolution of particle sizedistribution curves for Ottawa sand in one-dimensionalcompression is shown in Fig. 4.11 (Hagerty et al.,1993). Hence, the coordination number dominates oversize-dependent particle strength. Larger particles havehigher coordination numbers because they are in con-

tact with many smaller particles. The very smallestparticles have a lower coordination number becausethere are fewer smaller particles available for contact.Hence, the largest particles in the aggregate becomeprotected by the surrounding newly formed smallerparticles, and smaller particles are more likely to break

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Figure 4.12 Weight–volume relationships for a saturated clay-granular soil mixture.

or move. Further details on particle breakage effectson compression behavior of sands are given in Chap-ter 10.

4.4 DOMINATING INFLUENCE OF THE CLAYPHASE

In general, the more clay in a soil, the higher the plas-ticity, the greater the potential shrinkage and swell, thelower the hydraulic conductivity, the higher the com-pressibility, the higher the cohesion, and the lower theinternal angle of friction. Whereas surface forces andtheir range of influence are small relative to the weightand size of silt sand particles, the behavior of smalland flaky clay mineral particles is strongly influencedby surface forces, as discussed in Chapter 6. Water isstrongly attracted to clay particle surfaces, also dis-cussed in Chapter 6, and results in plasticity, whereasnonclay particles have much smaller specific surfaceand less affinity for water and do not develop signifi-cant plasticity, even when in finely ground form.

If it is assumed as a first approximation that all ofthe water in a soil is associated with the clay phase,the amount of clay required to fill the voids of thegranular phase and prevent direct contact betweengranular particles can be estimated for any water con-tent. The weight and volume relationships for the dif-ferent phases of a saturated soil are shown in Fig. 4.12.In this figure W represents weight, V is volume, C isthe percent clay by weight, GSC is the specific gravityof clay particles, w is the water content in percent, w

is the unit weight of water, and GSG is the specificgravity of the granular particles. The volume of voidsin the granular phase is eGVGS, where eG is the voidratio of the granular phase and VGS is the volume ofgranular solids, given by

C Wse V � 1 � e (4.5)� �G GS G100 G SG w

The volume of water plus volume of clay is given by

w W C WS SV � V � � (4.6)W C 100 100 G w SC w

If clay and water completely fill the voids in the gran-ular phase, then

w W C W C Wss � � 1 � e (4.7)� � G100 100 G 100 G w SC w SG w

which simplifies to

w C C eG� � 1 � (4.8)� �100 100G 100 GSC SG

The void ratio of a granular material composed ofbulky particles is of the order of 0.9 in its loosest pos-sible state. The specific gravity of the nonclay fractionin most soils is about 2.67, and that of the clay fractionis about 2.75. Inserting these values in Eq. (4.8) gives

C � 48.4 � 1.42w (4.9)

This relationship indicates that for water contents typ-ically encountered in practice, say 15 to 40 percent,only a maximum of about one-third of the soil solidsneed be clay in order to dominate the behavior by pre-venting direct interparticle contact of the granular par-ticles. In fact, since there is a tendency for clayparticles to coat granular particles, the clay can signif-icantly influence properties. For example, just 1 or 2percent of highly plastic clay present in gravel used asa fill or aggregate may be sufficient to clog handlingand batching equipment.

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ATTERBERG LIMITS 95

Figure 4.13 Plasticity chart.

4.5 ATTERBERG LIMITS

Atterberg limits are extensively used for identification,description, and classification of cohesive soils and asa basis for preliminary assessment of their mechanicalproperties. The potential usefulness of the Atterberglimits in soil mechanics was first indicated by Terzaghi(1925a) when he noted that ‘‘the results of the simpli-fied soil tests (Atterberg limits) depend precisely onthe same physical factors which determine the resis-tance and the permeability of soils (shape of particles,effective size, uniformity) only in a far more complexmanner.’’

Casagrande (1932b) developed a standard device fordetermination of the liquid limit and noted that thenonclay minerals quartz and feldspar did not developplastic mixtures with water, even when ground to sizessmaller than 2 �m. Further studies led to the formationof a soil classification system based on the Atterberglimits for identification of cohesive soils (Casagrande,1948). This system was adopted, with minor modifi-cations, as a part of the Unified Classification System.A plot of plasticity index as a function of liquid limitthat is divided into different zones, as shown in Fig.4.13, is termed the plasticity chart. This chart formsan essential part of the Unified Soil Classification Sys-tem.

Although both the liquid and plastic limits are easilydetermined, and their qualitative correlations with soilcomposition and physical properties are quite well es-tablished, fundamental interpretations of the limits andquantitative relationships between their values andcompositional factors are more complex.

Liquid Limit

The liquid limit test is a form of dynamic shear test.Casagrande (1932b) deduced that the liquid limit cor-responds approximately to the water content at whicha soil has an undrained shear strength of about 2.5 kPa.Subsequent studies have indicated that the liquid limitfor all fine-grained soils corresponds to shearing resis-tance of about 1.7 to 2.0 kPa and a pore water suctionof about 6 kPa (Russell and Mickle, 1970; Wroth andWood, 1978; Whyte, 1982).

Liquid limit values are determined using both theCasagrande liquid limit device and the fall cone device.Different standards adopt different devices and, there-fore, correlations based on liquid limit should be usedwith some caution. The variation of undrained shearstrength with water content can be obtained from aseries of fall cone tests and solutions are available us-ing the theory of plasticity for various geometries usedin fall cones (Houlsby, 1982; Koumoto and Houlsby,

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Table 4.4 Hydraulic Conductivity at Liquid Limit for Several Clays

Soil TypeLiquid Limit,

wL (%)

Void Ratio atLiquid Limit,

eL

HydraulicConductivity(10�7 cm/s)

Bentonite 330 9.240 1.28Bentonite � sand 215 5.910 2.65Natural marine soil 106 2.798 2.56Air-dried marine soil 84 2.234 2.42Oven-dried marine soil 60 1.644 2.63Brown soil 62 1.674 2.83

From Nagaraj et al. (1991).

2001). Furthermore, with the aid of critical state soilmechanics (see Chapter 11), some other engineeringproperties, such as compressibility, can be deduced(Wood, 1990).

Values of hydraulic conductivity at the liquid limitfor several clays are given in Table 4.4, from Nagarajet al. (1991). The striking aspect of these data is that,although the water contents and void ratios at the liq-uid limit for the different clays vary over a very widerange, the hydraulic conductivity is very nearly thesame for all of them. This means that the effective poresizes controlling fluid flow must be about the same forall the clays at their liquid limit. Such a microfabric isconsistent with the cluster model for hydraulic con-ductivity discussed in Chapter 9. In this model, theindividual clay particles associate into aggregates orflocs, as shown schematically in Fig. 9.11. The size ofvoids between the clusters or aggregates controls theflow rate according to either model.

The approximately equal strengths, pore water suc-tions, and hydraulic conductivities for all clays at theirliquid limit can be explained by the concepts that (1)the aggregates or clusters are the basic units that in-teract to develop the strength, that is, the aggregatesact somewhat like single particles, (2) the average ad-sorbed water layer thickness is about the same on allparticle surfaces, and (3) the average size of interclus-ter pores is the same for all clays. Concept 2 providesthe key to why different clays have different values ofliquid limit. All clays have essentially the same surfacestructures, that is, a layer of oxygen atoms in tetrahe-dral coordination with silicon, or a layer of hydroxylsin octahedral coordination with aluminum or magne-sium. The forces of interaction between these surfacesand adsorbed water should be about the same for thedifferent clay minerals. Thus, the amount of water ad-sorbed per unit area of surface that corresponds to apore water suction of 6 kPa should be about the same.This means that the greater the specific surface, the

greater the total amount of water required to reducethe strength to that at the liquid limit. The specificsurface areas of the different clay minerals (Table 3.6)are consistent with the liquid limit values of differentclay minerals in Table 4.5. Additional support for thisconcept is given by the following relationship foundfor 19 British clays:

LL � 19 � 0.56A (�20%) (4.10)s

where LL is the liquid limit and As is the specific sur-face in square meters per gram (Farrar and Coleman,1967).

The effects of electrolyte concentration, cation va-lence and size, and dielectric constant of the pore fluidon the liquid limit of kaolinite and montmorillonite areillustrated and discussed by Sridharan (2002). The ef-fects are generally consistent with the above interpre-tation and can be explained also through double-layer(see Chapter 6) influences on swelling, flocculationand deflocculation of clay particles, and shear strength.

Plastic Limit

The plastic limit has been interpreted as the water con-tent below which the physical properties of the waterno longer correspond to those of free water (Terzaghi,1925a) and as the lowest water content at which thecohesion between particles or groups of particles issufficiently low to allow movement, but sufficientlyhigh to allow particles to maintain the molded posi-tions (Yong and Warkentin, 1966). Whatever the struc-tural status of the water and the nature of theinterparticle forces, the plastic limit is the lowerboundary of the range of water contents within whichthe soil exhibits plastic behavior; that is, above theplastic limit the soil can be deformed without volumechange or cracking and will retain its deformed shape;below the plastic limit it cannot. Plastic limit values

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INFLUENCES OF EXCHANGEABLE CATIONS AND pH 97

Table 4.5 Atterberg Limit Values for the Clay Minerals

Minerala

LiquidLimit(%)

PlasticLimit(%)

ShrinkageLimit(%)

Montmorillonite (1) 100–900 50–100 8.5–15Nontronite (1)(2) 37–72 19–27Illite (3) 60–120 35–60 15–17Kaolinite (3) 30–110 25–40 25–29Hydrated halloysite (1) 50–70 47–60Dehydrated halloysite (3) 35–55 30–45Attapulgite (4) 160–230 100–120Chlorite (5) 44–47 36–40Allophane (undried) 200–250 130–140

a(1) Various ionic forms. Highest values are for monovalent; lowestare for di- and trivalent. (2) All samples 10% clay, 90% sand and silt.(3) Various ionic forms. Highest values are for di- and trivalent; lowestare for monovalent. (4) Various ionic forms. (5) Some chlorites arenonplastic.

Data Sources: Cornell University (1950), Samuels (1950), Lambeand Martin (1955), Warkentin (1961), and Grim (1962).

for different clay minerals are listed in Table 4.5. Theundrained shear strength at the plastic limit is reportedto be in the ranges of 100 to 300 kPa with an averagevalue of 170 kPa (Sharma and Bora, 2003).

Liquidity Index

The liquidity index (LI) is defined by

water content � plastic limitLI � (4.11)

plasticity index

wherein the plasticity index is given by PI � LL �PL. The liquidity index is useful for expressing andcomparing the consistencies of different clays. It nor-malizes the water content relative to the range of watercontent over which a soil is plastic. It correlates wellwith compressibility, strength, and sensitivity proper-ties of fine-grained soils as illustrated in later chaptersof this book.

4.6 ACTIVITY

Both the type and amount of clay influence a soil’sproperties, and the Atterberg limits reflect both of thesefactors. To separate them, the ratio of the plasticityindex to the clay size fraction (percentage by weightof particles finer than 2 �m), termed the activity, isvery useful (Skempton, 1953):

plasticity indexActivity � (4.12)

% � 2 �m

For many clays, a plot of plasticity index versus claycontent yields a straight line passing through the originas shown for four clays in Fig. 4.14. The slope of theline for each clay gives the activity. Approximate val-ues for the activities of different clay minerals arelisted in Table 4.6.

The greater the activity, the more important the in-fluence of the clay fraction on properties and the moresusceptible their values to changes in such factors astype of exchangeable cations and pore fluid composi-tion. For example, the activity of Belle Fourche mont-morillonite varies from 1.24 with magnesium as theexchangeable cation to 7.09 for sodium saturation ofthe exchange sites. On the other hand, the activity ofAnna kaolinite only varies from 0.30 to 0.41 for sixdifferent cation forms (White, 1955).

4.7 INFLUENCES OF EXCHANGEABLECATIONS AND pH

Cation type exerts a controlling influence on theamount of swelling of expansive clay minerals in thepresence of water. For example, sodium and lithiummontmorillonite may undergo almost unrestrictedinterlayer swelling provided water is available,the confining pressure is small, and the electrolyte

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Figure 4.14 Relationship between plasticity index and clay fraction (from Skempton, 1953).

Table 4.6 Activities of Various Clay Minerals

Mineral Activity

Smectites 1–7Illite 0.5–1Kaolinite 0.5Halloysite (2H2O) 0.5Halloysite (4H2O) 0.5Attapulgite 0.5–1.2Allophane 0.5–1.2

concentration is low. On the other hand, divalent andtrivalent forms of montmorillonite do not expand be-yond a basal spacing of about 17 A and form multi-particle clusters or aggregates, regardless of otherenvironmental factors.

In soils composed mainly of nonexpansive clay min-erals, adsorbed cation type is of the greatest impor-tance in influencing the behavior of the material insuspension and the nature of the fabric in sedimentsthat form. Monovalent cations, particularly sodium andlithium, promote deflocculation, whereas clay suspen-

sions ordinarily flocculate in the presence of divalentand trivalent cations.

pH influences interparticle repulsions because of itseffects on clay particle surface charge. Positive edgecharges can exist in low pH environments. These ef-fects are of greatest importance in kaolinite, lesserimportance in illite, and relatively unimportant insmectite. In kaolinite, the pH may be the single mostimportant factor controlling the fabric of sedimentsformed from suspension.

The influences of cations and pH are examined fur-ther in Chapter 6.

4.8 ENGINEERING PROPERTIES OF CLAYMINERALS

Different groups of clay minerals exhibit a wide rangeof engineering properties. Within any one group, therange of property values may also be great. It is afunction of particle size, degree of crystallinity, typeof adsorbed cations, pH, the presence of organic mat-ter, and the type and amount of free electrolyte in thepore water. In general, the importance of these factorsincreases in the order kaolin � hydrous mica (illite) �

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ENGINEERING PROPERTIES OF CLAY MINERALS 99

Table 4.7 Mineral Composition of Different Particle SizeRanges in Soils

ParticleSize(�m)

PredominatingConstituents

CommonConstituents

RareConstituents

0.1 Montmoril-loniteBeidellite

Mica inter-mediates

Illite (traces)

0.1–0.2 Mica inter-mediates

KaoliniteMontmo-rillonite

IlliteQuartz

(traces)0.2–2.0 Kaolinite Illite

Mica inter-mediates

MicasHalloysite

QuartzMontmo-rillonite

Feldspar

2.0–11.0 MicasIllites

QuartzKaolinite

Halloysite(traces)

Feldspars Montmo-rillonite(traces)

From Soveri (1950).

smectite. The chlorites exhibit characteristics in the ka-olin–hydrous mica range. Vermiculites and attapulgitehave properties that usually fall in the hydrous mica–smectite range.

Because of the influences of the above composi-tional factors, only typical ranges of property valuesare given in this section. Factors that determine theactual values in any case are analyzed in more detailin subsequent chapters.

Atterberg Limits

Plasticity values for different clay minerals are listedin Table 4.5 in terms of ranges in the liquid, plastic,and shrinkage limit values. Most of the values weredetermined using samples composed of particles finerthan 2 �m. Several general conclusions can be madeconcerning the Atterberg limits of the clay minerals.

1. The liquid and plastic limit values for any oneclay mineral species may vary over a wide range.

2. For any clay mineral, the range in liquid limitvalues is greater than the range in plastic limitvalues.

3. The variation in values of liquid limit among dif-ferent clay mineral groups is much greater thanthe variation in plastic limits.

4. The type of adsorbed cation has a much greaterinfluence on the high plasticity minerals (e.g.,montmorillonite) than on the low plasticity min-erals (e.g., kaolinite).

5. Increasing cation valence decreases the liquidlimit values of the expansive clays but tends toincrease the liquid limit of the nonexpansive min-erals.

6. Hydrated halloysite has an unusually high plasticlimit and low plasticity index.

7. The greater the plasticity the greater is the shrink-age on drying (the lower the shrinkage limit).

Particle Size and Shape

Different clay minerals occur in different size ranges(Table 3.6) because mineralogical composition is a ma-jor factor in determining particle size. There is someconcentration of different clay minerals in differentbands within the clay size range (less than 2 �m), asindicated in Table 4.7. The shapes of the most commonclay minerals are platy, except for halloysite, whichoccurs as tubes (Fig. 3.21). Particles of kaolinite arerelatively large, thick, and stiff (Fig. 3.13). Smectitesare composed of small, very thin, and filmy particles(Fig. 3.25). Illites are intermediate between kaoliniteand smectite (Fig. 3.29) and are often terraced and thin

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Figure 4.15 Ranges in effective stress failure envelopes forpure clay minerals and quartz (from Olson, 1974). Reprintedwith permission of ASCE.

Figure 4.16 Strength envelopes for a range of soil types(from Bishop, 1966).

at the edges. Attapulgite, owing to its double silicachain structure, occurs in lathlike particle shapes (Fig.3.31).

Hydraulic Conductivity (Permeability)

Mineralogical composition, particle size and size dis-tribution, void ratio, fabric, and pore fluid character-istics all influence the hydraulic conductivity. Thisproperty is considered in detail in Chapter 9. Over thenormal range of water contents (plastic limit to liquidlimit), the hydraulic conductivity of all the clay min-erals is less than about 1 � 10�7 m/s and may rangeto values less than 1 � 10�12 m/s for some of themonovalent ionic forms of smectite minerals at lowporosity. The usual measured range for natural claysoils is about 1 � 10�8 to 1 � 10�10 m/s. For clayminerals compared at the same water content, the hy-draulic conductivities are in the order smectite (mont-morillonite) � attapulgite � illite � kaolinite.

Shear Strength

There are many ways to measure and express the shearstrength of a soil, as described in most geotechnicalengineering textbooks. In most cases, a Mohr failureenvelope, where shear strength (usually peak, criticalstate, or residual) is plotted as a function of the directeffective stress on the failure plane, or a modified Mohrdiagram, in which maximum shear stress is plotted ver-sus the average of the major and minor principal ef-fective stresses at failure, is used. A straight line is fitto the resulting curve over the normal stress range ofinterest and the shear strength � is given by an equationof the form

� � c� � �� tan �� (4.13)n

where is the effective normal stress on the shear��nplane, c� is the intercept for equals zero, often called��nthe cohesion, and �� is the slope, usually called thefriction angle.

Effective stress strength envelopes are useful for re-lating strength to composition. Zones that encompassthe effective stress failure envelopes, based on peakstrength, for pure clay minerals and quartz are shownin Fig. 4.15. The increase in shear strength with in-crease in effective stress, that is, the friction angle, isgreatest for the nonclay mineral quartz, followed indescending order by kaolinite, illite, and montmoril-lonite. The ranges in the position of a failure envelopefor a given mineral result from differences in such fac-tors as fabric, adsorbed cation, pH, and overconsoli-dation ratio. A similar pattern of failure envelopes forsome natural soils is shown in Fig. 4.16. The finer

grained the soil and the greater the amount of clay, thesmaller the inclination of the failure envelope.

From a number of studies [e.g., Hvorslev (1937,1960), Gibson (1953), Trollope (1960), and Schmert-mann and Osterberg (1960), and Schmertmann(1976)], it has been believed that the total strength ofa clay is composed of two distinct parts: a cohesionthat depends only on void ratio (water content), and africtional contribution, dependent only on normal ef-fective stress. Evaluation of these two parts was doneby measurement of the strength of two samples bothat the same void ratio or water content, but at differentlevels of effective stress. This condition is obtained byusing one normally consolidated and one overconsol-idated sample. The strength parameters determined inthis way, often termed the Hvorslev parameters or true

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Figure 4.17 Residual friction angles for clay–quartz mixtures and natural soils (from Ken-ney, 1967).

cohesion and true friction, show increasing cohesionand decreasing friction with increasing plasticity andactivity of the clay.

However, two samples of the same clay at the samevoid ratio but different effective stresses are known tohave different structures, as discussed in Chapter 8.Thus, they are not equivalent, and the strength testsmeasure the effects of both effective stress and struc-ture differences. Furthermore, tests over large rangesof effective stress show that actual failure envelopesare curved in the manner of Fig. 4.16 and that thecohesion intercept is either zero or very small, exceptfor cemented soils. Thus, a significant true cohesion,if defined as strength in the absence of normal stresson the failure plane, does not exist in the absence ofchemical bonding. These considerations are discussedin more detail in Chapter 11.

Even the largest of the friction angle values for clayminerals is significantly less than the residual value forcohesionless soils, wherein values of drained frictionangle are generally in the range of 30� to 50�. Theresidual strengths of some quartz–clay mixtures areshown in Fig. 4.17. If each mineral were an equallyimportant contributor to strength, then the curve for agiven mixture should be symmetrical about the 50 per-cent point, as is the case for kaolinite and hydrous micawith no salt in the pore water. In the other mixtures,however, the clay phase begins to dominate at claycontents less than 50 percent. This is because with ex-pansive clay minerals (montmorillonite) or flocculatedfabrics (30 g salt / liter) the ratio of volume of wet clayto volume of quartz is greater than the ratio of dryvolumes. It is further illustration of the dominating in-fluence of the clay phase discussed earlier.

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Figure 4.18 Compression and unload–reload indices as a function of plasticity index (fromKulhawy and Mayne, 1990). Reprinted with permission from EPR1.

Compressibility

The compressibility of saturated specimens of clayminerals increases in the order kaolinite � illite �smectite. The compression index Cc, which is definedas the change in void ratio per 10-fold increase in con-solidation pressure, is in the range of 0.19 to 0.28 forkaolinite, 0.50 to 1.10 for illite, and 1.0 to 2.6 formontmorillonite, for different ionic forms (CornellUniversity, 1950). The more compressible the clay, themore pronounced the influences of cation type andelectrolyte concentration on compressibility.

Compression index values for a number of differentnatural clays are shown in Fig. 4.18 as a function ofplasticity index (Kulhawy and Mayne, 1990). The val-ues for pure clays plot generally within the definedranges in Fig. 4.18. The compression index for un-loading and reloading is about 20 percent of the valuefor virgin compression.

As both compressibility and hydraulic conductivityare strong functions of soil composition, the coefficientof consolidation cv is also related to composition be-cause cv is directly proportional to hydraulic conduc-tivity and inversely proportional to the coefficient ofcompressibility.4 Values of cv determined in one study

4 The coefficient of compressibility av is the negative of the rate ofchange of void ratio with effective stress.

(Cornell University, 1950) were in the ranges of 0.06� 10�8 to 0.3 � 10�8 m2/s for montmorillonite, 0.3 �10�8 to 2.4 � 10�8 m2/s for illite, and 12 � 10�8 to90 � 10�8 m2/s for kaolinite. Coefficients of consoli-dation for kaolinite, illite, montmorillonite, halloysite,and two-mineral mixtures of these clays ranged from1 � 10�8 m2/s for pure montmorillonite to 378 � 10�8

m2/s for pure halloysite in another study (Kondner andVendrell, 1964). Individual minerals did not influencethe coefficient of consolidation in direct proportion tothe amounts present.

Approximate ranges of the coefficient of consoli-dation for natural clays are given in Fig. 4.19. Theabove values for pure clays and clay mineral mixturesare within the same general ranges. One conclusionthat can be drawn from the comparability of compres-sion index and coefficient of consolidation values fornatural clays with those for pure clays is that the clayphase dominates the compression and consolidationbehavior, with the nonclay material playing a passiverole as relatively inert filler.

Swelling and Shrinkage

The actual amount of volume change of a soil in re-sponse to a change in applied stress depends on theenvironmental factors listed in Section 4.1 as well ason the cation type, electrolyte type and concentration,

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Figure 4.19 Coefficient of consolidation as a function ofliquid limit (from NAVFAC, 1982).

(Sur

char

geP

ress

ure

- 1p.

s.i.)

(Sur

char

geP

ress

ure

- 1p.

s.i.)

(Surc

harg

ePr

essu

re- 1

p.s.

i.)

(Surcharge Pressure - 6.94

p.s.i.)

Figure 4.20 Four correlations between swelling potentialand plasticity index (from Chen, 1975).

and pore fluid dielectric constant. However, the poten-tial total amount of swell or shrinkage is determinedby the type and amount of clay. From a considerationof the clay mineral structures and interlayer bonding(Chapter 3), it would be expected that smectite andvermiculite should undergo greater volume changes onwetting and drying than do kaolinite and hydrous mica.Experience indicates clearly that this is indeed thecase. In general, the swelling and shrinking propertiesof the clay minerals follow the same pattern as theirplasticity properties, that is, the more plastic the min-eral, the more potential swell and shrinkage. Illustra-tions of the influences of adsorbed cation type and porefluid composition are given in Chapter 10 and by Srid-haran (2002).

Because of the many problems encountered in theperformance of structures founded on high volumechange soils, numerous attempts have been made todevelop reliable methods for their identification. Themost successful of these are based on the determina-tion of some factor that is related directly to the claymineral composition, such as shrinkage limit, plasticityindex, activity, and percentage finer than 1 �m.

Simple, unique correlations between swell or swellpressure and these parameters that reflect only the typeand amount of clay are not possible because of thestrong dependence of the behavior on initial state(moisture content, density, and structure) and the otherenvironmental factors. This is illustrated by Fig. 4.20,which shows four different correlations between swell-ing potential and plasticity index (Chen, 1975). Thetwo curves showing the Chen correlations were ob-tained for different natural soils compacted to dry unitweights between 100 and 110 pounds per cubic foot(15.7 and 17.3 kN/m3) at water contents between 15and 20 percent. The large influence of surcharge pres-

sure during swelling is clearly shown. The tests bySeed et al. (1962b) were done using artificial mixturesof sand and clay minerals compacted at optimum watercontent using Standard AASHTO compactive effort al-lowed to swell under a surcharge pressure of 1 psi (7kPa). The measurements by Holtz and Gibbs (1956)were made using both undisturbed and remolded sam-ples allowed to swell from an air-dry state to saturationunder a surcharge of 1 psi (7 kPa).

The results of the tests on artificial sand–clay min-eral mixtures obtained by Seed et al. (1962b) correlatewell with compositional factors that reflect both thetype and amount of clay, that is, the activity A, definedas PI/ C, and the percent clay size C (% � 2 �m),according to

�5 2.44 3.44S � 3.6 � 10 A C (4.14)

where S is the percent swell for samples compactedand tested as indicated above. A chart based on thisrelationship is shown in Fig. 4.21. For compacted nat-ural soils the swelling potential could be related to theplasticity index with an accuracy of �35% accordingto

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Figure 4.21 Classification chart for swelling potential (mod-ified from Seed et al., 1962b).

Figure 4.22 Effect of amount and type of clay on ‘‘steady-state’’ creep rate (see Chapter 12).

�3 2.44S � 2.16 � 10 (PI) (4.15)

Somewhat different relationships have been found tobetter classify the swell potential of some soils, and nosingle relationship is suitable for all conditions. Thus,while the above relationships and plots such as Figs.4.20 and 4.21 illustrate the influences of compositionalfactors and provide preliminary guidance about the po-tential magnitude of swelling, reliable quantification ofswell and swell pressure in any case should be basedon the results of tests on representative undisturbedsamples tested under appropriate conditions of con-finement and water chemistry.

Time-Dependent Behavior

Different soil types undergo varying amounts of time-dependent deformations and stress variations withtime, as exhibited by secondary compression, creep,and stress relaxation. The potential for these phenom-ena depends on compositional factors, whereas the ac-tual amount in any case depends on environmentalfactors. For example, it is known that retaining wallswith wet clay backfills must be designed for at-restearth pressures because of stress relaxation along a po-tential failure plane that results in increased pressureon the wall. On the other hand, if dry clay is used, andif it is maintained dry, then designs based on activepressures are possible because time-dependent in-creases in pressure will be negligible.

In general, the greater the organic content and thewetter and more plastic the clay, the more pronouncedis the time-dependent behavior. Both the type andamount of clay are important, as indicated, for exam-ple, by the variation of creep rate with clay content forthree different clay mineral–sand mixtures, as shownin Fig. 4.22. In these tests, environmental factors wereheld constant by preparing all specimens to the sameinitial conditions (isotropic consolidation of saturatedsamples to 200 kPa) and application of a creep stressequal to 90 percent of the strength determined by anormal strength test. The variation in creep rate forthese specimens as a function of plasticity index isshown in Fig. 4.23. The correlation is reasonablyunique because the plasticity index reflects both thetype and amount of clay.

4.9 EFFECTS OF ORGANIC MATTER

Organic matter in soil may be responsible for highplasticity, high shrinkage, high compressibility, low

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CONCLUDING COMMENTS 105

Figure 4.23 Relationship between clay content, plasticity in-dex, and creep rate.

hydraulic conductivity, and low strength. Soil organicmatter is complex both chemically and physically, andmany reactions and interactions between the soil andthe organic matter are possible (Oades, 1989). It mayoccur in any of five groups: carbohydrates; proteins;fats, resins, and waxes; hydrocarbons; and carbon. Cel-lulose (C6H10O5) is the main organic constituent ofsoil. In residual soils organic matter is most abundantin the surface horizons. Organic particles may rangedown to 0.1 �m in size. The specific properties of thecolloidal particles vary greatly depending upon parentmaterial, climate, and stage of decomposition.

The humic fraction is gel-like in properties and neg-atively charged (Marshall, 1964). Organic particles canstrongly adsorb on mineral surfaces, and this adsorp-tion modifies both the properties of the minerals andthe organic material itself. Soils containing significantamounts of decomposed organic matter are usuallycharacterized by a dark gray to black color and an odorof decomposition. At high moisture contents, decom-

posed organic matter may behave as a reversible swell-ing system. At some critical stage during drying,however, this reversibility ceases, and this is oftenmanifested by a large decrease in the Atterberg limits.This is recognized by the Unified Soil ClassificationSystem, which defines an organic clay as a soil thatwould classify as a clay (the Atterberg limits plotabove the A line shown in Fig. 4.13) except that theliquid limit value after oven drying is less than 75 per-cent of the liquid limit value before drying (ASTM,1989).

Increasing the organic carbon content by only 1 or2 percent may increase the limits by as much as anincrease of 10 to 20 percent in the amount of materialfiner than 2 �m or in the amount of montmorillonite(Odell et al., 1960). The influences of organic mattercontent on the classification properties of a soft clayfrom Brazil are shown in Fig. 4.24.

The maximum compacted densities and compressivestrength as a function of organic content of both nat-ural samples and mechanical mixtures of inorganicsoils and peat are shown in Figs. 4.25 and 4.26, re-spectively. Both the compacted density and strengthdecrease significantly with increased organic contentand the relationships for natural samples and themixtures are about the same. Increased organic contentalso causes an increase in the optimum water contentfor compaction.

The large increase in compressibility as a result ofhigh organic content in clay is illustrated by the datain Fig. 4.27 for the clay whose classification propertiesare shown in Fig. 4.24. In Fig. 4.27 CR is the com-pression ratio, defined as CC / (1 � e0) expressed as apercentage, and C� is the secondary compression ratio,defined as the change in void ratio per 10-fold increasein time after the end of primary consolidation.

The effect of organic matter on the strength andstiffness of soils depends largely on whether the or-ganic matter is decomposed or consists of fibers thatcan act as reinforcement. In the former case, both theundrained strength and the stiffness, or modulus, areusually reduced as a result of the higher water contentand plasticity contributed by the organic matter. In thelatter, the fibers can act as reinforcements, thereby in-creasing the strength.


Knowledge of soil composition is a useful indicator ofthe probable ranges of geotechnical properties andtheir variability and sensitivity to changes in environ-mental conditions. Although quantitative values ofproperties for analysis and design cannot be derivedfrom compositional data alone, information on com-

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Figure 4.24 Influence of organic content on classification properties of Juturnaiba organicclay, Brazil (from Coutinho and Lacerda, 1987).

position can be helpful for explaining unusual behav-ior, identification of expansive soils, selection ofsampling and sample handling procedures, choice ofsoil stabilization methods, and prediction of probablefuture behavior.

For example, if it is known that a soil to be used inearthwork construction contains either hydrated halloy-site, organic matter, or expansive minerals, then air-drying laboratory samples prior to testing is likely toresult in erroneous data on mechanical properties andmust be avoided. If a soil contains a large amount ofactive clay minerals, then it can be anticipated thatproperties will be sensitive to changes in chemical en-vironment. Compositional data on the soil and porewater are useful to estimate the dispersion and erosionpotential of a soil (Chapter 8) and the risk of instabilityas a result of leaching and solutioning processes.

In many cases, the effects of composition on behav-ior are reflected by information on particle size, shape,and size distribution of the coarse fraction, and theAtterberg limits of the fine fraction. On large projectsand whenever unusual behavior is encountered, how-ever, compositional data are valuable aids for interpre-tation of observations. Furthermore, the influences ofcompositional and structural factors are not always ad-equately reflected by the usual classification properties,

and more direct evaluation of their significance isneeded. Examples of some soil types in which thesefactors may be especially important are decomposedgranite, tropical residual soils, volcanic ash soils, col-lapsing soils, loess, and carbonate sand, as discussedin more detail by Mitchell and Coutinho (1991).


1. Show that the loosest and densest packings of uni-form size particles give void ratios of 0.91 and 0.34,respectively. What is the coordination numbers(number of particle contacts for each particle) foreach packing?

2. Explain why smaller particles are stronger thanlarger particles and why angular particles are moresusceptible to breakage than round particles.

3. Using Figs. 4.8 and 4.11, show how the maximumand minimum void ratio changes with applied loadas particles progressively break and the coefficientof uniformity Cu increases. Plot the data in e–log�v space and discuss the result.

4. Using Eq. (4.8), derive a relationship between C(the percentage of clay) versus w (water content)

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Figure 4.25 Maximum dry density as a function of organiccontent for a natural soil and soil–peat mixtures (from Frank-lin et al., 1973). Reprinted with permission of ASCE.

Figure 4.27 Effect of organic content on the compressibilityproperties of Juturnaiba organic clay, Brazil (from Coutinhoand Lacerda, 1987).

Figure 4.26 Unconfined compressive strength as a functionof organic content for a natural soil and soil–peat mixtures(from Franklin et al., 1973). Reprinted with permission ofASCE.

for different values of eG (the void ratio of the gran-ular phase). Discuss the sensitivity of eG on sand–clay mixture packing. What happens if silt is mixedinstead of clay?

5. Using the reported undrained shear strengths at liq-uid limit and plastic limit, derive a relationship be-tween the compression index Cc and plasticity indexPI. Assume that the ratio of undrained shearstrength to vertical effective stress, su / , is 0.3.��v

Compare the result with the data presented in Fig.4.18.

6. Assuming the thickness of adsorbed water layer is100 A, estimate the amount of free water per gramof clay for the following conditions and discuss theresults:a. Montmorillonite at its liquid limit with mono-

valent adsorbed cations (specific surface � 840m2/g of dry clay), liquid limit � 900 percent

b. Montmorillonite at its plastic limit with mono-valent adsorbed cations (specific surface � 840m2/g of dry clay), plastic limit � 100 percent

c. Montmorillonite at its liquid limit with divalentadsorbed cations (specific surface � 50 m2/g ofdry clay), liquid limit � 100 percent

d. Montmorillonite at its plastic limit with divalentadsorbed cations (specific surface � 50 m2/g ofdry clay), plastic limit � 50 percent

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e. Kaolinite at its liquid limit (specific surface �15 m2/g of dry clay), liquid limit � 70 percent

f. Kaolinite at its plastic limit (specific surface �15 m2/g of dry clay), plastic limit � 30 percent

7. By examining the data presented in Figs. 4.24 and4.29, discuss why organic clays exhibit larger com-pressibility compared to inorganic clays (see Fig.4.18).

8. Assume that you are able to determine accurate,reliable quantitative values for all details of the min-eralogical, chemical, and biological constituents ofa given soil. All particle sizes, shapes, and distri-butions are also known. Speculate on your abilityto predict the volume change, strength, and per-meability properties of this soil over a range of wa-ter contents. Give reasons for why you would havelow or high confidence in your predictions.

9. In light of what is known about the dependence ofengineering properties on soil composition—bothof the particles and of the other phases present in a

soil—discuss the strengths and weaknesses of theUnified Soil Classification System (USCS) in pro-viding a clear and unambiguous picture of the prob-able behavior of the following soil types. Indeveloping your answer, be specific concerningwhat is measured and the terms of reference usedin the USCS and what is most important in deter-mining any property being discussed. (Note: Someof the information in Chapter 8 may be useful indeveloping your answer to this question.)a. Clean sandb. Decomposed granitec. Calcareous sandd. Organic silte. Expansive clayf. Glacial tillg. Loessh. Dispersive clayi. Volcanic ashj. Estuarine mud

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109

CHAPTER 5

Soil Fabric and ItsMeasurement

5.1 INTRODUCTION

Although soils are composed of discrete soil particlesand particle groups, a soil mass is almost alwaystreated as a continuum for engineering analysis anddesign. Nonetheless, the specific values of propertiessuch as strength, permeability, and compressibility de-pend on the size and shape of the particles, their ar-rangements, and the forces between them. Thus, tounderstand a property requires knowledge of these fac-tors. Furthermore, new theories of particulate mechan-ics and computational methods based on these theoriesare now becoming available. With these theories andmethods it may ultimately be possible to predict themechanical behavior of soil masses in terms of thecharacteristics of the particles themselves, although at-taining this goal appears somewhat far off.

Particle arrangements in soils remained largely un-known until suitable optical, X-ray diffraction, andelectron microscope techniques made direct observa-tions possible starting in the mid-1950s. Interest thencentered mainly on clay particle arrangements andtheir relationships to mechanical properties. In the late1960s, knowledge expanded rapidly, sparked by im-proved techniques of sample preparation and the de-velopment of the scanning electron microscope. In theearly 1970s attention was directed also at particle ar-rangements in cohesionless soils. From this work camea realization that characterization of the properties ofsands and gravels cannot be done in terms of densityor relative density alone, as had previously beenthought. Particle arrangements and stress history mustbe considered in these materials as well.

In the 1970s and 1980s, micromechanics theorieswere developed that aimed to relate microstructure tomacroscopic behavior. Various homogenization tech-

niques that incorporate small-scale features such asinhomogeneity and microfractures into continuummodels became available (Mura, 1987; Nemat-Nasserand Hori, 1999). Increased computational speeds al-lowed simulation of an assembly of individual soil par-ticles by modeling particle contact behavior, and thisled to the development of numerical methods such asthe discrete/distinct element method and contact dy-namics (Cundall and Strack, 1979; Moreau, 1994;Cundall, 2001). In the early developments, simulationswere limited to an assembly of two-dimensional cir-cular disks. However, it is now possible to performsimulations with various three-dimensional particleshapes, complex contact models, and pore fluid inter-actions. These ‘‘digital’’-type studies offer possibilitiesfor systematic investigation of soil fabric effects onmechanical properties in comparison to ‘‘laboratory’’-type studies, which contain inherent errors associatedwith measuring soil fabrics of different specimens.Furthermore, mechanical responses under the stresspaths that are difficult to apply in the laboratory canbe investigated using distinct element methods.

Other innovations in the past two decades have ledto improved material measurement techniques andtheir interpretation using computers. These include theenvironmental scanning electron microscopy (ESEM),nanoindentation and probing, complex digital imageanalysis, magnetic resonance imaging (MRI), X-Raytomography, and laser-aided tomography. Some ofthem have been used to characterize the microscopicproperties of soils (Oda and Iwashita, 1999).

The more established methods for studying and,where possible, quantifying the arrangements of par-ticles, particle groups, and voids in different soils aredescribed and illustrated in this chapter. Some ele-

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110 5 SOIL FABRIC AND ITS MEASUREMENT

Figure 5.1 Modes of particle associations in clay suspen-sions and terminology. (a) Dispersed and deflocculated, (b)aggregated but deflocculated (face-to-face association, orparallel or oriented aggregation), (c) edge-to-face flocculatedbut dispersed, (d ) edge-to-edge flocculated but dispersed, (e)edge-to-face flocculated and aggregated, (ƒ ) edge-to-edgeflocculated and aggregated, and (g) edge-to-face and edge-to-edge flocculated and aggregated. From An Introduction toClay Colloid Chemistry, by H. van Olphen, 2nd ed., Copy-right � 1977 by John Wiley & Sons. Reprinted with per-mission from John Wiley & Sons.

ments and applications of the newer methods are in-troduced in later chapters.

5.2 DEFINITIONS OF FABRICS AND FABRICELEMENTS

The term fabric refers to the arrangement of particles,particle groups, and pore spaces in a soil. The termstructure is sometimes used interchangeably with fab-ric. It is preferable, however, to use structure to referto the combined effects of fabric, composition, and in-terparticle forces. Methods for determination of soilfabric are described and examples of different fabrictypes are given in the following sections. The impor-tance of soil fabric as a factor determining soil prop-erties and behavior is discussed and illustrated inChapter 8. In practice, special problems, unusual soils,and the need to ensure that measured properties prop-erly reflect the in situ conditions may require appli-cation of these testing and interpretation methods.

It is necessary to consider the size, the form, andthe function of different fabric units and to keep inmind the scale at which the fabric is of interest. Forexample, a carefully compacted clay liner for an im-poundment may have uniformly and closely packedparticle groups within it, thus giving a material withvery low hydraulic conductivity. If, however, the linerbecomes broken into sections measuring a meter or soin each direction as a result of shrinkage cracking, thenleakage through it will be dominated totally by flowthrough the cracks, and the small-scale fabric is un-important. Similarly, the strength of intact, homoge-neous soft clay will be influenced greatly by theparticle arrangements on a microscale, whereas that ofstiff fissured clay will be controlled by the propertiesalong the fissures.

Particle Associations in Clay Suspensions

Many soil deposits are formed by deposition fromflowing or still water. Accordingly, knowledge of par-ticle associations in suspensions is a good startingpoint for understanding how soil fabrics are formedand changed throughout the history of a soil. Cleansands and gravels are usually comprised of single grainarrangements, and these are discussed in Section 5.3.Particle associations in clay suspensions may be morecomplex. They can be described as follows and as il-lustrated in Fig. 5.1 (van Olphen, 1977):

1. Dispersed No face-to-face association of clayparticles

2. Aggregated Face-to-face (FF) association ofseveral clay particles

3. Flocculated Edge-to-edge (EE) or edge-to-face(EF) association of aggregates

4. Deflocculated No association between aggre-gates

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DEFINITIONS OF FABRICS AND FABRIC ELEMENTS 111

Figure 5.2 Schematic representation of elementary particlearrangements (Collins and McGown, 1974). (a) Individualclay platelet interaction, (b) individual silt or sand particleinteraction, (c) clay platelet group interaction, (d ) clothed siltor sand particle interaction, and (e) partly discernible particleinteraction.

Thicker and larger particles result from FF associa-tion. The EF and EE associations can produce card-house structures that are quite voluminous untilcompressed.

The terms flocculated and aggregated are often usedsynonymously in a generic sense to refer to multipar-ticle assemblages, and the terms deflocculated and dis-persed are used synonymously in a generic sense torefer to single particles or particle groups acting in-dependently.

Particle Associations in Soils

Particle associations in sediments, residual soils, andcompacted clays assume a variety of forms; however,most of them are related to combinations of the con-figurations shown in Fig. 5.1 and reflect the differencein water content between a suspension and a densersoil mass. Fine-grained soils are almost always com-posed of multiparticle aggregates. Overall, three maingroupings of fabric elements may be identified (Collinsand McGown, 1974):

1. Elementary Particle Arrangements Singleforms of particle interaction at the level of indi-vidual clay, silt, or sand particles

2. Particle Assemblages Units of particle organi-zation having definable physical boundaries anda specific mechanical function, and which consistof one or more forms of the elementary particlearrangements

3. Pore Spaces Fluid and/or gas filled voidswithin the soil fabric

Schematic illustrations of each of the fabric featuresin these three classes are shown in Figs. 5.2 through5.4. Electron photomicrographs illustrating some of thefeatures are shown in Fig. 5.5. Figure 5.6 shows theoverall fabric of undisturbed Tucson silty clay, a fresh-water alluvial deposit. The features shown in the fig-ures are sufficient to describe most fabrics, although anumber of additional terms have also been used to de-scribe the same or similar features.

Cardhouse is an edge-to-face arrangement formingan open fabric similar to the edge-to-face flocculatedbut dispersed arrangement of Fig. 5.1c (Goldschmidt,1926). A domain (Aylmore and Quirk, 1960, 1962) orpacket or book (Sloane and Kell, 1966) is an aggregateof parallel clay plates. An array of such fabrics istermed a turbostratic fabric and is similar to the inter-weaving bunches of Fig. 5.3h. An edge-to-face asso-ciation of packets or books is termed a bookhouse andis similar to the arrangement of Fig. 5.1e. A cluster isa grouping of particles or aggregates into larger fabric

units (Olsen, 1962; Yong and Sheeran, 1973). In a fab-ric composed of groupings of clusters, it is useful torefer to intracluster and intercluster pore space and tocluster and total void ratios. The term ped (Brewer,1964) has a similar meaning to cluster.

Fabric Scale

The fabric of a soil may be viewed relative to threelevels of scale. From smallest to largest they are:

1. Microfabric The microfabric consists of theregular aggregations of particles and the verysmall pores between them. Typical fabric unitsare up to a few tens of micrometers across.

2. Minifabric The minifabric contains the aggre-gations of the microfabric and the interassem-

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Figure 5.3 Schematic representations of particle assemblages (Collins and McGown, 1974).(a) connectors, (b) connectors, (c) connectors, (d ) irregular aggregations by connector as-semblages, (e) irregular aggregations in a honeycomb, (ƒ ) regular aggregation interactingwith particle matrix, (g) interweaving bunches of clay, (h) interweaving bunches of clay withsilt inclusions, (i) clay particle matrix, and ( j ) granular particle matrix.

blage pores between them. Minifabric units maybe a few hundred micrometers in size.

3. Macrofabric The macrofabric may containcracks, fissures, root holes, laminations, and thelike that correspond to the transassemblage poresshown in Fig. 5.6.

Soil mechanical and flow properties depend on de-tails of these three levels of fabric to varying degrees.For example, the hydraulic conductivity of a fine-grained soil is almost totally dominated by the macro-

and minifabrics. Time-dependent deformations such ascreep and secondary compression are controlled moststrongly by the mini- and microfabric.

5.3 SINGLE-GRAIN FABRICS

Sand and gravel particles are sufficiently large andbulky that they ordinarily behave as independent units.Attempts to describe the stress–deformation behaviorof granular soils using particulate mechanics theories

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SINGLE-GRAIN FABRICS 113

Figure 5.4 Schematic representation of pore space types (Collins and McGown, 1974).

[e.g., Newland and Allely (1957), Rowe (1962, 1973),Horne (1965), Matsuoka (1974), Murayama (1983),Nemat-Nasser and Mehrabadi (1984), and Wan andGuo (2001)] have met with some success. The devel-opment of discrete element methods for numericalmodeling of granular soils has greatly extended thepotential for these methods as discussed in Section 5.1.These theories are based on elastic distortion of par-ticles and the sliding and rolling of particles, usuallyassumed of spherical or disk shape. In real granularsoils, the irregular particle shapes and distribution ofsizes mean that packing is usually far from regular.Nonetheless, the theories and computations can pro-vide valuable insights into behavior, and knowledge ofthe characteristics of ideal systems can be useful forinterpreting data on real soils (see Chapter 11).

Direct Observation of Cohesionless Soil Fabric

The study of the fabric of a cohesionless soil is usuallydone by optical means. The particles are large enoughto be easily seen in the petrographic microscope. Thinsections can be made after impregnation of a sampleby a suitable resin or plastic. Water-soluble materialsare available for use in initially saturated sands. Afterthe resin or plastic has hardened, thin sections can beprepared.

In some cases, sand samples can be dried prior toimpregnation since sand fabrics are not generally af-fected by capillary stresses. A procedure for doing thisto enable study of the fabrics produced in MontereyNo. 0 sand by different methods of compaction isgiven by Mitchell et al. (1976).

Packing of Equal-Sized Spheres

Regular packing of spheres of the same size providesinsight into the maximum and minimum possible den-sities, porosities, and void ratios that are possible insingle-grain fabrics. Five different possible packing ar-rangements are shown in Fig. 5.7, and properties of thearrangements shown are listed in Table 5.1. The rangeof possible porosities is from 25.95 to 47.64 percent,and the corresponding range of void ratios is from 0.35to 0.91.

Random packings of equal size spheres can be con-sidered to be composed of clusters of simple packings,each present in an appropriate proportion to give theobserved porosity. The relationship between coordi-nation number N and porosity n in such systems is

N � 26.486 � 10.726/n (5.1)

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Figure 5.5 Scanning electron photomicrograph features of undisturbed soil fabrics (Collinsand McGown, 1974). (a) Partly discernible particle systems in Lydda silty clay, Israel (fresh-water alluvial deposit); (b) grain–grain contacts in Ford silty loess, England (aeolian deposit);(c) connector assemblages in Breidmerkur silty till, Iceland (glacial ablation deposit); (d )particle matrix assemblage in Immingham silty clay, England (estuarine deposit); (e) regularaggregation assemblage in Holon silty clay, Israel (consisting of elementary particle arrange-ments interacting with each other and silt) (freshwater alluvial deposit); (ƒ ) interweavingbunch assemblage in Hurlford organic silty clay, Scotland (freshwater lacustrine deposit);and (g) irregular aggregation assemblage in Sundland silty clay, Norway (marine deposit).

Glass balls allowed to fall freely form an anisotropicassembly, with the balls tending to arrange themselvesin chains (Kallstenius and Bergau, 1961). The numberof balls per unit area in contact with a vertical planecan be different from the number in contact with ahorizontal plane. The same behavior is observed forsand pluviated through air and water.

Spontaneous segregation and stratification has beenobserved when granular mixtures of particles of twodifferent predominant sizes are dumped into a pile(Makse et al., 1997; Fineberg, 1997). When a mixtureof sizes is poured into a pile, the larger particles tend

to accumulate near the base. Makse and co-workers’(1997) experiments produced the interesting additionalresult that if the large grains in a binary mixture havea greater angle of repose than the small grains, thenthe mixture stratifies into alternating layers of smalland large grains. If the small grains have a larger angleof repose than the large grains, then segregation with-out stratification results. This type of behavior is rel-evant to such geoengineering problems as the stabilityof dumped mine waste piles, geological formationssusceptible to static liquefaction, and the processingand transport of granular materials.

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Particle Packings in Granular Soils

Particle sizes in soil vary, and as a result, smaller par-ticles can occupy pore spaces between larger particles.This results in a tendency toward higher densities andlower void ratios than for uniform spheres. On theother hand, irregular particle shapes produce a ten-dency toward lower densities and higher porosities andvoid ratios. The net result is that the range of porositiesand void ratios in real soils with single-grain fabricsmay not be much different from that for uniform

spheres shown by the values in Table 5.1, that is, po-rosity in the range of 26 to 48 percent and void ratioin the range of 0.35 to 0.91. This is illustrated by thedata in Table 5.2. The lower values of porosity anddensity and higher unit weight for silty sand and gravelcan be attributed to silt filling the large voids betweenthe gravel particles.

Many studies have shown that a given cohesionlesssoil can have different fabrics at the same void ratioor relative density. Characterization of this fabric can

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Figure 5.6 Overall microfabric in Tucson silty clay, United States (freshwater alluvial de-posit) (Collins and McGown, 1974).

be done in terms of grain shape factors, grain orien-tations, and interparticle contact orientations (Lafeber,1966; Oda, 1972a; Mahmood and Mitchell, 1974;Mitchell et al., 1976). More recently, application ofimage analysis techniques (Section 5.8) has led to bet-ter understanding and quantification of fabric features.

The orientation of grains in a sand deposit can bedescribed in terms of the inclination of the particleaxes to a set of reference axes. For example, the ori-entation of the particle shown in Fig. 5.8 can be de-scribed by the angles � and �. In most studies,however, a thin section is studied to give the orienta-tions of apparent long axes. The long axes of particlesare referred to a single horizontal reference axis by anangle �.1 The spatial orientation of the thin section it-

1 This method underestimates the value of L /W for elongate particleshaving their long axis out of the plane of the thin section.

self with respect to the sample and to the field depositis also an essential part of the fabric description.

Orientations of long axes for a large number ofgrains can be expressed by a histogram or rose dia-gram. A frequency histogram for a sand having a meanaxial ratio equal to 1.65 and placed by tapping the sideof a vertical, cylindrical mold is shown in Fig. 5.9. Theorientation of each grain was assigned to one of the15� intervals between 0� and 180�. The V-section refersto a thin section from a vertical plane (oriented parallelto the cylinder axis). The H-section refers to orienta-tions in the horizontal plane.

Orientations of long axes in the vertical plane fortwo samples of well-graded crushed basalt [mean(length)/(width) � 1.64] are shown by the rose dia-grams in Figs. 5.10 and 5.11. In this study, the orien-tations of at least 400 grains were measured for eachsample, and the orientation of each was assigned to

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Figure 5.7 Ideal packings of uniform spheres: (a) simple cubic, (b) cubic tetrahedral, (c)tetragonal sphenoidal, (d ) pyramidal, and (e) tetrahedral.

Table 5.1 Properties of Ideal Packings of Uniformly Sized Spheres

Type of PackingCoordination

NumberLayer Spacing(R � radius) Volume of Unit

Porosity(%) Void Ratio

Simple cubic 6 2R 8R3 47.64 0.91Cubical–tetrahedral 8 2R R343 39.54 0.65Tetragonal–sphenoidal 10 R3 6R3 30.19 0.43Pyramidal 12 R2 4 R32 25.95 0.35Tetrahedral 12 R22/3 R342 25.95 0.35

one of the eighteen 10� intervals between 10� and 180�.A completely random distribution would yield thedashed circles shown in the figures. There is a strongpreferred orientation in the horizontal direction in thesample prepared by pouring (Fig. 5.10). Dynamic com-

paction, however, resulted in a more nearly randomfabric (Fig. 5.11).

Interparticle contact orientations and their distribu-tion influence deformation and strength properties andanisotropy. These orientations can be described in

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Table 5.2 Maximum and Minimum Void Ratios, Porosities, and Unit Weights for Several Granular Soils

Void Ratio

emax emin

Porosity (%)

nmax nmin

Dry Unit Weight(kN m�3)

d min d max

Uniform spheres 0.91 0.35 47.6 26 — —Standard Ottawa sand 0.80 0.50 44 33 14.5 17.3Clean uniform sand 1.0 0.40 50 29 13.0 18.5Uniform inorganic silt 1.1 0.40 52 29 12.6 18.5Silty sand 0.90 0.30 47 23 13.7 20.0Fine to coarse sand 0.95 0.20 49 17 13.4 21.7Micaceous sand 1.2 0.40 55 29 11.9 18.9Silty sand and gravel 0.85 0.14 46 12 14.0 22.9

Modified from Lambe and Whitman (1969).

Figure 5.8 Three-dimensional orientation of a sand particle.

Figure 5.9 Frequency histograms of long particle axis orientations in two planes for auniform fine sand. Reprinted from Oda (1972a), with permission of The Japanese Societyof SMFE.

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CONTACT FORCE CHARACTERIZATION USING PHOTOELASTICITY 119

Figure 5.10 Particle orientation diagram for crushed basalt.Vertical section through a sample prepared by pouring. Den-sity is 1600 kg/m3 and the relative density is 62 percent.

Figure 5.11 Particle orientation diagram for crushed basalt.Vertical section through a sample prepared by dynamic com-paction. Density is 1840 kg/m3 and the relative density is 90percent.

terms of a perpendicular Ni to the tangent plane at thepoint of contact. As most fabric characterization stud-ies are done in a two-dimensional plane, and actualparticle contact points rarely occur in the analyzedplane, measurement of contact normals can be proneto detection errors.

The orientation of Ni is defined by angles �� and ��as shown in Fig. 5.12. A procedure for determinationof the angular distributions of normals E(��, ��) isgiven by Oda (1972a). For a fabric with axial sym-metry around the vertical axis, the function E(��, ��)is independent of �, so the distribution of E(��) as afunction of �� can be used to characterize the distri-bution of interparticle contact normals. Contact normaldistributions for four sands deposited in water andcompacted by tapping on the sides of their containersare shown in Fig. 5.13. The horizontal dashed linesrepresent the distributions for an isotropic fabric. Ineach case there is a greater proportion of contact planenormals in the near vertical direction; that is, there isa preferred orientation of contact planes near the hor-izontal.

Various methods to quantify long axis and contactdistributions are available (Oda, 1972a; Fisher et al.,1987; Shih et al., 1998). The measured statistical dis-tributions can be converted to a tensor that has thesame dimensionality as stresses and strains (Satake,1978; Kanatani, 1984; Oda et al., 1985; Kuo et al.,1998). One notable measure is the fabric tensor (Odaet al., 1982b) that characterizes the contact normal di-rections. This tensor and its evolution with plasticstrains are used in development of micromechanicstheories as well as continuum-based constitutive mod-els (e.g., Tobita, 1989; Muhunthan et al., 1996; Yimsiriand Soga, 2000; Wan and Guo, 2001; Li and Dafalias,2002).

The mean value of the particle coordination numberand its standard deviation are additional important fab-ric features in granular soils. The coordination numberis the number of adjacent particles in contact with anygiven particle, and it is dependent on particle size,shape, size distribution, and void ratio. Relationshipsbetween the different orientation and packing param-eters and mechanical properties of cohesionless soilsare given in Chapter 8.

5.4 CONTACT FORCE CHARACTERIZATIONUSING PHOTOELASTICITY

Photoelasticity is a phenomenon in which light goingthrough a photoelastic material (such as glass, rubber,and polymer) is polarized by the internal stresses ofthe material. The basic concept is that the speed oflight depends on the direction of the plane of oscilla-tion due to stress-induced optical anisotropy of the ma-terial. The planes of the limiting velocities coincidewith the direction of the principal stresses. Utilizingthis technique, the analysis of a photoelastically sen-sitive particle assembly under different boundary load-ing conditions gives information about the internalforce structure through particle contacts. Averaging thecontact forces over a number of particles in a regionof interest gives the average effective stress. The down-side of this technique is that actual soil particles cannotbe used. However, the force information obtained froma transparent particulate assembly is useful for under-standing how actual soil particle systems are likely tobehave.

Light propagates in a vacuum or in air at a speed Cof 3 � 108 m/s. In other transparent materials, thespeed V is lower and the ratio C /V is called the re-fractive index. In photoelastic materials, the change inrefractive index in the i direction (ni) is proportional tothe change in normal stress �i in the same direction; ni � Kso �i, where Kso is the stress-optical material

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Figure 5.12 Characterization of interparticle contact orientation.

Figure 5.13 Probability density functions of E(�) for (a)crushed chert, (b) Toyoura sand, (c) Soma sand, and (d ) To-chigi sand. The crushed chert and Toyoura sand are mainlyrodlike or flat particles. Tochigi sand has spherical particles.Soma sand is intermediate in particle shape (from Oda,1978). Reprinted by permission.

constant. Hence, the velocity becomes direction depen-dent when the material is stressed in an anisotropicmanner.

Using a polarizer, the incoming light is polarizedalong a well-defined plane. If another polarizer isplaced along the polarized light, complete extinctionof the light can be achieved by making the filteringdirection perpendicular to that of the first polarizer.When the polarized light goes through a stressed trans-parent material, two polarized lights are generated inthe direction of principal strains (also the principalstress directions in an elastic material). The velocity ofeach component is inversely proportional to the differ-ent refractive indices of its particular plane, and therewill be a relative retardation �:

� � (n � n )l � K (� � � )l (5.2)max min so max min

where l is the material thickness, nmax and nmin are therefractive indices of the two polarized lights, and �max

and �min are the maximum and minimum principlestress, respectively.

A polarizing analyzer can be placed along the po-larized lights and it will transmit only one componentof each of these waves. The polarized waves will in-terfere, and the light intensity of the polarized lightcoming out of the analyzer will be a function of � andthe angle between the analyzer and direction of prin-

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MULTIGRAIN FABRICS 121

-1 -0.5 0 0.5 10

0.5

1

1.5

2

(a) (b)

Figure 5.14 Photoelastic image of a circular disk squeezed between two contacts: (a) the-oretically expected image and (b) actual image (from Howell et al., 1999).

cipal strains. The light intensity becomes zero whenthe angle becomes zero and hence the principal strainsdirections can be determined. Optical filters known asquarter-wave plates can be added in the path of lightpropagation to produce circularly polarized light. Bydoing so, the image observed is not influenced by thedirection of principal strains, but the intensity I viewedby a circular polariscope depends on � by the follow-ing equation:

2I � I sin (�� /�) (5.3)0

where I0 is a constant and � is the wavelength of thelight. The light intensity becomes zero when � � N�(N � fringe order � 1, 2, ...), and hence the magnitudeof principal stress difference at a given point can beevaluated from Eq. (5.3). Photoelastic images of a cir-cular disk squeezed between two contacts are shownin Fig. 5.14 (Howell et al., 1999).

The forces applied to particles are not equal. Instead,the spatial distribution of forces varies significantly dueto random positions of the particles. Figure 5.15 showsimages in an assemblage of pentagonal-shaped disksunder (a) geostatic stresses by gravity and (b) bothgravity loading and point loading at the center of themodel (Geng et al., 2001). A chainlike force distribu-tion, indicated by large light intensity paths, existseven under geostatic stress conditions. Strong forcechains can develop in an assembly of pentagonal-shaped polymer particles as shearing progresses (Geng

et al., 2003). A complicated network of force chainsdevelops in the direction of the maximum principalstress.

Microscopic investigations of the development ofcontact force distribution under different loading con-ditions provide physical insights to understand defor-mation behavior of granular materials. Further detailsare given in Chapter 11.

Photoelasticity investigations can also be performedusing three-dimensional particle assemblages. Al-though the actual material may be transparent, the par-ticles become opaque due to refraction and reflectionof light at the particle surfaces, which are often opti-cally damaged. This adds difficulty in examining thecontact force distributions. However, if the pores arefilled with a fluid that has the same refractive index asthe photoelastic material, the assembly becomes moretransparent. Figure 5.16 shows the force distribution incrushed glass particles when a cone penetrometer ispushed into the material (Allersma, 1999). Again, de-velopment of a strong force network is evident.

5.5 MULTIGRAIN FABRICS

In Section 5.2, it was emphasized that single-grain fab-rics are rare in soils containing clay-size particles. Thisis often true also for silts (particle sizes in the rangeof 2 to 74 �m). For example, experiments have shownthat silt-size quartz particles sedimented in water can

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Figure 5.15 Photoelastic images of pentagonal shape diskassembly under (a) geostatic stresses by gravity and (b) bothgravity loading and point loading at the center of the model(from Geng et al., 2001).

Figure 5.16 Cone penetration test in photoelastic particles(from Allersma, 1999).

Figure 5.17 Schematic diagram of a honeycomb fabric insilt.have a void ratio as large as 2.2. Quartz particles in

this size range may be somewhat platy and can accountfor a part of this high void ratio as compared to anupper limit of about 1.0 for single-grain assemblagesof bulky particles. However, silt-size particles formmultigrain arrangements during slow sedimentation,because they are sufficiently small that their arrange-ments can be influenced by surface force interactions.An open honeycomb type of arrangement, as shownschematically in Fig. 5.17, is thought to exist in somesilts (Terzaghi, 1925a). Loose fabrics such as this aremetastable and subject to sudden collapse or liquefac-tion under the action of rapidly applied stresses.

Multigrain fabrics of clays and clay–nonclay mix-tures form because clay particle surface forces are sig-nificant relative to clay particle weight; clays can ad-

sorb on nonclay particle surfaces, and clay surfaces areoften chemically reactive. In addition, clay particlegroups in many soils may be remnants of a preexistingrock from which the soil was derived.

5.6 VOIDS AND THEIR DISTRIBUTION

Different types of pores are illustrated in Figs. 5.4 and5.6. The pore sizes and their distribution complementthe particle and particle group sizes and their distri-bution. Emphasis is usually placed on the solid phaserather than the liquid and gas phases when describing

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SAMPLE ACQUISITION AND PREPARATION FOR FABRIC ANALYSIS 123

properties and behavior. However, the pores and voidsdetermine the fluid and gas conductivity propertiesthat, in turn, control such important processes as therate of fluid and chemical transport, generation of ex-cess pore pressures during deformation, consolidationrate, the ease and rate of drainage, capillary pressuredevelopment, and the potential for liquefaction underdynamic loading. Methods for determining and char-acterizing pore sizes and their distribution are de-scribed in Section 5.9.

5.7 SAMPLE ACQUISITION ANDPREPARATION FOR FABRIC ANALYSIS

Obtaining representative soil samples with minimaldisturbance is essential if reliable measurements of en-gineering properties are to be made. The same consid-erations apply in the selection and preparation ofsamples for the study of fabric. Accordingly, the sam-pling and preparation phases of fabric study are criti-cal, and special methods are many times needed.Proven methods for reliable determination of fabriccan also be used for evaluation of the effects of dif-ferent sampling procedures used in engineering prac-tice, although there does not appear to be much recordof this having been done.

Both direct and indirect methods are used to studythe fabric and fabric features of soils, as listed in Table5.3. An illustrative schematic diagram prepared byR. N. Yong that summarizes methods for analysis ofsoil composition and fabric using various parts of theelectromagnetic spectrum is shown in Fig. 5.18. In in-terpreting the results from any of these methods, judg-ment is required to be sure that the conclusions pertainto properties and behavior of interest. For example,discontinuities, fractures, and anisotropy on a macro-scale can override the influences of microfabric details.

Of the methods listed in Table 5.3, optical and elec-tron microscopy, X-ray diffraction, and pore size dis-tribution offer the advantage of providing direct(usually) unambiguous information about specific fab-ric features, provided the samples are representativeand the sample preparation procedures have not de-stroyed the original fabric. On the other hand, thesetechniques are limited to small samples, and they aredestructive of the samples studied. The other tech-niques are nondestructive, at least in principle, and canbe used for the study of soil fabric in situ and for thestudy of changes in fabric that accompany compres-sion, shear, and fluid flow. However, with most of thesemethods interpretation is seldom straightforward or un-ambiguous. The use of several methods of fabric anal-

ysis may be appropriate in some cases in order toobtain information of more than one type or level ofdetail.

Sample Preparation for Fabric Analysis

Acoustical, dielectric, thermal, and magnetic measure-ments can be made directly on samples in their undis-turbed, wet state. Optical and electron microscopy,X-ray diffraction, and porosimetry require that the porefluid be removed, replaced, or frozen. To do this with-out disturbance of the original fabric is difficult, andin most cases there is no way to determine how muchdisturbance there may have been.

Pore Fluid Removal Air drying without significantdisruption of the natural fabric may be possible forsoils that do not undergo much shrinkage. For softsamples at high water content, oven drying may causeless fabric change than air drying, evidently becausethe longer time required for air drying allows forgreater particle rearrangement (Tovey and Wong,1973). On the other hand, the stresses induced duringoven drying may result in some particle breakage.

Water removal by drying at the critical point has alsobeen used. If the temperature and pressure of the sam-ple are raised above the critical values, which for waterare 374�C and 22.5 MPa, respectively, the liquid andvapor phases are indistinguishable. The pore water canthen be distilled off without the presence of air–waterinterfaces that can lead to shrinkage. The high tem-perature and pressure may change the clay particles,however. To avoid this, replacement by carbon dioxidehas been used. The critical temperature and pressureof carbon dioxide are 31.1�C and 7.19 MPa, respec-tively. The procedure requires prior impregnation ofthe sample with acetone, which may cause swelling inpartly saturated and expansive soils (Tovey and Wong,1973). Both critical point and freeze-drying cause lesssample disturbance and shrinkage than do air or ovendrying, but they are more difficult and time consuming.

Freeze-drying can be used for removal of water.Sublimation of the ice in a soil that has been rapidlyfrozen avoids the problem of air–water interfaces andshrinkage that accompany water removal by drying.Sample size must be small, usually thinner than about3 mm, if disruption due to nonuniform freezing is tobe avoided. Quick freezing is best done in a liquid thathas been cooled to its melting point in liquid nitrogen,such as isopentane at �160�C or Freon 22 at �145�C.This avoids gaseous bubbling caused by direct immer-sion in liquid nitrogen at �196�C (Delage et al., 1982).The freezing temperature should be less than �130�Cto avoid formation of crystalline ice. Sublimation of

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124

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125

Polarized LightMicrograph

Replica TransmissionElectron Micrographor Diffraction Pattern

Scanning ElectronMicrograph

Figure 5.18 Methods for examining mineralogy, fabric, and structure of soils using parts ofthe electromagnetic spectrum (prepared by R. N. Yong, McGill University Soil MechanicsLaboratory).

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Table 5.3 Techniques for Study of Soil Fabric

Method BasisScale of Observations and Features

Discernable

Optical microscope(polarizing)

Direct observation of fracturesurfaces of thin sections

Individual particles of silt size andlarger, clay particle groups,preferred orientation of clay,homogeneity on a millimeterscale or larger, large pores, shearzones

Useful upper limit of magnificationabout 300�

Electron microscope Direct observation of particlesor fracture surfaces throughsoil sample (SEM)observation of surfacereplicas (TEM)

Resolution to about 100 A; largedepth of field with SEM; directobservation of particles; particlegroups and pore space; details ofmicrofabric; environmental SEMcan be used to observespecimens containing waterand gas

X-ray diffraction Groups of parallel clay platesproduce stronger diffractionthan randomly orientedplates

Orientation in zones several squaremillimeters in area and severalmicrometers thick; best in singlemineral clays

Pore size distribution (1) Forced intrusion of anonwetting fluid (usuallymercury)

(1) Pores in range from �0.01 to�10 �m

(2) Capillary condensation (2) 0.1 �m maximumWave propagation Particle arrangement, density,

and stress influences wavevelocity

Anisotropy; measures fabricaveraged over a volume equal tosample size

Dielectricdispersion andelectricalconductivity

Variation of dielectricconstant and conductivitywith frequency

Assessment of anisotropy,flocculation and deflocculation,and properties; measures fabricaveraged over a volume equal tosample size

Thermal conductivity Particle orientations anddensity influence thermalconductivity


Magneticsusceptibility

Variation in magneticsusceptibility with change ofsample orientation relativeto magnetic field


Mechanical Propertiesstrength moduluspermeabilitycompressibilityshrinkage and swell

Properties reflect influences offabric; see Chapter 11

Fabric averaged over a volumeequal to sample size; anisotropy;macrofabric features in somecases

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METHODS FOR FABRIC STUDY 127

the water is then done at temperatures between �50and �100�C rather than at the initial freezing temper-ature to increase the rate of water vapor removal. Attemperatures less than �100�C the vapor pressure ofthe ice, about 10�5 torr, may be less than the capabilityof the vacuum system.

The freezing process may produce fabric changes invery high water content systems such as a 10 percentby weight slurry of bentonite in water (Kumai, 1979).However, with more typical saturated clays at consis-tencies likely to be encountered in geotechnical inves-tigations, the effects of freeze-drying on the fabric aresmall. Additional considerations in sample preparationby freeze-drying are given by Tovey and Wong (1973)and Gillott (1976).

Pore Fluid Replacement If thin sections are re-quired, as for optical microscopy or when dryingshrinkage must be minimized, but the presence of amaterial in pore spaces is not objectionable, replace-ment of the pore water may be necessary. Various res-ins and plastics have been used for this purpose.High-molecular-weight ethylene glycol such as Car-bowax 6000 is miscible with water in all proportionsand has been used for many studies. Carbowax 6000melts at 55�C but is solid at lower temperatures.

Impregnated samples are prepared by immersing anundisturbed cube sample, 10 to 20 mm on a side, inmelted Carbowax at 60 to 65�C. The top surface of thespecimen should be left exposed to vapor for the firstday of immersion to allow escape of trapped gases andprevent specimen rupture. The wax should be changedafter 2 or 3 days to ensure water-free wax in the samplepores. Replacement of all water by the Carbowax isusually complete in a few days. After removal fromthe liquid wax and cooling, the sample is ready forsectioning.

Thin sections are prepared by grinding using emerycloth or abrasive powders and standard thin-sectiontechniques. However, heat, water, or other water-soluble liquids cannot be used at any stage of thegrinding or section mounting process. Measurementsby X-ray diffraction have shown that Carbowax re-placement of water has essentially no effect on the fab-ric of wet kaolinite (Martin, 1966).

Gelatins or water-soluble resins may be used in lieuof Carbowax, or the sample may be impregnated withmethanol or acetone before replacement with resins orplastics. Further details on resin impregnation aregiven by Smart and Tovey (1982) and Jang et al.(1999).

Preparation of Surfaces for Study

Surfaces chosen for study should reflect the originalfabric of the soil and not the preparation method.

Grinding or cutting air-dried and Carbowax-treatedsamples may result in substantial particle rearrange-ment at the surface, thus making them of little valuefor study by the electron microscope. To overcome thisproblem, successive peels from the surface of a driedspecimen using adhesive tape can be used to exposethe original fabric. Alternatively, the surface may becoated with a resin solution that partly penetrates thesample. After hardening, the resin is peeled away re-vealing an undisturbed fabric. A comparison of sur-faces before and after this procedure is shown in Fig.5.19.

The disturbed zone at the surface of Carbowax-treated samples extends to a maximum depth of about1 �m in kaolinite (Barden and Sides, 1971). As thinsections used for polarizing microscope study are ofthe order of 30 �m thick, this disturbed zone is of littleconsequence. It is also insignificant for X-ray diffrac-tion studies.

Fracture surfaces in dried specimens are sometimestaken as representative of the undisturbed fabric. Ad-ditional preparation, such as gentle blowing of the sur-face or peeling is needed following fracture because(1) there may be loose particles on the surface, and (2)a fracture surface may be more representative of aplane of weakness than of the material as a whole. Analternative approach to avoid these problems is to frac-ture a frozen wet specimen as described by Delage etal. (1982).

The method of sample preparation should be se-lected after consideration of scale of fabric features ofinterest, method of observation to be used, and the soiltype and state as regards water content, strength, dis-turbance, and so forth. With these factors in mind, theprobable effects of the preparation methods on the fab-ric can be assessed.

5.8 METHODS FOR FABRIC STUDY

Once suitable samples and surfaces have been pre-pared, direct study of different fabric features is pos-sible using one or more of several methods, asindicated in Fig. 5.18. Details of these methods arediscussed in this section as well as the advantages andlimitations of each.

Polarizing Microscope

Individual particles of silt and sand can be seen usingpetrographic and binocular microscopes, and the sizes,orientations, and distributions of particles and porespaces can be described systematically. Thin sectionsor polished surfaces can be used for two-dimensional

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Figure 5.19 Effect of surface preparation on fabric seen by the scanning electron microscope(a) before peeling and (b) after one peeling, �5000 (from Tovey and Wong, 1973).

Figure 5.20 Pore pattern of a section from a stony tableland soil from Woomera, Australia.Pores in white, clay matrix in gray, and silt sand grains in black (from Lafeber, 1965).Reprinted with permission of AJSR.

analyses. Three-dimensional analyses require a seriesof parallel cross sections.

Many petrographic techniques and special treat-ments are available to aid in identification of featuresof interest (e.g., Stoopes, 2003). Rose diagrams can beused to represent two-dimensional planar patterns.Three-dimensional patterns can be represented usingstereo net projections. As an illustration of two-dimensional representation, Fig. 5.20 shows the porepattern in a section of a stony desert tableland soil fromnear Woomera, Australia, which suggests some degree

of preferred orientation. Rose diagrams are shown inFig. 5.21 of both pore orientation (white figure) andsilt and sand grain orientation (black figure). Consid-erable preferred orientation of both pores and particlesis evident.

It is not usually possible to see individual clay par-ticles with the polarizing microscope because of limi-tations in resolving power and depth of field. Practicalresolution is to a few micrometers using magnificationsup to about 300 times. If, however, clay plates arealigned parallel to each other in a group, then they

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L1

L1

RR

s1

s1

s2

s2

Figure 5.21 Distribution of elongated pores (white figure) and of elongated skeleton grains(black figure) in different directions for the pattern in Fig. 5.20. The broken circle representsan even distribution of lengths over all directions. s1 and s2 are the major maxima of theelongated pores, L1 is the major maximum of elongated grains, and R is the reference di-rection (from Lafeber, 1965). Reprinted with permission of AJSR.

Figure 5.22 Thin section of varved clay under polarizedlight (courtesy of Division of Building Research, NationalResearch Council, Canada).

Table 5.4 Orientation Scale for Clay AggregatesViewed in Plane Polarized Light

Birefringence Ratio Particle Parallelism

1.0 Random1.0–0.9 Slight0.9–0.5 Medium0.5–0.1 Strong

0 Perfect

From Morgenstern and Tchalenko (1967c).

behave optically as one large particle with definite op-tical properties.

The optical axes and the crystallographic axes of theclay minerals are almost coincident. For plate-shapedparticles, the refractive indices in the a and b directionsare approximately equal, but different from that in thec-axis direction. The difference in refractive indicesalong different optical axes of a crystal determines theoptical property termed the birefringence.

If a group of parallel particles is viewed in planepolarized light looking down the c axis, a uniform fieldis seen as the group is rotated around the c axis. If thesame particle group is viewed with the c axis normalto the direction of the light, no light is transmittedwhen the basal planes are parallel to the direction ofpolarization, and a maximum is transmitted when theyare at 45� to it. Thus there are four positions of ex-tinction and illumination when the sample is viewedusing light passed through crossed nicols and the mi-croscope stage is rotated through 360�. For rod-shapedparticles in parallel orientation, a uniform field is ob-served looking down the long axis, whereas illumina-tion and extinction are seen when looking normal tothis axis. Use of a tint plate in the microscope is oftenhelpful because the resulting retardation of light wavesresults in distinct different colors for extinction andillumination.

If particle orientation is less than perfect or if the c-axis direction of a group of parallel plates is other thannormal to the direction of light, then the minimum in-tensity is finite and the maximum intensity is less thanfor perfect orientation. The ratio of minimum intensityImin to maximum intensity Imax is called the birefrin-gence ratio �.

Photometric measurements of the birefringence ratiocan be used to quantify clay particle orientation (Wu,1960; Morgenstern and Tchalenko, 1967a). Althoughthere may be difficulties in photometric methods whendealing with other than monomineral materials with

singular orientations of particles (Lafeber, 1968), thesemiquantitative scale proposed by Morgenstern andTchalenko (1967c) given in Table 5.4 is useful.

A vertical section taken through varved clay isshown in Fig. 5.22. The upper half shows the winter-deposited clay varve and the lower half the summer-deposited silt varve. Strong preferred orientation of the

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Figure 5.23b Details of Fiddler’s Ferry shear zone (Mor-genstern and Tchalenko, 1967c). F is a fragment of ambientmaterial; the hatched areas indicate the shear matrix wherethe birefringence ratio � � 0.45; and the direction of hatch-ing is the average particle orientation over the stippled areaswhere � � 1.00.

Figure 5.23a Photograph of Fiddler’s Ferry shear zone(from Morgenstern and Tchalenko, 1967c).

clay is evident by comparison of illumination on theleft and extinction on the right. Were the clay platesoriented randomly throughout, the thin section wouldhave had the same appearance at both orientations. Theupper portion of the silt varve is also seen to containsome zones of well-oriented clay. A series of planarpores is also visible. These pores probably were de-veloped during impregnation of the sample or prepa-ration of the thin section.

Optical microscope study of fabric provides a viewof some features that are too small to be seen by eye,too large to be appreciated using an electron micro-scope, but important to understanding soil behavior.Some of these features include distributions of silt andsand grains, silt and sand particle coatings, homoge-neity of fabric and texture, discontinuities of varioustypes, and shear planes (e.g., Mitchell, 1956; Morgen-stern and Tchalenko, 1967b, 1967c; McKyes andYong, 1971; Oda and Kazama, 1998). A thin sectionfrom a shear zone through a soft silty clay at the siteof a foundation failure under an embankment at Fid-dler’s Ferry on the floodplain of the Mersey River,England, is shown in Fig. 5.23a. Details of the shearzone deduced from the photomicrograph are shown inFig. 5.23b.

Electron Microscope

The electron microscope can reveal clay particles andtheir arrangements directly. The practical limit of res-

olution of the transmission electron microscope (TEM)is less than 10 A, and atomic planes can be seen. Thepractical limit of the scanning electron microscope(SEM) is about 100 A; however, lesser magnificationis sufficient to resolve details of clay particles andother very small soil constituents. The major advan-tages of the SEM relative to the TEM are the muchgreater depth of field, the wide, continuous range ofpossible magnifications (about 20� to 20,000�), andthe ability to study surfaces directly. Either surface rep-licas or ultra-thin sections are needed for the TEM. Themain advantage of the TEM relative to the SEM is itshigher limit of resolution. Historical developmentsalong with its application to clay minerals and aggre-gates examination are given by McHardy and Birnie(1987) for SEM and Nadeau and Tait (1987) for TEM.

Both types of electron microscopy require an evac-uated sample chamber (1 � 10�5 torr), so wet soilscannot be studied directly unless they are housed in aspecial chamber. Cold stages are available, so frozenmaterials may be studied. It is usually necessary tocoat SEM sample surfaces with a conducting film toprevent surface charging and loss of resolution. Gold

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Figure 5.24 Microfabrics of artificial clay sediments. Scalebar � 2 �m for all micrographs: (a) kaolinite in distilledwater, (b) kaolinite in 0.5 N NaCl, (c) illite in distilled water,(d ) illite in 0.5 M NaCl, (e) montmorillonite in distilled wa-ter, and (ƒ) montmorillonite in 0.5 NaCl (from Osipov andSokolov, 1978).

Figure 5.25 Honeycomb microfabrics: (a) recent lacustrinesilt from Lake Vozhe and (b) recent marine silt from theBlack Sea (from Sergeyev et al., 1980). Reprinted with per-mission from Blackwell Scientific Publications, Ltd.

placed in a very thin layer (20 to 30 nm) in a vacuumevaporator is often used.

The main difficulty in the electron microscope studyof fabric is the preparation of sample surfaces, surfacereplicas, or ultra-thin sections that retain the undis-turbed fabric of the original soil. In general, the higherthe water content and void ratio of the original sample,the greater the likelihood of disturbance. Soils contain-ing expansive clay minerals may undergo changes inmicrofabric as a result of removal of interlayer water,or there may be shrinkage. The dry–fracture–peeltechnique and the freeze–fracture technique appear thebest of the available methods for obtaining represen-tative sample surfaces.

That careful techniques are successful in preservingdelicate fabrics is evidenced by Fig. 5.24, which showsthe microstructures of six artificial clay sediments (Os-ipov and Sokolov, 1978). These samples were obtainedby gradual sedimentation of clay particles �1 �m in

size from a 1 percent suspension followed by freeze-drying. When sedimented in distilled water, the sedi-ment porosities were kaolinite 96 percent, illite 90percent, and montmorillonite 83 percent. When sedi-mented in electrolyte solution, the porosities were 97,98 and 99 percent, respectively. The photomicrographsreflect the very high porosities of all samples and thatthe flocculating effect of the salt solution had a signif-icant effect on the initial microfabric.

Undisturbed silt microfabrics are shown in Fig. 5.25.These silty clay microfabrics are formed under condi-tions of uninterrupted sediment accumulation and havequite high porosities (60 to 90 percent). Sediments ofthis type are very compressible and weak.

Progressive collapse of microfabric of a sensitiveChamplain clay with increasing vertical loading isshown in Fig. 5.26 (Delage and Lefebvre, 1984). Thepreconsolidation pressure of the clay was 54 kPa. TheSEM photos were taken along the vertical plane andthe distribution of macropores at each loading stagewas derived from the photos as shown in the figure.Aggregate structure is apparent at the intact stage be-low the preconsolidation pressure. At a loading of 124

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(a) (b) (c) (d)

10 μm intact 10 μm 124 kPa 10 μm 421kPa 10 μm 1452 kPa

Pores Solid particlesVoids due topulling out ofparticles

Figure 5.26 SEM photographs of a sensitive Champlain clay under consolidation at (a)intact state, (b) 124 kPa, (c) 421 kPa, and (d ) 1452 kPa. The preconsolidation pressure ofthe clay is 54 kPa (from Delage and Lefebvre, 1984).

kPa, the collapse of macropores in the horizontal di-rection is observed. Aggregates are also aligning in thehorizontal direction. As the loading increases (421 and1452 kPa), aggregates become less apparent by thecomplete collapse of macropores and the particles arealigning in the horizontal direction. Although the fieldof view at high magnification is limited, mosaics ofphotomicrographs may be prepared to show larger fab-ric features. Such a composite is shown in Fig. 5.6.

Accessories are available for the SEM to enable de-termination of the elemental composition of specificmaterials under observation (McHardy and Birnie,1987; Bain et al., 1994). Further details on the tech-niques of electron microscopy used to examine thestructures of soils can be found in Smart and Tovey(1981, 1982).

Environmental SEM

Conventional SEM samples have to be dry, vacuumcompatible, and electrically conductive. To examineliquid and hydrated samples, the pressure has to be atleast 612 Pa, the minimum vapor pressure required tomaintain liquid water at 0�C. An environmental scan-ning electron microscope (ESEM) allows wet, natural,and nonconductive samples to be examined by havingthe specimen chamber at higher pressure separatedfrom the high-vacuum electron optical regions in

which the SEM electromagnetic lens must exist. Thispressure differentiation is achieved by a special devicecalled a pressure-limiting aperture. Examination ofsamples can be done under a range of gaseous envi-ronments (H2O, CO2, N2, etc.), relative humidities (0to 100 percent), pressures (up to 6.7 kPa), and tem-peratures (�180 to 1500�C). ESEM images are takenusing an electrical current detector that collects andprocesses signals generated by ionized gas molecules(usually water vapour) in the specimen chamber. Sec-ondary electrons emitted by the sample collide withgas molecules, which then cause ionization of the gas,creating positive ions and additional secondary elec-trons. The cascading amplification of the signal fromthe original secondary electrons enables the secondaryelectron detector to create an image. The positive ionsare attracted to the negatively charged sample surfaceand suppress the charging artefacts. This charge sup-pression allows imaging of nonconductive samples.

A significant feature of ESEM is its ability to ob-serve liquids inside the samples. The rate of sublima-tion and condensation of water can be controlled bymanipulating the pressure and temperature. Figure 5.27is an ESEM image of a sample containing illite clays(left side) and quartz grains (right side). Water dropletswere placed on the sample by condensation of distilledwater present as a gaseous phase in the testing cham-

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Figure 5.27 ESEM image of illite clay (left side) and quartzgrains (right side). Water droplets placed on the samplesshow that the quartz surface is hydrophilic and the illite sur-face is hydrophobic (from Buckman et al., 2000).

Figure 5.28 ESEM images showing swelling process of bentonite clay in a sand–bentonitemixture (from Komine and Ogata, 2004).

ber. The photo shows the wettability of fluids on soilminerals. Spherical water droplets are observed on theclay surface, indicating that this illite is hydrophobic.Quartz sand, on the other hand, is hydrophilic as lowdomed droplets of water are formed on the surface.

As pressure and temperature can be varied in thespecimen chamber, the ESEM allows studies of dy-namic changes in samples such as wetting, drying, ab-sorption, melting, corrosion, and crystallization. Figure5.28 shows ESEM images of the swelling of bentonitein a sand–bentonite mixture (Komine and Ogata,2004). Initially, the bentonite particles are attached tothe sand grains and macropores can be observed. As

water is added to the specimen, the bentonite swells tocompletely fill the macropores.

Image Analysis

Image analyzers can be used with both optical andelectron microscopes for quantification of fabric fea-tures. Digital imaging cameras can resolve reflected ortransmitted light from the sample into pixels. Theamount of light per pixel is then converted into ananalog signal. After the entire image is acquired, theanalog signal for each pixel is converted to digital formfor analysis, manipulation, and storage. Image analysisoffers greatly increased potential for quantitative de-scription of different fabric elements. Details of themethod are beyond the scope of this book. Examplesof image analysis of soil specimens are given by Frostand Wright (1993), Tovey and Hounslow (1995), andFrost and McNeil (1998).

X-ray Diffraction

As discussed in Section 3.22, crystallographic planesin minerals refract X-rays at an intensity that dependson (1) the amount of mineral in the volume of soilirradiated and (2) the proportion of the mineral grainsthat are properly oriented. For clay minerals, parallelorientation of plates enhances the basal reflections butdecreases the intensity of reflection from lattice planesoriented in other directions. The intensity of (001) re-flections provides a measure of clay particle orienta-tion.

The relative heights of basal peaks for different sam-ples of the same material give a measure of particle

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orientation differences. A fabric Index (FI) based onareas of diffraction peaks is defined as (Gillott, 1970):

FI � V / (P � V) (5.4)

where V is the area of the basal peak in a section cutperpendicular to the orientation plane, and P is the areaof the same peak from a section cut parallel to theplane of parallel orientation of particles. The value ofFI ranges from zero for perfect preferred orientation to0.5 for perfectly random orientation. A similar proce-dure that retains the concept of peak areas, but doesnot require their exact measurement, is given by Yo-shinaka and Kazama (1973).

The peak ratio (PR), defined as the ratio of the (002)reflection to that of the (020) reflection, can also beused as a measure of orientation. The PR has the ad-vantages of being independent of the particle concen-tration within the total soil and of minimizing theeffects of mechanical and instrumentation variables(Martin, 1966). The PR of kaolinite with completelyrandom particle orientations is about 2.0. For maxi-mum parallel orientation the PR is about 200. The rea-sons for choosing the (002) and (020) reflections arethat (1) they are strong and (2) the corresponding 2�values are not too far apart, thus ensuring that aboutthe same sample volume will be irradiated for deter-mination of both peaks.

X-ray diffraction methods had the advantage ofquantification of data in a way that was not possiblewith optical and electron microscope methods. How-ever, the development of image analysis techniques foruse with the latter has largely overcome this problem.X-ray methods have some disadvantages, including (1)difficult interpretation in multimineral soils, (2) thedata are weighted in favor of the fabric nearest thesample surface, and (3) the soil volume irradiated willusually include both microfabrics and minifabrics, andthe results will average rather than distinguish them.

Thus, X-ray diffraction is best suited for fabric anal-ysis of single mineral clays in which particle orienta-tions over regions the size of the X-ray beam (a fewmillimeters) are of interest or in conjunction with othermethods that can provide detail on the character of themicrofabric.

Transmission X-Ray and Computed TomographyScan

By detecting differences in electron density in mate-rials, transmission X-ray is a useful and nondestructivemethod for the study of soil stratigraphy, homogeneity,and macrofabric. X-radiographs of samples while stillin sample tubes provide information about the above

features as well as on texture and disturbance (Kenneyand Chan, 1972). A number of laboratories routinelyX-ray sample tubes prior to selection of samples forremoval and testing for determination of deformationand strength properties. The procedure is simple, rapid,and inexpensive (apart from the initial cost of theequipment).

X-radiography is also useful for the study of defor-mation patterns in soils. Lead shot is placed in regularpatterns in samples or in blocks of soil used for modeltests. The positions of the shot are determined at var-ious stages throughout a test by comparison of succes-sive radiographs. The results can be used to locateshear zones and compute strains and their variationthroughout the material.

X-ray computed tomography (CT) allows construc-tion of a three-dimensional density profile insidea material by assembling X-ray radiographic two-dimensional images taken at different angles. The res-olution of a CT scanner is determined by thedimensions of a source and a detector as well as theirpositions in relation to the test specimen. The tech-nique has been used to examine the locations of shearzones within a specimen as local dilation inside theshear band gives low electron density (Desrues et al.,1996; Otani et al., 2000; Alshibi et al., 2003; Otaniand Obara, 2004). Figure 5.29 shows the locations ofshear zones in cylindrical sand specimens that weresheared to different axial strains in triaxial compres-sion. The specimens showed strain-softening behaviorand exhibited uniform bulging with no apparent singleor multiple shear bands. The CT images were taken atstrains greater than the peak axial strain of approxi-mately 2 percent. No apparent shear zones are ob-served at an axial strain of 4.6 percent, indicating thatthe strain softening was due to dilation throughout thespecimens. As the axial strain increased, however,shear zones with large local void ratio appeared insidethe specimens. The following two shear zone structuresare apparent (Desrues et al., 1996; Alshibi et al., 2003):

1. Cone-Shaped Shear Zone The images of thehorizontal plane show black circles appearing atthe center, and they become smaller in diameterfrom the boundary toward the middle height ofthe specimen (Fig. 5.29a). This suggests a cone-shaped shear zone from the midheight to theboundary. The tip of the cone is at the midheightand the symmetry exists at the central axis of thespecimen.

2. Conjugate-Inclined Shear Zones The horizon-tally sliced images show radially oriented linesgenerating outward from the circle (Fig. 5.29a).These are the inclined lines in the vertically

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PORE SIZE DISTRIBUTION ANALYSIS 135

Figure 5.29 CT scans of a dense sand specimen under triaxial compression: (a) Horizontalslice at the midheight, (b) vertical slice, and (c) 3D image (from Alshibi et al., 2003).

sliced images (Fig. 5.29b). Close examination ofthese lines reveal that there are several pairs ofconjugate shear bands at two different inclinedangles as shown in Fig. 5.29c.

Further details of shear bands are given in Chapter11. Other noninvasive techniques reported to observeparticle packing arrangements include nuclear mag-netic resonance imaging (Ehrichs et al., 1995; Ng andWang, 2001) and laser-aided tomography (Matsushimaet al., 2002).

5.9 PORE SIZE DISTRIBUTION ANALYSIS

The shape and distribution of voids are one of the threemost important measures of fabric, along with contactdistributions and particle orientations. Pore informationcan be obtained by volumetric pore size distribution

determinations and from image analysis of thin sec-tions and SEM pictures.

Volumetric Pore Size Distribution Determinations

Volumetric pore size distributions can be determinedusing forced intrusion of a nonwetting fluid, a capillarycondensation method based on interpretation of ad-sorption and desorption isotherms, and by removal ofwater by suction or air pressure.

The maximum pore size that can be measured usingthe capillary condensation method is about 0.1 �m.With the possible exception of intraaggregate poresmost soil pores are larger, so this method is of limitedusefulness. The mercury intrusion method, however, isuseful for measurement of pore sizes from about 0.01�m to several tens of micrometers. The basis of themethod is that a nonwetting fluid (fluid-to-solid contactangle �90�) will not enter pores without application of

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Figure 5.30 Pore size distributions in crushed basalt as affected by compaction method.

pressure. For pores of cylindrical shape, the capillarypressure equation applies, and

4� cos �d � � (5.5)

p

where d is the diameter of pore intruded, � is the sur-face tension of the intruding fluid, � is the contact an-gle, and p is the applied pressure.

The volume of mercury intruded into an evacuateddry sample that is about 1 g in weight is measuredusing successively higher pressures. The total volumeof mercury intruded at any pressure gives the total vol-ume of pores with an equivalent diameter larger thanthat corresponding to that pressure. The surface tensionof mercury is 4.84 � 10�4 N/mm at 25�C. The contactangle � is about 140�; measurements by Diamond(1970) gave 139� for montmorillonite and 147� forother clay mineral types.

Limitations of the mercury intrusion method are:

1. Pores must be dry initially. Freeze-dried samplesare often used to minimize the effect of volumechange upon drying.

2. Isolated pores are not measured.3. Pores accessible only through smaller pores will

not be measured until the smaller pores are pen-etrated.

4. The apparatus may not have the capacity to pen-etrate the smallest pores in a sample.

In spite of these limitations, pore size distributionsdetermined by the mercury intrusion method can pro-vide useful information about factors influencing fabricand fabric–property interrelationships. An example isshown in Fig. 5.30. The data are in the form of cu-mulative volumes of pore space intruded for a pore ofthe indicated size and larger. It may be seen that thepores cover a range of sizes and that changes in densityand sample preparation method result in changes inpore size distributions.

Pore size distributions may be estimated for sands,which are too coarse for mercury intrusion, by deter-mination of the pore water volume that is drained ei-ther by application of suction to the sample or byapplication of air pressure to the pore water. Equation(5.5) applies. The surface tension of water, 7.5 � 10�5

N/mm at ordinary temperature, and a contact angle �of 0� should be used.

Image Analysis

The spatial distribution of local voids inside a soilspecimen can be obtained by analyzing the images ob-tained from thin sections. Generally, two image anal-ysis methods are available: (1) method of polygons and(2) mean free path. In the first method the centroids of

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INDIRECT METHODS FOR FABRIC CHARACTERIZATION 137

Figure 5.31 Image analysis methods to determine void fabric: (a) polygon method (afterBhatia and Soliman, 1990) and (b) mean free path method (Kuo et al., 1998).

particles are located and linked to produce polygons,representing individual void elements as shown in Fig.5.31a. Using this method, Bhatia and Soliman (1990)found that looser specimens of sand exhibited a greatervariability in local void ratio than denser specimens.Frost and Jang (2000) used this method to quantify thevariation of local void distribution produced by differ-ent preparation methods. Moist tamped specimens hada higher standard deviation of local void ratio for thesame mean void ratio than air-pluviated specimens.

The mean free path method measures the mean freepath between particles by use of a scanning line thatpasses through both particles and voids as shown inFig. 5.31b. The spacing and orientation of the line arevaried, and a representative void is then produced bysumming over the void lines found on a number ofscanned lines in each direction (Kuo et al., 1998). Us-ing this method, Masad and Muhunthan (2000) foundthat larger local voids exist in the horizontal directionthan the vertical for a pluviated specimen.

5.10 INDIRECT METHODS FOR FABRICCHARACTERIZATION

All physical properties of a soil depend in part on thefabric; therefore, the measurement of a property pro-vides indirect measure of the fabric. Some of the mea-surements that are particularly useful are listed in Table5.3 and are discussed briefly in this section.

Elastic Wave Propagation

The propagation velocities of compression and shearwaves through a soil depend on the density, confining

stress, and fabric of the soil. According to elastic the-ory, which is applicable to soils for the small defor-mations associated with wave propagation, the shearwave (S-wave) velocity Vs and the compression wave(P-wave) velocity Vp are related to the shear modulusG and the constrained modulus M by

V � G /� (5.6)s

and

V � M /� (5.7)p

where � is the mass density.The constrained modulus M is related to the more

familiar Young’s modulus according to

1 � �M � E (5.8)

(1 � �)(1 � 2�)

in which � is Poisson’s ratio. Young’s modulus andthe shear modulus are related to each other by

E � 2(1 � �)G (5.9)

The moduli depend on the applied effective stresses,stress history, void ratio, and plasticity index. For co-hesionless soils the modulus varies approximately asthe square root of the effective confining pressure. Forcohesive soils the modulus varies as the effective con-fining pressure to a power between 0.5 and 1.0. Thesmall strain shear modulus of soil depends on contactstiffness and fabric state. Therefore, the change inshear wave velocity with confining pressure provides

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0 0.2 0.4 0.6 0.8 1

B-value

Vs = 212 (ms)

vb

= 0.25v

b= 0.5

vb

= 0.35v

b= 0.4

Vw = 1492 (m/s)

Dr = 30%σo' = 98 kPa

Vp

Vs

Toyoura sandAir pluviation

Vp2 = Vs

2[ 43– –––––––––]+

2(1 + vb)

3(1 – 2νb) (1 – B)

Vp

& V

s(m

/s)

2000

1500

1000

500

0

Figure 5.32 Variation in P- and S-wave velocities with Bvalue in loose Toyoura sand under an isotropic compressionstress of 98 kPa (after Tsukamoto et al., 2002).

insight on the pressure dependency of contact stiffness.Equations (5.6) and (5.7) assume isotropic elasticity. Ifthe material is viscoelastic, the wave velocities becomefrequency dependent. Solutions for various viscoelasticmodels are given by Santamarina et al. (2001).

If two samples of the same soil have the same massdensity and are under the same effective confiningpressure but have different fabrics, they will have dif-ferent modulus values. This difference will be reflectedby differences in shear and compression wave veloci-ties. These velocities can be measured, and this pro-vides a means for assessing fabric. The shear wavevelocity is the more useful of the two because shearwaves are only transmitted through the solid grainstructure of the soil mass, that is shear waves cannotbe transmitted through water. Anisotropic soil structureand stress states can be detected on the basis of dif-ferent shear wave velocities in different directions. Fur-ther details of the relationships between small strainmoduli and compositional and environmental factorsare given in Chapter 11.

If the material is dry, the bulk modulus of the skel-eton can be derived using both shear wave and com-pression wave velocity measurements. If the materialincludes water, the P-wave velocity depends on theelastic properties of soil solids and water, saturation,and porosity. For fully saturated conditions, solutionsare available for two-phase media (Biot, 1956a, 1956b;Stoll, 1989; Mavko et al., 1998; Santamarina et al.,2001). The solutions show that there are two P-wavesand one S-wave. The fast P-wave and S-wave are thestandard waves and the velocities have weak depend-ency on frequency. The slow P-wave (or Biot wave),which is associated with the diffusional process of wa-ter flow in deforming porous media, especially at lowfrequency, and is very difficult to detect (Plona, 1980;Nakagawa et al., 1997). Hence, the fast P-wave and S-wave are commonly used to characterize the soil.

In fully saturated condition, the fast P-wave propa-gates with a velocity that is 10 to 15 percent fasterthan the velocity through water. This is because thestiffness of the soil skeleton contributes to increasingP-wave velocity. In very loose saturated soil, the P-wave velocity is essentially controlled by the bulkmodulus of water and has a value of about 1500 m/s.When air is introduced, P-wave velocity decreases.Even with a small amount of air, the reduction is dra-matic due to a large decrease in bulk modulus of thefluid–air mixture. The effect of B-value (or water sat-uration ratio Sw) on P- and S-wave velocities of Toy-oura sand specimen (Dr � 30 percent) is shown in Fig.5.32 (Tsukamoto et al., 2002). The fast P-wave veloc-ity at B � 0.95 (Sw � 100 percent) is 1700 m/s,

whereas that at B � 0.05 (Sw � 90 percent) is only500 m/s. The S-wave velocity, on the other hand, isindependent of the water saturation. Kokusho (2000)derives the following relationship that relates the fastP-wave velocity to B value:

4 2(1 � � )bV � V � (5.10)p s 3 3(1 � � )(1 � B)b

where �b is Poisson’s ratio of soil skeleton. Equation(5.10) is plotted in Fig. 5.32 for different �b values.There is a dramatic decrease in P-wave velocity witheven a very small decrease in B value from fully sat-urated conditions.

Dielectric Dispersion and Electrical Conductivity

The flow of electricity through a soil is a composite of(1) flow through the soil particles alone, which issmall, because the solid phase is a poor conductor, (2)flow through the pore fluid alone, and (3) flow throughboth solid and pore fluid. The total electrical flow alsodepends on the porosity, tortuosity of flow paths, andconditions at the interfaces between the solid and liq-uid phases. These factors are, in turn, dependent on theparticle arrangements and the density. Thus, a simple

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INDIRECT METHODS FOR FABRIC CHARACTERIZATION 139

Figure 5.33 Dielectric and conductivity dispersion charac-teristics of saturated illite (Grundite) (from Arulanandan etal., 1973).

measurement of electrical conductivity would seem arapid and reliable means for evaluation of soil fabric.

However, electrical measurements in soils are com-plicated by the fact that if direct current is used, thenthere will be electrokinetic coupling phenomena, suchas electroosmosis, and electrochemical effects that cancause irreversible changes in the system, as discussedin Chapter 9. On the other hand, if alternating current(AC) is used, then the measured responses depend onfrequency. Thus the application of electrical methodsand interpretation of the data require careful consid-eration of how the measurement method may influencewhat is being measured. At the same time, however,measurement of the frequency dependence of electricalproperties can be useful for evaluation of fabric and asan index for engineering properties.

The capacitance C and the resistance R can be mea-sured relatively easily. If electrical flow is in one di-mension only, then the electrical conductivity � isgiven by

� � L / (RA) (5.11)

where L is the sample length and A is the cross-sectional area.

The capacitance can be converted to the relative di-electric constant D (see Chapter 6) using

D � CL / (A� ) (5.12)0

where �0 is the permittivity of vacuum (8.8542 � 10�12

C2 J�1 m�1).In fine-grained materials such as clays, the applica-

tion of an AC field causes the electrical charges thatare concentrated adjacent to particle surfaces to moveback and forth with amplitude dependent on such fac-tors as type of charge, association of charge with sur-faces, particle arrangement, and strength and frequencyof the field. These oscillating charges contribute to apolarization current that can be measured. The numberof charges per unit volume times the average displace-ment is the polarizability. The magnitude of the po-larizability is determined by the composition andstructure of the material and is reflected by the dielec-tric constant.

Phenomena contributing to polarization include di-pole rotation, accumulation of charges at interfaces be-tween particles and their suspending medium, ionatmosphere distortion, coupling of flows, and distortionof a molecular system. The extent to which polariza-tion can develop depends on ease of charge movementand time available for displacement. With increase infrequency the dielectric constant may decrease and the

conductivity may increase. These changes are termedanomalous dispersion. Several regions of anomalousdispersion may develop over the frequency range fromzero to microwave (�1011 Hz). Different polarizationmechanisms cease to be effective above different fre-quency values, thus accounting for the successiveregions of anomalous dispersion. Electrolyte solutionsalone do not exhibit dispersion effects at frequenciesless than 108 Hz, but clays do in the radio frequencyrange. For example, the conductivity and dielectric dis-persion behavior of saturated illite are shown in Fig.5.33.

The electrical response characteristics in the low-frequency range depend on particle size and size dis-tribution, water content, direction of current flowrelative to the direction of preferred particle orienta-tion, type and concentration of electrolyte in the porewater, particle surface characteristics, and sample dis-turbance. Relationships between dielectric propertiesand compositional and state parameters such as poros-ity, particle shape, fabric anisotropy, and specific sur-face area are given by Arulanandan (1991). The theoryis based on Maxwell’s (1881) relationship between po-rosity and the dielectric properties of a mixture of so-lution and spherical particles, and its extension toellipsoidal particles that are all oriented in one direc-tion by Fricke (1953). Extensive discussion of electro-magnetic properties of soils is given in Santamarina etal. (2001).

The formation factor appears in the relationshipsused to describe soil properties and state in terms ofelectrical properties. The formation factor is the ratioof the electrical conductivity of the pore water to theelectrical conductivity of the wet soil. It is a nondi-mensional parameter that depends on particle shape,

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long axis orientation, porosity, and degree of satura-tion. If a soil has an anisotropic fabric, then the for-mation factor is different in different directions.

Thermal Conductivity

Heat transfer through soils is through soil grains, wa-ter, and pore air. As the thermal conductivity of soilminerals is about 2.9 W/(m � �C), and the values forwater and air are 0.6 and 0.026 W/(m � �C), respec-tively, heat transfer is mainly through the soil particles.Accordingly, the lower the void ratio, the greater thenumber and area of interparticle contacts and thehigher the degree of saturation, the higher is the ther-mal conductivity. The thermal conductivity of a typicalsoil is likely to be in the range of 0.5 to 3.0 W/(m ��C). This property is considered in more detail in Sec-tion 9.6.

Thermal conductivity can be determined using a rel-atively simple transient heat flow method in which aline heat source, called a thermal needle, is insertedinto the soil. The needle contains both a heating wireand a temperature sensor. When heat is introduced intothe needle at a constant rate, the temperatures T2 andT1 at times t2 and t1 are related to the thermal conduc-tivity k according to

4 ln(t ) � ln(t )2 1k � � (5.13)Q T � T2 1

where Q is the heat input between t1 and t2. Thismethod and factors influencing the results are de-scribed by Mitchell and Kao (1978).

Differences in thermal conductivity in different di-rections provide a measure of soil anisotropy. Forexample, the ratios of thermal conductivity in thehorizontal direction kh to that in the vertical directionkv for three clays with preferred particle orientations inthe horizontal direction were in the range of 1.05 to1.70, depending on the clay type, consolidation pres-sure, and sample disturbance (Penner, 1963b). For theprobe in the vertical position in a cross anisotropicfabric, the value of k determined from Eq. (5.13) is kh.For the probe in the horizontal direction, a value of ki

is measured that is related to kv and kh according to(Carlslaw and Jaeger, 1957)

2kik � (5.14)v kh

Thermal probe measurements can also be used todetect differences in density at different locations inthe same material (Bellotti et al., 1991) and for eval-uation of changes in density, water content, and struc-

ture caused by mechanically and environmentallyinduced changes in state of the soil.

Mechanical Properties

The mechanical properties of soil, including stress–deformation behavior, strength, compressibility, andpermeability, depend on fabric in ways that are rea-sonably well understood, as considered in Chapter 8.Therefore, information about fabric can be deducedfrom measurements of these properties and known in-terrelationships between properties and fabric.

5.11 CONCLUDING COMMENT

Fabric analyses are useful in research to show howmechanical properties are dependent on particle asso-ciations and arrangements. Fabric information can beused to deduce details of the depositional and postdep-ositional history of a deposit. The effects of differentsampling methods can be assessed through the studyof fabric changes. Insights can be gained into the me-chanics of strength mobilization, the nature of peakand residual strengths, and the stress–strain behaviorof soils from fabric studies.

The indirect methods for fabric study are often use-ful for determination of properties, homogeneity, andanisotropy in situ. They may be of value also for as-sessing whether reconstituted samples used for labo-ratory testing correctly duplicate the field conditions.The particulate nature of soil and the many possibleassociations of discrete particles and particle groupsmean that a soil of given composition can have manydifferent fabrics and exist over a very wide range ofstates, each having its own unique set of geotechnicalproperties.


1. Two samples of the same remolded clay have beenconsolidated from the liquid limit to the same watercontent. One was consolidated under an isotropicset of stresses and the other under anisotropicstresses. What differences in fabric would you an-ticipate? Why?

2. Two slurries of the same clay, one with flocculatedclay particles and the other with deflocculated par-ticles, have been consolidated under an effectivestress of 100 kPa. Which will have the higher (a)void ratio, (b) sensitivity, (c) strength? Explain youranswer.

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Exhibit 5.1 Soil fabrics.

3. A series of shrinkage tests was done on a fine-grained soil mass, and it was found that the shrink-age was a maximum in the Z direction and was aminimum in all directions lying in a plane perpen-dicular to the Z direction.a. Was the soil mass likely to have been isotropi-

cally consolidated or anisotropically consoli-dated?

b. If anisotropically consolidated, what was the ma-jor principal stress direction?

c. Would you expect the soil to be isotropic withrespect to hydraulic conductivity? Why? If ani-sotropic, in which direction would the hydraulicconductivity be greatest? Why?

4. Could X-ray diffraction alone be used to distinguishamong the fabrics shown in Exhibit 5.1? Explainyour answer. Pertinent geometrical parameters oftypical X-ray diffractometers are: distance from X-ray source to sample � 17 cm, divergence of X-raybeam � 1�, angle of incidence of X-ray beam tothe sample surface in the range of 10� to 35�.

5. You are analyzing a new type of laboratory strengthtest that imposes unusual boundary conditions onthe sample being tested. What methods of fabricstudy would you use to examine the location, di-rection, thickness, and fabric of shear zones withinspecimens? What would these methods tell you?

6. Several methods for study and characterization ofsoil fabric are listed in Table 5.3. Indicate some

specific soil types and states for which each of thesemethods might be useful for gaining insights andunderstanding of the macro- and microfabrics andtheir influences on volume change, strength, andpermeability properties.

7. To obtain an essentially undisturbed sample of co-hesionless soil from the field that preserves the insitu fabric is usually impossible without resortingto expensive and time-consuming procedures suchas ground freezing or injection followed by settingof a grout or resin. Suppose that you do not havethe time or budget that will allow this, but wish toreconstitute disturbed specimens of the soil in thelaboratory by forming them in such a way that theywill have fabrics that reasonably duplicate the un-disturbed condition in the field. Suggest practicallaboratory procedures that might be used, startingwith dry and disturbed soil of the type indicated, toreproduce specimens that could then be used forfabric studies and measurements of mechanicalproperties:a. Beach sandb. Alluvial depositc. Wind-blown dune sandd. Uniform sand placed as a hydraulic fille. Uniform sand placed as a hydraulic fill and then

densified using vibratory probesf. Sand fill placed as a pavement base and densified

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Gloria

Cuadro de texto

FALTA EL CAPITULO 6

173

CHAPTER 7

Effective, Intergranular, andTotal Stress

7.1 INTRODUCTION

The compressibility, deformation, and strength prop-erties of a soil mass depend on the effort required todistort or displace particles or groups of particles rel-ative to each other. In most engineering materials,resistance to deformation is provided by internalchemical and physicochemical forces of interactionthat bond the atoms, molecules, and particles together.Although such forces also play a role in the behaviorof soils, the compression and strength properties de-pend primarily on the effects of gravity through selfweight and on the stresses applied to the soil mass.The state of a given soil mass, as indicated, for ex-ample, by its water content, structure, density, or voidratio, reflects the influences of stresses applied in thepast, and this further distinguishes soils from mostother engineering materials, which, for practical pur-poses, do not change density when loaded or unloaded.

Because of the stress dependencies of the state, agiven soil can exhibit a wide range of properties. For-tunately, however, the stresses, the state, and the prop-erties are not independent, and the relationshipsbetween stress and volume change, stress and stiffness,and stress and strength can be expressed in terms ofdefinable soil parameters such as compressibility andfriction angle. In soils with properties that are influ-enced significantly by chemical and physicochemicalforces of interaction, other parameters such as cohe-sion may be needed.

Most problems involving volume change, deforma-tion, and strength require separate consideration of thestress that is carried by the grain assemblage and thatcarried by the fluid phases. This distinction is essentialbecause an assemblage of grains in contact can resistboth normal and shear stress, but the fluid and gas

phases (usually water and air) can carry normal stressbut not shear stress. Furthermore, whenever the totalhead in the fluid phases within the soil mass differsfrom that outside the soil mass, there will be fluid flowinto or out of the soil mass until total head equality isreached.

In this chapter, the relationships between stresses ina soil mass are examined with particular reference tostress carried by the assemblage of soil particles andstress carried by the pore fluid. Interparticle forces ofvarious types are examined, the nature of effectivestress is considered, and physicochemical effects onpore pressure are analyzed.

7.2 PRINCIPLE OF EFFECTIVE STRESS

The principle of effective stress is the keystone ofmodern soil mechanics. Development of this principlewas begun by Terzaghi about 1920 and extended forseveral years (Skempton, 1960a). Historical accountsof the development are described in Goodman (1999)and de Boer (2000). A lucid statement of the principlewas given by Terzaghi (1936) at the First InternationalConference on Soil Mechanics and Foundation Engi-neering. He wrote:

The stresses in any point of a section through a mass ofsoil can be computed from the total principal stresses, �1,�2, �3, which act in this point. If the voids of the soil arefilled with water under a stress u, the total principalstresses consist of two parts. One part, u, acts in the waterand in the solid in every direction with equal intensity. Itis called the neutral stress (or the pore water pressure).The balance � �1 � u, � �2 � u, and � �3 �� 1 2 3

u represents an excess over the neutral stress u, and it hasits seat exclusively in the solid phase of the soil.

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174 7 EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS

This fraction of the total principal stresses will be calledthe effective principal stresses . . . . A change in the neutralstress u produces practically no volume change and haspractically no influence on the stress conditions for failure. . . . Porous materials (such as sand, clay, and concrete)react to a change of u as if they were incompressible andas if their internal friction were equal to zero. All the meas-urable effects of a change of stress, such as compression,distortion and a change of shearing resistance are exclu-sively due to changes in the effective stresses and��, ��1 2

Hence every investigation of the stability of a saturated��.3

body of soil requires the knowledge of both the total andthe neutral stresses.

In simplest terms, the principle of effective stressasserts that (1) the effective stress controls stress–strain, volume change, and strength, independent of themagnitude of the pore pressure, and (2) the effectivestress is given by �� u for a saturated soil.1

There is ample experimental evidence to show thatthese statements are essentially correct for soils. Theprinciple is essential to describe the consolidation of aliquid-saturated deformable porous solid, as was donefor the one-dimensional case by Terzaghi and furtherdeveloped for the three-dimensional case by otherssuch as Biot (1941). It is also an essential concept forthe understanding of soil liquefaction behavior duringearthquakes.

The total stress � can be directly measured or com-puted using the external forces and the body force dueto weight of the soil–water mixture. A pore water pres-sure, denoted herein by u0, can be measured at a pointremote from the interparticle zone. The actual pore wa-ter pressure in the interparticle zone is u. We knowthat at equilibrium the total potential or head of thewater at the two points must be equal, but this doesnot mean that u � u0, as discussed in Section 7.7. Theeffective stress is a deduced quantity, which in practiceis taken as �� u0.

7.3 FORCE DISTRIBUTIONS IN APARTICULATE SYSTEM

The term intergranular stress has become synonymouswith effective stress. Whether or not the intergranularstress is indeed equal to � � u cannot be ascertained��iwithout more detailed examination of all the interpar-

1 The terms � and �� are the principal total and effective stresses.For general stress conditions, there are six stress components (�11,�22, �33, �12, �23, and �31), where the first three are the normal stressesand the latter three are the shear stresses. In this case, the effectivestresses are defined as � �11 � u, � �22 � u, � �33 �� 11 22 33

u, � , � and �� , � � � .12 12 23 23 31 31

ticle forces in a soil mass. Interparticle forces at themicroscale can be separated into the following threecategories (Santamarina, 2003):

1. Skeletal Forces Due to External Loading Theseforces are transmitted through particles from theforces applied externally [e.g., foundation load-ing) (Fig. 7.1a)].

2. Particle Level Forces These include particleweight force, buoyancy force when a particle issubmerged under fluid, and hydrodynamic forcesor seepage forces due to pore fluid movingthrough the interconnected pore network (Fig.7.1b).

3. Contact Level Forces These include electricalforces, capillary forces when the soil becomesunsaturated, and cementation-reactive forces (Fig.7.1c).

When external forces are applied, both normal andtangential forces develop at particle contacts. All par-ticles do not share the forces or stresses applied at theboundaries in equal manner. Each particle has differentskeletal forces depending on the position relative to theneighboring particles in contact. The transfer of forcesthrough particle contacts from external stresses wasshown in Fig. 5.15 using a photoelastic model. Strongparticle force chains form in the direction of majorprincipal stress. The evolution and distribution of in-terparticle skeletal forces in soils govern the macro-scopic stress–strain behavior, volume change, andstrength. As the soil approaches failure, buckling ofparticle force chains occurs and shear bands developdue to localization of deformation. Further discussionof microbehavior in relation to deformation andstrength is given in Chapter 11.

Particle weights act as body forces in dry soil andcontribute to skeletal forces, observed in the photo-elastic model shown in Fig. 5.15. When the pores arefilled with fluids, the weight of the fluids adds to thebody force of the soil–fluids mixture. However, hydro-static pressure results from the fluid weight, and theuplift force due to buoyancy reduces the effectiveweight of a fluid-filled soil. This leads to smaller skel-etal forces for submerged soil compared to dry soil.Seepage forces that result from additional fluid pres-sures applied externally produce hydrodynamic forceson particles and alter the skeletal forces.

7.4 INTERPARTICLE FORCES

Long-range particle interactions associated with elec-trical double layers and van der Waals forces are dis-

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INTERPARTICLE FORCES 175

External Load

InterparticleForces

InterparticleForces

(a)

Body Force

Buoyancy Forceif Saturated

Seepage

Viscous Drag bySeepage Flow

(b)

Capillary Force orCementation-reactiveForce

Electrical Forces

(c)

Figure 7.1 Interparticle forces at the particle level: (a) skeletal forces by external loading,(b) particle level forces, and (c) contact level forces (after Santamarina, 2003).

cussed in Chapter 6. These interactions control theflocculation–deflocculation behavior of clay particlesin suspension, and they are important in swelling soilsthat contain expanding lattice clay minerals. In densersoil masses, other forces of interaction become impor-tant as well since they may influence the intergranularstresses and control the strength at interparticle con-tacts, which in turn controls resistance to compressionand strength. In a soil mass at equilibrium, there mustbe a balance among all interparticle forces, the pres-sure in the water, and the applied boundary stresses.

Interparticle Repulsive Forces

Electrostatic Forces Very high repulsion, the Bornrepulsion, develops at contact points between particles.It results from the overlap between electron clouds,and it is sufficiently great to prevent the interpenetra-tion of matter.

At separation distances beyond the region of directphysical interference between adsorbed ions and hy-dration water molecules, double-layer interactions pro-vide the major source of interparticle repulsion. Thetheory of these forces is given in Chapter 6. As notedthere, this repulsion is very sensitive to cation valence,electrolyte concentration, and the dielectric propertiesof the pore fluid.

Surface and Ion Hydration The hydration energyof particle surfaces and interlayer cations causes largerepulsive forces at small separation distances betweenunit layers (clear distance between surfaces up to about2 nm). The net energy required to remove the last few

layers of water when clay plates are pressed togethermay be 0.05 to 0.1 J/m2. The corresponding pressurerequired to squeeze out one molecular layer of watermay be as much as 400 MPa (4000 atm) (van Olphen,1977).

Thus, pressure alone is not likely to be sufficient tosqueeze out all the water between parallel particle sur-faces in naturally occurring clays. Heat and/or highvacuum are needed to remove all the water from a fine-grained soil. This does not mean, however, that all thewater may not be squeezed from between interparticlecontacts. In the case of interacting particle corners,edges, and faces of interacting asperities, the contactstress may be several thousand atmospheres becausethe interparticle contact area is only a very small pro-portion (�� 1%) of the total soil cross-sectional areain most cases. The exact nature of an interparticle con-tact remains largely a matter for speculation; however,there is evidence (Chapter 12) that it is effectively solidto solid.

Hydration repulsions decay rapidly with separationdistance, varying inversely as the square of the dis-tance.

Interparticle Attractive Forces

Electrostatic Attractions When particle edges andsurfaces are oppositely charged, there is attraction dueto interactions between double layers of opposite sign.Fine soil particles are often observed to adhere whendry. Electrostatic attraction between surfaces at differ-ent potentials has been suggested as a cause. When the

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gap between parallel particle surfaces separated by dis-tance d at potentials V1 and V2 is conductive, there isan attractive force per unit area, or tensile strength,given by (Ingles, 1962)

�6 24.4 � 10 (V � V )1 2 2F � N/m (7.1)2d

where F is the tensile strength, d is in micrometers,and V1 and V2 are in millivolts. This force is indepen-dent of particle size and becomes significant (greaterthan 7 kN/m2 or 1 psi) for separation distances lessthan 2.5 nm.

Electromagnetic Attractions Electromagnetic at-tractions caused by frequency-dependent dipole inter-actions (van der Waals forces) are described in Section6.12. Anandarajah and Chen (1997) proposed a methodto quantify the van der Waals force between particlesspecifically for fine-grained soils with various geomet-ric parameters such as particle length, thickness, ori-entation, and spacing.

Primary Valence Bonding Chemical interactionsbetween particles and between the particles and adja-cent liquid phase can only develop at short range. Co-valent and ionic bonds occur at spacings less than 0.3nm. Cementation involves chemical bonding and canbe considered as a short-range attraction.

Whether primary valence bonds, or possibly hydro-gen bonds, can develop at interparticle contacts with-out the presence of cementing agents is largely amatter of speculation. Very high contact stresses be-tween particles could squeeze out adsorbed water andcations and cause mineral surfaces to come close to-gether, perhaps providing opportunity for cold weld-ing. The activation energy for soil deformation is high,in the range characteristic for rupture of chemicalbonds, and strength behavior appears in reasonableconformity with the adhesion theory of friction (Chap-ter 11). Thus, interatomic bonding between particlesseems possible. On the other hand, the absence of co-hesion in overconsolidated silts and sands arguesagainst such pressure-induced bonding.

Cementation Cementation may develop naturallyfrom precipitation of calcite, silica, alumina, iron ox-ides, and possibly other inorganic or organic com-pounds. The addition of stabilizers such as cement andlime to a soil also leads to interparticle cementation. Iftwo particles are not cemented, the interparticle forcecannot become tensile; they loose contact. However, ifa particle contact is cemented, it is possible for someinterparticle forces to become negative due to the ten-sile resistance (or strength) of the cemented bonds.

There is also an increase in resistance to tangentialforce at particle contacts. However, when the bondbreaks, the shear capacity at a contact reduces to thatof the uncemented contacts.

An analysis of the strength of cemented bondsshould consider three cases: (i) failure in the cement,(ii) failure in the particle and (iii) failure at the ce-ment–particle interface. The following equation can bederived (Ingles, 1962) for the tensile strength �T perunit area of soil cross section:

1 n� � Pk (7.2)� �T n1 � e

A� i1

where P is the bond strength per contact zone, k is themean coordination number of a grain, e is the voidratio, n is the number of grains in an ideal breakageplane at right angles to the direction of �T, and Ai isthe total surface area of the ith grain.

For a random and isotropic assembly of spheres ofdiameter d, Eq. (7.2) becomes

Pk� � (7.3)T 2�d (1 � e)

For a random and isotropic assembly of rods of lengthl and diameter d

Pk� � (7.4)T �d(l � d /2)(1 � e)

Bond strength P is evaluated in the following way (Fig.7.2) for two cemented spheres of radius R. It may beshown that

(R � cos �)� cosh � R sin � (7.5)

�

so for known �, � can be computed. Then, for cementfailure,

2P � � � �� (7.6)c

where �c is the tensile strength of the cement; forsphere failure,

2P� � � � �(��) (7.7)s

where �� R sin �, and �s is the tensile strength ofthe sphere, and for failure at the interface

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INTERPARTICLE FORCES 177

Figure 7.2 Contact zone failures for cemented spheres.

sin � 2P� � � � � 2�R (1 � cos �) (7.8)1 �

where �1 is the tensile strength of the interface bond.In principle, Eq. (7.6), (7.7), or (7.8) can be used toobtain a value for P in Eq. (7.2) enabling computationof the tensile strength �T of a cemented soil.

The behavior of cemented soils can depend on thetiming of cementation development. Artificially ce-mented soils are often loaded after cementation hasdeveloped, whereas cementation develops during or af-ter overburden loading in natural soils. In the formercase, the particles and cementation bonding are loadedtogether and contact forces can become negative de-pending on the tensile resistance of cementation bond-ing. The distribution and magnitude of skeletal forcesare therefore influenced by both geometric arrange-ment of particles and the cementation bonding at theparticle contacts. In the latter case, on the other hand,the contact forces induced by external loading are de-veloped before cementation coats the already loadedparticles. In this case, it is possible that cementationcreates extra forces at particle contacts. In some ce-

mented natural materials, if the soil is unloaded fromhigh overburden stress, elastic rebound may disrupt ce-mented bonds.

Cementation allows interparticle normal forces tobecome negative, and, therefore, the distribution andevolution of skeletal forces may be different than inuncemented soils, even though the applied externalstresses are the same. Thus, the stiffness and strengthproperties of a soil are likely to differ according towhen and how cementation was developed. How toaccount for this in terms of effective stress is not yetclear.

Capillary Stresses Because water is attracted tosoil particles and because water can develop surfacetension, suction develops inside the pore fluid when asaturated soil mass begins to dry. This suction acts likea vacuum and will directly contribute to the effectivestress or skeletal forces. The negative pore pressure isusually considered responsible for apparent and tem-porary cohesion in soils, whereas the other attractiveforces produce true cohesion.

When the soil continues to dry, air starts to invadeinto the pores. The air entry pressure is related to thepore size and can be estimate using the following equa-tion, assuming a capillary tube as shown in Fig. 7.3a:

2� cos �awP � (7.9)c rp

where is the capillary pressure at air entry, �aw isPc

the air–water interfacial tension, � is contact angle de-fined in Fig. 7.3, and rp is the tube radius. For purewater and air, �aw depends on temperature, for exam-ple, it is 0.0756 N/m at 0�C, 0.0728 N/m at 20�C, and0.0589 N/m at 100�C. If the capillary pressure Pc

(� ua � uw, where ua and uw are the air and waterpressures, respectively) is larger than then air in-P ,c

vades the pore.2 Since soil has pores with various sizes,the water in the largest pores is displaced first followedby smaller pores. This leads to a macroscopic modelof the soil–water characteristic curve (or the capillarypressure–saturation relationship), as discussed in Sec-tion 7.11.

If the water surrounding the soil particles remainscontinuous [termed the ‘‘funicular’’ regime by Bear(1972)], the interparticle force acting on a particle withradius r can be estimated from

2 It is often assumed that ua � 0 (for gauge pressure) or 1 atm (forabsolute pressure). However, this may not be true in cases such asrapid water infiltration when air in the pores cannot escape or the airboundary is completely blocked.

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Capillary TubeRepresenting a Pore

2rp

dc

θ

(a) (b)

ua

uwPc = ρw gdc =

rp

^ 2σawcosθ

Figure 7.3 Capillary tube concept for air entry estimation: (a) capillary tube and (b) bundleof capillary tubes to represent soil pores with different sizes.

22�r � cos �aw2 ˆF � �r P � (7.10)c c rp

where rp is the size of the pore into which the air hasentered. Since the fluid acts like a membrane with neg-ative pressure, this force contributes directly to theskeletal forces like the water pressure as shown in Fig.7.4a.

As the soil continues to dry, the water phase be-comes disconnected and remains in the form of me-nisci or liquid bridges at the interparticle contacts[termed the ‘‘pendular’’ regime by Bear (1972)]. Thecurved air–water interface produces a pore water ten-sion, which, in turn, generates interparticle compres-sive forces. The force only acts at particle contacts incontrast to the funicular regime, as shown in Fig. 7.4b.The interparticle force generally depends on the sep-aration between the two particles, the radius of the liq-uid bridge, interfacial tension, and contact angle (Lianet al., 1993). Once the water phase becomes discontin-uous, evaporation and condensation are the primarymechanisms of water transfer. Hence, the humidity ofthe gas phase and the temperature affect the water va-por pressure at the surface of water menisci, which inturn influences the air pressure ua.

7.5 INTERGRANULAR PRESSURE

Several different interparticle forces were described inthe previous section. Quantitative expression of the in-

teractions of all these forces in a soil is beyond thepresent state of knowledge. Nonetheless, their exis-tence bears directly on the magnitude of intergranularpressure and the relationship between intergranularpressure and effective stress as defined by �� u.

A simplified equation for the intergranular stress ina soil may be developed in the following way. Figure7.5 shows a horizontal surface through a soil at somedepth. Since the stress conditions at contact points,rather than within particles, are of primary concern, awavy surface that passes through contact points (Fig.7.5a) is of interest. The proportion of the total wavysurface area that is comprised of intergrain contact areais very small (Fig. 7.5c).

The two particles in Fig. 7.5 that contact at point Aare shown in Fig. 7.6, along with the forces that act ina vertical direction. Complete saturation is assumed.Vertical equilibrium across wavy surface x–x is con-sidered.3 The effective area of interparticle contact isac; its average value along the wavy surface equals thetotal mineral contact area along the surface divided bythe number of interparticle contacts. Define area a as

3 Note that only vertical forces at the contact are considered in thissimplified analysis. It is evident, however, that applied boundary nor-mal and shear stresses each induce both normal and shear forces atinterparticle contacts. These forces contribute both to the develop-ment of soil strength and resistance to compression and to the slip-ping and sliding of particles relative to each other. These interparticlemovements are central to compression, shear deformations, and creepas discussed in Chapters 10, 11, and 12.

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INTERGRANULAR PRESSURE 179

(a)

Soil Particles

ContinuousWater Film

Negative pore pressure acts allaround the particles

(b)

Suction forces act only at particlecontacts and the magnitude of theforces depends on the size of liquidbridges.

LiquidBridges

Soil Particles

InterparticleForces

Pores of Radiusrp Filled with Air

Air

Figure 7.4 Microscopic water–soil interaction in unsaturated soils: (a) funicular regime and(b) pendular regime.

Figure 7.6 Forces acting on interparticle contact A.

Figure 7.5 Surfaces through a soil mass.

the average total cross-sectional area along a horizontalplane served by the contact. It equals the total hori-zontal area divided by the number of interparticle con-tacts along the wavy surface. The forces acting on areaa in Fig. 7.6 are:

1. �a, the force transmitted by the applied stress �,which includes externally applied forces andbody weight from the soil above.

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2. u(a � ac), the force carried by the hydrostaticpressure u. Because a �� ac and ac is very small,the force may be taken as ua. Long-range,double-layer repulsions are included in ua.

3. A(a � ac) � Aa, the force caused by the long-range attractive stress A, that is, van der Waalsand electrostatic attractions.

4. A�ac, the force developed by the short-range at-tractive stress A�, resulting from primary valence(chemical) bonding and cementation.

5. Cac, the intergranular contact reaction that is gen-erated by hydration and Born repulsion.

Vertical equilibrium of forces requires that

�a � Aa � A�a � ua � Ca (7.11)c c

Division of all terms by a converts the forces tostresses per unit area of cross section,

ac� � (C � A�) � u � A (7.12)a

The term (C � A�)ac /a represents the net force acrossthe contact divided by the total cross-sectional area(soil plus water) that is served by the contact. In otherwords, it is the intergrain force divided by the grossarea or the intergranular pressure in common soil me-chanics usage. Designation of this term by gives��i

�� A � u (7.13)i

Equations analogous to Eqs. (7.11), (7.12), and (7.13)can be developed for the case of a partly saturated soil.To do so requires consideration of the pressures in thewater uw and in the air ua and the proportions of areaa contributed by water aw and by air aa with the con-dition that

a � a � a i.e., a → 0w a c

The resulting equation is

aw�� A � u � (u � u ) (7.14)i a w aa

In the absence of significant long-range attractions,this equation is similar to that proposed by Bishop(1960) for partially saturated soils

�� u � �(u � u ) (7.15)i a a w

where � � aw /a. Although it is clear that for a dry soil� � 0, and for a saturated soil � � 1.0, the usefulnessof Eq. (7.15) has been limited in practice because ofuncertainties about � for intermediate degrees of sat-uration. Further discussion of the effective stress con-cept for unsaturated soils is given in Section 7.12.

Limiting the discussion to saturated soils, two ques-tions arise:

1. How does the intergranular pressure relate to��ithe effective stress as defined for most analyses,that is, �� u?

2. How does the intergranular pressure relate to��ithe measured quantity, � � � u0, that is taken��mas the effective stress, recalling (Section 7.2) thatpore pressure can only be measured at points out-side the true interparticle zone?

Answers to these questions require a more detailedconsideration of the meaning of fluid pressures in soils.

7.6 WATER PRESSURES AND POTENTIALS

Pressures in the pore fluid of a soil can be expressedin several ways, and the total pressure may involveseveral contributions. In hydraulic engineering, prob-lems are analyzed using Bernoulli’s equation for thetotal heads and head losses associated with flow be-tween two points, that is,

2 2p v p v1 1 2 2Z � � � Z � � � h (7.16)1 2 1–2 2g 2gw w

where Z1 and Z2 are the elevations of points 1 and 2,p1 and p2 are the hydrostatic pressures at points 1 and2, v1 and v2 are the flow velocities at points 1 and 2,w is the unit weight of water, g is the acceleration dueto gravity, and h1–2 is the loss in head between points1 and 2. The total head H (dimension L) is

2p vH � Z � � (7.17)

2gw

Flow results only from differences in total head;conversely, if the total heads at two points are thesame, there can be no flow, even if Z1 Z2 and p1 p2. If there is no flow, there is no head loss and h1–2

� 0.The flow velocity through soils is low, and as a re-

sult v2 /2g → 0, and in most cases it may be neglected.Therefore, the relationship

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WATER PRESSURE EQUILIBRIUM IN SOIL 181

p p1 2Z � � Z � � h (7.18)1 2 1–2 w w

is the basis for evaluation of pore pressures and anal-ysis of seepage through soils and other porous media.

Although the absence of velocity terms is a factorthat seems to simplify the analysis of flows and pres-sures in soils, there are other considerations that tendto complicate the problem. These include:

1. The use of several terms to describe the status ofwater in soils, for example, potential, pressure,and head.

2. The possible existence of tensions in the pore wa-ter.

3. Compositional differences in the water frompoint-to-point and adsorptive force fields fromparticle surfaces.

4. Differences in interparticle forces and the energystate of the pore fluid from point to point owingto thermal, electrical, and chemical gradients.Such gradients can cause fluid flows, deforma-tions, and volume changes, as considered in moredetail in Chapter 9.

Some formalism in definition and terminology isnecessary to avoid confusion. The status of water in asoil can be expressed in terms of the free energy rel-ative to free, pure water (Aitchison, et al., 1965). Thefree energy can be (and is) expressed in different ways,including

1. Potential (dimensions—L2T�2: J/kg)2. Head (dimensions—L: m, cm, ft)3. Pressure (dimensions—ML�1 T�2: kN/m2, dyn/

cm2, tons/m2, atm, bar, psi, psf)

If the free energy is less than that of pure waterunder the ambient air pressure, the terms suction andnegative pore water pressure are used.

The total potential (head, pressure) of soil water isthe potential (head, pressure) in pure water that willcause the same free energy at the same temperature asin the soil water. An alternative definition of total po-tential is the work per unit quantity to transport re-versibly and isothermally an infinitesimal amount ofpure water from a pool at a specified elevation at at-mospheric pressure to the point in soil water underconsideration.

The selection of the components of the total poten-tial � (total head H, total pressure P) is somewhatarbitrary (Bolt and Miller, 1958); however, the follow-ing have gained acceptance for geotechnical work(Aitchison, et al., 1965):

1. Gravitational potential �g (head Z, pressure pz)corresponds to elevation head in normal hydrau-lic usage.

2. Matrix or capillary potential �m (head hm, pres-sure p) is the work per unit quantity of water totransport reversibly and isothermally an infinites-imal quantity of water to the soil from a poolcontaining a solution identical in composition tothe soil water at the same elevation and externalgas pressure as that of the point under consider-ation in the soil. This component corresponds tothe pressure head in normal hydraulic usage. Itresults from that part of the boundary stressesthat is transmitted to the water phase, from pres-sures generated by capillarity menisci, and fromwater adsorption forces exerted by particle sur-faces. A piezometer measures the matrix poten-tial if it contains fluid of the same compositionas the soil water.

3. Osmotic (or solute) potential �s (head hs, pres-sure ps) is the work per unit quantity of water totransport reversibly and isothermally an infinites-imal quantity of water from a pool of pure waterat a specified elevation and atmospheric pressureto a pool containing a solution identical in com-position to the soil water, but in all other respectsidentical to the reference pool. This componentis, in effect, the osmotic pressure of the soil wa-ter, and it depends on the composition and abilityof the soil particles to restrain the movement ofadsorbed cations. The osmotic potential is nega-tive, that is, water tends to flow in the directionof increasing concentration.

The total potential, head, and pressure then become

� � � � � � � (7.19)g m s

H � Z � h � h (7.20)m s

P � p � p � p (7.21)z s

At equilibrium and no flow there can be no varia-tions in �, H, or P within the soil.

7.7 WATER PRESSURE EQUILIBRIUM IN SOIL

Consider a saturated soil mass as shown in Fig. 7.7.Conditions at several points will be analyzed in termsof heads for simplicity, although potential or pressurecould also be used with the same result. The system isassumed at constant temperature throughout. At point0, a point inside a piezometer introduced to measure

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Figure 7.7 Schematic representation of a saturated soil for analysis of pressure conditions.

pore pressure, Z � 0, hm � hm0, and hs0 � 0 if purewater is used in the piezometer. Thus,

H � 0 � h � 0 � h0 m0 m0

It follows that

P � h � u (7.22)0 m0 w 0

the measured pore pressure.Point 1 is at the same elevation as point 0, except it

is inside the soil mass and midway between two clayparticles. At this point, Z1 � 0, but hs 0 because theelectrolyte concentration is not zero. Thus,

H � 0 � h � h1 m1 s1

If no water is flowing, H1 � H0, and

h � h � hm1 s1 m0

Also, because p1 � p0 � u0

u � h � h (7.23)0 m1 w s1 w

At point 2, which is between the same two clay par-ticles as point 1 but closer to a particle surface, therewill be a different ion concentration than at 1. Thus,at equilibrium, and assuming Z2 � 0,

u0h � h � h � h � h �m2 s2 m1 s1 m0 w

A similar analysis could be applied to any point in thesystem. If point 3 were midway between two clay par-ticles spaced the same distance apart as the particleson either side of point 1, then hs3 � hs1, but Z3 0.Thus,

u0 � Z � h � h � Z � h � h (7.24)3 m3 s3 3 m3 s1w

A partially saturated system can also be analyzed,but the influences of curved air–water interfaces mustbe taken into account in the development of the hm

terms.The conclusions that result from the above analysis

of component potentials are:

1. As the osmotic and gravitational componentsvary from point to point in a soil at equilibrium,

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MEASUREMENT OF PORE PRESSURES IN SOILS 183

the matrix or capillary component must also varyto maintain equal total potential. The concept thathydrostatic pressure must vary with elevation tomaintain equilibrium is intuitive; however, theidea that this pressure must vary also in responseto compositional differences is less easy to vi-sualize. Nonetheless, this underlies the wholeconcept of water flow by chemical osmosis.

2. The total potential, head, and pressure are meas-urable, and separation into components is possi-ble experimentally, although it is difficult.

3. A pore pressure measurement using a piezometercontaining pure water gives a pressure u0 � wh,where h is the pressure head at the piezometer.When referred back to points between soil par-ticles, u0 is seen to include contributions fromosmotic pressures as well as matrix pressures.Since osmotic pressures are the cause of long-range repulsions due to double-layer interactions,measured pore water pressures may include con-tributions from long-range interparticle repulsiveforces.

7.8 MEASUREMENT OF PORE PRESSURES INSOILS

Several techniques for the measurement of pore waterpressures are available. Some are best suited for lab-oratory use, whereas others are intended for use in thefield. Some yield the pore pressure or suction by directmeasurement, while others require deduction of thevalue using thermodynamic relationships.

1. Piezometers of Various Types Water in the pi-ezometer communicates with the soil through aporous stone or filter. Pressures are determinedfrom the water level in a standpipe, by a manom-eter, by a pressure gauge, or by an electronicpressure transducer. A piezometer used to mea-sure pressures less than atmospheric is usuallytermed a tensiometer.

2. Gypsum Block, Porous Ceramic, and FilterPaper The electrical properties across a spe-cially prepared gypsum block or porous ceramicblock are measured. The water held by the blockdetermines the resistance or permittivity, and themoisture tension in the surrounding soil deter-mines the amount of moisture in the block(Whalley et al., 2001). The same principle can beapplied by placing a dry filter paper on a soilspecimen and allowing the soil moisture to ab-sorb into the paper. When the suction in the filterpaper is equal to the suction in the soil, the two

reach equilibrium, and the suction can be deter-mined by the water content of the filter paper.These techniques are used for measurement ofpore pressures less than atmospheric.

3. Pressure-Membrane Devices An exposed soilsample is placed on a membrane in a sealedchamber. Air pressure in the chamber is used topush water from the pores of the soil through themembrane. The relationship between water con-tent and pressure is used to establish the relation-ship between soil suction and water content.

4. Consolidation Tests The consolidation pressureon a sample at equilibrium is the soil water suc-tion. If the consolidation pressure were instanta-neously removed, then a negative water pressureor suction of the same magnitude would beneeded to prevent water movement into the soil.

5. Vapor Pressure Methods The relationship be-tween relative humidity and water content is usedto establish the relationship between suction andwater content.

6. Osmotic Pressure Methods Soil samples areequilibrated with solutions of known osmoticpressure to give a relationship between watercontent and water suction.

7. Dielectric Sensors Such as Capacitance Probesand Time Domain Reflectometry Soil moisturecan be indirectly determined by measuring thedielectric properties of unsaturated soil samples.With the knowledge of soil water characteristicsrelationship (Section 7.11), the negative porepressure corresponding to the measured soilmoisture can be determined. The capacitanceprobe measures change in frequency response ofthe soil’s capacitance, which is related to dielec-tric constants of soil particle, water, and air. Thecapacitance is largely influenced by water con-tent, as the dielectric constant of water is largecompared to the dielectric constants of soilparticle and air. Time domain reflectrometrymeasures the travel time of a high-frequency,electromagnetic pulse. The presence of water inthe soil slows down the speed of the electromag-netic wave by the change in the dielectric prop-erties. Volumetric water content can therefore beindirectly measured from the travel time mea-surement.

Piezometer methods are used when positive porepressures are to be measured, as is usually the case indams, slopes, and foundations on soft clays. The othermethods are suitable for measurement of negative porepressures or suction. Pore pressures are often negativein expansive and partly saturated soils. More detailed

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descriptions and comparisons of these and other meth-ods are given by Croney et al. (1952), Aitchison et al.(1965), Richards and Peter (1987), and Ridley et al.(2003).

7.9 EFFECTIVE AND INTERGRANULARPRESSURE

In Section 7.5, it was shown that the intergranular pres-sure is given by

�� A � u (7.25)i

where u is the hydrostatic pressure between particles(or hmw in the terminology of Section 7.7). General-ized forms of Eq. (7.24) are

u � Z � h � h (7.26)0 w m w s w

and

u � h � u � Z � h (7.27)m w 0 w s w

Thus, Eq. (7.25) becomes, for the case of no elevationdifference between a piezometer and the point in ques-tion (i.e., Z � 0),

�� A � u � h (7.28)i 0 s w

Because the quantity hsw is an osmotic pressure andthe salt concentration between particles will invariablybe greater than at points away from the soil (such asin a piezometer), hsw will be negative. This pressurereflects double-layer repulsions. It has been termed Rin some previous studies (Lambe, 1960; Mitchell,1962). If hsw in Eq. (7.28) is replaced by the absolutevalue of R, we obtain

�� A � u � R (7.29)i 0

From Eq. (7.25), it was seen that the intergranularpressure was dependent on long-range interparticle at-tractions A as well as on the applied stress � and thepore water pressure between particles u. Equation(7.29) indicates that if intergranular pressure is to��ibe expressed in terms of a measured pore pressure u0,then the long-range repulsion R must also be taken intoaccount. The actual hydrostatic pressure between par-ticles u � u0 � R includes the effects of long-rangerepulsions as required by the condition of constant to-tal potential for equilibrium.

In the general case, therefore, the true intergranularpressure � � � A � u0 � R and the conventionally��i

defined effective stress �� u0 differ by the netinterparticle stress due to physicochemical contribu-tions,

�� A � R (7.30)i

When A and R are both small, as would be true ingranular soils, silts, and clays of low plasticity, or incases where A � R, the intergranular and effectivestress are approximately equal. Only in cases whereeither A or R is large, or both are large but of signifi-cantly different magnitude, would the intergranular andeffective stress be significantly different. Such a con-dition appears not to be common, although it might beof importance in a well-dispersed sodium montmoril-lonite, where compression behavior can be accountedfor reasonably well in terms of double-layer repulsions(Chapter 10).4

The derivation of Eq. (7.30) assumed vertical equi-librium, with contributing forces parallel to each other,that is, the intergranular stress is the sum of the��iskeletal forces (defined as �� u0) and the elec-trochemical stress (A � R), as illustrated in Fig. 7.8a.This implies that the deformation induced by the elec-trochemical stress (A � R) is equal to the deformationinduced by the skeletal forces at contacts [i.e., a ‘‘par-allel’’ model as described by Hueckel (1992)]. Thechange in pore fluid chemistry at constant confinement(��) leads to changes in intergranular stresses re-(��),i

sulting in changes in shear strength, for example.An alternative assumption can be made; the total

deformation of soil is the sum of the deformations ofthe particles and in the double layers as illustrated inFig. 7.8b. The effective stress �� is then equal to theelectrochemical stress (R � A):

�� R � A � �� u (7.31)i 0

This is called the ‘‘series’’ model (Hueckel, 1992), andthe model can be applicable for very fine soils at highwater content, in which particles are not actually incontact with each other but are aligned in a parallelarrangement. Increase in intergranular stress or ef-��ifective stress �� changes the interparticle spacing,which may contribute to changes in strength propertiesupon shearing.

4 A detailed analysis of effective stress in clays is presented by Chat-topadhyay (1972), which leads to similar conclusions, including Eq.(7.29). was termed the true effective stress and it governed the��ivolume change behavior of Na–montmorillonite.

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ASSESSMENT OF TERZAGHI’S EQUATION 185

Skeletal Forceσ� = σ _ u0

ElectrochemicalForce A _ R

σi�

σi�

Deformation atthe Contact

σi� = σ _ u0 + A _ R

(a)

Total Deformationat the Contactσ�i

σi�

σi� = σ _ u0 = A _ R

(b)

Particle Deformationby Skeletal Force

ElectrochemicalForce A _ R

Skeletal Forceσ� = σ _ u0

Electrochemical Force

Skeletal Force

Skeletal Force Electrochemical Force

Skeletal ForceElectrochemical Force Electrochemical Force

Skeletal Force

Figure 7.8 Contribution of skeletal force (� � u0) and electrochemical force (A � R) tointergranular force �i: (a) parallel model and (b) series model.

Since the particles are arranged in parallel as wellas nonparallel manner, the chemomechanical couplingbehavior of actual soils can be far from the predictionsmade by the above two models. In fact, Santamarina(2003) argues that the impact of skeletal forces by ex-ternal forces, particle-level forces, and contact-levelforces on soil behavior is different, and mixing bothtypes of forces in a single algebraic expression in termsof effective stress can lead to incorrect prediction [e.g.,Eq. (7.15) for unsaturated soils and Eq. (7.30) for soilswith measurable interparticle repulsive and attractiveforces].

7.10 ASSESSMENT OF TERZAGHI’S EQUATION

The preceding equations and discussion do not confirmthat Terzaghi’s simple equation is indeed the effectivestress that governs consolidation and strength behaviorof soils. However, its usefulness has been establishedfrom the experience of many years of successful ap-plication in practice. Skempton (1960b) showed thatthe Terzaghi equation does not give the true effectivestress but gives an excellent approximation for the case

of saturated soils. Skempton proposed three possiblerelationships for effective stress in saturated soils:

1. The true intergranular pressure for the case whenA � R � 0

�� (1 � a )u (7.32)c

in which ac is the ratio of contact area to totalcross-sectional area.

2. The solid phase is treated as a real solid that hascompressibility Cs and shear strength given by

� � k � � tan � (7.33)i

where � is an intrinsic friction angle and k is atrue cohesion. The following relationships werederived: For shear strength,

a tan �c�� 1 � u (7.34)� �tan ��

where �� is the effective stress angle of shearingresistance. For volume change,

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Table 7.1 Compressibility Values for Soil, Rock,and Concrete

Material

Compressibilitya

per kN/m2 � 10�6

C Cs Cs /C

Quartzitic sandstone 0.059 0.027 0.46Quincy granite (30 m deep) 0.076 0.019 0.25Vermont marble 0.18 0.014 0.08Concrete (approx.) 0.20 0.025 0.12Dense sand 18 0.028 0.0015Loose sand 92 0.028 0.0003London clay (over cons.) 75 0.020 0.00025Gosport clay (normally cons.) 600 0.020 0.00003

After Skempton (1960b).aCompressibilities at p � 98 kN/m2; water Cw � 0.49

� 10�6 per kN/m2.

Cs�� 1 � u (7.35)� �C

where C is the soil compressibility.3. The solid phase is a perfect solid, so that � � 0

and Cs � 0. This gives

�� u (7.36)

To test the three theories, available data were studiedto see which related to the volume change of a systemacted upon by both a total stress and a pore waterpressure according to

V� �C �� (7.37)

V

and also satisfied the Coulomb equation for drainedshear strength �d :

� � c� � �� tan �� (7.38)d

when both a total stress and a pore pressure are acting.It may be noted that this approach assumes that theCoulomb strength equation is valid a priori.

The results of Skempton’s analysis showed that Eq.(7.32) was not a valid representation of effective stress.Equations (7.34) and (7.35) give the correct results forsoils, concrete, and rocks. Equation (7.36) accountswell for the behavior of soils but not for concrete androck. The reason for this latter observation is that insoils Cs /C and ac tan � / tan �� approach zero, and,thus, Eqs. (7.34) and (7.35) reduce to Eq. (7.36). Inrock and concrete, however, Cs /C and ac tan � / tan ��are too large to be neglected. The value of tan � / tan�� may range from 0.1 to 0.3, ac clearly is not negli-gible, and Cs /C may range from 0.1 to 0.5 as indicatedin Table 7.1.

Effective stress equations of the form of Eqs. (7.32),(7.34), (7.35), and (7.36) can be generalized to the gen-eral form (Lade and de Boer, 1997):

�� u (7.39)

where � is the fraction of the pore pressure that givesthe effective stress.5 Different expressions for � pro-posed by several researchers are listed in Table 7.2.

5 A more general expression has been proposed as �ij � � �iju,��ijwhere �ij is the tensor that accounts for the constitutive characteristicsof the solid such as complex kinematics associated with anisotropicelastic materials (Carroll and Katsube, 1983; Coussy, 1995; Did-wania, 2002).

A more rigorous evaluation of the contribution ofsoil particle compressibility to effective stress wasmade by Lade and de Boer (1997) using a two-phasemixture theory. The volume change of the soil skeletoncan be separated into that due to pore pressure incre-ment u and that due to the change in confining pres-sure (� � u) (or � � u). The effective stressincrement �� is defined as the stress that produces thesame volume change,

CV �� V � V � CV ( � � u)0 sks sku 0

� C V u (7.40)u 0

where Vsks is the volume change of soil skeleton dueto change in confining pressure, Vsku is the volumechange of soil skeleton due to pore pressure change,V0 is the initial volume, C is the compressibility of thesoil skeleton by confining pressure change, and Cu isthe compressibility of the soil skeleton by pore pres-sure change. Rearranging Eq. (7.40) leads to

Cu �� 1 � u (7.41)� �C

Lade and de Boer (1997) used this equation to de-rive an effective stress equation for granular materialsunder drained conditions. Consider a condition inwhich the total confining pressure is constant [ (� �

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ASSESSMENT OF TERZAGHI’S EQUATION 187

Table 7.2 Expressions for � to Define Effective Stress

Pore Pressure Fraction � Note Reference

1 Terzaghi (1925b)n n � porosity Biot (1955)

1 � ac ac � grain contact area per unit area of plane Skempton and Bishop (1954)

1 � ac

tan �

tan ��

Equation (7.34) Skempton (1960b)

1 �Cs

CEquation (7.35); for isotropic elastic

deformation of a porous material; for solidrock with small interconnected pores andlow porosity (Lade and de Boer, 1997)

Biot and Willis (1957), Skempton(1960b), Nur and Byerlee (1971), Ladeand de Boer (1997)

1 � (1 � n)Cs

CEquation (7.43) Suklje (1969); Lade and de Boer (1997)

After Lade and de Boer (1997).

Figure 7.9 Variation of � with stress for quartz sand andgypsum sand (Lade and de Boer, 1997).

u) � 0], but the pore pressure changes by u.6 Thevolume change of soil skeleton caused by change inpore pressure ( Vsku) is attributed solely from the vol-umetric compression of the solid grains ( Vgu). Hence,

V C V u � C (1 � n)V u V orsku u 0 s 0 gu

C � C (1 � n)u s (7.42)

where Cs is the compressibility of soil grains due topore pressure change and n is the porosity. SubstitutingEq. (7.42) into (7.41) gives

Cs �� 1 � (1 � n) u or �C

Cs� � 1 � (1 � n) (7.43) �C

Figure 7.9 shows the variations of � with stress forquartz sand and gypsum sand (Lade and de Boer,1997). For a stress level less than 20 MPa, � is essen-tially one. Thus, Terzaghi’s effective stress equation,while not rigorously correct, is again shown to be anexcellent approximation in almost all cases for satu-rated soils (i.e., solid grains and pore fluid are consid-ered to be incompressible compared to soil skeletoncompressibility).

6 An example of this condition is a soil under a seabed, in which thesea depth varies. This condition is often called the ‘‘unjacked con-dition.’’

Can the effective stress concept also be applied forundrained conditions where drainage is prevented?That is, when an isotropic total stress load of �iso isapplied, is u equal to �iso? Using a two-phase mix-ture theory, the total stress increment ( �iso) is sepa-rated into partial stress increments for the solid phase( �s) and the fluid phase ( �ƒ) (Oka, 1996). Consid-ering that the macroscopic volumetric strains by twophases are equal but of opposite sign for undrained

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θ

θ

Solid Surface

AirWater(reference fluid)

Air

Solid surface

(a)

Water(reference fluid)

(b)

(c)

Air

Water

Solid

Figure 7.10 Wettability of two fluids (water and air) on asolid surface: (a) contact angle less than 90�, (b) contact an-gle more than 90�, and (c) unsaturated sand with water as thewetting fluid and air as the nonwetting fluid.

conditions, Oka (1996) showed that the partial stressesare related to the total stress as follows:

C � Cs � � �ƒ iso(C /n) � (1 � 1/n)C � Cs l (7.44)

[(1/n) � 1]C � (C /n) � Cs l � � �s iso(C /n) � (1 � 1/n)C � Cs l

where n is the porosity, C is the compressibility of soilskeleton, Cs is the compressibility of soil particles, andCl is the compressibility of pore fluid.

If the excess pore pressure generated by undrainedisotropic loading � is u, the partial stress incrementfor the fluid phase becomes (Oka, 1996)

� � n u (7.45)ƒ

Combining Eqs. (7.45) and (7.46),

C � Cs u � � (7.46)isoC � C � n(C � C )s l s

The multiplier in the right-hand side of the aboveequation is in fact Bishop’s pore water pressure coef-ficient B (Bishop and Eldin, 1950).7 For typical soils(Cs � 1.9 � 2.7 � 10�8 m2 /kN, Cl � 4.9 � 10�9

m2/kN, C � 10�5 � 10�4 m2/kN), so the values of Bare roughly equal to 1. Hence, it can be concluded thatTerzaghi’s effective stress equation is also applicablefor undrained conditions for most soils.

7.11 WATER–AIR INTERACTIONS IN SOILS

Wettability refers to the affinity of one fluid for a solidsurface in the presence of a second or third fluid orgas. A measure of wettability is the contact angle,which was introduced in Eq. (7.9). Figure 7.10 illus-trates a drop of the reference liquid (water for Fig.7.10a and air for Fig. 7.10b) resting on a solid surfacein the presence of another fluid (air for Fig. 7.10a andwater for 7.10b). The interface between the two fluidsmeets the solid surface at a contact angle �. If the angleis less than 90�, the reference fluid is referred to as thewetting fluid for a given solid surface. If the angle isgreater than 90�, the reference liquid is referred to asthe nonwetting phase. The figure shows that water and

7 A similar equation for B value has been proposed by Lade and deBoer (1997).

air are the wetting and nonwetting fluid, respectively.8

The environmental SEM photos in Fig. 5.27 showedthat water can be either wetting or nonwetting fluiddepending soil mineralogy.

The contact angle is a property related to interac-tions of solid and two fluids (water and air, in thiscase).

� � �as wscos � � (7.47)�aw

where �as is the interfacial tension between air andsolid, �ws is the interfacial tension between waterand solid, and �aw is the interfacial tension between

8 Some contaminated sites contain non-aqueous-phase liquids(NAPLs). In general, NAPLS can be assumed to be nonwetting withrespect to water since the soil particles are in general primarilystrongly water-wet. Above the water table, it is usually appropriateto assume that the water is the wetting fluid with respect to NAPLand that NAPL is a wetting fluid with respect to air, implying thatthe wettability order is water � NAPL � air. Below the water table,water is the wetting fluid and NAPL is the nonwetting fluid.

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WATER–AIR INTERACTIONS IN SOILS 189

Volumetric Water Content θ w

0.1 0.2 0.3 0.4 0.5 0.60.010-1

100

101

102

103

104

105

106

1

2

3

5

4

6

7

1 Dune Sand2 Loamy Sand3 Calcareous Fine Sandy Loam4 Calcareous Loam5 Silt Loam Derived from Loess6 Young Oligotrophous Peat Soil7 Marine Clay

Mat

ric s

uctio

n u a

– u

w (

kPa)

Figure 7.11 Soil–water characteristic curves for some Dutchsoils (from Koorevaar et al., 1983; copied from Fredlund andRahardjo, 1993).

air and water. The microscopic scale distribution ofwater and air is illustrated in Fig. 7.10c, whereby it isassumed that water is wetting the grain surfaces.

The aforementioned discussion on wettability andcontact angle assumes static water drops on solid sur-faces. It has been observed for movement of water rel-ative to soil that the ‘‘dynamic’’ contact angle formedby the receding edge of a water droplet is generallyless than the angle formed by its advancing edge.

Matric suction (or capillary pressure) refers to thepressure discontinuity across a curved interface sepa-rating two fluids. This pressure difference exists be-cause of the interfacial tension present in the fluid–fluid interface. Matric suction is a property that causesporous media to draw in the wetting fluid and repelthe nonwetting fluid and is defined as the differencebetween the nonwetting fluid pressure and the wettingfluid pressure. For a two-phase system consisting ofwater and air, the matric suction � is

� � u � u (7.48)n w

where un is the pressure of the nonwetting fluid (air)and uw is the pressure of the wetting fluid (water).

Assuming that the soil pores have a cylindricalshape, like a bundle of capillary tubes as illustrated inFig 7.3b, the interface between two liquids in each tubeforms a subsection of a sphere. The capillary pressureis then related to the tube radius, contact angle, andthe interfacial tension between the two liquids. Thepressure drop across the interface is directly propor-tional to the interfacial tension and inversely propor-tional to the radius of curvature. It follows that higherair pressure is required for air to enter water-saturatedfine-grained than coarse-grained materials.

Soil contains a range of different pore sizes, whichwill drain at different capillary pressure values. Thisleads to a soil–water characteristic relationship inwhich the matric suction is plotted against the volu-metric water content (or sometimes water saturationratio) such as shown in Fig. 7.11.9 The curves are oftendetermined during air invasion into a previously water-saturated soil. As the volumetric water content de-creases, as a result of drainage or evaporation, thematric suction increases. When water infiltrates intothe soil (wetting or imbibition), the conditions reverse,with the volumetric water content increasing and ma-tric suction decreasing. Usually drainage and wetting

9 The soil–water characteristic curve is referred to by a variety ofnames depending on different disciplines. They include moisture re-tention, soil–water retention, specific retention, and moisture char-acteristic.

processes do not follow the same curve and the volu-metric water content versus matric suction curves ex-hibit hysteresis during cycles of drainage and wettingas shown in Fig. 7.12a. One cause of hysteresis is theexistence of ‘‘ink bottle neck’’ pores at the microscopicscale as shown in Fig. 7.12b. Larger water-filled porescan remain owing to the inability of water to escapethrough smaller openings below in the case of drainageor above in the case of evaporation. Another cause isirreversible change in soil fabric and shrinkage duringdrying.

The curves in Fig. 7.11 have two characteristicpoints—the air entry pressure �a and residual volu-metric water content �r as defined in Fig. 7.12a. Theentry pressure is the matric suction at which the airbegins to enter the pores and the pores become inter-connected (Corey, 1994). At this point, the air per-meability becomes greater than zero. Corey (1994)also introduced the term ‘‘displacement pressure’’ (�d

in Fig. 7.12b) and defined it as the matric suction atwhich the first water desaturation occurs during adrainage cycle.10 The entry pressure is always slightly

10 For the Dense NAPL–water two-phase system (often Dense NAPLis the nonwetting fluid and water is the wetting fluid), the displace-ment pressure may be important to examine the potential of DNAPLinvading into a noncontaminated water-filled porous media.

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Water Content

Initial drainageCurve

Main WettingCurve

ScanningCurve

Main Drying Curve

Hysteresis ScanningCurve

(a)

θ r

ψa

θ r Residual Water Content

ψa Air Entry Value

Draining

Wetting

(b)

ψd

ψd Displacement pressure

Suc

tion

Figure 7.12 Hysteresis of a soil–water characteristic curve: (a) effect of hysteresis and (b)ink bottle effect: a possible physical explanation for the hysteresis.

greater than the displacement pressure because porethroats smaller than the maximum must be penetratedto establish air connectivity. The air entry pressure ismuch greater for fine-grained than for coarse-grainedsoils because of their smaller pore sizes.

Residual water content �r is defined as the watercontent that cannot be further reduced by the increasein matric suction. At this stage, the water phasebecomes essentially discontinuous and the regimechanges from the funicular to pendular state, as de-scribed in Section 7.4. However, this does not meanthat the soil cannot have a degree of saturation lessthat the residual saturation because residual water cancontinue to evaporate. Hence, it is important to notethat the residual saturation defined here is a mathe-matical fitting parameter without a specific quantitativevalue.

The shape of the soil–water characteristic curve de-pends on many factors, including the grain size distri-bution, soil fabric, the contact angle, and the interfacialtension [see Eq. (7.11)]. If the material is uniform witha narrow range of pore sizes, the curve has three dis-tinct parts: a straight part up to the air entry pressure,a relatively horizontal middle part, and an end part thatis almost vertical (soil 1 in Fig. 7.11). On the otherhand, if the material is well graded, the curve issmoother (soils 3, 4, and 5 in Fig. 7.11). The capillarypressure increases gradually as the water saturation de-creases and the middle part is not horizontal. Many

algebraic formulas have been proposed to fit the mea-sured soil-water characteristic relations. The most pop-ular ones are (a) the Brooks–Corey (1966) equation:

� � � when � � � (7.49)m d

�1/�� r� � � when � � � (7.50)� �d d� � �m r

where �m is the volumetric water content at fullsaturation and � is the curve-fitting parameter calledthe pore size distribution index and (b) the van Gen-uchten equation (1980):

�1 / m 1�m� � �r� � � � 1 (7.51) � � �0 � � �m r

where �0 and m are curve-fitting parameters.Various modifications have been proposed to these

equations to include behaviors such as hysteresis, non-wetting fluid trapping, and three-phase conditions.

7.12 EFFECTIVE STRESS IN UNSATURATEDSOILS

Although it seems clear that the volume change andstrength behavior of partly saturated soils are con-

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EFFECTIVE STRESS IN UNSATURATED SOILS 191

(ua_uw)/(ua

_uw)b

(ua_uw)b = Air Entry Value

(a) (b)

S (%)

1. CompactedBoulder Clay2. Compacted Shale3. Breadhead silt4. Silt5. Silty clay6. Sterrebeek silt7. White clay

Degree of Saturation

Coe

ffici

entχ

χ =(ua – uw)(ua – uw)

– 0.55

Coe

ffici

entχ

Figure 7.13 Variation of parameter � with the degree of water saturation Sr for differentsoils: (a) � versus water saturation (after Gens, 1996) and (b) � versus suction (after Khaliliand Khabbaz, 1998).

Applied Pressure (kPa )

Voi

d R

atio

e

10 100 10000.64

0.68

0.72

0.76

0.80

0.84

Air Dry (8 specimens)

Soaked at Constant Void Ratio

Soaked at Constant AppliedPressure

Initially Soaked Test

Figure 7.14 Oedometer compression curves of unsaturatedsilty soils (after Jennings and Burland, 1962 in Leroueil andHight, 2002).

trolled by an effective stress that is not the same as thetotal stress, the appropriate formulation for the effec-tive stress is less certain than for a fully saturated soil.As noted earlier, Bishop (1960) proposed Eq. (7.15)(assuming �� ):��i

�� u � �(u � u ) (7.52)a a w

The term � � ua is the net total stress. The termua � uw represents the soil water suction that adds tothe effective stress since uw is negative. Thus, theBishop equation is appealing intuitively because neg-ative pore pressures are known to increase strength anddecrease compressibility. Using Eq. (7.52), the shearstrength of unsaturated soil can be expressed as

� � {(� � u ) � �(u � u )}tan �� (7.53)a a w

where �� is the effective friction angle of the soil.However, difficulties in the evaluation of the parameter�, its dependence on saturation (� � 1 for saturatedsoils and � � 0 for dry soils), and that the relationshipbetween � and saturation is soil dependent, as shownin Fig. 7.13a, all introduce problems in the applicationof Eq. (7.53). Since water saturation is related to matricsuction as described in Section 7.11, it is possible that� depends on matric suction as shown in Fig. 7.13b.Nonetheless, because of the complexity in determining�, the attempt to couple total stress and suction to-gether into a single equivalent effective stress is un-certain (Toll, 1990).

Limitations in Bishop’s equation were highlightedby Jennings and Burland (1962) in their experimentsinvestigating the volume change characteristics of un-saturated soils. Figure 7.14 shows that the oedometercompression curve of air-dry silt falls above that ofsaturated silt. Also, as shown in the figure, some air-dry samples were consolidated at four different pres-sures (200, 400, 800, and 1600 kPa) and then soaked.

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Preconsolidationpressure

25 50 100 200 4000.95

1.00

1.05

1.10

1.15

1.20

1.25

σ _ua (kPa)

ua_ uw (kPa)

300 kPa

200 kPa

100 kPa0 kPa

Curves are Averages ofSeveral Tests

Voi

d R

atio

e

Figure 7.15 Isotropic compression tests of compacted kaolin(after Wheeler and Sivakumar, 1995 in Leroueil and Hight,2002).

The void ratio decreased upon soaking and the finalstate was very close to the compression curve of thesaturated silt. Additional tests in which constant vol-ume during soaking was maintained by adjusting theapplied load were also done. Again, after equilibrium,the state of soaked samples was close to the compres-sion curve of the saturated silt. Soaking reduces thesuction and, hence, Bishop’s effective stress decreases.This decrease in effective stress should be associatedwith an increase in void ratio. However, the experi-mental observations gave the opposite trend (i.e., a de-crease in void ratio is associated with irreversiblecompression). The presence of meniscus water lensesin the soil before wetting was stabilizing the soil struc-ture, which is not taken into account in Bishop’s equa-tion (7.52).

An alternative approach is to describe the shearstrength/deformation and volume change behavior ofunsaturated soil in terms of the two independent stressvariables � � ua and ua � uw (Coleman, 1962; Bishopand Blight, 1963; Fredlund and Morgenstern, 1977;Fredlund, 1985; Toll, 1990, Fredlund and Rahardjo,1993; Tarantino et al., 2000). Figure 7.15 shows theresults of isotropic compression tests of compacted ka-olin. Different compression curves are obtained forconstant suction conditions, and relative effects of � �ua and ua � uw on volume change behavior can beobserved. Furthermore, the preconsolidation pressure(or yield stress) increases with suction.

On this basis, the dependence of shear strength � onstress is given by equations of the form

� � a(� � u ) � b(u � u ) (7.54)a a w

in which a and b are material parameters that may alsodepend on degree of saturation and stress. For exam-ple, Fredlund et al. (1978) propose the following equa-tion:

b� � (� � u )tan �� (u � u )tan � (7.55)a a w

where �b is the angle defining the rate of increase inshear strength with respect to soil suction. An exampleof this parameter as a function of water content, fric-tion angle, and matric suction is given by Fredlund etal. (1995).

Similarly, the change in void ratio e of an unsat-urated soil can be given by (Fredlund, 1985)

� � a (� � u ) � a (u � u ) (7.56)t a m a w

where at is the coefficient of compressibility with re-spect to changes in � � ua and am is the coefficient ofcompressibility with respect to changes in capillarypressure. A similar equation, but with different coef-ficients, can be written for change in water content.For a partly saturated soil, change in water content andchange in void ratio are not directly proportional.

The two stress variables, or their modifications thatinclude porosity and water saturation, have been usedin the development of elasto-plastic-based constitutivemodels for unsaturated soils (e.g., Alonso et al., 1990;Wheeler and Sivakumar, 1995; Houlsby, 1997; Gallip-oli et al., 2003). The choice of stress variables is stillin debate; further details on this issue can be found inGens (1996), Wheeler and Karube (1996), Wheeler etal. (2003), and Jardine et al. (2004).

Bishop’s � parameter in Eq. (7.52) is a scalar quan-tity, but microscopic interpretation of water distributionin pores can lead to an argument that � is directionaldependent (Li, 2003; Molenkamp and Nazemi,2003).11 During the desaturation process, the numberof soil particles under a funicular condition decreases,and they change to a pendular condition with furtherdrying. For particles in the funicular region, the suctionpressure acts all around the soil particles like the waterpressure as illustrated in Fig. 7.4a. Hence, the effect isisotropic even at the microscopic level. However, oncethe microscopic water distribution of a particle changesto the pendular condition, the capillary forces only acton a particle at locations where water bridge forms andthe contribution to the interparticle forces becomes

11 A microstructural analysis by Li (2003) suggests the following ef-fective stress expression:

�� u � � � (u � u )ij ij a ij ij a w

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more or less point wise, as shown in Fig. 7.4b. Asdescribed in Section 7.3, the magnitude of capillaryforce depends on the size of the water bridge and theseparation of the two particles, and hence, the contactforce distribution in the particle assembly becomes de-pendent not only on pore size location and distributionbut also on the relative locations of particles to oneanother (or soil fabric). It is therefore possible that thedistribution of the pendular-type capillary forces be-comes directional dependent.

In clayey soils, water is attracted to clay surface byelectrochemical forces, creating large matric suction.Although uw � u0 is used in practice, the actual porepressure u acting at interparticle contacts may be dif-ferent from u0, as discussed in Section 7.9. The con-tribution of the long-range interparticle forces tomechanical behavior of unsaturated clayey soils re-mains to be fully evaluated.


The concepts in this chapter provide insight into themeanings of intergranular pressure, effective stress,and pore water pressure and the factors controllingtheir values. Because soils behave as particulate ma-terials and not as continua, knowledge of these stressesand of the factors influencing them is a necessary pre-requisite to the understanding and quantification ofcompressibility, deformation, and strength in constitu-tive relationships for behavior. Various interparticleforces have been identified and their possible effectson soil behavior are highlighted.

The effective stress in a soil is a function of its state,which depends on the water content, density, and soilstructure. These factors are, in turn, influenced by thecomposition and ambient conditions. The relationshipsbetween soil structure and effective stress are devel-oped further in Chapter 8. Chemical, electrical, andthermal influences on effective pressures and fluidpressures in soils have not been considered in the de-velopments in this chapter. They may be significant,however, as regards soil structure stability fluid flow,volume change, and strength properties. They are an-alyzed in more detail in subsequent chapters.

An understanding of the components of pore waterpressure is important to the proper measurement ofpore pressure and interpretation of the results. Inclu-sion of the effect of pore water suction and air or gaspressure on the mechanical behavior of unsaturatedsoils requires modification of the effective stress equa-tion used for saturated soils. Complications arise fromthe difficulty in the choice of stress variables and intreatment of contact-level forces (i.e., capillary forces

in the pendular regime) in the macroscopic effectivestress equations.


1. A sand in the ground has porosity n of 0.42 andspecific gravity Gs of 2.6. It is assumed that thesevalues remain constant throughout the depth. Thewater table is 4 m deep and the groundwater is un-der hydrostatic condition. The suction–volumetricwater content relation of the sand is given by soil1 in Fig. 7.11.a. Calculate the saturated unit weight and dry unit

weight.b. Evaluate the unit weights at different saturation

ratios Sw.c. Plot the hydrostatic pore pressures with depth

down to a depth of 10 m and evaluate the satu-ration ratios above the water table.

d. Along with the hydrostatic pore pressure plot,sketch the vertical total stress with depth usingthe unit weights calculated in parts (a) and (b).

e. Estimate the vertical effective stress with depth.Use Bishop’s equation (7.52) with � � Sw. Com-ment on the result.

2. Repeat the calculations done in Question 1 with soil5 in Fig. 7.11. The specific gravity of the soil is2.65. Comment on the results by comparing themto the results from Question 1.

3. Using Eq. (7.3), estimate the tensile strength of asoil with different values of tensile strengths of ce-ment, sphere, and interface. The soil has a particlediameter of 0.2 mm and the void ratio is 0.7. As-sume k / (1 � e) � 3.1. Consider the following twocases: (a) � � 0.0075 mm and � � 5� and (b)� � 0.025 and � � 30�. Comment on the results.

4. Compute the following contact forces at differentparticle diameters d ranging from 0.1 to 10 mm.Comment on the results in relation to the effectiveand intergranular pressure described in Section 7.9.a. Weight of the sphere, W � �Gswd3, where Gs

1–6is the specific gravity (say 2.65) and w is theunit weight of water.

b. Contact force by external load, N � d2��, where�� is the external confining pressures applied.The equation is approximate for a simple cubicpacking of equal size spheres (Santamarina,2003). Consider two cases, (i) �� 1 kPa (�depth of 0.1 m) and (ii) �� 100 kPa (� depthof 10 m).

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c. Long-range van der Waals attraction force, A �Ahd / (24t2), where Ah is the Hamaker constant(Section 6.12) and t is the separation betweenparticles (Israelachvili, 1992, from Santamarina,2003). Use Ah � 10�20 N-m and t � 30 A.

5. Discuss why it is difficult to measure suction usinga piezometer-type tensiometer for long-term moni-toring of pore pressures. Describe the advantages ofother indirect measurement techniques such as po-rous ceramic and dielectric sensors.

6. For the following cases, compare the effectivestresses calculated by the conventional Terzaghi’sequation and by the modified equation (7.39) withvalues presented in Fig. 7.8. Discuss the possibleerrors associated with effective stress estimation byTerzaghi’s equation.a. Pile foundation at a depth of 20 m.b. A depth of 5 km from the sea level where the

subsea soil surface is 1 km deep.

7. Give a microscopic interpretation for why an un-saturated soil can collapse and decrease its volumeupon wetting as shown in Fig. 7.14 even though theBishop’s effective stress decreases.

8. Clay particles in unsaturated soils often aggregatecreating matrix pores and intraaggregate pores. Airexists in the matrix pores, but the intraaggregatepores are often saturated by strong water attractionto clay surfaces. The total potential of unsaturatedsoil can be extended from Eq. (7.19) to � � �g ��m � �s � �p, where �p is the gas pressure poten-tial.12 Discuss the values of each component of theabove equation in the matrix pores and the intraag-gregate pores.

12 This was proposed by a Review Panel in the Symposium on Mois-ture Equilibrium and Moisture Changes in Soils Beneath CoveredAreas in 1965.

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195

CHAPTER 8

Soil Deposits—Their Formation,Structure, GeotechnicalProperties, and Stability

8.1 INTRODUCTION

Long before methods were available to confirm spe-cific soil fabrics and structures, hypotheses were ad-vanced about them, their formation, and their stabilityin an attempt to account for such phenomena asstrength loss of clays on remolding, differences inproperties of soils deposited in different environments,collapsing soils and soil liquefaction, creep and sec-ondary compression, pore pressure generation duringdeformation, anisotropy, thixotropic hardening, and themobilization of friction and cohesion.

Two soils can have the same fabrics but differentproperties if the forces between particles and particlegroups are not the same. Fabric stability is sensitive tochanges in stresses and chemical environment. To takeboth fabric and its stability into account, the termstructure is used. Particles, particle groups, and theirassociations, together with interparticle forces and ap-plied stresses, determine the overall soil structure.

The term structure is also used to account for dif-ferences between the properties of a soil in its naturalstate and of the same soil at the same void ratio butthoroughly remolded, or between the soil in its naturalstate and after remolding and the reapplication of theoriginal stress state. Thoroughly remolded and re-worked soil is said to be destructured. Virtually everynatural, undisturbed soil has structure. As emphasizedby Leroueil and Vaughan (1990), the structure can beas significant in determining engineering behavior ascan such important factors as porosity and stress his-tory.

How residual and transported soil deposits areformed, how the formative processes and subsequentchanges over time act to produce unique types of soil

structures with characteristic properties, how theseproperties and the associated behavior are interelated,and why these processes and properties are relevantto geotechnical applications are the subjects of thischapter.

8.2 STRUCTURE DEVELOPMENT

Early Concepts

Early ideas about soil fabric and structure were largelyspeculative because techniques for direct observationof particles had not yet been developed. There wasparticular interest in the development of explanationsfor the loss of strength that accompanied the distur-bance of many natural clays at constant water content.This sensitivity of the undisturbed structure, which isquantified as the ratio of the undisturbed to fully re-molded strength at the same water content, can be greatenough to give the strength loss due to remoldingshown in Fig. 8.1.

Terzaghi (1925a) theorized that adsorbed water lay-ers had a high viscosity near particle surfaces and wereresponsible for strong adhesion between mineral grainsat points of contact between particles. Disturbance ofthe clay caused contacts to rupture, more water to fillin around the old contact points, and the strength todrop. Different adsorbed ions were also recognized aspossibly responsible for differences in strength andsensitivity (Terzaghi, 1941). Goldschmidt (1926) hy-pothesized that particles in sensitive clay are arrangedin a ‘‘cardhouse’’ that collapses on remolding.

A load-carrying skeleton consisting of highly com-pressed ‘‘bond clay’’ trapped between silt and fine sand

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196 8 SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY

Figure 8.1 Strength loss of a clay that is extremely sensitiveto remolding. Clay that becomes fluid on remolding is termedquick clay (photograph courtesy of Haley and Aldrich, Inc.).

particles was suggested by Casagrande (1932a) as re-sponsible for marine clay sensitivity. Such a fabric isassumed to form by simultaneous deposition of floc-culated clay particles and silt and sand grains in thesaltwater environment. The clay deposited in the inter-stices between the elements of the skeleton, termedmatrix clay, is assumed to be only partly consolidatedand remain at high water content. Remolding mixesthe matrix and bond clays, thereby destroying the pri-mary load-carrying structure and causing a reductionin strength.

Winterkorn and Tschebotarioff (1947) suggestedthat sensitivity resulted from a cementation similar tothat in loess and sandstone. This cementation was at-tributed to slow recrystallization or formation of ce-menting materials from inorganic substances of lowsolubility.

In the years since the formulation of these ideas ofsoil structure, it has been possible to determine fabricsand compositions in more detail and, along with a bet-ter understanding of the stress–deformation–strength

properties of soil, to interrelate structure and proper-ties. Modern concepts of soil structure and its impor-tance in geotechnics began to be formulated in theearly 1950s, for example, Lambe (1953) and in thecomprehensive review of clay microstructure given byBennett and Hurlbut (1986).

General Considerations in Structure Development

A soil’s structure is composed of a fabric and inter-particle force system that reflect all facets of the soilcomposition, history, present state, and environment.Structure-determining factors and processes are sum-marized in Fig. 8.2. Initial conditions dominate thestructure of young deposits at high porosity or freshlycompacted soils, whereas older soils at lower porosityare likely to be influenced more by the postdeposi-tional changes.

Single-grain fabrics are uncommon in soils contain-ing clay. Complex fabric units of micrometer-to-millimeter size or greater consisting of skeleton grains,clay aggregates, and pores are characteristic of mostfine-grained soil structures.

The principle of chemical irreversibility of clay fab-ric (Bennett and Hurlbut, 1986) applies generally tofine-grained soil deposits. This principle recognizesthat the chemical environment is critical during the in-itial stages of sediment fabric formation in water. How-ever, after the initial flocculation of particles anddeposition, the chemistry is much less important in in-fluencing fabric changes and subsequent states. Me-chanical energy rather than chemical energy becomesthe dominant factor influencing subsequent behavior.

Residual Soils

The texture of residual soils formed by the in-placeweathering of crystalline rocks may be quite similar tothat of the parent rock. Clay particles may form coat-ings over silt and sand grains as a result of repeatedwetting and drying. Open, porous fabrics form in somezones, while dense, low-porosity fabrics form in oth-ers, and heterogeneity is common.

Intense weathering and leaching, coupled with anabundance of aluminum and iron oxides, produces fab-rics and textures ranging from open granular to denseand clayey in tropical and subtropical soils. Concre-tions and nodules are common in some of these ma-terials. For example, a red kaolinitic clay from Kenyais composed of ‘‘crumbs’’ made up of ‘‘subcrumbs’’that can in turn break up into ‘‘sub-subcrumbs’’ thatcontain a random arrangement of individual particles(Barden, 1973). Pores are in two classes: irregularpores of about 1 �m and very small pores of about5 nm.

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STRUCTURE DEVELOPMENT 197

Figure 8.2 Structure-determining factors and processes.

Alluvial Soils

Alluvial soils can be deposited in marine, brackish wa-ter, or freshwater basins. Single clay particles are rare,and flocculated fabrics of particle groups can form inwater over the full range of salinities. Edge-to-faceflocculated and aggregated arrangements, similar toFig. 5.3e, are common in marine clays, with dispersedgroups and turbostratic groups, similar to inter-weaving bunches (Fig. 5.3h) found mainly in brackishwater clays (Collins and McGown, 1974).

Silt and sand grains are reasonably evenly distrib-uted, except in varved or stratified clays, and the largergrains are not usually in contact with each other. Openinitial fabrics are characteristic of water-laid sediments,with the degree of openness dependent on clay min-eralogy, particle size, and water chemistry, includingboth the total salt content and the monovalent/divalentcation ratio. The intensity of flocculation may be lessin brackish and freshwater deposits, so subsequentconsolidation can cause greater preferred orientation ofplaty particles and particle groups than in saltwaterclays. Very slow accumulation rates allow for morestability in open fabrics than is possible when the sed-iment accumulates rapidly.

Aggregates in illitic clay contain particle arrange-ments ranging from random to booklike. Booklikeaggregates are most common in kaolinite. The concen-tration and type of adsorbed cations usually controlsthe basic fabric units in smectite. Na–montmorillonitecan separate into unit layers, and an interwoven net-

work of filmy particles may form. Ca–montmorilloniteparticles are usually made up of several unit layers.Some heavily consolidated montmorillonites exhibitsurprisingly little preferred orientation.

There is little or no preferred particle orientation insoft marine and brackish water illitic clays, exceptwithin aggregates, whereas in soft freshwater clays,particles larger than 0.5 �m align with their long axesnormal to the direction of the consolidation pressure.In clay sediments derived from preexisting shale, theaggregates themselves may be small rock fragmentswithin which the clay plates are intensely oriented.

The open packing of sensitive postglacial clay maybe due in part to the presence of very small quartzparticles of platy morphology (Krinsley and Smalley,1973; Smalley et al., 1973). Below a critical size ofabout a cleavage mechanism appears to exist, so platyparticles of quartz and possibly other nonclay mineralsform as a result of grinding.

Organic matter in the form of microscopic animaland plant fragments, microorganisms, and organiccompounds can have a profound effect on the structureand properties of postglacial clays (Soderblom, 1966;Pusch, 1973a, 1973b). The number of bacteria in theoceans is from 1 � 109 to 3 � 1011 per m3 at depthsof 10 to 50 m beneath the surface (Reinheimer, 1971).It is probable that microorganisms were prevalent inthe ocean at the time postglacial clays were formed aswell. As organic material and clay surfaces interacted,organic matter was attached to the sedimentary aggre-

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gates. In the new environment most of the organismsdied or became dormant because of the absence of nu-trients, subsequently contributing humic acids, fulvicacids, and humus. Either aggregating or dispersing ten-dencies result, depending on the environment. Electronmicrographs of ultrathin sections (Pusch, 1973a) showorganic matter both as fluffy bodies and as distinct ob-jects associated with aggregates.

Fabric anisotropy as a result of one-dimensionalcompression after deposition will ordinarily result insome anisotropy of mechanical properties. Currents,waves, and slopes may also cause preferred orienta-tions of particles. An example for Portsea Beach sandis shown in Fig. 8.3. The long axes of elongate parti-cles show preferred orientations parallel to the coast-line and dipping landward at an angle of about 10�.

Aeolian Soils

Wind-deposited soils such as loess are characterizedby particles in the silt and fine sand ranges, althoughsmall amounts of clay are often present. These depos-its, which are usually partly saturated, are often subjectto collapse if saturated. The loose metastable fabric ismaintained by clay and light carbonate cementation atgrain contacts. The overall macrofabric can be de-scribed as bulky granular.

Directional, preferred orientation in Vicksburg (Mis-sissippi) loess was observed and described by Matal-ucci et al. (1969). The long axes of grains concentratedin an azimuth direction of 285� to 289�, with an incli-nation of 3� to 8�. A prevailing wind direction of 290�at the time of deposition was deduced from the thin-ning pattern of the loess in the area, thus accountingfor the observed three-dimensional anisotropy.

Glacial Deposits

The wide range of particle sizes within and amongglacial soils, as well as their widely varying rates ofdeposition from meltwater, produces a range of fabrictypes. The presence of small, platy quartz particles de-rived by glacial grinding was noted earlier. Many siltyand sandy ablation tills have a multimodal grain sizedistribution, with coarser particles distributed througha fine-particle matrix (McGown, 1973). The fabric ofthe matrix is variable. Many fabric forms are similarto those observed in collapsing soils (Barden et al.,1973).

Boulder clays differ from soft, sedimentary clays inthat they contain a wider range of grain sizes, withsome particles extending into the gravel to boulderranges, and they are much denser. Many boulder clayshave been subjected to high vertical and tangentialstresses as a result of readvancing ice sheets. Poor sort-ing and the presence of a large number of different

mineral types are characteristic of these materials.Well-developed domains of clay are common, andthere may be soft clay zones that bridge over somepores caused by the arching action of the large parti-cles. High past stresses on some boulder clays havedeveloped macrofabric features that include shearzones and shear planes.

Remolded and Compacted Soil Fabrics

The fabric immediately after remolding or compactinga soil depends on several factors, including strength ofpreexisting fabric units, compaction method, and com-paction or remolding effort. The general effects of dis-turbance and remolding at constant water content areto break down flocculated aggregations, destroy shearplanes, eliminate large pores, and produce a more ho-mogeneous fabric (on a macroscopic scale). Whetheror not there will be a preferred direction of particleorientation depends on the methods used. When well-defined shear planes are formed, there usually is analignment of platy particles or particle groups alongthe shear plane.

Under anisotropic consolidation conditions, platesalign with their long axes in the plane acted on by themajor principle stress. An isotropic (hydrostatic) con-solidation stress produces an isotropic fabric, providedthe fabric was isotropic at the start of consolidation.

Soil compaction can be done using different meth-ods, including impact, kneading, vibratory, and static.The method used and the initial state of the soil canhave profound effects on the fabrics of both sands andclays and on the properties of the compacted soil. Inclays, the water content is important; it controls theease with which particles and particle groups can berearranged under the compactive effort.

A major factor in formation of fabric in a compactedfine-grained soil is whether or not the compaction ram-mer induces large shear strains. If the hammer (impactcompaction), tamper (kneading compaction), or piston(static compaction) does not penetrate the soil, as isusual for compaction dry of optimum water content,then there may be a general alignment of particles orparticle groups in horizontal planes. If the soil is suf-ficiently wet of optimum that the compaction rammerpenetrates the soil surface as a result of a bearing ca-pacity failure under the rammer face, there is an align-ment of particles along the failure surfaces. A seriesof such zones is developed as a result of successiverammer blows, and a folded or convoluted fabric mayresult, as shown, for example, by Fig. 8.4.

Effects of Postformational Changes

As listed in Fig. 8.2, a large number of postformationalfactors can modify the initial structure of a soil.

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STRUCTURE DEVELOPMENT 199

Figure 8.3 Fabric and particle orientation in Portsea Beach sand (Lafeber and Willoughby,1971). (a) Vertical cross section (perpendicular to the coastline) where B is the dip directionof bedding plane, H is the horizontal plane, and I is the imbrication plane. (b) Distributionof long axis orientations.

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Figure 8.4 Microfabric of Takahata kaolin compacted wetof optimum using impact compaction �1000. Reprinted fromYoshinaka and Kazama (1973) with permission of The Jap-anese Society of SMFE.

Time Chemical diffusion and chemical reactionsare time dependent. Following deposition, remolding,or compaction, the interparticle forces, and thereforethe mechanical properties, can also change simply asa result of pore pressure redistribution in the new en-vironment.

Seepage and Leaching The flow of fluids througha soil can do at least four things:

1. Move particles.2. Cause compression due to seepage forces.3. Remove chemicals, colloids, and microorganisms

by leaching.4. Introduce chemicals, colloids, and microorgan-

isms.

Precipitation/Cementation Precipitation of mate-rials onto particle surfaces, at interparticle contacts,and in pores can produce cementation. A fabric ofpartly discernable particle groups may form.

Weathering In the zone of weathering, some ma-terials are broken down and others are formed.Changes in pore water chemistry influence the inter-particle forces and flocculation–deflocculation tenden-cies. Weathering can disrupt the initial soil fabric.

Cyclical wetting and drying and freezing and thaw-ing disrupt weak particle assemblages and intergroupassociations. Wetting generally means weakening andmay lead to collapse of some structures, particularlythose with open fabrics where particles are only

weakly bonded, such as in loess. Shrinkage associatedwith drying collapses open particle arrangements andcreates domain-type aggregates in some soils and ten-sion cracking in others. Drying concentrates clayaround sand and silt particles and between their contactpoints. Ice lens formation in frost-susceptible soils canopen cracks and fissures, followed later by collapse onthawing.

Pressure and Consolidation Consolidation underpressure usually strengthens the structure through de-crease in porosity and the formation of stronger inter-particle contacts. However, in some soils that possessbonding and cementation in their initial states, consol-idation stresses greater than some critical value canbreak down the structure, thus causing weakening andcollapse.

Temperature Transformations of structure associ-ated with leaching, precipitation, cementation, weath-ering, and pressure increase develop more rapidly athigh temperatures than at low temperatures.

Shearing Shearing collapses some structures,whereas in others, such as heavily overconsolidatedclay, it may change the structure significantly only inthe immediate vicinity (a few millimeters) of the shearplane.

Unloading Stress relief as a result of unloading canallow elastic rebound of particles and particle groupsand the onset of swelling. Some very stiff materialsmay split and/or spall after unloading.

The following sections of this chapter describe anddiscuss the structures, properties, and stability of manyof the soils identified above in more detail.

8.3 RESIDUAL SOILS

Our geotechnical understanding of residual and tropi-cal soils is much less developed than it is for sedi-mentary sands, clays, silts, and tills. This is becauseby far the greatest amount of what might be termed‘‘classical’’ geotechnical engineering has developedfrom research and projects involving sedimented soils,that is, materials that have been eroded, transported,and redeposited in a new environment. Much workwith these materials has been in areas of temperateclimate. However, the need for knowledge and under-standing of the engineering behavior of tropical resid-ual soils is great, owing to the extensive constructionworldwide in areas covered by these soils.

Residual soils differ from sedimentary soils in thatthey have formed in place in response to the localparent material, climate, topography, and drainageconditions. They may retain elements of the parentmaterial structure; they are usually nonuniform and

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RESIDUAL SOILS 201

Figure 8.5 Schematic diagram of a typical tropical residualsoil profile (from Little, 1969).

characterized by highly variable thickness or depth tobedrock. Frequently encountered residual soils includetropical soils, saprolite, and decomposed granite.

Various engineering classification systems are avail-able, and they can be categorized into three types(Wesley, 1988): (a) methods based on weathering pro-file, (b) methods based on pedological classification(see Section 8.4), and (c) methods for specific localsoils. Discussion of these systems is given by Wesley(1988) and Wesley and Irfan (1997). Due to the greatdiversity in residual soil types and properties, devel-opment of a single engineering classification systemthat has universal applicability is unlikely.

Tropical Soils

In regions of high temperature and abundant rainfall,rock weathering is intensive and is characterized bythe rapid breakdown of feldspars and ferromagnesianminerals, the removal of silica and bases (Na2O, K2O,MgO), and the concentration of iron and aluminumoxides. This process is termed laterization (Gidigasu,1972; Grant, 1974; and others) and involves leachingof SiO2 and deposition of Fe2O3 and Al2O3. A lateriteis a soil whose ratio of SiO2 to Al2O3 is less than 1.33,whereas a lateritic soil has a ratio between 1.33 and2.00 (Bawa, 1957).

With abundant rainfall, high temperature, gooddrainage, and crystalline parent materials, feldsparsweather initially to kaolinite, hydrated iron and alu-minum oxides (sesquioxides) are formed, and the moreresistant quartz and mica particles may remain. Asweathering proceeds, the content of kaolinite de-creases, and the hydrated iron and aluminum oxides(goethite and gibbsite) progressively alter to hematite(Fe2O3). Because of the high iron concentration, theresulting soils, termed oxisols, are usually red.

The tropical weathering of volcanic ash and rockleads to formation of allophane and halloysite, alongwith the sesquioxides of iron and aluminum. Smectites(montmorillonites) may also form in the early stagesof weathering of volcanic materials. Ultimately, kao-linite and gibbsite may form. Soils formed from weath-ering of volcanic ash and rocks are termed andisols.

Allophane as a clay mineral type is described inChapter 3. The term allophane soil is also used to referto andisols. They occur commonly in the Caribbean,the Andes, and the Pacific areas of the United States,Indonesia, Japan, and New Zealand. A comprehensivepresentation of the structure and properties of allo-phane soils is given by Maeda et al. (1977) and Wesley(1977).

A typical deep weathering profile in the tropics isshown schematically in Fig. 8.5. Boundaries between

the layers are not always clearly defined, and there areseveral systems for classifying them based on the de-gree of weathering and engineering properties (Little,1969; Deere and Patton, 1971; Tuncer and Lohnes,1977).

Owing to their compositions, structures, and for-mational histories, laterites and andisols have severalunique properties relative to those of typical sand andclay deposits formed from transported sediments(Mitchell and Sitar, 1982).

1. Cemented particle aggregates and clusters sus-ceptible to mechanical breakdown are common.Continued mechanical working or the removal ofsesquioxides from such soils can result in sig-nificant changes in properties. The effects ofremolding and sesquioxide removal on theclassification properties of a lateritic soil areshown in Table 8.1.

2. Air drying may cause clay size particles to formaggregates of silt and sand size and a loss ofplasticity, as shown by the data in Table 8.2. Thesignificant decrease in plasticity that resulted

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Table 8.1 Physical Properties of Unremolded, Remolded, andSesquioxide-Free Lateritic Soil

Property Unremolded RemoldedSesquioxide

Free

Liquid limit (%) 57.8 69.0 51.3Plastic limit (%) 39.5 40.1 32.1Plasticity index (%) 18.3 28.0 19.2Specific gravity 2.80 2.80 2.67Proctor density

(kN/m3)13.3 13.0 13.8

Optimum moisturecontent (%)

35.0 34.5 29.5

From Townsend et al. (1971).

Table 8.2 Effect of Air Drying on Index Properties of a Hydrated Laterite Clay from the Hawaiian Islands

Index Properties

Wet(at NaturalMoistureContent)

Moist(Partial Air

Drying)

Dry(Complete

Air Drying) Remarks

Sand content (%) 30 42 86 Dispersion prior to hydrometer testwith sodium silicate

Silt content (%)(0.05–0.005 mm)

34 17 11

Clay content (%)(�0.005 mm)

36 41 3

Liquid limit (%)Plastic limit (%)Plasticity index (%)

245135110

217146

71

NPNPNP

Soaking in water for 7 days didnot cause regain of plasticitylost due to the air drying

After Willis (1946); in Gidigasu (1974). Reprinted with permission from Elsevier Science Publishers.

from drying a number of different tropical soilsis shown in Fig. 8.6.

3. Drying may cause hardening, and this hardeningmay be irreversible in some cases. British Stan-dard BS1377 (1990) recognizes the irreversiblechanges that occur during drying and recom-mends that tropical residual soils be tested intheir natural state wherever possible.

4. The compacted dry density, plasticity index, andcompressibility of tropical residual soils arelikely to be less than the values for temperatesoils of comparable liquid limit. On the otherhand, the strength and permeability may behigher.

5. Tropical residual soils commonly are heteroge-neous in structure and texture.

6. Soils in tropical areas exist at water contentshigher than those that are desirable for mostearthwork construction. As a result, difficulties insoil handling and compaction are common.

The yielding and strength of residual soils reflect theirbonded structure. The preconsolidation pressure mayhave no connection with the stress history or overbur-den pressure on the soil. Typical preconsolidation pres-sure values of residual soils are given in Table 8.3.After yielding, residual soils exhibit large compressi-bility as a result of structure degradation and particlebreakage. A relationship between compression indexand in situ void ratio for several soils is given in Fig.8.7. Extensive discussion on the mechanical behaviorof residual soils in relation to their bonded structure isgiven by Vaughan (1988).

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RESIDUAL SOILS 203

Figure 8.6 Effect of drying on the Atterberg limits of some tropical soils (from Morin andTodor, 1975).

Table 8.3 Yield Stresses of Various Residual SoilsObtained from Odometer or K0 Triaxial Tests

Soil Type and Location Yield Stress (kPa)

Halloysite and allophone, PapuaNew Guinea 100–350

Volcanic clay 110–270Gneiss, basalt, and sandstone,

Brazil 60–450Granite, basalt, and sandstone,

Brazil 50–200Halloysite and allophone, Japan 200–550Granite, gneiss, and schist, USA 50–150Gneiss, Venezuela 50–300Volcanic ash, Indonesia and New

Zealand 200–500

After Fookes (1997).1.0 2.0 3.0 4.0

Gurl. Venezuela (Field)

From Volcanic Ash (Italy)

From Basalt (Brazil)

Seprolitic (Sea USA)

Sensitivity 8Sensitivity 4

Tuccarul, various(Brazil)

From Basalt(Brazil)

Com

pres

sion

Inde

x, C

c

Soft Clay (Canada)

Lateritic(Brazil)

From Gneiss

(Brazil)

Alloph

ane

and

Hallo

ysite

(Pap

a New

Gui

nea)

In Situ Void Ratio

1.5

1.0

0.5

Figure 8.7 Relationship between compression index, mea-sured by odometer tests and initial void ratio (after Vaughan,1988).

Saprolite

Saprolite is derived from the in situ decomposition ofparent rock and typically contains soil-like componentsand partially weathered and/or fresh rock components.Saprolites usually retain some visible remnant rockstructure, such as schistosity, relict joints, and parentrock fabric. Often the contact between saprolitic soiland the underlying parent rock is gradational and in-distinct. Although saprolites may retain much of theirrocklike appearance, they break down easily into asoil-like material. The cracks and joints in a saproliteare often filled with clay, and this can result in lowresistance to sliding when wet.

Decomposed Granite

Selective and progressive decomposition of unstableminerals in granitic bedrock breaks up the rock byspheroidal weathering, disintegration, and disaggrega-tion. Granitic rock may weather to depths of 30 m ormore and may contain mixtures of solid rock and re-sidual debris throughout most of the profile. The pro-portion of solid rock usually decreases gradually fromthe base upward.

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Figure 8.8 Zones of a mature profile of decomposed granite.

Granitic rock weathers in general accordance withBowen’s reaction series. Biotite decomposes first,followed by plagioclase feldspar. When part of theplagioclase has decomposed and breakdown of theorthoclase begins, the rock breaks into fragments ofdecomposed granite called gruss. When most of theorthoclase has weathered to kaolinite, the gruss crum-bles to silty sand, which typically contains mica flakes.Apart from some mechanical breakdown, the quartzfragments remain unchanged.

Decomposed granite profiles generally contain fourzones as shown in Fig. 8.8. The deepest zone consistsof angular granitic blocks. The amount of residual de-bris is small, although the rock may be relativelyhighly altered. The next zone above contains abundantangular to subangular core stones in a matrix of grussand residual debris. The upper middle zone is the mostvariable part of the weathering profile and typicallycontains about equal amounts of rounded core stones,gruss, and residual debris. The topmost zone usuallyconsists of an unstructured mass of clayey sand witha highly variable grain size distribution.

Construction can be difficult in areas underlain bydecomposed granite. The bedrock profile is highly ir-regular, and competent bedrock may be located at vari-able depths below the ground surface. The core stonescan present significant obstacles to excavation. Seem-ingly sound pieces of rock and gravel break downwhen excavated or used in earthwork construction. Thepresence of mica may cause cohesionless soils com-posed of decomposed granite to be highly compressi-ble.

Decomposed granite can be used successfully as anembankment fill material provided it is rememberedthat particles may undergo substantial breakage underrelatively low stresses. Breakage is greatest in materi-

als that are coarse and uniformly graded, and forhighly angular particles and particles with high intra-granular void content. Consequences of this may in-clude substantial reductions in the peak frictionalstrength with increasing confining pressure. For ex-ample, Yapa et al. (1995) found a reduction in frictionangle of 25 percent in densely compacted specimensand about 15 percent in loose specimens over the con-fining pressure range from 100 to 1500 kPa. Frictionangles assigned to decomposed granites used in 12 em-bankment dam fills constructed in California in the1960s were conservatively selected and ranged from29� to 38�. Compaction to greater than 90 percent mod-ified Proctor maximum relative compaction at opti-mum water content is recommended to minimizesettlement due to postconstruction hydrocompressionwhen the fill is wetted.

During the 1995 Kobe, Japan, earthquake, many re-claimed land sites in Kobe liquefied extensively. Thesoil used for reclamation was decomposed granitecalled Masado, which is a well-graded material withparticles ranging from gravels to fines. The liquefac-tion of this soil was surprising because of its higheruniformity coefficient and greater dry density thansandy soils. The weak and crushable character of Ma-sado particles is considered to be one of the causes.The undrained cyclic shear strength of the decomposedgranite was found to be much smaller than that of agravelly soil that had a similar particle size distributionbut with strong particles (Kokusho et al., 2004).

Colluvial Soils

Colluvium is soil that has formed in place but subse-quently has been transported down slope by gravity.Colluvial soils frequently consist of abundant parentrock fragments in a heterogeneous clayey to sandy ma-trix. They are often found on hillsides and may accu-mulate in topographic depressions or swales. Slopestability problems may be associated with thick accu-mulations of colluvium. For example, the colluviumsin Hong Kong can be up to 30 m thick, often exist ina loose state on steep slopes, and have been responsiblefor catastrophic landslides leading to significant loss oflife. (Philipson and Brand, 1985).

Pyritic Soils

Pyrite (FeS2) bearing rocks and soils are responsiblefor foundation heave, concrete degradation, steel cor-rosion, environmental damage, acid drainage, acceler-ated weathering of rock, and loss of strength andstability of geomaterials. Sulfur occurs in rock and soilin the forms of sulfide (S� or S2�), sulfate (SO4

2�), andorganic sulfur. The amount of sulfide sulfur (also

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SURFICIAL RESIDUAL SOILS AND TAXONOMY 205

known as pyritic sulfur) in a material is a good indi-cator of the potential for weathering. Sulfide-inducedheave has occurred in materials containing as little as0.1 percent sulfide sulfur (Belgeri and Siegel, 1998).

Products of pyrite oxidation include sulfate miner-als, insoluble iron oxides, such as goethite (FeOOH)and hematite (Fe2O3), and sulfuric acid (H2SO4). Sul-furic acid can dissolve other sulfides, heavy metals,and the like that are present in the oxidation zone, thusallowing the effects of oxidation to increase as theprocess builds upon itself. Sulfate crystals form in cap-illary zones and localize along discontinuities due toreduced confining stress in these regions. Volume in-crease from the growth of sulfate minerals along bed-ding planes is a dominant factor in the vertical heavethat occurs in shale and other layered materials. Theproduction of sulfates by pyrite oxidation also in-creases the potential for further deleterious reactions,such as the formation of gypsum (CaSO4 � 2H2O) andother expansive sulfate minerals (e.g., ettringite).

Pyrite oxidation processes proceed in the followingway:

7 2� 2� �–FeS � O � H O → Fe � 2SO � 2H2 2 2 2 4

2� 1 � 3� 1– –Fe � O � H → Fe � H O4 2 2 2

3� �Fe � 3H O → Fe(OH) � 3H2 3

3� 2�FeS � 14Fe � 8H O → 15Fe2 2

2� �� 2SO � 16H4

These reactions are usually catalyzed by microbial ac-tivity. The sulfuric acid that is produced is often thesource of acid rock drainage (ARD) and acid minedrainage (AMD).

Gypsum forms when sulfate ions react with calciumin the presence of water,

H SO � CaCO � H O → CaSO � 2H O � CO2 4 3 2 4 2 2

and is accompanied by very large volume increases, asthe products of pyrite oxidation reactions are signifi-cantly less dense than the initial sulfide (pyrite). Pyrite,of specific gravity (Gs � 4.8–5.1), reacts with calcite(Gs � 2.7) to create gypsum (Gs � 2.3) (Hawkins andPinches, 1997).

Mitigation options that are useful for preventing orreducing sulfide-induced problems include controllingthe pyrite oxidation process, use of restraining forcesto prevent ground movement, design measures that al-low for movement, and removal or neutralization ofacid. A recent review of geotechnical problems, heave

mechanisms, and mitigation strategies associated withpyrite-bearing soils and rocks is given by Bryant et al.(2003).

8.4 SURFICIAL RESIDUAL SOILS ANDTAXONOMY

Agricultural soil maps are often available for areaswhere engineering data are lacking. They can be usefulfor preliminary assessments of surficial soils and theirproperties. These soils are of particular importance inhighway, airfield, and land development projects. Sur-face soils are classified so that they can be aggregatedinto categories that are useful for understanding gen-esis, properties, and behavior, especially in relation toagriculture. All soils in the United States (more than11,000 in 1980) and numerous soils in other countrieshave been classified according to soil taxonomy (SoilSurvey Staff, 1975).

Soil taxonomy is a multicategory system of soil clas-sification that includes 10 orders, about 47 suborders,200 great groups, 1000 subgroups, 2000 families, and10,000 series. Unlike most classification systems, eachcategory of soil taxonomy carries elements of thehigher category so that when a soil is classified at thefamily level, the family name indicates the order, sub-order, great group, and subgroup to which the soilbelongs. The soil family name also may contain infor-mation on particle size, mineralogy, mean annual soiltemperature, pH, soil slope, and soil depth.

Soil orders and suborders of the world are related toclimate. The orders and their characteristics are givenbelow. The general characteristics of residual soil pro-files and the definitions of specific horizons within pro-files are given in Section 2.7 and Table 2.4.

Entisols (recent soils) are generally without profiledevelopment and include alluvial deposits of clay togravel, deep, soft mineral deposits such as sand dunes,loess, glacial drift, and masses of rock fragments fromimperfectly weathered, consolidated rocks. Entisolsinclude some recent, young soils formed in poorlydrained areas. In general, geotechnical engineers en-counter these soils more than any other because largeconstruction activities tend to concentrate in areaswhere these soils accumulate, such as in river valleysand in areas bounded by water. The majority of largeurban areas are located in such regions. To understandthe characteristics of these soils requires considerationof transportation, deposition, and postdepositional sed-imentary processes. These topics are considered inSection 2.8.

Vertisols (inverted soils) are deep and clayey and areknown also as black cotton, black earth, and blackland

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soils. They are associated with a climate that has verydry and very wet seasons. The texture of all horizonsis clayey, and the dominant clay mineral is smectite.The soils are expansive.

Inceptisols, or new soils, include tundra and selectedsoils of marshes, swamps, and flat areas. Tundra is adark gray, peaty accumulation over gray mottled min-eral horizons. The soil is poorly drained and boggy.The clay mineral content is low. Permafrost (perma-nently frozen soil) is frequently present in the substra-tum. Humic-gley inceptisols are mineral soils formedin poorly drained areas that possess a sticky, compact,gray, or olive-gray B or C horizon. The A horizon maycontain 5 to 10 percent organic matter.

Aridisols (arid soils) are characterized by surface ac-cumulations of salts from upward movement of water,and usually consist of several centimeters of soil overa calcareous parent material. The soils may be alkaline,with high concentrations of soluble salts of calcium,magnesium, and sodium near the surface. Illite andsmectite are common in these soils.

Mollisols generally form in cool areas having annualrainfall of 400 to 650 mm. They typically have a darkA1 horizon, and the horizon boundaries are indistinct.Smectites predominate in the clay fraction over illite.There may be local accumulations of sepiolite, paly-gorskite, and attapulgite, and calcium salts may bepresent.

Spodosols are found south of the tundras in areaswhere rainfall exceeds 600 mm/yr, and summers areshort and cool. Spodosols are characterized by mod-erate humus accumulation, a thin A1 horizon, and astrongly eluviated A2 horizon. The B horizon is darkbrown to reddish brown and often cemented by organiccompounds and iron oxides. The texture of all horizonsexcept O is often sandy. The soils are acid, have a lowcation exchange capacity, and illite dominates the clayfraction.

Alfisols are found south of the spodosol region andeast of the prairies in northeastern United States andsoutheastern Canada and in the humid, temperate areasof western Europe and eastern Asia, where rainfall av-erages 750 to 1300 mm annually. These soils are char-acterized by a thin A1 horizon (50 to 150 mm) and awell-developed gray to yellowish A2 horizon. The Bhorizon is gray to reddish brown, darker, and of finertexture than either the A or C horizons. They are acidsoils, and kaolinite is the dominant clay mineral.

Ultisols are found in areas of high temperature andhigh rain (1000 to 1500 mm/yr). Leaching is great,and mineral decay is rapid. Surface accumulation oforganic matter is small, and the leached A horizon is

deep. A relatively thick B horizon may be brightly col-ored (red and yellow) as a result of oxidation and hy-dration of iron. The B horizon has more than twice theclay content of the A horizon. The cation exchangecapacity is low in all horizons, and the clay fraction iscomposed mainly of kaolinite, illite, and quartz. Manylateritic soils of subtropical regions are ultisols.

Oxisol is an iron oxide and aluminum oxide-rich,highly weathered clayey material that changes irre-versibly to concretions, hardpans, or crusts when de-hydrated. Clay minerals are rapidly broken down andremoved. What little clay remains is usually kaolinitic.Deposits of these soils may be up to 30 m or more indepth and may range in texture from friable soils tohard rock. Some oxisols are strong and resistant tobreakdown; however, others may lose their granularcharacteristics when worked, becoming soft, clayey,and impervious. Most laterites of the tropics are oxi-sols.

Histosols, or organic soils, are bog soils whose char-acteristics depend largely on the nature of the vegeta-tion from which they form.

An 11th order, andisols was also proposed to ac-commodate the soil developed from volcanic ash.

8.5 TERRESTRIAL DEPOSITS

Aeolian Deposits

Of the various sediment transporting agents, wind isthe only one that can move material uphill for anydistance. Wind is most easily able to move sand. It isnot a universal agent of erosion, as its effects are re-stricted to areas of a particular climate such as desertsor to specific places such as beaches and plowed fields.The load suspended by the wind, which is composedprimarily of silt-size particles, is carried high above theground and may be transported for great distances. Thebed load, moved by saltation and traction, movesslowly and as a unit.

Deposition from wind occurs with reduction in windvelocity. Consequently, accumulations are found in thelee of desert areas. Coarser particles of sand, carriedby saltation and traction, pile in dunes with their longaxis parallel to the wind. Loess deposits, composed ofsilt-size particles, are of particular interest because oftheir unique structure and properties and are describedmore fully in Section 8.16.

Glacial Deposits

Several types of deposit form from glacial melting, aslisted in Table 8.4. Moraines are dropped directly from

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TERRESTRIAL DEPOSITS 207

Table 8.4 Deposits of the Glacial Environment

I. Ice Deposited MaterialA. Sediments

1. Boulder clay or till (drift includes glacial and glacio-fluvial sediments)2. Erratics

B. Structures1. Moraines

a. Lateral moraine—ribbon of debris on sides of glacierb. Medial moraine—merging of inner lateral moraines of two joining glaciersc. Englacial moraine—material within iced. Subglacial moraine—material at sole of glaciere. Ground moraine—deposited subglacial morainef. Terminal or end moraine—ridge of deposits built up at end of glacierg. Recessional moraine—terminal moraine of receding glacier

2. DrumlinsMounds of boulder clay formed under deep ice

II. Glacio-Fluvial Deposited MaterialA. Sediments

1. Coarse gravel to clay, progressively sorted dams and deltas2. Crudely bedded gravel and sand in kames and eskers

B. Structures1. Alluvial fans for glaciers terminating on land2. Outwash plains merged with fans3. Deltas for glaciers terminating in standing water4. Kettle holes caused by melting of stranded ice blocks5. Kames—mounds of crudely bedded sand and gravel caused by stream from melting ice6. Esker—winding ridge of sand and gravel from meltwater stream in ice tunnel or from receding ice

III. Glacial Lake Deposited MaterialA. Sediments

1. Sands to clay2. Poor sorting and stratification of channel deposits3. Excellent stratification of lake floor deposits

B. Structures1. Overflow channels where lake water escaped2. Shore line deposits and terraces from waves and currents3. Deltas4. Lake floor sediments including varved clays

the melting ice. There are several types of moraine,depending on where the material is dumped relative tothe ice mass, as indicated in the table. Moraines usu-ally contain a wide range of unsorted particle sizes,and the material is known as till. When large amountsof boulders and clay are present, the deposit is referredto as boulder clay. Some glacial moraines are denselycompacted owing to compression under advancing icemasses.

Glacio-fluvial deposits are transported from themelting point by flowing meltwater; kames and eskers(Fig. 8.9) are examples. Kames and eskers are poorly

sorted gravel and sand deposits. Many lateral morainesand dead ice deposits are mixed glacial and glacio-fluvial deposits.

Glacial lake deposits are quiet water sediments thatare usually composed of fine-grained materials. Varvedclay is an example (see Fig. 2.13). The formation andcharacteristics of varved clay are discussed in Section2.8.

The characteristics of a specific glacial deposit de-pend on the type and erodability of the parent material,the type and distance of transportation, gradients, andpressures. For example, bottom moraines are usually

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Figure 8.9 Glacio-fluvial sediments (Selmer-Olsen, 1964).

finer grained and more consolidated than lateral or endmoraines. Finely ground (silt and clay size) rock flouris produced by the grinding action of the ice and maybe a major constituent of postglacial marine and lakeclays found in Canada and Scandinavia.

More extensive and detailed information on glaciersand the characteristics of glacial deposits can be foundin Leggett and Hatheway (1988) and West (1995),among many other texts and references.

Alluvial Deposits

Alluvial deposits form from pluvial (high rain area)and fluvial (river) deposition and are generally char-acterized by laterally discontinuous, lenticular bedsthat are oriented downstream and have different parti-cle size characteristics. Gravels are often in contactwith sand and silt.

Deposition from streams results from a decrease inslope, increased resistance to flow, a decrease in streamdischarge, or a discharge into the more quiet waters ofoceans and lakes. As the slope flattens, the stream losesenergy, and all particles larger than a certain size aredumped in a jumble of large and small particles. Theflow then slips to one side following the steepest slope.The channel may subsequently fill, and the flow shiftsagain. When this process occurs at the base of a slope,the result is an alluvial fan, a temporary feature that isa symmetrical pile of material spread out radially fromthe point of slope change.

In advanced stages of stream development, thestream occupies only a small part of a broad, flat val-

ley. As the stream overflows its banks during floodstage, friction against the ground surface outside thechannel decreases the energy of the water, and a layerconsisting mainly of sands and gravels is dropped. Thisprocess leads to the formation of natural levees.

The alluvial valley of the lower Mississippi River isillustrative of alluvial deposits and their complexity.The valley covers and extends from Cairo, Illinois, tothe Gulf of Mexico. All types of deposits from sandsto highly plastic clays may be found at some pointwithin the valley. The fall of sea level during the laststages of glaciation led to scouring of a valley beneaththe present floodplain surface. Rising sea at the end ofthe glacial period resulted in deposition of sands andgravels in the bottom of the valley followed by finermaterial above. In the 25,000 years since the last gla-ciation, the Mississippi River has changed from anoverloaded, shallow, braided stream to a deep, single-channel, and meandering river.

The variety of deposits found within the MississippiRiver Valley is great, and their interrelationships arecomplex; however, each can be accounted for in a log-ical way in terms of the factors governing its deposi-tion and history, as described by Kolb and Shockley(1957).

The coarser materials were laid down initially in thebottom of the valley. Occasional lenses of clay, sandysilt, and silty sand are found in these substratum de-posits. The depths to these materials vary from about3 m in the north to 30 m in the southern part of theriver, and the thickness varies from 15 to 125 m in thesame direction.

Braided stream deposits are usually remote frompresent large streams. Most are relatively dense, sandysilts and clayey sands. Natural levees rise to 5 m ormore above the floodplain and decrease in grain sizeaway from the crest and in a downstream direction.

Point bar deposits composed of silts and silty sandsform on the inside of river bends during high-waterperiods. Clayey swales with high organic and watercontents form between the bars and the original riv-erbank. The alternating pervious bars and imperviousswales have been responsible for seepage problems inconnection with artificial levees. Abandoned sectionsof the river, left behind as oxbow lakes, fill with weakand compressible clay and silty clay layers with thick-nesses up to 30 m or more. Abandoned river coursesmany miles long fill with materials similar to those ofthe oxbow lakes.

Medium- to high-plasticity clays, often organic,termed backswamp deposits, form in shallow areasduring flood stage. Because of desiccation between pe-riods of deposition, they have water contents lowerthan the abandoned channel deposits.

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MARINE DEPOSITS 209

Lacustrine and Paludal Deposits

Lacustrine, or lake, deposition can occur under fresh-water or saline conditions. Gravity settling of sedi-ments discharged into saline lakes may be acceleratedby flocculation of clay particles. Saline deposition canlead to precipitation of salt beds, or evaporite deposits.

Freshwater lacustrine deposits are generally fine-grained, quiet water deposits, except for narrow shorezones of sand. As an example, large shallow lakes,present in much of the western United States duringPleistocene time, have resulted in the formation of lat-erally continuous and thick clay beds. The Corcoranclay, which covers an area of about 15,000 km2 inCalifornia’s San Joaquin Valley, forms an extensiveconfining bed and aquiclude in the valley and is a sig-nificant feature influencing groundwater development.

Paludal, or swamp, deposits usually consist of plas-tic silts, muds, and clays with high water content andorganic matter. Difficult problems may be associatedwith these deposits because of their low strength andhigh compressibility and from the formation of marshgas.

8.6 MIXED CONTINENTAL AND MARINEDEPOSITS

Littoral Deposits

Littoral deposits form in the tidal zone and consist oftidal lagoon, tidal flat, and beach sediments. Lagoonsediments include fine-grained sands and silts in thechannels and organic-rich silt and clay in the quiet ar-eas. Organic matter and carbonates may be abundant.Tidal flat deposits consist of fine-grained dark muds,with lenses or stringers of sand and gravel, and arefree of intermediate-size sediments. Beach depositsconsist of clean fine- to coarse-grained sand with oc-casional stringers of gravel.

Estuarine Deposits

Estuaries are semienclosed coastal bodies of water thathave a free connection with the sea. The sedimentsconsist of channel muds, silts, and sands deposited inresponse to seasonal river processes and tidal rhythms.Estuarine sediments typically grade seaward into fine-grained tidal deposits and landward into coarser-grained river (alluvial) deposits. Fine-grained tidal flatswith salt marshes often fringe estuaries.

Deltaic Deposits

Deltas form at the mouth of rivers where they enterthe sea. They build up where there is no tidal or current

action capable of removing the sediment as fast as itis deposited. Deltas build forward from the coastlinein a complex process that leads to the formation of anumber of separate channels, isolated lagoons, levees,marshy ground, and small streams. As a result, deltasmay consist of coarse and fine material, organic matter,and marl (a loose or friable deposit of sand, silt, orclay containing calcium carbonate). Coarse and finematerials alternate owing to the continual shifting ofthe stream. Suspended silt and clay in the main streamis flocculated by salts in the seawater to form marinemud in the seaward delta face, which is later coveredby alluvial, lacustrine, and beach deposits as the deltagrows.

The complex formations of the Mississippi Riverdelta reflect the composite effects of the advancingdelta and the encroaching sea. Pleistocene sedimentsconsisting of dense clays, sands, and gravels underliethe delta. Sand and shell beaches, often 5 m high ormore, are among the most suitable deltaic formationsfor foundation support. Conversely, difficult geotech-nical problems are associated with fine-grained and or-ganic delta sediments because of their low strength andhigh compressibility.

8.7 MARINE DEPOSITS

An averaged and idealized profile through the marineenvironment is shown in Fig. 8.10. The continentalshelf extends from low tide to an average water depthof about 130 m (nearly 450 ft). The steeper continentalslope (average of 4� leads down to the more gentlysloping continental rise. The average water depth inthe deep ocean is more than 3500 m (11,500 ft).

There are three main types of marine sediments:lithogenous (derived from terrestrial, volcanic, or cos-mic sources), biogenous (remains of marine organ-isms), and hydrogenous (precipitates from the seawateror interstitial water). An engineering classification sys-tem that incorporates compositional and depositionalcharacteristics of these sediments was developed byNoorany (1989) as shown in Fig. 8.11. This system ispatterned after the Unified Soil Classification System,the most widely used system for classification of ter-restrial soils for engineering purposes.

Biogenous sediments, formed from the remains ofmarine plants and animals, cover about half of the con-tinental shelves, more than half of the deep-sea abyssalplains, and parts of the continental slopes and rises(Noorany, 1989). They are abundant as coarse-grainedbioclastic sediments in shallow waters of the coastalzones in tropical regions (between 30�N and 30�S lat-itude).

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Figure 8.10 Idealized profile of the continental margin, with vertical exaggeration (afterHeselton, 1969).

Neritic Deposits

The neritic, or continental shelf, environment extendsto water depths of up to 200 m. In shallow water, dep-osition occurs when the intensity of wave-caused tur-bulence decreases. Generally there is a decrease inparticle size and increased influences of biological andchemical factors in the seaward direction, although thesediment distributions may be irregular due to tidalcurrents and seasonal climatic variations. Neritic de-posits reflect sediment source areas and climatic con-ditions, with sandstone, shale, and limestone typicallypresent in shelf areas. With the exception of the bi-ogenous sediments, the physical properties of conti-nental shelf deposits are essentially the same as thoseof comparable terrestrial soils.

Calcareous Sands Calcareous bioclastic sands areformed from the skeletal remains of corals, shells ofmollusks, and algae. They are widely distributed in the

oceans in tropical and subtropical regions of the world.Most consist of porous or hollow particles. An electronphotomicrograph of a calcareous sand is shown in Fig.8.12. Special geotechnical features of the calcareoussediments are (Semple, 1988) that they are composedof weak, angular particles, particle sizes and size dis-tributions are variable, there is uneven cementationover short distances, and they have high void ratio rel-ative to silicate sediments. As a result, these materialsmay be the source of special geotechnical problems.For example, the side friction developed on drivenpiles in calcareous sands is often very much lower thananticipated based on the behavior of piles in quartzsand (Noorany, 1985; Murff, 1987; Jewell et al., 1988).

Bathyal Deposits

The bathyal environment includes the continental slopeand the continental rise. Bathyal sediments are typi-

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211

Figure 8.11 Chart for classification of marine sediments (from Noorany, 1989). Reprintedwith permission of ASCE.Co

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Figure 8.12 Electron photomicrographs of calcareous sandfrom Guam. Magnification is 45� (courtesy of I. Noorany).

cally fine sand, silt, and mud of high water content andlow shear strength. The tectonic setting of the depo-sitional area and the characteristics of the continentalsource materials largely control the distribution, ge-ometry, and properties of these sediments.

Erosion, transport, and deposition of these sedimentsmay be caused by the frictional effects of contour-following undercurrents that result in thick sequencesof sediment ‘‘drift’’ consisting of alternating thin layersof very fine sands, silts, and muds (Leeder, 1982). Ap-preciable quantities of sediments can be transportedfrom the continental slope and rise to the deep-oceanabyssal plains by slumps, debris flows, and turbidityflows.

Detailed exploration of the ocean margins indicatesthat debris flows are probably a much more importantdepositional process on the seafloor than has been pre-viously suspected. For example, debris flow depositsof enormous extent have been identified that were gen-erated by large sediment slides on the northwesternAfrican continental margin. The flow traveled on aslope as flat as 0.1� for a distance of several hundredkilometers. The deposits cover an area of about 30,000km2 and originated from a massive slump of about 600km3 on the upper continental rise where a prominent

slide scar now exists. The exact triggering mechanismsfor such events are unknown in most cases; however,earthquakes are believed to be the cause of some ofthem.

Abyssal Deposits

Deep-ocean (abyssal) deposits consist primarily ofbrown clays and calcareous and silicious oozes, withthicknesses of 300 to 600 m. Terrigenous deposits arederived from land, whereas pelagic sediments settlefrom the water alone and contain the shells and skeletalremains of tiny marine organisms and plants. Accu-mulation rates range from less than a millimeter perthousand years in the deep sea to a few tens of centi-meters per year in near-shore areas close to the mouthsof large rivers (Griffin et al., 1968). Oozes containmore than 50 percent biotic material.

Calcareous ooze, composed of empty shells or tests,covers about 35 percent of the seafloor for waterdepths up to about 5 km. It is usually nonplastic, creamto white in color, and composed of easily crushedsand- to silt-size particles. Brown clay is found beneathmost of the deeper ocean areas. Its origin is believedto be atmospheric dust and fine material circulated byocean currents. About 60 percent of this material isfiner than 60 �m, and the clay fraction contains chlo-rite, smectite, illite, and kaolinite, with illite often themost abundant. Brown clays have high water contents,moderate-to-high plasticity, and low strength. Siliceousooze, composed of plant remains, is found mainly inthe Antarctic, northeast of Japan, and in some areas ofthe equatorial Pacific.

Except near their surface, deep-sea deposits are nor-mally consolidated and highly compressible. There isan apparent overconsolidation of the near-surface ma-terial at many locations. This evidently reflects bond-ing developed as a result of the extremely slow rate ofdeposition and physicochemical effects (Noorany andGizienski, 1970). Much of the available data on themechanical properties of deep-seafloor soils pertains tomaterial from the upper 6 m.

8.8 CHEMICAL AND BIOLOGICAL DEPOSITS

Evaporite deposits formed by precipitation of saltsfrom salt lakes and seas as a result of the evaporationof water are sometimes found in layers that are up toseveral meters thick. The major constituents of sea-water, their relative proportions, and some of the moreimportant evaporite deposits are listed in Table 8.5. Insome areas alternating layers of evaporite and clay or

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FABRIC, STRUCTURE, AND PROPERTY RELATIONSHIPS: GENERAL CONSIDERATIONS 213

Table 8.5 Major Constituents of Seawater and Evaporite Deposits

Ion Grams per LiterPercent by Weight

of Total Solids Important Evaporite Deposits

Sodium, Na�

Magnesium, Mg2�

Calcium, Ca2�

Potassium, K�

Strontium, Sr2�

Chloride, Cl�

Sulfate, So42�

Bicarbonate, HCO3�

Bromide, Br�

Fluoride, F�

Boric Acid, H3BO3

10.561.270.400.380.013

18.982.650.140.0650.0010.026

34.485

30.613.691.161.100.04

55.047.680.410.19—0.08

100.00

Anhydrite CaSO4

Barite BaSO4

Celesite SrSO4

Kieserite MgSO � H O4 2

Gypsum CaSO � 2H O4 2

Polyhalite Ca K Mg(SO ) � 2H O2 2 4 2

Bloedite Ma Mg(SO ) � 4H O2 4 2 2

Hexahydrite MgSO � 6H O4 2

Epsomite MgSO � 7H O4 2

Kainite K Mg (Cl/SO ) � 11H O4 4 4 2

Halite NaClSylvite KClFlourite CaF2

Bischofite MgCl � 6H O2 2

Carnallite KMgCl � 6H O3 2

Adapted from data by Degens (1965).

other fine-grained clastic sediments are formed duringcyclic wet and dry periods.

Many limestones have been formed by precipitationor from the remains of various organisms. Because ofthe much greater solubility of limestones than of mostother rock types, they may be the source of specialproblems caused by solution channels and cavities un-der foundations.

More than 12 percent of Canada is covered by apeaty material, termed muskeg, composed almost en-tirely of decaying vegetation. Peat and muskeg mayhave water contents of 1000 percent or more, they arevery compressible, and they have low strength. Thespecial properties of these materials and methods foranalysis of geotechnical problems associated withthem are given by MacFarlane (1969), Dhowian andEdil (1980), and Edil and Mochtar (1984).

Chemical sediments and rocks in freshwater lakes,ponds, swamps, and bays are occasionally encounteredin civil engineering projects. Biochemical processesform marls ranging from relatively pure calcium car-bonate to mixtures with mud and organic matter. Ironoxide is formed in some lakes. Diatomite or diatoma-ceous earth is essentially pure silica formed from theskeletal remains of small (up to a few tenths of a mil-limeter) freshwater and saltwater organisms. Com-pacted fills of diatomaceous earth can have very lowdry unit weights (1.0 to 1.2 Mg/m3) and high moisturecontents (40 percent or more). The material may be-have as a dense granular material at stresses below

about 50 kPa, owing to the roughness and interlockingof the diatoms, but becomes more compressible underhigher stresses owing to crushing of the diatoms (Day,1995).

8.9 FABRIC, STRUCTURE, AND PROPERTYRELATIONSHIPS: GENERAL CONSIDERATIONS

The variety of possible soil fabrics and the many pos-sible interparticle force systems associated with eachmean that the potential number of soil structures isalmost limitless. The mechanical properties of a soilreflect the influences of the structure to a degree thatdepends on the soil type, the structure type, and theparticular property of interest. The effects of structurecan be of equal importance to those of initial void ratioand stress. In this sense, structure refers to the differ-ences between the actual void ratio and effective stressand the corresponding values for the same soil in thedestructured state. The difference between void ratiounder a given effective stress for a soil with somestructure, which is the case for consolidation of virtu-ally all sediments from a high void ratio, and the voidratio of a completely destructured soil is illustrated inFig. 8.13.

It is possible that a soil can be at state to the rightof the virgin compression curve in Fig. 8.13 as a resultof bonding by chemical cementation or aging effects.Thus the full range of possible states in void ratio–

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Figure 8.13 The influence of metastable fabric on void ratio under and effective consoli-dation pressure.

Figure 8.14 Possible states in void ratio–effective stress space.

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FABRIC, STRUCTURE, AND PROPERTY RELATIONSHIPS: GENERAL CONSIDERATIONS 215

Figure 8.15 (a) One-dimensional compression curves forseveral clays. (b) Normalized compression curves definingthe intrinsic compression line (ICL) (from Burland, 1990).

effective stress space is greater than shown in Fig.8.13, as may be seen in Fig. 8.14. Virgin compressionfrom an initial state at o to a is followed by the de-velopment of bonding, which enables the soil to resistadditional compressive stress a–b. At point b the soilis under effective stress . The completely destruc-��btured soil under the same stress would be at point d.The difference in void ratios between the structuredsoil at b and the destructured soil at d results from abonding contribution b–c and a fabric contributionc–d.

Figure 8.15a shows one-dimensional compressioncurves for various reconstituted clays with a widerange of plasticities. The void index, was proposed byBurland (1990) for correlating the compression behav-ior of different clays and for assessing the influence ofstructure on properties. The void index Iv is defined as

e � e*100I � (8.1)v C*c

in which e is the void ratio, is the ‘‘intrinsic’’ voide*100

ratio under an effective vertical stress of 100 kPa inthe one-dimensional odometer test, and is the in-C*ctrinsic compression index. The intrinsic properties aredetermined for a reconstituted samples of clay thathave been prepared at a water content of about 1.25times the liquid limit. The intrinsic compression curvescan be normalized as shown in Fig. 8.15b.

Knowledge of the intrinsic compression curve isuseful because the departure of a compression curvefor the soil in its natural state from the intrinsic com-pression curve indicates the existence of soil structureresisting the applied load. Figure 8.16a shows the sed-imentation compression curves of several marinedeposits reported by Skempton (1970). The watercontents (or void ratios) of naturally sedimented clayswere plotted against the in situ vertical effective over-burden stress. The normalized compression curves,termed the sedimentation compression line (SCL), areshown in Fig. 8.16b along with the intrinsic compres-sion curve, termed the intrinsic compression line(ICL).

At a given void ratio, the effective overburden pres-sure carried by a sedimented clay is approximately fivetimes the pressure that can be resisted by the equivalentreconstituted clay owing to the fabric and soil structuredeveloped during sedimentation and postdepositionalprocesses. For instance, the compression curves of afreshwater glacial lake clay lie well above the sedi-mentation compression line and the intrinsic compres-sion line before yielding as shown in Fig. 8.17. Oncethe loading exceeds the preconsolidation pressure, the

soil structure degrades and the compression curvesmove toward the intrinsic compression curve. A gen-eralized view of in situ states of natural soils in relationto the void index and vertical overburden pressure isgiven in Fig. 8.18 (Chandler et al., 2004).

Several principles relate the fabric and structure ofa soil to the mechanical properties of interest in engi-neering:

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Figure 8.16 (a) Compression curves for several clays (from Skempton, 1970). (b) Normal-ized compression curves for clays in (a) showing the intrinsic compression line (ICL) andsedimentation compression line (SCL).

1. Under a given effective consolidation pressure,a soil with a flocculated fabric is less dense thanthe same soil with a deflocculated structure.

2. At the same void ratio, a flocculated soil withrandomly oriented particles and particle groupsis more rigid than a deflocculated soil.

3. Once the maximum precompression stress hasbeen reached, a further increment of pressurecauses a greater change in fabric of a flocculatedsoil structure than in a deflocculated soil struc-ture.

4. The average pore diameter and range of poresizes is smaller in deflocculated and/or destruc-tured soils than in flocculated and/or undis-turbed soils.

5. Shear displacements usually orient platy parti-cles and particle groups with their long axesparallel to the direction of shear.

6. Anisotropic consolidation stresses tend to alignplaty particles and particle groups with theirlong axes in the major principal plane.

7. Stresses are usually not distributed equallyamong all particles and particle groups. Some

particles and particle groups may be essentiallystress free as a result of arching by surroundingfabric elements, as discussed further in Chapter11.

8. Two samples of a soil without cementation canhave a different structure at the same void ratio-effective stress coordinates if they have differentstress histories. In Fig. 8.19, a sample initiallyat point a on the virgin compression curve candeform to point b as a result of disturbance andreconsolidation or by secondary compressionunder stress stained for a long time. A sam-��aple initially at c can reach point b as a result ofunloading from . The stress–deformation��cproperties of the two samples will differ. Theoverconsolidation ratio (OCR), defined as theratio of the maximum past consolidation effec-tive stress to the present overburden effectivestress is a good measure of stress history. TheOCR of sample 2 in Fig. 8.19 is �� /��.c a

9. Volume change tendencies determine pore pres-sure development during undrained deforma-tion.

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SOIL FABRIC AND PROPERTY ANISOTROPY 217


10. Changes in structure of a saturated soil at con-stant volume are accompanied by changes in ef-fective stress. These effective stress changes areimmediate.

11. Changes in structure of a saturated soil at con-stant effective stress are accompanied bychanges in void ratio. The change in void ratiois not immediate but depends on the time forwater to drain from or enter the soil.

Figure 8.20 illustrates points 9, 10, and 11. For anysaturated, destructured soil there is a unique relation-ship between combinations of void ratio and effectiveconsolidation pressure termed the critical state orsteady state line, as discussed in more detail in Chapter11. If the soil is on this line, there is no tendency forchange in volume during shear deformation. However,if the state of the soil is in the region above and to theright of the critical state line it will either contract if

the rate of deformation is slow or positive pore pres-sures will be generated if deformation is rapid. On theother hand, if the soil is initially at a state in the di-lative zone, slow deformation will be accompanied byswelling and rapid deformation will be accompaniedby generation of negative pore pressures. In general,normally consolidated to slightly overconsolidatedclays and saturated loose sands are contractive,whereas heavily overconsolidated clays and densesands are dilative.

8.10 SOIL FABRIC AND PROPERTYANISOTROPY

Anisotropic consolidation, shear, directional transpor-tation components, method of remolded or compactedsoil preparation, and compaction of soil in layers eachmay produce anisotropic fabrics. Fabric anisotropy on

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Figure 8.17 Compression curves for freshwater glacial lake clay at pressures below andabove yield (from Burland, 1990).

Figure 8.19 Illustration of different paths to reach the samepresent void ratio–effective stress state.

Figure 8.18 Void index in relation to stress states for dif-ferent clay types (from Chandler et al., 2004).

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Figure 8.20 Initial state in relation to the critical-state or steady-state line and its influenceon pore pressure or volume changes during deformation.

a macroscale usually leads to mechanical property an-isotropy, and the property differences in different di-rections may be significant. Examples of anisotropicfabrics in sands are given in Figs. 5.9 and 5.10.

Some examples are presented in this section to il-lustrate the general nature and magnitudes of aniso-tropy in properties that may be associated with ahomogeneous anisotropic fabric. These considerationsare separate from property anisotropy caused by strat-ification of different soil layers, although the latter maybe very important in the field, especially with respectto fluid flow. Additional analysis and discussion of theeffects of fabric and stress anisotropy on soil stress–deformation and strength are given in Chapter 11.

Sands and Silts

The strength of crushed basalt, both along and acrossthe direction of preferred orientation of grains, isshown in Fig. 8.21. Preferred orientation of the some-what elongated particles (mean particle length to widthratio � 1.64) was obtained by pouring the soil into ashear box. Intense preferred orientation was obtainedat moderate relative densities, as shown by Fig. 5.11.At the lower relative densities the strength was about40 percent greater across the plane of particle orien-tation than along it. As shown by Fig. 8.21, this dif-ference decreased with increasing density, and forrelative densities above 90 percent, the strengths in thetwo directions were the same. This is consistent with

the finding that as the density increased the intensityof preferred orientation decreased. The sample stiff-ness, as measured by the ratio of stress to shear dis-placement at 50 percent of peak strength, was abouttwice as high for shear across the direction of preferredorientation than parallel to it.

Figure 8.22 shows the variation in friction angle asa function of the loading direction in plane strain andtriaxial compression in relation to the initial beddingplane measured on dense Toyoura sand specimens(Park and Tatsuoka, 1994). The term � is the angle ofthe bedding plane relative to the maximum principalstress direction, and the measured friction angles arenormalized by the friction angle in plane strain com-pression with � � 90�. The friction angle is the lowestwhen the loading direction is approximately at � � 30�.This is partly because the failure shear plane coincideswith the bedding plane. The friction angles in triaxialcompression are generally less than those in plainstrain compression due to the intermediate stress effect(see Chapter 11). Less bedding effect is also observedin triaxial compression because multiple shear planesat different directions are often produced in triaxialcompression samples, whereas fewer, but more dis-tinct, shear plane are observed in plane strain com-pression.

The orientations of contact planes between particleshave significant influence on the stress–strain and vol-ume change behavior of granular soils when they are

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Figure 8.21 Effect of shear direction on strength of samplesof crushed basalt prepared by pouring into a shear box (fromMahmood and Mitchell, 1974).

Figure 8.22 Variation of friction angles in plane strain andtriaxial compression as a function of principal stress directionrelative to bedding plane orientation (from Park and Tat-suoka, 1994).

sheared in different directions. The contact plane ori-entation can be represented by the normal to the plane��, as shown in Fig. 5.12. Probability density functionsE(�) of these normals for four sands are shown in Fig.5.13. The fabric of each sand was formed by pouringthe sand through water into a cylindrical mold fol-lowed by tapping to attain the desired density. FromFig. 5.13 it may be noted that there was considerableanisotropy in particle contact orientations for sandswith rodlike or flat particles and for sands with nearlyspherical particles.

Triaxial compression tests were done on samples ofthese sands with different maximum principal stressdirections � relative to the original horizontal plane.The results of these tests for Toyoura sand (b in Fig.5.13) are shown in Fig. 8.23. Toyoura sand is com-posed of elongated, flat particles having an axial ratioof 1.65, but similar results were obtained also for theTochigi sand (Fig. 5.13d). The results of these andother tests reported by Oda (1972a) included tests atdifferent relative densities. They illustrate importantaspects of anisotropic granular soil fabric on mechan-ical properties, for example:

1. The stress–strain and volume change behaviorare different for different principal stress direc-tions.

2. The effects of fabric anisotropy are somewhatgreater in sand with elongated grains than in sandwith more spherical grains.

3. The deformation modulus and dilation decreaseas the angle � decreases from 90� to 0� for sandfabric formed by pluviation.

4. The stress–strain–volume change properties ofdense sand tested at � � 0� are comparable tothose for loose samples tested at � � 90�.

5. The secant modulus at 50 percent of peakstrength decreases with decreasing values of �.The ratio of E50 for � � 90� to that at � � 0� is2 to 3 for dense sand.

Overall, the major influence of anisotropy of gran-ular soil fabric, as measured by both particle long axisorientations and interparticle contact orientations, is togive different volume change (dilatancy) tendencies,which, in turn, give different stress–deformation andstrength behavior for different directions of loading.

Fabric and mechanical property anisotropy are alsofound in undisturbed sands and silts in the field. Un-disturbed samples of Vicksburg loess exhibit up to 12percent higher strength when sheared perpendicular tograin orientation than parallel to it (Matalucci et al.,1970). The friction angle measured in triaxial tests de-creased from 34� to 31� for dry loess and from 24� to

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Figure 8.23 Effect of initial fabric anisotropy on stress–strain and volume change behaviorof Toyoura sand. Angle � is between major principal stress direction and the original hori-zontal plane (from Oda, 1972a). Reprinted with permission of The Japanese Society ofSMFE.

21� for moist samples as the direction of the majorprincipal stress was changed from normal to the pre-ferred orientation of particles to 45� to it.

Anisotropic fabric in undisturbed Portsea Beachsand is shown in Fig. 8.3. The effect of this anisotropyon the behavior in triaxial compression was studied by

testing undisturbed samples1 cut as shown in Fig. 8.24.

1 To handle undisturbed sand samples, Lafeber and Willoughby(1971) used a two-stage replacement of the original seawater by pol-yethylene glycol (Carbowax 4000). Triaxial tests were done after firstheating the samples to melt the Carbowax.

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Figure 8.24 Orientations of triaxial cylinders of Portsea Beach sand in relation to in situconditions (Lafeber and Willoughby, 1971).

Table 8.6 Effect of Sample Orientation on SecantModulus of Undisturbed Samples of Portsea BeachSand

SampleAxis

Direction

SampleAxis

Azimuth

SecantModulus(kN/m2)

StandardDeviation(kN/m2)

Vertical 5.41 � 104 �0.27 � 104

Horizontal Parallel tocoastline 4.01 � 104 �0.24 � 104

Horizontal 30� withcoastline 3.85 � 104 �0.18 � 104

Horizontal 60� withcoastline 3.76 � 104 �0.23 � 104

Horizontal Perpendicu-lar tocoastline 3.55 � 104 �0.53 � 104

Data from Lafeber and Willoughby (1971).

Values of mean secant modulus for samples at differentorientations are given in Table 8.6. There are signifi-cant differences among samples tested in different di-rections, and there is no horizontal plane of isotropyfor deformation modulus.

Collectively, the results of studies of the effects offabric anisotropy on properties of granular soils showthe following:

1. Anisotropic fabric, as indicated by particle ori-entations and interparticle contact orientations, islikely in natural deposits, compacted fills, andlaboratory samples.

2. Anisotropic fabrics produce anisotropic mechan-ical properties.

3. Strengths and deformation moduli are higher forshear directions across planes of preferred ori-entation than along them.

4. The magnitude of strength and modulus aniso-tropy depends on density and the extent to whichparticles are platy and elongated. Differences inpeak strength of the order of 10 to 15 percentmay exist when the axial ratios of particles are1.6 or greater.

5. Differences in moduli in different directions aregreater than differences in peak strength. Moduliin different directions may differ by a factor of 2or 3.

6. The effect of fabric anisotropy on mechanicalproperty anisotropy is primarily through differ-ences in volume change tendencies for defor-mation in different directions.

Clays

Clay fabric anisotropy studies in clays have dealtmainly with effects on strength and hydraulic conduc-tivity. Undrained strength anisotropy results from stressanisotropy during consolidation, apart from any pos-

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SAND FABRIC AND LIQUEFACTION 223

sible fabric anisotropy. In terms of the effective stressstrength parameters c� and ��, analysis of the effectsof stress anisotropy by Brinch-Hansen and Gibson(1949) leads to

c c�u � cos �� (1 � K ) sin ��(2A � 1)0 ƒp p2c c ��u u 2� � (1 � K ) cos 45 � � � � � � �0p p 2

2 1/21 � K0� � � �2(8.2)

where cu is undrained shear strength, p is vertical con-solidation pressure, K0 is the coefficient of lateral Earthpressure at rest, and � is the inclination of the failureplane to the horizontal. The pore pressure parameter

is defined asAƒ

uƒA � (8.3)ƒ ( � � � )1 3 ƒ

where uƒ is the change in pore water pressure at fail-ure, and ( �1 � �3)ƒ is the deviator stress at failure.

The degree of mobilization of c� and �� at peakstress difference and the strain at failure in an un-drained test vary with orientation of principal stresses.Data on the variation of undrained compressivestrength with orientation of the failure plane are sum-marized in Fig. 8.25. Strengths in the vertical and hor-izontal directions may differ by as much as 40 percentas a result of fabric anisotropy. The differences in un-drained strength in the different directions result fromdifferences in pore pressures developed during shear(Duncan and Seed, 1966; Bishop, 1966; Nakase andKamei, 1983; Kurukulasuriya et al., 1999). The effec-tive stress strength parameters are independent of sam-ple orientation. The drained strength is independent ofshear stress orientation relative to fabric orientation, asdemonstrated by tests on kaolin (Duncan and Seed,1966; Morgenstern and Tchalenko, 1967b). Stresspaths for two samples from a clay with anisotropicfabric but isotropic initial stresses are shown schemat-ically in Fig. 8.26.

The facts that both the effective stress strength pa-rameters and the drained strength are independent offabric anisotropy, but that pore pressures developed inundrained shear are strongly influenced by anisotropy,suggest that the effect of fabric anisotropy on strengthis the same for both sands and clays. Changes in stressorientation relative to fabric orientation influence vol-

ume change tendencies. This, in turn, influences thedilatancy contribution to the strength of sands and thevolume changes in drained deformation and the porepressures in undrained shear of clays.

Anisotropy of soil fabric and natural stratificationare responsible for higher hydraulic conductivities inthe horizontal direction than in the vertical directionfor most soil deposits, and this topic is discussed inmore detail in Section 9.3.

8.11 SAND FABRIC AND LIQUEFACTION

If saturated sand is at a void ratio above the critical-state or steady state line (Fig. 8.20) and sheared rap-idly, it will try to densify. As water cannot escape fromthe pores instantaneously, the collapsing structure willtransfer normal stress to the pore water. The accom-panying decrease in effective stress reduces the shearstrength to a low value, and the soil mass liquefies.Cyclic loading due to earthquakes is perhaps the mostcommon cause of dynamic liquefaction. The resistanceto liquefaction depends on characteristics of the sand,including gradation, particle size, and particle shape;relative density; confining pressure; and initial stressstate. A comprehensive review of the state of knowl-edge of the causes and effects of soil liquefactionduring earthquakes was published by the NationalResearch Council (NRC, 1985) and by Kramer (1996).

Liquefaction depends on a sand’s resistance to de-formation and the degree to which rapidly appliedshear stresses cause a tendency for the structure to re-duce in volume or collapse. Since samples of the samesand at the same density but having different fabricshave different stress–strain and volume change prop-erties, see Section 8.8, it follows that different fabricsshould influence liquefaction resistance as well. Figure8.27 shows for three sands that preparation of samplesby two different methods produced distinctly differentresistances to liquefaction, as measured by the numberof load cycles to cause liquefaction at a particular valueof cyclic stress ratio. The cyclic stress ratio for thesetests was defined as the ratio of half the cyclic deviatorstress to the initial effective confining pressure.

The differences in liquefaction behavior result fromdifferences in the sand fabric owing to different samplepreparation methods (Mitchell et al., 1976). Resultssimilar to those in Fig. 8.27 are shown in Fig. 8.28 forsamples of Monterey No. 0 sand at a relative densityof 50 percent prepared by three different methods.Similar behavior was measured for samples of thesame sand at a relative density of 80 percent (Muliluset al., 1977). Monterey No. 0 sand is a uniform me-

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Figure 8.25 Variation of compressive strength with orientation of failure plane (from Dun-can and Seed, 1966). Reprinted with permission of ASCE.

Figure 8.26 Stress paths in triaxial compression for differently oriented samples for claywith anisotropic fabric.

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SAND FABRIC AND LIQUEFACTION 225

Figure 8.27 Influence of sand sample preparation method on liquefaction resistance (fromMulilis et al., 1977). Reprinted with permission of ASCE.

Figure 8.28 Liquefaction resistance of Monterey No. 0 sand prepared to a relative densityof 50 percent by three methods (Mulilus et al., 1977).

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Figure 8.29 Influence of sample preparation method ondrained triaxial compression behavior of Monterey No. 0sand at 50 percent relative density.

dium sand with rounded to subrounded grains consist-ing predominantly of quartz with some feldspar andmica.

That the fabrics were different for the different prep-aration methods was determined by analysis of particlelong axis and interparticle contact on normal orienta-tions measured on thin sections cut through thesamples. Pluviation resulted in distinct preferredorientation of particle long axes in the horizontal di-rection. Moist vibration produced the most random ori-entation of particle long axes, with moist tampinggiving intermediate values. The results of static triaxialcompression tests (Fig. 8.29) showed stress–strain andvolume change behavior consistent with the observedfabrics and liquefaction resistance. That is, the weakestand least dilative material was that prepared by drypluviation, and the strongest and most dilative materialwas prepared by moist vibration.

From results such as these, it is clear that relativedensity by itself is insufficient for characterization ofthe sand properties. This means that sand samples re-constituted in the laboratory ordinarily cannot be usedfor determination of properties that are representative

of undisturbed sand in the field since the field fabricis not usually known, and undisturbed samples are vir-tually impossible to obtain. It also explains partiallywhy such heavy reliance is placed on the results of insitu tests such as the standard penetration test and thecone penetration test for assessment of the in situ liq-uefaction resistance of sand deposits.

Of several laboratory methods that can be used toprepare sand samples, pluviation usually produces themost compressible and weakest fabrics at any relativedensity. Thus this method can be used to obtain a lowerbound or most conservative estimate of the propertiesthat the same sand at the same relative density canhave in the undisturbed state in the field. Most sandsin situ are stronger because of prestressing effects, ag-ing, and cementation. The difference between the plu-viated sample lower bound values and the actual in situvalues can be large. A corollary of this is that undis-turbed sand deposits can suffer a stress loss on distur-bance; that is, they are sensitive in the same way asmany clay deposits owing to loose metastable struc-tures.

8.12 SENSITIVITY AND ITS CAUSES

As noted at the beginning of this chapter, early con-cepts of fabric and structure in geotechnical engineer-ing were developed, at least in part, to explain the lossof undrained strength when undisturbed clay is re-molded. Although virtually all normally consolidatedsoils exhibit some amount of sensitivity, quick clay, asillustrated in Fig. 8.1, is the most sensitive. Large de-posits of this material, which turns into a heavy viscousfluid on remolding, are found in previously glaciatedareas of North America and Scandinavia.

The ratio of peak undisturbed strength (Sup) to re-molded strength (Sur), as determined by the unconfinedcompression test, was used initially as the quantitativemeasure of sensitivity St (� Sup /Sur) (Terzaghi, 1944).The remolded strength of some clay is so low, how-ever, that unconfined compression test specimens can-not be formed. Therefore, the vane shear test is oftenused to measure sensitivity, both in the field and in thelaboratory, as is also the Swedish fall-cone test (Swed-ish State Railways, 1922; Karlsson, 1961).

Several classifications of sensitivity have been pro-posed; one of them is given in Table 8.7. Marine clayswith high salinity may exhibit considerable sensitivityup to 30 (Torrance, 1983). Clays become quick notbecause the undisturbed strength becomes very highbut because the remolded strength becomes very low.Salt leaching is a requirement for the development ofvery high sensitivity of more than 100. Leaching de-

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SENSITIVITY AND ITS CAUSES 227

Table 8.7 Classification of Clay Sensitivity Values

St

Insensitive �1.0Slightly sensitive clays 1–2Medium sensitive clays 2–4Very sensitive clays 4–8Slightly quick clays 8–16Medium quick clays 16–32Very quick clays 32–64Extra quick clays �64

From Rosenqvist (1953).

Figure 8.30 Photomicrograph of undisturbed Leda clay, airdried. Picture width is 8 �m (Tovey, 1971).

creases the liquid limit of low-activity clays and con-sequently the remolded strength, while the void ratioremains essentially constant or decreases only a smallamount.

Composition of Sensitive Clays

Quick clays may not differ from clays of low sensitiv-ity in terms of mineral composition, grain size distri-bution, or fabric. Most quick clays are postglacialdeposits, with the mineralogy of the clay fraction dom-inated by illite and chlorite and that of the nonclayfraction by quartz and feldspar. Amphibole and calciteare also common. The activity of quick clays is usuallyless than 0.5. The pore fluid composition and thechanges in composition that have developed betweenthe time of deposition and the present are of paramountimportance. Changes in the type and amount of elec-trolyte, organic compounds, and small quantities ofsurface-active agents are controlling factors in the de-velopment of quick clay.

Fabric of Sensitive Clays

With the possible exception of strongly cemented soils,the undisturbed fabric of sensitive clays is composedof flocculated assemblages of particles or aggregates.Electron photomicrographs show open and flocculatedparticle arrangements in medium sensitive to quickclays. The contribution of fabric to high sensitivity isthrough open networks of particles and aggregates thatare linked by unstable connections. The fabric of un-disturbed Leda clay is shown in Fig. 8.30. A very widerange of particle sizes may be seen.

The microfabric of quick clay and that of adjacentzones of much less sensitive clay may be the same.Thus, while an open flocculated fabric is necessary, itis not a sufficient condition for quick clay develop-ment. Some preferred orientation might develop in

quick clays as a consequence of delayed or secondarycompression. This compression can be accelerated asa result of leaching of salts during formation of thedeposit (Torrance, 1974).

Causes of Sensitivity

At least six different phenomena may contribute to thedevelopment of sensitivity:

1. Metastable fabric2. Cementation3. Weathering4. Thixotropic hardening5. Leaching, ion exchange, and change in the

monovalent/divalent cation ratio6. Formation or addition of dispersing agents

Metastable Fabric When particles and particlegroups flocculate and/or pack inefficiently, the initialfabric after deposition is open and involves someamount of edge-to-edge and edge-to-face associationsin a cardhouse arrangement of elongate and platy par-ticles. A consequence of this is well illustrated by thesedimentation compression line relative to the intrinsiccompression line in Fig. 8.16b. During consolidationthis fabric can carry effective stress at a void ratiohigher than would be possible if the particles and par-ticle groups were arranged in an efficient, parallel ar-ray. When saturated soil is mechanically remoldedfrom a state such as represented by point 1 in Fig. 8.13,the fabric is disrupted, effective stresses are reducedbecause of the tendency for the volume to decrease,and the strength is less.

If the original consolidation stress is reapplied, thenthere will be additional consolidation, and the void ra-

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Figure 8.31 Stress–strain characteristics of kaolinite–sandmixtures illustrating the effects of disturbance.

tio will decrease to a point as represented by 2 in Fig.8.13. Mechanical remolding and reapplication ofstresses will cause consolidation to point 3, and con-tinued repetition of the process will lead ultimately toa minimum void ratio for the fully destructured soil atn. Thus, if the soil is at any state within the shadedzone of Fig. 8.13, it will have some degree of metas-tability of structure and could be further consolidatedif disturbed and recompressed.

Sensitivity values resulting from metastable particlearrangements were measured in undrained triaxial testson saturated kaolinite samples consolidated from highinitial water content (Houston, 1967). They decreasedfrom 12 at high water content and low consolidationpressure to 2 at low water content and high consoli-dation pressure. Consolidated, undrained triaxial com-pression tests on saturated sand–kaolinite mixturesconsolidated initially under an effective stress of 200kPa gave the results shown in Fig. 8.31. The loss instrength due to disturbance was accompanied by alarge increase in pore water pressure and decrease in

effective stress to almost zero from the initial value of200 kPa. This illustrates the interdependence of effec-tive stress and structure, as well as the effects of struc-ture metastability.

A point of practical importance is that the continu-ing generation of metastable fabrics following distur-bance explains why some sand deposits have beenobserved to reliquefy at the same locations in succes-sive earthquakes.

Cementation Many soils contain carbonates, ironoxide, alumina, and organic matter that may precipitateat interparticle contacts and act as cementing agents.On disturbance, the cemented bonds are destroyedleading to a loss of strength. Four naturally cementedCanadian clays tested by Sangrey (1970) had sensitiv-ities of 45 to 780.

Late glacial plastic clay from near Lilla Edit in theGota Valley of Sweden has a sensitivity of 30 to 70.The apparent preconsolidation pressure as determinedby odometer tests is much greater than the maximumpast overburden pressure (Bjerrum and Wu, 1960).When consolidation pressure greater than this apparentmaximum past pressure is applied, there is a markedreduction in cohesion. This was interpreted to resultfrom a rupture of cemented interparticle bonds thatwere created by carbonation of microfossils and or-ganic matter and precipitation of pore water salts atparticle contacts. Removal of carbonates, gypsum, andiron oxide by leaching with EDTA (a disodium salt ofethylene-diaminetetraacetic acid) resulted in a markedreduction in the apparent preconsolidation pressure ofquick clay from Labrador (Bjerrum, 1967).

A quasi-preconsolidation effect (Leonards and Ra-miah, 1960) results if clay remains under constantstress for a long period. Whether or not the additionalresistance is due to a true chemical cementation is de-batable; however, the effect is the same, and an in-crease in sensitivity results.

Weathering Weathering processes change the typesand relative proportions of ions in solution, which, inturn, can alter the flocculation–deflocculation tenden-cies of the soil after disturbance. Some change in theundisturbed strength is also probable; however, the ma-jor effect on sensitivity is usually through change inthe remolded strength. Strengths and sensitivities maybe increased or decreased, depending on the nature ofthe changes in ionic distributions (Moum et al., 1971).

Thixotropic Hardening Thixotropy is an isother-mal, reversible, time-dependent process occurring un-der conditions of constant composition and volumewhereby a material stiffens while at rest and softens orliquefies upon remolding. The properties of a purelythixotropic material are shown in Fig. 8.32. Thixo-

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Figure 8.32 Properties of a purely thixotropic material.

tropic hardening may account for low to medium sen-sitivity and for a part of the sensitivity of quick clays(Skempton and Northey, 1952).

The mechanism of thixotropic hardening is ex-plained as follows (Mitchell, 1960). Sedimentation,remolding, and compaction produce soil structurescompatible with these processes. Once the externallyapplied energy of remolding or compaction is re-moved, however, the structure is no longer in equilib-rium with the surroundings. If the interparticle forcebalance is such that attraction is somewhat in excessof repulsion, there will be a tendency toward floccu-lation of particles and particle groups and for reorgan-ization of the water–cation structure to a lower energystate. Both effects, which have been demonstrated ex-perimentally, take time because of the viscous resis-tance to particle and ion movement.

The effect of time after disturbance on the pressurein the pore water is particularly significant. Severalstudies show that there is a continual decrease in porewater pressure, or increase in pore water tension, withtime after compaction or remolding. Figure 8.33 andRipple and Day (1966) show that shear of thixotropicclay pastes causes an abrupt decrease in pore watertension (increase in pore water pressure) followed byslow regain during periods of rest. The concurrenttime-dependent increase in effective stress accounts forthe observed increase in undrained strength.

The importance of thixotropic hardening in contrib-uting to the sensitivity of clay in the field is impossibleto determine. Laboratory studies start with a specificpresent composition and density. The initial state of aclay deposit in nature is usually far different than atthe present time, and the history of an undisturbed claybears little resemblance to that of a remolded sample

of the same clay that is allowed to rest at constantwater content and pore fluid composition. However, theresults of studies on samples allowed to harden startingfrom present composition suggest that sensitivities upto about 8 or so may be possible due to thixotropy(Skempton and Northey, 1952; Seed and Chan, 1957;Mitchell, 1960).2

Leaching and Changes in Monovalent/Divalent Cat-ion Ratios Reduction in salinity of marine clay byleaching is an essential first step in the development ofquick clay, as first suggested by Rosenqvist (1946).Freshwater leaching following a drop in sea level orrise in land level results in removal of the seawaterenvironment. Percolating freshwater in silt and sandlenses is sufficient to remove salt from the clay bydiffusion without the requirement that the water flowthrough all the pores of intact clay (Torrance, 1974).

Although leaching causes little change in fabric, theinterparticle forces are changed, resulting in a decreasein undisturbed strength of up to 50 percent, and sucha large reduction in remolded strength that quick clayforms. The large increase in interparticle repulsion isresponsible for the deflocculation and dispersion of theclay on mechanical remolding. It results in part fromthe decrease in electrolyte concentration causing in-crease in double-layer thickness. Changes in strengthand the increase in sensitivity accompanying the leach-ing of salt from a Norwegian marine clay are shownin Fig. 8.34. The relationship between sensitivity andsalt content for several Norwegian marine clays isshown in Fig. 8.35. Confirmation of the leaching hy-pothesis was obtained by means of leaching tests onartificially sedimented clays (Bjerrum and Rosenqvist,1956). Asrum clay sedimented in saltwater (35 g/liter)and then leached of salt exhibited an increase in sen-sitivity from 5 to 110. A sample sedimented in fresh-water had a sensitivity of 5 to 6.

Although leaching of salt is necessary, it may not besufficient for the development of quick clay. The saltcontent of Champlain clay in eastern Canada rarelyexceeds 1 to 2 g/liter and is usually less than 1 g/liter,yet the sensitivities of different samples range from aslow as 10 to over 1000 (Eden and Crawford, 1957;Penner, 1963c, 1964, 1965). The reason for this largerange is that the essential condition for developmentof quick clay is an increase in interparticle repulsions.Considerations in Chapter 6 show that the type of cat-ions and the relative amounts of monovalent anddivalent cations have a controlling influence onequilibrium particle arrangements.

2 Sherard (1975, personal communication) indicated that thixotropicstrength ratios of up to 100 have been measured in Champlain clay.

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Figure 8.33 Effect of shear on pore water tensions for various clays (after Day, 1955).

The electrokinetic or zeta potential in Champlainclay, as determined using electroosmosis (see Chapter9), correlates well with sensitivity, as shown in Fig.8.36 (Penner, 1965). The electrokinetic potential is ameasure of the double-layer potential, with higher val-ues associated with thicker double layers and highersensitivity. For clays of low salinity (�1 or 2 g salt /liter of pore water) the sensitivity correlates well withthe percent of monovalent cations in the pore water,

also shown in Fig. 8.36. The percent monovalent cat-ions in the pore water is given by

� �Na � K� 100

� � 2� 2�Na � K � Ca � Mg

with all concentrations in milliequivalents per liter. Thedependence of sensitivity on monovalent to total cation

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Figure 8.34 Changes in properties of a normally consoli-dated marine clay when subjected to leaching by freshwater(Bjerrum, 1954).

ratio was also shown by Moum et al. (1971). An anal-ysis in terms of sodium adsorption ratio (Section 6.15)leads to a similar result (Balasubramonian and Mor-genstern, 1972).

The percent monovalent cation in seawater is onlyabout 75 on a meq/liter basis. Thus, according to therelationship in Fig. 8.36, if seawater is leached withoutchange in the relative concentrations of Na�, K�,Mg2�, and Ca2�, very high sensitivities cannot develop.Selective removal of divalent cations is necessary. Inquick clay, Ca2� and Mg2� are removed from the sys-tem, possibly by organic matter (Soderblom, 1969;Lessard and Mitchell, 1985). The mechanism by whichthese changes occur as deduced by Lessard (1981) issummarized as follows.

Organic matter from marine organisms deposits si-multaneously with the illite, feldspar, and quartz thatconstitute the bulk of a postglacial marine clay. Ironoxide minerals are also present in small quantities. Asthe depth of burial increases with continued deposition,so does the distance to oxygen supply from the sea-water above.

Bacterial oxidation of the organic matter depletesthe oxygen content of the pore water, and an anaerobicenvironment develops that reduces ferric oxides to sol-uble ferrous iron. Simultaneously, sulfates in the porewater are reduced to hydrogen sulfide by the organicmatter with the aid of sulfate-reducing bacteria. Theformation of iron sulfide materials then follows:

2�Fe � H S → black amorphous FeS2

→ slowly crystallizes → FeS (pyrite)2

The amount of FeS and FeS2 produced is limited bythe rate of diffusion of sulfate from the overlying sea-water and/or by the amount and reactivity of detritaliron.

Carbon dioxide generated by the bacterial oxidationof organic matter produces an increase in alkalinity(pH increase) and decrease in the amount of dissolvedCa2� and Mg2�, as the latter precipitate as Mg–calcite.All of these transformations can occur in a period ofonly several years.

If the deposit is uplifted above sea level, sulfate be-comes scarce, oxidation of organic matter is slow be-cause of the depleted O2 content, and sulfides remainstable. Freshwater leaching decreases the salt content,which in combination with the low Ca2� and Mg2�

concentrations that result from the sulfate reductionprocesses, provides the necessary conditions for theexistence of a quick clay, that is, low-salt content, highpercentage of monovalent cations in the adsorbed lay-ers on the clay particles, and high pH.

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Figure 8.35 Relationship between sensitivity and salt concentration for some Norwegianclay deposits (Bjerrum, 1954).

Aging of Quick Clay Samples

Important changes in the properties of quick clays havebeen observed to develop with time after sampling,including increases in remolded strength and liquidlimit and decrease in the liquidity index, all withoutchange in water content. For example, the changes thatoccurred in remolded quick clay from Outardes-2 inQuebec over a 1-year period are shown in Fig. 8.37.Changes such as these mean that laboratory tests onaged samples can give results that are misleading rel-ative to the clay properties in situ. The liquidity index,see Section 4.5, is useful for expressing and comparingthe consistencies of different clays, as it normalizes thewater content relative to the plasticity index.3

3 Similarly, the void index, Iv [Eq. (8.1)] is often used for correlatingthe compression behavior of different clays and for assessing theinfluence of structure on properties (Burland, 1990; Cotecchia andChandler, 2000; Jardine et al., 2004).

e � e*100I �v C*c

From studies on the quick clay from LaBaie, Que-bec, it was possible to explain the transformations thatcause changes in properties after sampling, such asthose shown in Fig. 8.37 (Lessard and Mitchell, 1985).Geotechnical properties of the LaBaie clay determinedwithin one month after sampling are shown in Fig.8.38. This clay is composed primarily of rock flourcontaining plagioclase, K-feldspar, quartz, amphibole,and calcite, with about 10 percent illite and traceamounts of kaolinite and chlorite.

Samples of the LaBaie clay were stored under dif-ferent conditions. The changes in remolded strength,liquidity index, pH, and concentrations of several iontypes as a function of storage time are shown in Fig.8.39. These results show that aging leads to increasesin both pore water salinity and the concentrations ofdivalent cations in the pore water and decreases in pH.Collectively, the compositional changes are responsiblefor increase in remolded strength (Fig. 8.37) and de-crease in liquidity index (Fig. 8.39) because eachdepresses the double layer, thereby decreasing theinterparticle repulsive forces. The remolded strength

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Figure 8.36 Relationship between sensitivity and monova-lent cations in low-salt-content clays and between sensitivityand electrokinetic potential (data from Penner, 1965).

correlates well with both the concentration of divalentcations and the total cation concentration, as shown inFig. 8.40. The method of storage (see Fig. 8.39) doesnot affect the correlations shown in Fig. 8.40; rather,it influences the time required for the chemical con-centration changes to occur.

These changes in chemistry and properties arecaused by the following sequence of events. Whenquick clay is sampled or exposed, some contact withthe air and oxygen is inevitable. This air causes someof the remaining organic matter to oxidize and formcarbonic acid, which, in turn, dissolves calcium car-bonate, thus increasing the concentrations of calciumand bicarbonate in the pore water. Even extremely lowpartial pressures of O2 are sufficient to initiate oxida-tion phases of the sulfur cycle. The oxidation of pyrite

forms sulfuric acid and ferric hydroxide. The reactionscan be rapid at high pH. Slow transformation ofFe(OH)3 to yellow goethite (FeO–OH) may give abrownish color to the clay.

The sulfuric acid reacts with the Mg–calcite to in-crease the concentrations of Ca2� and Mg2� in the porewater and in the adsorbed complex on the clay parti-cles. Concurrently, sodium and potassium are dis-placed from the double layer to the pore water. Thesalinity increases, and the increase in concentrations ofthe divalent cations causes increases in the remoldedstrength and the liquid limit and decreases in the sen-sitivity and liquidity index. More complete descrip-tions of the reactions, including phase diagrams andreaction kinetics are given by Lessard (1981) and Les-sard and Mitchell (1985). An important role of bacteriain mediating the oxidation and reduction reactionsassociated with quick clay formation and aging issuggested. The importance of geochemical andmicrobiological processes in geotechnical engineeringhas been given little attention in the past. Future stud-ies of the phenomena and processes are likely to pro-vide important new insights and understanding.

Significance of Aging in Practice

The aging of quick clays shows how even seeminglysmall changes in environmental conditions can resultin significant changes in properties. These changes canoccur over times typical of those associated with thefield and laboratory phases of many projects, for ex-ample, from several weeks to a few months. If extremecare is not exercised during sample storage, laboratorytests may give misleading results. Simple pH measure-ments at the time of sampling and again at the time oftesting can provide a rapid and easy means for assess-ing whether aging processes have occurred. To mini-mize the aging effects the exposure of samples to airshould be minimized, thick wax caps should be usedwith rust-free sample tubes, and samples should bestored at low temperatures to slow down reaction rates.

Summary of Sensitivity-Causing Mechanisms

The six causes for the development of sensitivity dis-cussed above are summarized in Table 8.8. An estimateof the upper limit of sensitivity for each mechanism isalso given. Virtually all natural soils, including manysands, are sensitive in that they lose some strength ondisturbance and remolding. Exceptions are heavily ov-erconsolidated stiff fissured clays that can gain strengthbecause of the elimination of fissures and planes ofweakness. Quick clays are formed from soft glacialmarine clays only after removal of excess salt by leach-ing and further increase in double-layer repulsions as

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Figure 8.37 Changes in the remolded strength and consistency of a Canadian quick clay asa function of time (Lessard, 1978).

Figure 8.38 Geotechnical characteristics of the quick clay from LaBaie as a function ofdepth (after Lessard, 1981).

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PROPERTY INTERRELATIONSHIPS IN SENSITIVE CLAYS 235

Figure 8.39 Effect of time and storage conditions on theproperties of LaBaie quick clay.

Figure 8.40 Dependence of remolded strength on cationconcentration in LaBaie quick clay.

a result of an increase in the relative proportion ofmonovalent cations (mainly sodium) in the pore waterand increase in pH. More than one mechanism maycontribute to the total sensitivity of any one soil.

8.13 PROPERTY INTERRELATIONSHIPS INSENSITIVE CLAYS

The geotechnical properties of normally consolidated,noncemented sensitive clays fit a pattern that is pre-dictable in terms of sensitivity, liquidity index, and ef-fective stress using the concepts given in the precedingsections.

General Characteristics of Sensitive Clays

Glacial and postglacial clays of high and low sensitiv-ity exhibit significant differences, as shown by the pro-files in Fig. 8.41 for a normal clay from Drammen anda quick clay from Manglerud, both in Norway. One ofthe most important of these differences is that at Man-glerud the water content is well above the liquid limit;that is, the liquidity index is greater than 1.0. This ischaracteristic of quick clays.

Plasticity and Activity When normal clays are con-verted to highly sensitive or quick clays by the chem-ical changes described in Section 8.12, the liquid limit,plasticity index, and activity decrease. These changesare reflected by an increase in the liquidity index atconstant effective stress. The liquid limit of highly sen-sitive clay is usually less than 40 percent and rarelygreater than 50 percent. Plastic limit values are usuallyabout 20 percent. The activity of most normal inor-ganic marine clays is of the order of 0.5 to 1.0,whereas the activity of quick clays can be as low as0.15. The sensitivity of a given clay type usually cor-relates uniquely with liquidity index, as may be seenin Fig. 8.42 for Norwegian marine clays.

Pore Pressure Parameter, [Eq. (8.3)] High poreAƒ

pressures are developed when sensitive soils aresheared. For some quick clay, pore pressures as highas two times the peak deviator stress have been mea-sured. Loose sand may develop excess pore pressureequal to the initial confining effective stress whensheared rapidly without drainage, thereby losing itsstrength completely.

Undrained Shear Strength to Consolidation PressureRatio, Su /p The Su /p ratio (often indicated as the c /p ratio) decreases with increasing sensitivity, rangingfrom 0.3 or more for normally consolidated insensitiveclays to less than 0.1 for quick clays. This is illustratedby Fig. 8.43 for normally consolidated clay. In thisfigure the consolidation pressure p is taken as the over-

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Table 8.8 Summary of the Causes of Sensitivity in Soils

MechanismApproximate Upper Limit

of Sensitivitya Predominant Soil Types Affected

Metastable fabric Slightly quick (8–16) All soilsCementation Extra quick (�64) Soils containing Fe2O3, Al2O3, CaCO3, free

SiO2

Weathering Medium sensitive (2–4) All soilsThixotropic hardening Very sensitiveb ClaysLeaching, ion exchange, and change in

monovalent /divalent cation ratioExtra quick (�64) Glacial and postglacial marine clays

Formation or addition of dispersingagents

Extra quick (�64) Inorganic clays containing organic compoundsin solution or on particle surfaces

aAdjectival descriptions according to Rosenqvist (1953).bPertains to samples starting from present composition and water content. Role of thixotropy in causing sensitivity in

situ is indeterminate.

burden vertical effective stress, and CIUC means� ,vo

isotropically consolidated undrained compression testswere used for determination of strength.

Stress–Strain Relationships In general, strain atfailure decreases with increasing sensitivity. Somequick clays are quite brittle during unconfined loadingand fracture at very low strains, sometimes by axialsplitting. Further working of the fractured specimenmay cause it to turn into a fluid mass.

Compressibility The compressibility of highly sen-sitive clays is relatively low until the consolidationstress exceeds the preconsolidation pressure. It then in-creases sharply as shown by Fig. 8.44 for Champlainclay. As the void ratio reduces under higher consoli-dation pressures, the compressibility eventually as-sumes a lower value.

Property, Effective Stress, and Water ContentRelationships

Consolidation Because the initial structure dependson many factors and the volume changes under pres-sure are a function of structure, a soil does not have aunique consolidation curve. All states and compressioncurves must be above the curve for the fully destruc-tured material.

Strength of Normally Consolidated Soil The higherthe effective stress at a given water content, the greaterthe undrained strength because of increased frictionalresistance between particles. For constant effectivestress, strength increases with decreasing water contentbecause of increased dilatancy. Thus the general be-havior shown in Fig. 8.45 is observed.

Sensitivity As each point on the curves for fullydestructured soil in Figs. 8.13 and 8.14 represents com-pletely remolded material, the sensitivity at any pointon this curve must be unity. Thus this curve is a lineof constant sensitivity or sensitivity contour. Saturatedclay at a given water content and pore fluid composi-tion cannot be made weaker than its thoroughly re-molded strength. Therefore, a water content–effectivestress relationship to the left of that for the fully de-structured soil is not possible. The undisturbed strengthincreases with increasing effective stress at constantwater content (Fig. 8.45), and the sensitivity at allpoints to the right of the fully destructured soil curveis greater than 1. Thus, the maximum gradient of sen-sitivity increase is generally normal to the contour forthe fully destructured soil.

Pore Pressure Parameter, The pore pressure atAƒ

failure is controlled by the tendency of the soil to dilateor contract. Thus decreases with decreasing waterAƒ

content at constant initial effective stress. At constantwater content, the lower the effective stress, the easierit is for the soil to dilate since less energy is requiredfor expansion against low pressures than high. There-fore, the maximum gradient of is as shown in Fig.Aƒ

8.46.Strain at Failure Restrained dilation increases ef-

fective stress, thus increasing shearing resistance. Con-sequently, the deformation required to cause failureincreases with increasing dilation. On the other hand,strain at failure should decrease with increase in Aƒ

because varies inversely with dilation tendencies.Aƒ

Consequently, the maximum positive gradient of strain

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PROPERTY INTERRELATIONSHIPS IN SENSITIVE CLAYS 237

Figure 8.41 Soil profiles for marine clays of low and high sensitivity (from Bjerrum, 1954).

at failure should be opposite to the maximum gradientfor .Aƒ

Example of Relationships The results of triaxialcompression tests on kaolinite (Houston, 1967) illus-trate the above relationships. By consolidating differentsamples from several different initial water contentsand remolding and reconsolidating them in variousways, samples covering a range of initial effectivestress and water content values, each reflecting a dif-ferent structure, were obtained. The results of un-drained triaxial tests yield values of strength,

sensitivity, , and strain at failure. Contours based onAƒ

these values are shown in Fig. 8.47. The variations inthe measured values are in general accord with thepredictions stated previously.

Sensitivity–Effective Stress–Liquidity IndexRelationship

General relationships between sensitivity, effectivestress, and water content can be established based onnormalization of the remolded strength versus water

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Figure 8.42 Sensitivity as a function of liquidity index forNorwegian marine clays. Relationship was averaged frommany more data points than those shown (data from Bjerrum,1954).

Figure 8.43 Normalized undrained shear strength of nor-mally consolidated clay as a function of liquidity index (fromBjerrum and Simons, 1960). Reprinted with permission ofASCE.

Figure 8.44 Consolidation curves for Champlain (Leda)clay. Reproduced with permission from the National Re-search Council of Canada, from the Canadian GeotechnicalJournal, Vol. 3, pp. 61–73, 1966.

Figure 8.45 Gradient of strength increase with water contentand effective stress variation.

content relationship. The liquidity index (LI) providesa basis for this normalization. A unique relationshipbetween sensitivity, liquidity index, and effective stressexists if:

1. The LI–effective stress relationship is the samefor thoroughly remolded specimens of all clays.This relationship is the contour for a sensitivityof 1.0.

2. The relationship between remolded strength andliquidity index is the same for all clays.

3. At any value of liquidity index, the variation ofSu /p with effective consolidation pressure is thesame for all clays. This fixes the undisturbedstrength in terms of LI and effective stress.

These conditions hold sufficiently well for most sen-sitive clays. Remolded shear strength as a function of

liquidity index for several clays is shown in Fig. 8.48.The data points in this figure were based on fall-conetests for determination of the liquidity index. Thewider band of values reported by Houston and Mitchell(1969) resulted, at least in part, from the use of dif-ferent methods for determination of the strength andliquidity index values. A general relationship betweenthe undrained shear strength of the remolded clay andthe liquidity index for the heavy curve in Fig. 8.48 is

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DISPERSIVE CLAYS 239

Figure 8.46 Gradient of pore pressure parameter withAƒ

water content and effective stress variations.

1S � (kPa) (8.4)u 2(LI � 0.21)

The following equation that can be deduced fromSharma and Bora (2003) also fits the relationship de-fined by Eq. (8.4) well:

2 wLlog � � log � � � log (8.5)LL log(w /w ) wL p

In Eq. (8.5) � is the undrained strength and w, wL, andwp are the water content, liquid limit, and plastic limitvalues.

By averaging data for several clays, the relationshipbetween liquidity index, effective stress, and sensitivityshown in Fig. 8.49 is obtained. Figure 8.49 is also validfor moderately overconsolidated clays, provided thepreconsolidation pressure is used instead of the presenteffective stress. This is because the water content andundrained strength depend more on the preconsolida-tion pressure than on the present effective stress. Somedeviations from the values in Fig. 8.49 are to be ex-pected because of the extensive averaging used in itspreparation. These deviations may be greatest for extraquick clays because of the very low remolded strength,the difficulty in determining it accurately, and its con-trolling influence on the calculated value of sensitivity.Nonetheless, the relationships in Figs. 8.48 and 8.49can be used to estimate sensitivity and strength whenundisturbed samples or in situ strength data are not

available, to estimate changes in strength and sensitiv-ity due to change in effective stress or liquidity index,and as a guide for extrapolating a small amount of datato a larger pattern. A very similar approach that relatessensitivity, stress state, and void index Iv is proposedby Cotecchia and Chandler (2000) and Chandler(2000).

8.14 DISPERSIVE CLAYS

Some fine-grained soils are structurally unstable, easilydispersed, and, therefore, easily eroded. Soils in whichthe clay particles will detach spontaneously from eachother and from the soil structure and go into suspen-sion in quiet water are termed dispersive clays. Theconsequences of the exposure of dispersive clays towater may be several, as shown by Figs. 8.50 and 8.51.The surface erosion pattern on an excavated slope,which is characteristic of ‘‘badlands’’ topography, isshown in Fig. 8.50. Erosion tunnels in a flood controldike are shown in Fig. 8.51. Failures of this type haveoccurred in well-constructed, low homogeneous dams.

In each case shown, the soil contained readily dis-persed clay particles that went easily into suspensionin flowing water. Failures of this type have occurred inembankments, dams, and slopes composed of clayswith low-to-medium plasticity (CL and CL–CH) thatcontain montmorillonite. Dispersive piping in damshas occurred either on the first reservoir filling or, lessfrequently, after raising the reservoir to a higher level.

Dispersive clay failures are usually initiated whenwater flows into small cracks and fissures. When a res-ervoir is filled for the first time, settlement may accom-pany saturation of the soil, particularly if the soil wasplaced dry of optimum and not well compacted. Set-tlement below the phreatic surface and arching aboveit can result in crack formation. Water moving throughthe crack picks up dispersive clay particles, with therate of removal increasing as the seepage velocity andsize of opening increase. This is a fundamentally dif-ferent mechanism than erosive piping, which developsand works backward from the discharge face. Tunnel-ing has been initiated in soils with a hydraulic con-ductivity as low as 1 � 10�7 m/s.

Visual classification, Atterberg limits, and particlesize analyses do not provide a basis for differentiationbetween dispersive clays and ordinary erosion-resistantclays. However, relatively simple chemical tests, a dis-persion test, a ‘‘crumb’’ test, and the pinhole test (Sher-ard et al., 1976) can be used for identification ofdispersive clays.

In the pinhole test, distilled water is allowed to flowthrough a 1.0-mm-diameter hole drilled through acompacted specimen. If the soil is dispersive, the water

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Figure 8.47 Strength properties of normally consolidated kaolinite as a function of effectivestress and water content: (a) shear strength, (b) strain at failure, (c) pore pressure parameter

, and (d ) sensitivity.Aƒ

becomes muddy and the hole rapidly erodes. For non-dispersive clays the water remains clear and there isno erosion. The pinhole test and test procedure aredescribed in ASTM Standard D4647-93 (1998)(ASTM 2000).

As noted in Section 6.15, the exchangeable sodiumpercentage (ESP) is a strong indicator of potential dis-persive behavior, with an ESP greater than 2 indicatingpossible dispersion, and an ESP greater than 10 to 15

indicating probable dispersive clay behavior in soils ofrelatively low total salt concentration in the pore water.As determination of the ESP requires measurement ofboth the cation exchange capacity and the amount ofsodium in the exchange complex, it is not a simple orrapid method for identification of dispersive clay. Asimpler chemical measure of potential dispersivity,supported by the results of tests on many samples, wasproposed by Sherard et al. (1972, 1976) that is based

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DISPERSIVE CLAYS 241

Figure 8.48 Relation between shear strength of remoldedclay and liquidity index (from Leroueil et al., 1983). Repro-duced with permission from the National Research Councilof Canada.

Figure 8.50 Erosion pattern in excavated slope of sensitiveclay (courtesy of J. L. Sherard).

Figure 8.49 General relationships between sensitivity, liquidity index, and effective stress.

on the percent sodium in the saturation extract from asoil–water paste. This correlation is shown in Fig.8.52.

Many subsequent tests have shown, however, thatthe zones in Fig. 8.52 are not always reliable indicatorsof dispersibility. For example, Craft and Acciardi(1984) found that only 62.3 percent of 223 sampleswere classified correctly. This is not surprising because

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Figure 8.51 Erosion damage on the crest of 5-m-high floodcontrol dike caused by rain runoff concentrating in dryingcracks, Rio Zulia, Venezuela (courtesy of J. L. Sherard).

Figure 8.52 Relationship between dispersibility (susceptibility to colloidal erosion) and dis-solved pore water salts based on pinhole tests and field observations. SAR � sodium ab-sorption ratio, Eq. (6.33). Concentrations in meq/ liter (from Sherard et al., 1976). Reprintedwith permission of ASCE.

whether or not a soil will exhibit dispersive behaviordepends not only on its chemical and mineralogicalcomposition but also on its state, as reflected by watercontent, density, and structure, on the chemistry of thewater to which it is exposed, and on the specific con-ditions of exposure, including temperature, confining

pressure, and velocity of flowing water. The influenceof the chemistry of the water used for evaluation ofdispersibility was illustrated by the results of pinholetests on compacted samples of shale by Statton andMitchell (1977). A decrease in pH of the eroding waterto less than about 4, using hydrochloric acid, or anincrease to greater than about 11, using calcium hy-droxide or sodium hydroxide, caused a change fromdispersive to nondispersive behavior. Similarly, in-creasing the salt concentration of the water at its nat-ural pH of 6.3 to 0.1 N CaCl2 or 0.5 N NaCl causederosion of the dispersive clay to stop.

In the dispersion test the percentage of particles finerthan 5 �m is determined by hydrometer analyses ofsamples with and without dispersing agent in the sus-pension water (Sherard et al., 1972). The higher theratio of percentage material finer than 5 �m by weightmeasured in the test without dispersing agent to thatmeasured in the test with a dispersing agent, thegreater the probability of dispersion in the field. Thisratio, when expressed as a percentage, is termed thepercent dispersion. Values greater than 20 to 25 percentindicate that dispersion may be a problem. Valuesgreater than 50 percent are nearly always indicative ofsoils susceptible to severe erosion damage initiated byclay dispersion.

In the crumb test a small clod of the soil is placedin a beaker and submerged in water. If the soil clod is

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COLLAPSING SOILS AND SWELLING SOILS 243

initially dry, it will often slake. If it is dispersive, clayparticles will go into suspension in the quiet water, andthe zone around the clod will become cloudy.

Of the several tests developed for identification ofdispersive clays, the pinhole test is considered the mostreliable. But even with this test, it is important that thesamples correctly simulate the soil state and the watercomposition to be expected in the field.

Several methods can be used to mitigate the adverseeffects of dispersive soils. The addition of 2 to 3 per-cent hydrated lime during construction will usuallyconvert a soil to a nondispersive form. Filters that aredesigned to retain small particle sizes should be usedon the discharge side of dams and dam cores. For anexisting dam, in which tunneling erosion is expectedto develop, lime can be added at the upstream face tobe carried inward by the percolating water. Additionalstrategies were suggested and evaluated by Sherard andDecker (1977).

8.15 SLAKING

Most fine-grained soils slake after exposure to air andsubsequent unconfined immersion in water; an initiallyintact piece of soil will disintegrate into a pile of piecesor sediment of small particles. This disintegration maybegin immediately upon immersion or develop slowlywith time. Slaking usually is more rapid and vigorousin materials that have been dried prior to immersioncompared to the same material immersed at its initialwater content. Whether a material slakes or not hasbeen proposed as a basis for distinguishing betweensoil and rock (Morgenstern and Eigenbrod, 1974). Theslaking of hard clays and clay shale is a concern in thestability of open excavations and the shale durabilitywhen it is used as an aggregate or rockfill for construc-tion.

From controlled tests on relatively pure samples ofdifferent clays (Moriwaki and Mitchell, 1977) and onclay shales (Seedsman, 1986), four modes of disinte-gration were identified. These are:

1. Dispersion Slaking Particles of clay detachfrom the surface of the intact clay by dispersioninto the adjacent water.

2. Swelling Slaking Water is adsorbed by the clayand the material swells and softens.

3. Surface Slaking Aggregates of clay particlesspall off the surface and accumulate as sedimentin the adjacent water.

4. Body Slaking The material splits and disinte-grates into pieces, and the failure appears to de-velop from the inside out.

Three mechanisms are responsible for these modesof failure. Dispersion, which is dependent on the clayand water chemistry, was described in the precedingsection. Swelling slaking results from stress relief andwater intake due to water adsorption and osmoticforces. Compression of entrapped air in partially sat-urated soils is responsible for body slaking and, tosome extent, for surface slaking. Rapid water absorp-tion into the material compresses the air, which, inturn, exerts tensile stresses on the soil structure. If thestructural strength is insufficient to withstand thesestresses, then the material splits apart. Seedsman(1986) found that the slaking mechanism was relatedto the bulk density, and the higher the density the moreresistant the material to slaking by any mode.

8.16 COLLAPSING SOILS AND SWELLINGSOILS

Large areas of Earth’s surface, particularly in the Mid-west and Southwest United States, parts of Asia, SouthAmerica, and southern Africa, are covered by soils thatare susceptible to large decreases in bulk volume whenthey become saturated. Such materials are termed col-lapsing soils. Collapse may be triggered by water aloneor by saturation and loading acting together. Soils withcollapsible structures may be residual, water deposited,or aeolian. In most cases, the deposits have a loosestructure of bulky shaped grains, often in the silt-to-fine-sand range. Collapsible grain structures are leftbehind in residual soils as a result of leaching of sol-uble and colloidal material. Water- and wind-depositedcollapsing soils are usually found in arid and semiaridregions and are a consequence of the loose fabrics andweak structures that form.

Debris flows (mudflows and torrential stream depos-its) are deposited suddenly and locally, and may forma loose, metastable structure. Torrential stream sedi-ments, in particular, form a loose, poorly graded ma-terial. Some small amount of clay is present that servesas a binder for the deposit after it dries. Some cemen-tation may also develop because in the arid climateswhere such deposits form, water moves upward toevaporate, leaving behind its content of dissolved salts.If subsequently wetted, the loose structure can collapseand cause large settlements.

When a large canal was constructed through the SanJoaquin Valley during the 1960s to carry water fromnorthern California to southern California, it was nec-essary to cross many collapsible debris flow deposits.In order to minimize future settlements of the canaland appurtenant structures as a result of canal leakage,

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Figure 8.53 Loess deposit. Note vertical slopes.

Figure 8.54 Compression properties of Missouri River basinloess (from Clevenger, 1958). Reprinted with permission ofASCE.

extensive preponding was carried out before construc-tion of the canal.

Soils susceptible to large collapse as a result of wet-ting can be identified using a density criterion. If thedensity is sufficiently low that the void space is largerthan needed to hold the liquid limit water content, thencollapse problems are likely (Gibbs and Bara, 1967).If the void space is less than that needed for the liquidlimit water content, then collapse is not likely unlessthe soil is loaded.

Loess deposits are widespread throughout the mid-western United States and parts of Asia. This material,which is wind-blown silt, is light brown in color, crum-bly, and essentially devoid of stratification. The par-ticles are predominantly silt size and composed offeldspar and quartz. A small amount of clay, usuallyless than 15 percent, may be present. Smectite is theusual clay mineral type. Calcite may be present inamounts up to 30 percent and can act as weak cementthat precipitates along the sides of vertical root holesand at interparticle contacts. Densities of undisturbedloess may be as low as 1.2 g/cm3, and the naturalwater content of metastable deposits of loess is low,on the order of 10 percent. Most loesses plot near theA-line on the plasticity chart.

Because of vertical root holes formed by gradualburial of grassy plains, the absence of stratification,and light cementation, loess cleaves on vertical planes,and vertical faces cut in loess are quite stable, as shownin Fig. 8.53. In fact, if inclined slopes are cut, they willgradually erode back to a series of steplike verticalfaces.

The low density and light cementation of the loessstructure make it susceptible to collapse. When main-tained dry, it is reasonably strong and incompressible.The porous structure may persist even beneath 60 mof overburden. When saturated, however, loess depos-its may lose their stability. Compression due to satu-ration alone may be small, but with a surcharge, it maybe very large, as shown in Fig. 8.54. Watering lawnsaround new houses founded on loess has been knownto cause large settlements. If saturated loess deposits

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are subjected to dynamic loading, such as from anearthquake, there may be instantaneous liquefactionand large flow slides. The undisturbed density of a lo-ess deposit may be a fair indicator of the potentialsettlement and loss of strength that may result fromsaturation. Detailed information about the nature andbehavior of Mississippi loess, a widespread loess de-posit, is given by Krinitzky and Turnbull (1967).

8.17 HARD SOILS AND SOFT ROCKS

Among the continuum of soils and rocks that are en-countered in engineering and construction, very heav-ily overconsolidated fine-grained soils and mudstones,shales, and siltstones are sometimes among the mostdifficult to deal with. It is not always clear whethersuch materials should be treated as soil or rock. If be-havior is rocklike, the material can be used in earth-work construction like a rock and placed in thick liftswithout much compaction. If the shale is susceptibleto break down, however, it must be treated as a soiland placed in thin, well-compacted lifts. If considereda rock and subsequent deterioration under the actionsof stress, water, and chemical change causes break-down, loss of strength and increase in compressibility,then there can be failures. Conversely, if the durabilityand mechanical properties are too conservatively as-signed, then unnecessary overdesigns and excessivecosts may result.

Shale is a prime example of a material that illus-trates the soft rock-hard soil problem. According toTerzaghi et al. (1996):

Shale is a clastic sedimentary rock mainly composed ofsilt-size and clay-size particles. Most shales are laminatedand display fissility; the rock has a tendency to split alongrelatively smooth and flat surfaces parallel to the bedding.When fissility is completely absent, the clastic sedimentarydeposit is called mudstone, or clay rock.

Unweathered, intact shale, although considerablyweaker and less durable than most igneous and meta-morphic rocks, may still have adequate resistance andlong-term stability to be stable on cut slopes or to beused as an embankment fill or stable pavement sub-grade. On the other hand, many shales that appear in-tact and rocklike when exposed or excavated can haveproperties that deteriorate with time. The problems,then, are to determine whether degradation is likely,and if so, how much and how fast.

Degradation, apart from that caused by mechanicalprocesses such as unloading, compression, crushing,and shearing, is usually by slaking (see Section 8.15)initiated by exposure to air, moisture, and changedchemical environment. Cementation shales are likely

to be more durable over the long term than compactionshales, unless exposure to water and ions in solutionleads to dissolution of the cementing material. Pyriteor sulfates in sedimentary rocks can be the cause ofgeochemical processes, often catalyzed by microbio-logical activity, that result in heave and loss of theintact rock strength. This deterioration can occur intime periods as short as a few months. Chemically non-durable shales are likely to be especially troublesomein environments with pH less than 6. Recommenda-tions for identifying these materials are given by Noble(1977, 1983).

Knowledge of the geologic history of a deposit, themineralogical and chemical composition, and the newloading and exposure conditions provides initial in-sights about whether shales, siltstones, and sandstonescan be expected to degrade. Accelerated weatheringand durability tests are used to classify shale durability.Tests used for this purpose have been described andreviewed by Huber (1997). They include water adsorp-tion, wet–dry, freeze–thaw, jar slaking, crushing, pointload strength, ultrasonic disaggregation, and slakedurability tests in which the breakdown of shalesubmerged in a rotating wire basket (Franklin andChandra, 1972) is determined. The results of thesetests form the basis of several shale durability classi-fication systems that have as their goal to distinguishshales that cause problems from those that do not. Oneof the first such systems was developed by Underwood(1967) for engineering evaluations. Table 8.9, adaptedfrom Underwood’s study, is a listing of physical andcomposition properties associated with the indicatedtypes of unfavorable behavior. It may be seen that therange of most properties within which unfavorable be-havior is likely to develop is rather broad, which meansthat any single test or observation by itself is unlikelyto be sufficient for confirmation of favorable or unfa-vorable behavior.


This chapter is concerned with how residual and trans-ported soil deposits are formed, how the formativeprocesses and subsequent changes over time act toproduce unique types of soil structures with character-istic properties, and how these properties and the as-sociated behavior are interrelated. Several illustrationsof the relevance of these processes and properties togeotechnical applications are among the subjects ofthis chapter.

The structure of a soil depends on its fabric andinterparticle force system. It reflects all facets of thesoil’s composition, history, present state, and environ-mental influences. Soil particles come in a great variety

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246

Table 8.9 Properties and Conditions Likely to Cause Problems with Shale

Physical and Compositional Properties Probable in Situ Behavior

Lab tests and in situobservations

Unfavorable behaviorprobable for valuesin indicated range

High porepressure

Lowbearingcapacity

Tendency torebound

Slopestabilityproblems

Rapidslaking

Rapiderosion

Tunnelsupportproblems

Compressivestrength, kPa

�300–1800 � �

Modulus ofelasticity, MPa

�140–1400 � �

Cohesive strength,kPa

�30–700 � � �

Angle of internalfriction, deg.

�10–20 � � �

Dry unit weight,kN/m3

�11.0–17.3 � �(?)

Potential swell, % �3–15 � � � �Natural moisture

content, %�20–35 � �

Hydraulicconductivity, m/s

�10�5 � � �

Predominant clayminerals

Smectite or illite � �

Activity �0.75–2.0 �Wetting and drying

cyclesReduces to grain

sizes� �

Spacing of rockdefects

Closely spaced � � �(?) �

Orientation of rockdefects

Adverse � � �

State of stress �Existingoverburden

� � �

Adapted from Underwood (1967).

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of sizes, shapes, and compositions. The possible par-ticle arrangements (fabric) and stabilities of these ar-rangements (structure) are many; therefore, any singlesoil can exist in many different states, each of whichcan be viewed as a somewhat different material.

Geochemical and microbiological influences on thegeological processes and properties that are importantin geoengineering are only now beginning to be stud-ied and understood by geotechnical engineers. It islikely that knowledge drawn from these fields will bevery useful in the future.


1. Indicate whether each of the following statementsis True or False. Justify your answer with a briefstatement.a. Rearrangement of particles during shear pro-

vides an important contribution to the residualstrength of a highly plastic clay.

b. The relationship between critical void ratio andeffective confining pressure is the same for un-disturbed and reconstituted samples of the samesand.

c. The sensitivity of a clay can be explained by thechange in effective stress caused by remolding.

d. Collapse of structure in a saturated soil is usuallyaccompanied by an increase in effective stress.

e. Relative density is a suitable single parameter forcharacterizing sand properties.

f. Strength loss when a sensitive clay is disturbedis related to the liquidity index.

g. Marine clays have very high values of sodiumadsorption ratio and exchangeable sodium per-centage, which means that they are dispersiveclays.

h. Two samples of the same sand have the samerelative density and are confined under the samemean effective stress. Therefore, they have thesame stress–deformation, volume change, andstrength properties.

i. A compacted clay liner is to be used for contain-ment of nonpolar organic solvent wastes. Timecan be saved in determining the hydraulic con-ductivity of this clay by mixing the soil with thesolvent and then compacting samples for testing,rather than doing the compaction using water andthen using the solvents as permeants. Each pro-cedure will give the same result.

2. The results of unconfined compression tests on twosamples of kaolinite compacted by two differentmethods are shown in Fig. 11.20.a. Why is the peak strength greater by static com-

paction than by kneading compaction? (Knead-ing compaction is the type produced by asheepsfoot roller, and static compaction is pro-duced by a smooth steel roller.)

b. Why are the ultimate or residual strengths of thematerials prepared by the two methods thesame?

c. If this kaolinite were to be used for a structuralfill, which method of compaction would youspecify? Why?

d. If this kaolinite were to be used for the core ofan earth dam, which method of compactionwould you specify? Why?

e. If each material was saturated without furtherchange in dry unit weight and then sheared un-drained, sketch the curves of pore water pressureversus strain that you would expect to obtain foreach.

3. Given heavily overconsolidated clay under a presentvertical effective overburden stress of 200 kPa, themaximum past effective stress on the horizontalplane was 600 kPa. Consider this to be state I. Ithas been determined that this clay has a peak fric-tion angle �� of 30� and a residual friction angle

of 17�. There is no cementation of the clay struc-��rture. Rapid shear is defined as deformation at a ratefast enough so there can be no change in pore pres-sure in the shear zone. Slow shear is deformationat a rate slow enough that there can be no changein pore pressure in the shear zone.a. What is the overconsolidation ratio?b. Show paths on a diagram of shear stress versus

effective normal stress on the failure plane torepresent the following, and state for eachwhether the accompanying changes in volume( V) and pore pressure ( u) are positive, nega-tive, or zero:

i. Rapid shear from I to peak strengthii. Slow shear from I to peak strength

iii. Rapid shear from peak strength to residualstrength

c. What changes in fabric would you anticipate ingoing from I to peak strength and from peakstrength to residual strength?

d. Deep cuts in heavily overconsolidated claysometimes fail many years after they are made,and stability analyses have indicated that the av-

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erage strength at the time of failure correspondsto that at residual state.i. Account for the time delay.

ii. Is it reasonable to assume simultaneous de-velopment of residual strength at all pointsalong the failure surface? If not, how can thebehavior be explained? Take into accountstress–strain properties and water contentchanges that may be involved.

4. Suggest ways by which a quick clay might be sta-bilized in situ, that is, made less susceptible to largestrength loss.

5. It is shown in Fig. 8.48 that there is a unique re-lationship between remolded shear strength and li-quidity index that seems to be independent of theparticular clay. Explain why this should be so.

6. Which is easier to determine, the exchangeable so-dium percentage or the sodium adsorption ratio?Why?

7. Salt-affected soils are classified by agronomists asfollows:

Soil Group

ExchangeableSodium

PercentageUsual

pH

UsualStructural

State

Saline �15 �8.5Saline-alkali �15 �8.5Nonsaline alkali �15 8.5–10.0Nonsaline, nonalkali �15 �8.5

a. Complete the above table by filling in the lastcolumn on the right.

b. Which, if any, of these soil types may be a prob-lem soil? Why?

c. A practical form of the Gapon equation is

Na*� 0.17 (SAR)

Na* � Mg*

where SAR is the sodium adsorption ratio and *refers to the cation concentrations adsorbed onthe clay. At the time of construction of a smallearth dam, the soil was compacted and the waterin it contained the following cation concentra-tions:

�Na � 1.0 meq/liter2�Ca � 2.5 meq/liter2�Mg � 1.0 meq/liter

Comment on the probable structural state of thesoil at the time of construction.

d. The reservoir water to be stored behind this damwill contain the following cation concentrations:

�Na � 4.0 meq/liter2�Ca � 0.5 meq/liter2�Mg � 0.3 meq/liter

Comment on the possible consequences of pro-longed percolation by this water. Justify yourconclusions numerically.

8. State special geotechnical characteristics of thefollowing soil types and relate them to their(1) formational processes, (2) composition, (3) en-vironmental setting, and (4) structure. By all meansconsult references in addition to the relevant sec-tions in this book to enhance the quality of youranswers.a. Loessb. Organic clayc. Decomposed granited. Expansive soile. Pyrite-rich soilf. Loose sandg. Carbonate sandh. Glacial morainei. Saprolitej. Torrential stream deposits and mudflows

9. Manned missions to the Moon are likely to resumewithin the next several years for several purposes,including scientific studies, astronomical observa-tions, resource development, military advantage,and development of a launching platform for furtherspace exploration. The lunar soil and its propertieswill have important impacts on many aspects ofthese activities, especially facilities construction,their operation, and maintenance. Consider the fol-lowing aspects of the Moon and its surface envi-ronment:a. Lunar rocks are primarily basaltic.b. The gravitational field is one-sixth that of Earth.

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c. The lunar surface temperature ranges from�150�C at lunar midnight to �120�C at lunarnoon.

d. There is no free water.e. Atmospheric pressure is 10�13 Earth atmos-

pheres.f. There is much higher cosmic and solar radiation

on the Moon than on Earth.g. There is a high frequency of meteorite impact

compared to Earth.

Use principles relating to geologic and soil-formingprocesses, soil composition, surfaces, fabric, structure,and any other relevant concepts to make reasoned es-timates of or comments on the following:

a. Soil particle composition

b. Soil particle sizes and size distributionsc. Whether or not lunar soils will be cohesived. The nature and magnitude of lunar soil weath-

eringe. Local and regional variability of lunar soil com-

positions and densitiesf. Coefficient of friction between soil particles (see

Chapter 11)g. The ultimate bearing capacity of a cohesionless

soil on the Moon compared to that of the samesoil on Earth.

h. The optimum size of particles that might formmetastable honeycomb structures on the Moonas opposed to a finding by Terzaghi that silt-sizeparticles in the range of 6- to 20-�m diameterare most susceptible to this effect on Earth.

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251

CHAPTER 9

Conduction Phenomena

9.1 INTRODUCTION

Virtually all geotechnical problems involve soil or rockdeformations and stability and/or the flow throughearth materials of fluids, chemicals, and energy in var-ious forms. Flows play a vital role in the deformation,volume change, and stability behavior itself, and theymay control the rates at which the processes occur.Descriptions of these flows, predictions of flow quan-tities, their rates and changes with time, and associatedchanges in the properties and composition of both thepermeated soil and the flowing material are the sub-jects of this chapter.

Water flow through soil and rock has been most ex-tensively studied because of its essential role in prob-lems of seepage, consolidation, and stability, whichform a major part of engineering analysis and design.As a result, much is known about the hydraulic con-ductivity and permeability of earth materials. Chemi-cal, thermal, and electrical flows in soils are alsoimportant. Chemical transport through the ground is amajor concern in groundwater pollution, waste dis-posal and storage, remediation of contaminated sites,corrosion, leaching phenomena, osmotic effects in claylayers, and soil stabilization. Heat flows are importantrelative to frost action, construction in permafrost ar-eas, insulation, underground storage, thermal pollution,temporary ground stabilization by freezing, permanentground stabilization by heating, underground transmis-sion of electricity, and other problems. Electrical flowsare important to the transport of water and ground sta-bilization by electroosmosis, insulation, corrosion, andsubsurface investigations.

In addition to the above four flow types, each drivenby its own potential gradient, several types of coupled

flow are important under a variety of circumstances. Acoupled flow is a flow of one type, such as hydraulic,driven by a potential gradient of another type, such aselectrical.

This chapter includes a review of the physics of di-rect and coupled flow processes through soils and theirquantification in practical form, an evaluation of rele-vant parameters, their magnitudes, and factors influ-encing them, and some examples of applications.

9.2 FLOW LAWS AND INTERRELATIONSHIPS

Fluids, electricity, chemicals, and heat flow throughsoils. Provided the flow process does not change thestate of the soil, each flow rate or flux Ji (as shown inFig. 9.1) relates linearly to its corresponding drivingforce Xi according to

J � L X (9.1)i ii i

in which Lii is the conductivity coefficient for flow.When written specifically for a particular flow type andusing familiar phenomenological coefficients, Eq. (9.1)becomes, for cross section area A

Water flow q � k i A Darcy’s law (9.2)h h h

Heat flow q � k i A Fourier’s law (9.3)t t t

Electrical flow I � � i A Ohm’s law (9.4)e e

Chemical flow J � Di A Fick’s law (9.5)D c

In Eqs. (9.2) to (9.5) qh, qt, I, and JD are the water,heat, electrical, and chemical flow rates, respectively.

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252 9 CONDUCTION PHENOMENA

Figure 9.1 Four types of direct flow through a soil porousmass. A is the total cross-section area normal to flow; n isporosity.

Coefficients kh, kt, �e, and D are the hydraulic, thermal,electrical conductivities, and the diffusion coefficient,respectively. Typical ranges of values for these prop-erties are given later. The driving forces for flow aregiven by the respective hydraulic, thermal, electrical,and chemical gradients, ih, it, ie, and ic, respectively.

The terms in Eqs. (9.2) through (9.5) are identifiedin Fig. 9.1 and in Table 9.1, which also shows analogsbetween the various flow types. As long as the flowrates and gradients are linearly related, the mathemat-ical treatment of each flow type is the same, and theequations for flow of one type may be used to solveproblems of another type provided the property valuesand boundary conditions are properly represented. Twowell-known practical illustrations of this are the cor-respondence between the Terzaghi theory for clay con-solidation and one-dimensional transient heat flow, andthe use of electrical analogies for the study of seepageproblems.

9.3 HYDRAULIC CONDUCTIVITY

Darcy’s law1 states that there is a direct proportionalitybetween apparent water flow velocity vh or flow rateqh and hydraulic gradient ih, that is,

v � k i (9.6)h h h

q � k i A (9.7)h h h

where A is the cross-section area normal to the direc-tion of flow. The constant kh is a property of the ma-terial. Steady-state and transient flow analyses in soilsare based on Darcy’s law. In many instances, moreattention is directed at the analysis than at the value ofkh. This is unfortunate because no other property ofimportance in geotechnical problems is likely to ex-hibit such a great range of values, up to 10 orders ofmagnitude, from coarse to very fine grained soils, orshow as much variability in a given deposit as doesthe hydraulic conductivity. Some soils exhibit 2 or 3orders of magnitude variation in hydraulic conductivityas a result of changes in fabric, void ratio, and watercontent. These points are illustrated by Fig. 9.2 inwhich hydraulic conductivity values for a number ofsoils are shown.

Different units for hydraulic conductivity are oftenused by different groups or agencies; for example, cen-timeters per second by geotechnical engineers, feet peryear by groundwater hydrologists, and Darcys by pe-troleum technologists. Figure 9.3 can be used to con-vert from one system to another. The preferred unit inthe SI system is meters/second.

Theoretical Equations for Hydraulic Conductivity

Fluid flow through soils finer than coarse gravel is lam-inar. Equations have been derived that relate hydraulicconductivity to properties of the soil and permeatingfluid. A usual starting point for derivation of suchequations is Poiseuille’s law for flow through a roundcapillary, which gives the average flow velocity, vave,according to

2 Rpv � i (9.8)ave h8�

where � is viscosity, R is tube radius, and p is unit

1 This ‘‘law’’ was established empirically by Darcy based on the re-sults of flow tests through sands. Its general validity for the descrip-tion of hydraulic flow through most soil types has been verified bymany subsequent studies. Historical accounts of the development ofDarcy’s law are given by Brown et al. (2003).

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HYDRAULIC CONDUCTIVITY 253

Table 9.1 Conduction Analogies in Porous Media

Fluid Heat Electrical Chemical

Potential Total head h (m) Temperature T(�C)

Voltage V (volts) Chemical potential � orconcentration c (molm�3)

Storage Fluid volume W(m3/m3)

Thermal energy u(J /m3)

Charge Q (Coulomb) Total mass per unit totalvolume, m (mol/m3)

Conductivity Hydraulicconductivity kh

(m/s)

Thermalconductivity kt

(W/m/ �C)

Electrical conductivity �(siemens/m)

Diffusion coeff. D(m2/s)

Flow qh (m3/s) qt (J /s) Current I (amp) jD (mol/s)Flux qh/A (m3/s /m2) qt /A (J /s /m2) I /A (amp/m2) JD � jD/A (mol s�1 m�2)

Gradient (m/m)�h

i � �h �x(�C/m)

�Ti � �t �x

(v/m)�V

i � �e �x(mol m�4)

�ci � �c �x

Conduction Darcy’s law�h

q � �k Ah h �x

Fourier’s law�T

q � �k At t �x

Ohm’s law�V V

I � �� A �e �x R

Fick’s law�c

J � �D AD �xCapacitance Coefficient of

volume changeVolumetric heat

C(J / �C/m3)Capacitance C (farads �

coul/volt)Retardation factor, Rd

(dimensionless)

�dW aw vM � �dh 1 � e

kh

cv

dQC �

dT

Continuity�W qh� � � 0� ��t A

�u qt� � � 0� ��t A

�Q I� � � 0� �

�t A�(m)

� �J � 0D�tSteady state �2qh � 0 �2qt � 0 �2I � 0 �2JD � 0

Diffusion2�h k � hh� 2�t M �x

2�T k � Tt� 2�t C �x

2�V � � V� 2�t C �x

2�c D* � c� 2�t R �xD

k� c� �vM

k� a� �C

weight of the flowing fluid. Because the flow channelsin a soil are of various sizes, a characteristic dimensionis needed to describe average size. The hydraulic ra-dius RH

flow channel cross-section areaR �H wetted perimeter

is useful.For a circular tube flowing full,

2�R RR � � (9.9)H 2�R 2

so Poiseuille’s equation becomes

1 p 2q � R i a (9.10)cir H h2 �

where a is the cross-sectional area of the tube. Forother shapes of cross section, an equation of the sameform will apply, differing only in the value of a shapecoefficient Cs, so

2 Rp Hq � C i a (9.11)s h�

For a bundle of parallel tubes of constant but irreg-ular cross section contributing to a total cross-sectionalarea A (solids plus voids), the area of flow passages Aƒ

filled with water is

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Figure 9.2 Hydraulic conductivity values for several soils. Soil identification code: 1, com-pacted caliche; 2, compacted caliche; 3, silty sand; 4, sandy clay; 5, beach sand; 6, compactedBoston blue clay; 7, Vicksburg buckshot clay; 8, sandy clay; 9, silt—Boston; 10, Ottawasand; 11, sand—Gaspee Point; 12, sand—Franklin Falls; 13, sand–Scituate; 14, sand–PlumIsland; 15, sand–Fort Peck; 16, silt—Boston; 17, silt—Boston; 18, loess; 19, lean clay; 20,sand—Union Falls; 21, silt—North Carolina; 22, sand from dike; 23, sodium Boston blueclay; 24, calcium kaolinite; 25, sodium montmorillonite; 26–30, sand (dam filter) (FromLambe and Whitman (1969). Copyright � 1969 by John Wiley & Sons. Reprinted withpermission from John Wiley & Sons.

Figure 9.3 Hydraulic conductivity and permeability conversion chart.

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A � SnA (9.12)ƒ

where S is the degree of saturation and n is the poros-ity. For this condition the hydraulic radius is given by

A A L volume available for flowƒ ƒR � � �H P PL wetted area

Vw� (9.13)V Ss 0

where P is the wetted perimeter, L is the length of flowchannel in the direction of flow, Vs is the volume ofsolids and S0 is the wetted surface area per unit volumeof particles. The wetted surface area depends on theparticle sizes and the soil fabric and may be consideredas an effective surface area per unit volume of solids.It is less than the total specific surface area of the soilsince flow will not occur adjacent to all particle sur-faces.

For void ratio e and volume of solids Vs, the volumeof water Vw is

V � eV S (9.14)w s

Equation (9.11) becomes

ep p2 2q � C R Sni A � C R S i A� � � � � �s H h s H h� � 1 � e

(9.15)

and substitution for RH using Eqs. (9.13) and (9.14)gives

31 ep 3q � C S i A (9.16)� �� s h2S � 1 � e0

By analogy with Darcy’s law,

3 1 ep 3k � C S (9.17)� � � �h s 2� S 1 � e0

For full saturation, S � 1, and denoting Cs by 1/(k0T

2), where k0 is a pore shape factor and T is a tor-tuosity factor, Eq. (9.17) becomes

3� 1 eK � k � (9.18)� � � �h 2 2 k T S 1 � ep 0 0

This is the Kozeny–Carman equation for the permea-bility of porous media (Kozeny, 1927; Carman, 1956).The hydraulic conductivity kh has units of velocity

(LT�1), and the absolute or intrinsic permeability K hasunits of area (L2).

The effects of permeant properties are accounted forby the � /p term, provided the fabric of the soil is thesame in the presence of different fluids. The pore shapefactor k0 has a value of about 2.5 and the tortuosityfactor has a value of about in porous media con-2taining approximately uniform pore sizes.

For equal size spheres, S0 becomes 6/D (�surfacearea/volume of a sphere), where D is the diameter. Ifa soil is considered to consist of spheres of differentsizes, an effective diameter Deff can be computed fromthe particle size distribution (Carrier, 2003) accordingto

100%D � (9.19)eff �(ƒ /D )i ave,i

where fi is the fraction of particles between two sizes(Dli and Dsi) and Dave,i is the average particle size be-tween two sizes (� ); S0 can also be estimated0.5 0.5D Dli si

from the specific surface area. Methods for nonplasticsoils and clayey soils are given in Chapter 3 and alsoare summarized by Chapuis and Aubertin (2003). Var-ious modifications for S0 are available to take irregularparticle shapes (Loudon, 1952; Carrier, 2003) into ac-count.

The Kozeny–Carman equation accounts well for thedependency of permeability on void ratio in uniformlygraded sands and some silts; however, serious discrep-ancies are often found when it is applied to clays. Themain reasons for these discrepancies are that most claysoils do not contain uniform pore sizes and changes inpore fluid type are often accompanied by changes inthe clay fabric. Particles in clays are grouped in clus-ters or aggregates that have large intercluster pores andsmall intracluster pores. The influences of fabric andnonuniform pore sizes on the hydraulic conductivity offine-grained soils are discussed further later in this sec-tion.

If comparisons are made using materials having thesame fabric, the influence of permeant on hydraulicconductivity is quite well accounted for by the p /�term. If, however, a fine-grained soil is molded or com-pacted in different permeants, then the fabrics may bequite different, and the hydraulic conductivities forsamples at the same void ratio can differ greatly.

If Cs in Eq. (9.17) is taken as a composite shapefactor, and noting that total surface area per unit vol-ume is inversely proportional to particle size, then

3 ew2 3k � CD S (9.20)� �h s � 1 � e

where Ds is a characteristic grain size.

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Like the Kozeny–Carman equation, Eq. (9.20) de-scribes the behavior of cohesionless soils reasonablywell, but it is inadequate for clays. For a uniform sandwith bulky particles and a given permeant, Eqs. (9.17)and (9.20) indicate that kh should vary directly withe3 /(1 � e) and , and experimental observations sup-2Ds

port this.Despite the inability of the theoretical equations to

predict the hydraulic conductivity accurately in manycases, they do reflect the overwhelming importance ofpore size. Flow velocity depends on the square of poreradius, and hence the flow rate depends on radius tothe fourth power. The specific surface in the Kozeny–Carman equation and the representative grain size termin Eq. (9.20) are both measures of pore size. All otherfactors equal, the hydraulic conductivity depends farmore on the fine particles than on the large. A smallpercentage of fines can clog the pores of an otherwisecoarse material and result in a manyfold lower hydrau-lic conductivity. On the other hand, the presence offissures, cracks, root holes, and the like can result inenormous increases in the rate of water flow throughan otherwise compact soil layer.

Equation (9.20) predicts that the hydraulic conduc-tivity should vary with the cube of the degree of sat-uration, and some, but not all, experimental datasupport this, even in the case of fine-grained soils.Consideration of flow through unsaturated soils isgiven in Section 9.4.

Validity of Darcy’s Law

A basic premise of Darcy’s law is that flow is laminarand steady through saturated porous media. If particleand pore sizes and flow rates are sufficiently great, thenflow is turbulent, and Darcy’s law no longer applies.Turbulent flow conditions are likely in flows throughgravel and rockfill (Ahmed and Sunada, 1969; Ar-bhabhirama and Dinoy, 1973; George and Hansen,1992; Hansen et al., 1995; Li et al., 1998).2 Some mod-ification of Darcy’s law is needed also to account fornonsteady and wave-induced flows through sands, silts,

2 Flow transitions from laminar to turbulent flow when the Reynoldsnumber Re, defined as the ratio of inertial to viscous forces, exceedsa critical value. For flow through soils the critical value of interstitialflow Re is in the range of 1 to 10, with Re defined as (Khalifa et al.,2002)

4��vRe �

�(1 � n)Avd

in which � is fluid density, � is tortuosity (ratio of flow path meanlength to thickness), v is flow velocity, n is porosity, and Avd is theratio of pore surface area exposed to flow to the volume of solid.

and clays (Khalifa et al., 2002). These nonsteady andturbulent flow conditions are not treated herein.

As early as 1898, instances were cited in which hy-draulic flow velocity in fine-grained materials in whichlaminar flow can be expected increased more than pro-portionally with increases in gradient (King, 1898).The absence of water flow at finite hydraulic gradientsin ceramic filters of 0.1-�m average pore diameterwas reported by Derjaguin and Krylov (1944). Oakes(1960) found no detectable flow through a 30-cm-longsuspension of 6 percent Wyoming bentonite subjectedto a 50-cm head of water. Experiments by Miller andLow (1963) led to the conclusion that there was athreshold gradient for flow through sodium montmo-rillonite. Flow rates through clay-bearing sandstoneswere found to increase more than directly with gradi-ent up to gradients of 170 by von Englehardt and Tunn(1955). Deviations from Darcy’s law in pure and nat-ural clays up to gradients of 900 were measured byLutz and Kemper (1959). Apparent deviations fromDarcy’s law for flow in undisturbed soft clay are shownin Fig. 9.4.

The reported deviations from linearity between flowrate and hydraulic gradient are most significant in thelower range of gradients. Hydraulic gradients in thefield are seldom much greater than one. Thus, de-viations from Darcy’s law, if real, could have veryimportant implications for the applicability ofsteady-state and transient flow analyses, including con-solidation, that are based on it. Furthermore, gradientstypically used in laboratory testing are high, commonlymore than 10, and often up to several hundred. Thisbrings the suitability of laboratory test results as indi-cators of field behavior into question.

Three hypotheses have been proposed to account fornonlinearity between flow velocity and gradient: (1)non-Newtonian water flow properties, (2) particle mi-grations that cause blocking and unblocking of flowpassages, and (3) local consolidation and swelling thatis inevitable when hydraulic gradients are appliedacross a compressible soil. The apparent existence ofa threshold gradient below which flow was not de-tected was attributed to a quasi-crystalline water struc-ture. It is now known, however, that many of theeffects interpreted as resulting from unusual waterproperties can be ascribed to undetected experimentalerrors arising from contamination of measuring sys-tems (Olsen, 1965), local consolidation and swelling,and bacterial growth (Gupta and Swartzendruber,1962). Additional careful measurements by a numberof investigators (e.g., Olsen, 1969; Gray and Mitchell,1967; Mitchell and Younger, 1967; Miller et al., 1969;Chan and Kenney, 1973) failed to confirm the exis-tence of a threshold gradient in clays. Darcy’s law was

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Figure 9.4 Dependence of flow velocity on hydraulic gradient. Undisturbed soft clay fromSka Edeby, Sweden (from Hansbo, 1973).

obeyed exactly in several of these studies. Thus it isunlikely that unusual water properties are responsiblefor non-Darcy flow behavior.

On the other hand, particle migrations leading tovoid plugging and unplugging, electrokinetic effects,and chemical concentration gradients can cause appar-ent deviations from Darcy’s law. Analysis of interpar-ticle bond strengths in relation to the magnitude ofseepage forces shows that particles that are not partic-ipating in the load-carrying skeleton of a soil mass canbe moved under moderate values of hydraulic gradient.Soils with open, flocculated fabrics and granular soilswith a relatively low content of fines appear particu-larly susceptible to the movement of fine particles dur-ing permeation.

Internal swelling and dispersion of clay particlesduring permeation can cause changes in flow rate andapparent non-Darcy behavior. Tests on illite–siltmixtures showed that the hydraulic conductivity de-pends on clay content, sedimentation procedure,compression rate, and electrolyte concentration. Sub-sequent behavior was quite sensitive to the type andconcentration of electrolyte used for permeation andthe total throughput volume of permeant. Changes inrelative hydraulic conductivity that occurred while the

electrolyte concentration was changed from 0.6 to 0.1N NaCl are shown in Fig. 9.5. The cumulative through-put is the ratio of the total flow volume at any time tothe sample pore volume. The hydraulic conductivitiesfor these materials ranged from more than 1 � 10�7 toless than 1 � 10�9 m/s.

Practical Implications Evidence indicates thatDarcy’s law is valid, provided that all system variablesare held constant. However, unless fabric changes, par-ticle migrations, and internal void ratio redistributionscaused by effective stress and chemical changes canbe shown to be negligible, hydraulic conductivity mea-surements in the laboratory should be made under con-ditions of temperature, pressure, hydraulic gradient,and pore fluid chemistry as closely approximatingthose in the field as possible. This is particularly im-portant in connection with the testing of clays as po-tential waste containment barriers, such as slurry wallsand liners for landfills and impoundments (Daniel,1994). Microbial activities may be important as well,as they can lead to formation of biofilms, pore clog-ging, and large reductions in hydraulic conductivity asshown, for example, by Dennis and Turner (1998).

Unfortunately, duplication of field conditions is notalways possible, especially as regards the hydraulic

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Figure 9.5 Reduction in hydraulic conductivity as a result of internal swelling (from Hard-castle and Mitchell, 1974).

gradient. If hydraulic gradients are low enough to du-plicate those in most field situations, then the labora-tory testing time usually becomes unacceptably long.In such cases, tests over a range of gradients are de-sirable in order to assess the stability of the soil struc-ture against changes due to seepage forces.

Similarly, the gradients that are developed in labo-ratory consolidation tests on thin samples are manytimes greater than exist in thick layers of the same clayin the field. The variation of hydraulic gradient i withtime factor T during one-dimensional consolidation ac-cording to the Terzaghi theory is shown in Fig. 9.6.The solution of the Terzaghi equation gives excesspore pressure u as a function of position (z/H) andtime factor

� 2u Mz 20 �M Tu � sin e (9.21)� � �M Hm�0

where M � �(2m � 1)/2. Thus, the hydraulic gradientis

�� u 2u Mz 20 �M Ti � � cos e (9.22)�� z H Hm�0w w

If a parameter p is defined by

� Mz 2�M Tp � 2 cos e (9.23)� � �Hm�0

Eq. (9.22) becomes

u0i � p (9.24) Hw

The real gradient for any layer thickness or loadingintensity can be obtained by using actual values of u0

and H and the appropriate value of p from Fig. 9.6.For small values of u0 /wH, as is the case in the

field, for example, for u0 � 50 kPa, H � 5m, thenu0 /wH � 1, and the field gradients are low throughoutmost of the layer thickness during the entire consoli-dation process. On the other hand, for a laboratorysample of 10 mm thickness and the same stress in-crease, u0 /wH is 500, and the hydraulic gradients arevery large. In this case a gradient-dependent hydraulicconductivity could be the cause of significant differ-ences between the laboratory-measured and field val-ues of coefficient of consolidation. Constant rate ofstrain or constant gradient consolidation testing of suchsoils is preferable to the use of load increments be-cause lower gradients minimize particle migration ef-fects.

Anisotropy

Anisotropic hydraulic conductivity results from bothpreferred orientation of elongated or platy particles andstratification of soil deposits. Ratios of horizontal-to-vertical hydraulic conductivity from less than 1 tomore than 7 were measured for undisturbed samplesof several different clays (Mitchell, 1956). These ratioscorrelated reasonably well with preferred orientation ofthe clay particles, as observed in thin section. Ratiosof 1.3 to 1.7 were measured for kaolinite consolidatedone dimensionally from 4 to 256 atm, and 0.9 to 4.0

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Figure 9.6 Hydraulic gradients during consolidation according to the Terzaghi theory.

were measured for illite and Boston blue clay consol-idated over a pressure range up to more than 200 atm(Olsen, 1962). A ratio of approximately 2 was mea-sured for kaolinite over a range of void ratios corre-sponding to consolidation pressures up to 4 atm(Morgenstern and Tchalenko, 1967b). Thus, an averagehydraulic conductivity ratio of about 2 as a result ofmicrofabric anisotropy may be typical for many clays.

Large anisotropy in hydraulic conductivity as a re-sult of stratification of natural soil deposits or in earth-work compacted in layers is common. Varved clayshave substantially greater hydraulic conductivity in thehorizontal direction than in the vertical direction owingto the presence of thin silt layers between the thin claylayers. The ratio of horizontal values to vertical valuesdetermined in the laboratory, rk, is 10 � 5 for Con-necticut Valley varved clay (Ladd and Wissa, 1970).Similar values were measured for the varved clay inthe New Jersey meadows. Values less than 5 were mea-sured for New Liskeard, Ontario, varved clay (Chanand Kenney, 1973).

The practical importance of a high hydraulic con-ductivity in the horizontal direction depends on the dis-tance to a drainage boundary and the type of flow. Forexample, the rate of groundwater flow will clearly beaffected, as will the rate of consolidation when vertical

drains are used. On the other hand, lateral drainagebeneath a loaded area may not be greatly influencedby a high ratio of horizontal to vertical conductivity ifthe width of loaded area is large compared to the thick-ness of the drainage layer.

Fabric and Hydraulic Conductivity

The theoretical relationships developed earlier in thissection indicate that the flow velocity should dependon the square of the pore radius, and the flow rate isproportional to the fourth power of the radius. Thus,fabrics with a high proportion of large pores are muchmore pervious than those with small pores. For ex-ample, remolding several undisturbed soft clays re-duced the hydraulic conductivity by as much as afactor of 4, with an average of about 2 (Mitchell,1956). This reduction results from the breakdown of aflocculated open fabric and the destruction of largepores.

An illustration of the profound influence of com-paction water content on the hydraulic conductivity offine-grained soil is shown in Fig. 9.7. All samples werecompacted to the same density. For samples compactedusing the same compactive effort, curves such as thosein Fig. 9.8 are typical. For compaction dry of optimum,

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Figure 9.7 Hydraulic conductivity as a function of compac-tion water content for samples of silty clay prepared to con-stant density by kneading compaction.

Figure 9.8 Influence of compaction method on the hydraulicconductivity of silty clay. Constant compactive effort wasused for all samples.

clay particles and aggregates are flocculated, the resis-tance to rearrangement during compaction is high, anda fabric with comparatively large pores is formed. Forhigher water contents, the particle groups are weaker,and fabrics with smaller average pore sizes are formed.Considerably lower values of hydraulic conductivityare obtained wet of optimum in the case of kneadingcompaction than by static compaction (Fig. 9.8) be-cause the high shear strains induced by the kneadingcompaction method break down flocculated fabricunits.

Three levels of fabric are important when consid-ering the hydraulic conductivity of finer-grained soils.The microfabric consists of the regular aggregations ofparticles and the very small pores, perhaps with sizesup to about 1 �m, between them through which verylittle fluid will flow. The minifabric contains these ag-gregations and the interassemblage pores betweenthem. The interassemblage pores may be up to severaltens of micrometers in diameter. Flows through thesepores will be much greater than through the intraag-gregate pores. On a larger scale, there may be a ma-crofabric that contains cracks, fissures, laminations, orroot holes through which the flow rate is so great asto totally obscure that through the other pore spacetypes.

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Figure 9.9 Contours of constant hydraulic conductivity forsilty clay compacted using kneading compaction.

Figure 9.10 Cluster model for permeability prediction (after Ol-sen, 1962).

These considerations are of particular importance inthe hydraulic conductivity of compacted clays used asbarriers for waste containment. The controlling unitsin these materials are the clods, which would corre-spond to minifabric units. Acceptably low hydraulicconductivity values are obtained only if clods and in-terclod pores are eliminated during compaction (Ben-son and Daniel, 1990). This requires that compactionbe done wet of optimum using a high effort and amethod that produces large shear strains, such as bysheepsfoot roller.

The wide range of values of hydraulic conductivityof compacted fine-grained soils that results from thelarge differences in fabric associated with compactionto different water contents and densities is illustratedby Fig. 9.9. The grouping of contours means that se-lection of a representative value for use in a seepageanalysis is difficult. In addition, if it is required thatthe hydraulic conductivity of earthwork not exceed acertain value, such as may be the case for a clay linerfor a waste pond, then specifications must be carefullydrawn. In so doing, it must be recognized also thatother properties, such as strength, also vary with com-paction water content and density and that the com-paction conditions that are optimal for one propertymay not be suitable for the other. A procedure for thedevelopment of suitable specifications for compactedclay liners is given by Daniel and Benson (1990).

The primary reason equations such as (9.18) and(9.20) fail to account quantitatively for the variation ofthe hydraulic conductivity of fine-grained soils withchange in void ratio is unequal pore sizes (Olsen,1962). A typical soil has a fabric composed of small

aggregates or clusters as shown schematically in Fig.9.10. These aggregates of N particles each have anintracluster void ratio ec. The spaces between the ag-gregates comprise the intercluster voids and areresponsible for the intercluster void ratio ep. The totalvoid ratio eT is equal to the sum of ec and ep. Theclusters and intracluster voids comprise the microfa-bric, whereas the assemblage of clusters comprises theminifabric. Fluid flow in such a system is dominatedby flow through the intercluster pores because of theirlarger size.

The sizes of clusters depend on the mineralogicaland pore fluid compositions and the formational proc-ess. Conditions that favor aggregation of individualclay plates produce larger clusters than deflocculating,dispersing environments. There is general consistencywith the interparticle double-layer interactions de-scribed in Chapter 6. When a fine-grained soil issedimented in or mixed with waters of differentelectrolyte concentration or type or with fluids of dif-ferent dielectric constants, quite different fabrics result.This explains why the � / term in Eqs. (9.18) and(9.20) is inadequate to account for pore fluid differ-ences, unless comparisons are made using sampleshaving identical fabrics. This will only be the casewhen a pore fluid of one type replaces one of anothertype without disturbance to the soil.

The cluster model developed by Olsen (1962) ac-counts for discrepancies between the predicted andmeasured variations in flow rates through differentsoils. The following equation can be derived for theratio of estimated flow rate for a cluster model, qCM tothe flow rate predicted by the Kozeny–Carman equa-tion (9.18) qKC:

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3q (1 � e /e )CM c T2 / 3� N (9.25)4 / 3q (1 � e )KC c

Application of Eq. (9.25) requires assumptions forthe variations of ec with eT that accompany compres-sion and rebound. Olsen (1962) considered the relativecompressibility of individual clusters and cluster as-semblages. The compressibility of individual clustersis small at high total void ratios, so compression isaccompanied by reduction in the intercluster poresizes, but with little change in intracluster void ratio.This assumption is supported by the microstructurestudies of Champlain clay by Delage and Lefebvre(1984) Thus, the actual hydraulic conductivity de-creases more rapidly with decreasing void ratio duringcompression than predicted by the Kozeny–Carmanequation until the intercluster pore space is comparableto that in a system of closely packed spheres, whenthe clusters themselves begin to compress. Further de-creases in porosity involve decreases in both ec and eT.As the intercluster void ratio now decreases less rap-idly, the hydraulic conductivity decreases at a slowerrate with decreasing porosity than predicted by theKozeny–Carman equation. During rebound increase inporosity develops mainly by swelling of the clusters,whereas the flow rate continues to be controlled pri-marily by the intercluster voids.

Recent attempts to quantify saturation and hydraulicconductivity of fine-grained soils containing a distri-bution of particle sizes and fabric elements in terms ofpore-scale relationships have given promising results(Tuller and Or, 2003). Expressions for clay plate spac-ing in terms of surface properties and solution com-position derived using DLVO theory (see Chapter 6),combined with assumed geometrical representations ofclay aggregates and pore space in combination withsilt and sand components, are used in the formulation.

9.4 FLOWS THROUGH UNSATURATED SOILS

Darcy’s law [Eq. (9.7)] also applies for flow throughunsaturated soils such as those in the vadose zoneabove the water table where pore water pressures arenegative. However, the hydraulic conductivity is notconstant and depends on the amount and connectivityof water in the pores. For instance, Eq. (9.20) predictsthat hydraulic conductivity should vary as the cube ofthe degree of saturation.3 This relationship has been

3 The hydraulic conductivity can also be a function of volumetricmoisture content � or matric suction �. These variables are relatedto each other by the soil–water characteristic curve as described inChapter 7.

found reasonable for compacted fine-grained soils anddegrees of saturation greater than about 80 percent.

Similarly to Eq. (9.7), the unsaturated flow equationin the direction i can be written as

�� zv � �k(S) � (9.26)� �i �x �xi i

where k(S) is saturation-dependent hydraulic conduc-tivity, � is the matric suction equivalent head (L), and�z /�xi is the unit gravitational vector measured upwardin direction z (1.0 if xi is the direction of gravity z).When percolating water infiltrates vertically into drysoil, the hydraulic gradient near the sharp wetting frontcan be very large because of a large value of the �� /�x term. However, the wetting front becomes less sharpas the infiltration proceeds and the gravity term thendominates. The hydraulic gradient then is close to oneand the magnitude of flux is equal to the hydraulicconductivity k(S).

Using Eq. (9.26), the equation of mass conservationbecomes

�(nS) � �� z R� k(S) � � (9.27) � ��

�t �x �x �x �i i i w

where n is the porosity, �w is the density of the water,and R is a source or sink mass transfer term such aswater uptake by plant roots (ML�3).

If the soil is assumed to be incompressible and thereis no sink/sources (R � 0), Eq. (9.27) becomes

�S �� zn � k(�) � � ��

�� t �x �x �xi i i

�� zor C(�) � k(�) � (9.28) � ��

�t �x �x �xi i i

where C(�) � n(�S /��) and k(S) is converted to k(�)using the soil–water characteristic curve (S–� relation-ships). Equation (9.28) is called the Richards equation(Richards, 1931). For given S–� and k(�) relationshipsand initial /boundary conditions, the nonlinear govern-ing equation can be solved for � (often numerically bythe finite difference or finite element method).

The hydraulic conductivity of unsaturated soils canbe a function of saturation, water content, matric suc-tion, or others. Measured hydraulic conductivities ofwell-graded sand and clayey sand as a function of (a)matric suction and (b) saturation ratio are shown inFig. 9.11. Both figures are related to each other, as thematric suction is a function of saturation ratio by thesoil moisture characteristic curve as described in Sec-

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FLOWS THROUGH UNSATURATED SOILS 263

Sand

Rel

ativ

e P

erm

eabi

lity

k r

Sand

Sand

0 100

Rel

ativ

e P

erm

eabi

lity

k r

1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05Matric Suction (kPa)

1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05Matric Suction (kPa)

Clayey Sand > Sand

Clayey Sand

Sand > Clayey Sand

1.E+01

1.E-01

1.E-05

1.E-07

1.E-09

1.E-11

1.E-13

1.E-15

1.E-17

1.E-191.E-21

1.E-03

Hyd

raul

ic c

ondu

ctiv

ity (

m/s

)

1.E+01

1.E-01

1.E-05

1.E-07

1.E-09

1.E-11

1.E-13

1.E-15

1.E-17

1.E-191.E-21

1.E-03

Hyd

raul

ic C

ondu

ctiv

ity (

m/s

)

Saturation (%)

1.E+00

1.E-02

1.E-04

1.E-06

1.E-08

1.E-10

1.E-12

1.E-14

1.E-16

1.E+00

1.E-02

1.E-04

1.E-06

1.E-08

1.E-10

1.E-12

1.E-14

1.E-16

Saturation (%)

Clayey Sand

Clayey Sand

Sand

Clayey Sand

20 40 60 80

0 10020 40 60 80

(a) (b)(a)

(d)(c)

Figure 9.11 Hydraulic conductivity of partially saturated sand and clayey sand as a functionof matric suction and degree of saturation (from Stephens, 1996).

tion 7.12. Various methods to measure the hydraulicconductivity of unsaturated soils are available (Klute,1986; Fredlund and Rahardjo, 1993). However, themeasurement in unsaturated soils is more difficult toperform than in saturated soils because the hydraulicconductivity needs to be determined under controlledwater saturation or matric suction conditions.

A general expression for the hydraulic conductivityk of unsaturated soils can be written as

�gk � k K � k k (9.29)r r s�

where ks is the saturated conductivity, K is the intrinsicpermeability of the medium (L2) such as given by Eq.(9.18), � is the density of the permeating fluid (ML�3),g is the acceleration of gravity (LT�2), � is the dynamicviscosity of the permeating fluid (MT�1L�1), and ks isthe conductivity under the condition that the pores arefully filled by the permeating fluid (i.e., full saturation).The dimensionless parameter kr is called the relativepermeability, and the values range from 0 (� zero per-

meability, no interconnected path for the permeatingfluid) to 1 (� permeating fluid at full saturation). Theequation can be used for a nonwetting fluid (e.g., air)by substituting the values of � and � of the nonwettingfluid.

The data in Fig. 9.11a and 9.11b can be replottedas the relative permeability against matric suction inFig. 9.11c and against saturation ratio in Fig. 9.11d.The two different curves in Fig. 9.11d clearly showthat kr � S3 derived from Eq. (9.20) is not universallyapplicable. At very low water contents, the water inthe pores becomes disconnected as described in Chap-ter 7. Careful experiments show that the movement ofwater exists even at moisture contents of a few percent,but vapor transport becomes more important at this drystate (Grismer et al., 1986). Therefore, Eq. (9.20) isnot suitable for low saturations. One reason for thisdiscrepancy is that soil contains pores of various sizesrather than the assumption of uniform pore sizes usedto derive Eq. (9.20).

Considering that the soil contains pores of randomsizes, Marshall (1958) derived the following equation

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for hydraulic conductivity as a function of pore sizesfor an isotropic material:

2 2 2 2 2n r � 3r � 5r � � � � � (2m � 1)r1 2 3 mK � 2m 8

(9.30)

in which K is the specific hydraulic conductivity (per-meability) (L2), n is the porosity, m is the total numberof pore classes, and ri is the mean radius of the poresin pore class i. Pore sizes can be measured from dataon the amount of water withdrawn as the suction onthe soil is progressively increased. Using the capillaryequation, the radius of the largest water-filled pore un-der a suction of � (L) is given by

2�r � (9.31)

� g�w

in which � is the surface tension of water, �w is thedensity of water, and g is the acceleration of gravity.As it is usually more convenient to use moisture suc-tion than pore radius, Eq. (9.29) can be rewritten as

2 2� n�2 �2 �2K � [� � 3� � 5�1 2 32 2 22� g mw

�2� � � � � (2m � 1)� ] (9.32)m

The permeability K can be converted to the hydraulicconductivity k by multiplying the unit weight (�wg) di-vided by the dynamic viscosity of water �. This gives

2 2� n�2 �2 �2k � [� � 3� � 5�1 2 322� g� mw

�2� � � � � (2m � 1)� ] (9.33)m

Following Green and Corey (1971), the porosity nequals the volumetric water content of the saturatedcondition �S, and m is the total number of pore classesbetween �S and zero water content � � 0.

A matching factor is usually used in Eq. (9.33) toequate the calculated and measured hydraulic conduc-tivities. Matching at full saturation is preferable tomatching at a partial saturation point because it is sim-pler and gives better results. Rewriting Eq. (9.33) andintroducing a matching factor gives

l2 2k � �s S �2k(� ) � [(2j � 1 � 2i)� ]�i j2k 2� g� m j�1sc w

(i � 1, 2, . . . , l) (9.34)

in which k(�i) is the calculated hydraulic conductivityfor a specified water content �i; is i the last water con-tent class on the wet end, for example, i � 1 denotesthe pore class corresponding to the saturated watercontent �S, and i � l denotes the pore class correspond-ing to the lowest water content �L for which hydraulicconductivity is calculated; ks /ksc is the matching factor,defined as the measured saturated hydraulic conductiv-ity divided by the calculated saturated hydraulic con-ductivity; and l is the total number of pore classes (apore class is a pore size range corresponding to a watercontent increment) between � � �L and �S. Thus

m �S� (9.35)l � � �S L

A constant value of l is used at all water contents, andthe value of l establishes the number of pore classesfor which terms are included in the calculation at�2�j

saturation. Other pore size distribution models for un-saturated soils are available, and an excellent reviewof these models is given by Mualem (1986).

Equation (9.34) can be written in an integration formas (after Fredlund et al., 1994)

�2 pk � � � � xs Sk(�) � � dx (9.36)2�k 2� g� � (x)Lsc w

where suction � is given as a function of volumetricwater content �, and x is a dummy variable. The hy-draulic conductivity for fully saturated condition is cal-culated by assigning � � �S. For generality, the term

in Eq. (9.34) is replaced by , where p is a constant2 p� �S s

that accounts for the interaction of pores of varioussizes (Fredlund et al., 1994).

From Eq. (9.36), the relative permeability kr is afunction of water content as follows:

� �S� � x � � xk (�) � � dx � dx (9.37)�r 2 2

�r �r� (x) � (x)

Herein, the lowest water content �L is assumed to bethe residual water content �r. If the moisture content�–suction � relationship (or the soil–water character-istic curve) is known, the relative permeability kr canbe computed from Eq. (9.37) by performing a numer-ical integration. The hydraulic conductivity k is thenestimated from Eq. (9.29) with the knowledge of sat-urated hydraulic conductivity ks.

The use of the soil–water characteristic curve to es-timate the hydraulic conductivity of unsaturated soilsis attractive because it is easier to determine this curve

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THERMAL CONDUCTIVITY 265

in the laboratory than it is to measure the hydraulicconductivity directly. Apart from Eq. (9.37), the fol-lowing relative permeability function proposed by Mu-alem (1976) is often used primarily because of itssimplicity:

q 2� �s� � � d� d�rk (�) � � � (9.38)� � � � �r� �� (�) �(�)r rs r

where q describes the degree of connectivity betweenthe water-conducting pores. Mualem (1976) states thatq � 0.5 is appropriate based on permeability measure-ments on 45 soils. van Genuchten et al. (1991) substi-tuted the soil–water characteristic equation (7.52) intoEq. (9.38) and obtained the following closed-form so-lution4:

p 1 / m m 2� � � � � �r rk (�) � 1 � 1 �� r � � � � � �S r S r

(9.39)

Both Eq. (9.39) as well as Eq. (9.37) using the soil–water characteristic curve by Fredlund and Xing(1994) give good predictions of measured data asshown in Fig. 9.12.

The two hydraulic conductivity–matric suctioncurves shown in Fig. 9.11a cross each other at a matricsuction value of approximately 50 kPa (or 5 m abovethe water table under hydrostatic condition). Belowthis value, the hydraulic conductivity of sand is largerthan that of the clayey sand. However, as the matricsuction increases, the water in the sand drains rapidlytoward its residual value, giving a very low hydraulicconductivity. On the other hand, the clayey sand holdsthe pore water by the presence of fines and the hy-draulic conductivity becomes larger than that of thesand at a given matric suction.

If the sand is overlain by the clayey sand, then thematric suction at the interface is larger than 50 kPa,and the water infiltrating downward through the finerclayey sand cannot enter into the coarser sand layerbecause the underlying sand layer is less permeablethan the overlying clayey sand. The water will insteadmove laterally along the bedding interface. This phe-nomenon is called a capillary barrier (e.g., Zaslavskyand Sinai, 1981; Yeh et al., 1985; Miyazaki, 1988).The barrier will be maintained as long as the lateraldischarge along the interface (preferably inclined) is

4 m � 1 � 1 /n is assumed (van Genuchten et al., 1991). See Eq.(7.52).

larger than the vertically infiltrating water flow. How-ever, if the matric suction is reduced by large infiltra-tion, the barrier breaks and water enters into theinitially dry coarse layer. Solutions are available toevaluate the amount of water flowing laterally acrossthe capillary barrier interface at the point of break-through for a given set of fine and coarse soil hydraulicproperties and interface inclination (Ross, 1990; Steen-huis et al., 1991; Selkar, 1997; Webb, 1997).

Capillary barriers have received increased attentionas a means for isolating buried waste from ground-water flow and as part of landfill cover systems in dryclimates (Morris and Stormont, 1997; Selkar, 1997;Khire et al., 2000). The barrier can be used to divertthe flow laterally along an interface and/or to storeinfiltrating water temporarily in the fine layer so thatit can be removed ultimately by evaporation and tran-spiration. Capillary barriers are constructed as simpletwo-layer systems of contrasting particle size or mul-tiple layers of fine- and coarse-grained soils. If thethickness of the overlying fine layer is too small, cap-illary diversion is reduced because of the confiningflow path in the fine layer. The minimum effectivethickness is several times the air-entry head of the finesoil (Warrick et al., 1997; Smersrud and Selker, 2001).Khire et al. (2000) stress the importance of site-specificmetrological and hydrological conditions in determin-ing the storage capacity of the fine layer. The soil forthe underlying coarse layer should have a very largeparticle size contrast with the fine soil, but finesmigrations into the coarse sand should be avoided.Smesrud and Sekler (2001) suggest the d50 particle sizeratio of 5 to be ideal. The thickness of the coarse sandlayer does not need to be great, as the purpose of thelayer is simply to impede the downward water migra-tion.

9.5 THERMAL CONDUCTIVITY

Heat flow through soil and rock is almost entirely byconduction, with radiation unimportant, except for sur-face soils, and convection important only if there is ahigh flow rate of water or air, as might possibly occurthrough a coarse sand or rockfill. The thermal conduc-tivity controls heat flow rates. Conductive heat flow isprimarily through the solid phase of a soil mass. Valuesof thermal conductivity for several materials are listedin Table 9.2. As the values for soil minerals are muchhigher than those for air and water, it is evident thatthe heat flow must be predominantly through the sol-ids. Also included in Table 9.2 are values for the heatcapacity, volumetric heat, heat of fusion, and heat ofvaporization of water. The heat capacity can be used

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Predicted coefficientof permeability(drying)

Predicted coefficientof permeability(wetting)

Measured coefficientof permeability(drying)

Measured coefficientof permeability(wetting)

10

1

0.1

0.01

0.001

0.0001

Volumetric Water Content

Hyd

raul

ic C

ondu

ctiv

ity, k

× 10

(m/s

)

20 30 40 50 60

(a)

Hyd

raul

ic C

ondu

ctiv

ity, k

(cm

/day

)Figure 9.12 Comparisons of predicted and measured relationships between hydraulic con-ductivity and volumetric water content for two soils. (a) By Eq. (9.37) with the measureddata for Guelph loam (from Fredlund et al., 1994) and (b) by Eq. (9.39) with the measureddata for crushed Bandelier Tuff (van Genuchten et al., 1991).

to compute the volumetric heat using the simple rela-tionships for frozen and unfrozen soil given in the ta-ble. Volumetric heat is needed for the analysis of manytypes of transient heat flow problems. The heat of fu-sion is used for analysis of ground freezing and thaw-ing, and the heat of vaporization applies to situationswhere there are liquid to vapor phase transitions.

The denser a soil, the higher is its composite thermalconductivity, owing to the much higher thermal con-ductivity of the solids relative to the water and air.Furthermore, since water has a higher thermal conduc-tivity than air, a wet soil has a higher thermal conduc-tivity than a dry soil. The combined influences of soilunit weight and water content are shown in Fig. 9.13,which may be used for estimates of the thermal con-ductivity for many cases. If a more soil-specific valueis needed, they may be measured in the laboratory us-ing the thermal needle method (ASTM, 2000). Moredetailed treatment of methods for the measurement ofthe thermal conductivity of soils are given by Mitchelland Kao (1978) and Farouki (1981, 1982).

The relationship between thermal resistivity (inverseof conductivity) and water content for a partly satu-rated soil undergoing drying is shown in Fig. 9.14. Ifdrying causes the water content to fall below a certainvalue, the thermal resistivity increases significantly.This may be important in situations where soil is usedas either a thermally conductive material, for example,

to carry heat away from buried electrical transmissioncables, or as an insulating material, for example, forunderground storage of liquefied gases. The water con-tent below which the thermal resistivity begins to risewith further drying is termed the critical water content,and below this point the system is said to have lostthermal stability (Brandon et al., 1989).

The following factors influence the thermal resistiv-ity of partly saturated soils (Brandon and Mitchell,1989).

Mineralogy All other things equal, quartz sandshave higher thermal conductivity than sands con-taining a high percentage of mica.

Dry Density The higher the dry density of a soil,the higher is the thermal conductivity.

Gradation Well-graded soils conduct heat betterthan poorly graded soils because smaller grainscan fit into the interstitial spaces between thelarger grains, thus increasing the density and themineral-to-mineral contact.

Compaction Water Content Some sands that com-pacted wet and then dried to a lower water contenthave significantly higher thermal conductivitythan when compacted initially at the lower watercontent.

Time Sands containing high percentages of silica,carbonates, or other materials that can develop ce-

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ELECTRICAL CONDUCTIVITY 267

Table 9.2 Thermal Properties of Materialsa

ThermalConductivity Material Btu/h/ft2 / �F/ft W/m/K

Air 0.014 0.024Water 0.30 0.60Ice 1.30 2.25Snow(100 kg m�3)(500 kg m�3)

0.030.34

0.060.59

Shale 0.90 1.56Granite 1.60 2.76Concrete 1.0 1.8Copper 225 389Soil 0.15–1.5 (�1.0) 0.25–2.5 (�1.7)Polystyrene 0.015–0.035 0.03–0.06

Heat Capacity Material Btu/ lb/ �F kJ/kg/K

Water 1.0 4.186Ice 0.5 2.093Snow(100 kg m�3)(500 kg m�3)

0.050.25

0.211.05

Minerals 0.17 0.710Rocks 0.20–0.55 0.80–2.20

Volumetric Heat Material Btu/ft3 / �F kJ/m3/K

Unfrozen Soil d(0.17 � w /100) d(72.4 � 427w /100)SoilFrozen soil d(0.17 � 0.5w /100) d(72.4 � 213w /100)Snow(100 kg m�3)(500 kg m�3)

3.1315.66

2101050

Heat of Fusion Water 143.4 Btu/ lb 333 kJ/kgSoil 143.4(w /100)d Btu/ft3 3.40 � 104(w /100)d kJ/m3

Heat of Vaporization Water 970 Btu/ lb 2.26 MJ/kgSoil 970(w /100)d Btu/ft3 230(w /100)d MJ/m3

ad � dry unit weight, in lb/ft3 for U.S. units and in kN/m3 for SI units; w � water content in percent.

mentation may exhibit an increased thermal con-ductivity with time.

Temperature All crystalline minerals in soils havedecreasing thermal conductivity with increasingtemperature; however, the thermal conductivity ofwater increases slightly with increasing tempera-ture, and the thermal conductivity of saturatedpore air increases markedly with increasing tem-perature. The net effect is that the thermal con-ductivity of moist sand increases somewhat withincreasing temperature.

9.6 ELECTRICAL CONDUCTIVITY

Ohm’s law, Eq. (9.4), in which �e is the electrical con-ductivity, applies to soil–water systems. The electricalconductivity equals the inverse of the electrical resis-tivity, or

1 L� � (siemens/meter; S/m) (9.40)e R A

where R is the resistance ( ), L is length of sample

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Figure 9.13 Thermal conductivity of soil (after Kersten,1949).

Figure 9.14 Typical relationship between thermal resistivityand water content for a compacted sand.

(m), and A is its cross-sectional area (m2). The valueof electrical conductivity for a saturated soil is usuallyin the approximate range of 0.01 to 1.0 S/m. The spe-cific value depends on several properties of the soil,including porosity, degree of saturation, composition(conductivity) of the pore water, mineralogy as it af-

fects particle size, shape, and surface conductance, soilstructure, including fabric and cementation, and tem-perature.

Electrical measurements found early applications inthe fields of petroleum engineering, geophysical map-ping and prospecting, and soil science, among others.The inherent complexity of soil–water systems and thedifficulty in characterizing the wide ranges of particlesize, shape, and composition have precluded develop-ment of generally applicable theoretical equations forelectrical conductivity. However, a number of empiri-cal equations and theoretical expressions based onsimplified models may provide satisfactory results,depending on the particular soil and conditions. Theydiffer in assumptions about the possible flow paths forelectric current through a soil–water matrix, the pathlengths and their relative importance, and whethercharged particle surfaces contribute to the total currentflow.

Nonconductive Particle Models

Formation Factor The electrical conductivity ofclean saturated sands and sandstones is directly propor-tional to the electrical conductivity of the pore water (Ar-chie, 1942). The coefficient of proportionality depends onporosity and fabric. Archie (1942) defined the formationfactor, F, as the resistivity of the saturated soil, �T, dividedby the resistivity of the saturating solution, �W, that is,

� �T WF � � (9.41)� �W T

where �W and �T are the electrical conductivities of thepore water and saturated soil, respectively.

An empirical correlation between formation factor andporosity for clean sands and sandstones is given by

�mF � n (9.42)

where n is porosity, and m equals from 1.3 for loose sandsto 2 for highly cemented sandstones. An empirical relationbetween formation factor at 100 percent water saturationand ‘‘apparent’’ formation factor at saturation less than100 percent is

�WpF � (S ) (9.43)atS �1 ww �T

where p is a constant determined experimentally. Archiesuggested a value of p � 2; however, other published val-ues of p range from 1.4 to 4.6, depending on the soil and

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whether a given saturation is reached by wetting or bydrainage.

Capillary Model In this and the theoretical modelsthat follow, direct current (DC) conductivity is as-sumed, although they may apply to low-frequency al-ternating current (AC) models as well. Consider asaturated soil sample of length L and cross-sectionalarea A. If the pores are assumed to be connected andcan be represented by a bundle of tubes of equal radiusand length Le and total area Ae, where Ae � porosity� A, and Le is the actual length of the flow path, thenan equation for the formation factor as a function ofthe porosity n and the tortuosity T � Le /L is

2TF � (9.44)

n

For S � 1, and assuming that the area available forelectrical flow is nSA, then F � T2 /nS. In principle, ifF is measured for a given soil and n is known, a valueof tortuosity can be calculated to use in the Kozeny–Carman equation for hydraulic conductivity.

Cluster Model As discussed earlier in connectionwith hydraulic conductivity, the cluster model (Olsen,1961, 1962) shown in Fig. 9.10 assumes unequal poresizes. Three possible paths for electrical current flowcan be considered: (1) through the intercluster pores,(2) through the intracluster pores, and (3) alternatelythrough inter- and intracluster pores. On this basis thefollowing equations for formation factor as a functionof the cluster model parameters can be derived (Olsen,1961):

1 � e 1T2F � T (9.45)� �� e � e 1 � XT c

X � Y � Z (9.46)

2[(1 � e ) /(e � e )]T T cY � (9.47)2 21 � (T /T) [(1 � e ) /e (e � e )]c c c T c

2e TcZ � a (9.48)� �� e � e TT c c

in which T is the intercluster tortuosity, Tc is the intra-cluster tortuosity, and a is the effective cluster ‘‘contactarea.’’ The cluster contact area is very small except forheavily consolidated systems.

This model successfully describes the flow of cur-rent in soils saturated with high conductivity water. Insuch systems, the contribution of the surface conduc-

tance of clayey particles to the total current flow wouldbe small.

Conductive Particle Models

In conductive particle models the contribution of theions concentrated at the surface of negatively chargedparticles is taken into account. Two simple mixturemodels are presented below; other models can befound in Santamarina et al. (2001).

Two-Parallel-Resistor Model A contribution of sur-face conductance is included, and the soil–water sys-tem is equivalent to two electrical resistors in parallel(Waxman and Smits, 1968). The result is that the totalelectrical conductivity �T is

� � X(� � � ) (9.49)T W s

in which �s is a surface conductivity term, and X is aconstant analogous to the reciprocal of the formationfactor that represents the internal geometry.

This approach yields better fits of �T versus �W datafor clay-bearing soils. However, it assumes a constantvalue for the contribution of the surface ions that isindependent of the electrolyte concentration in the porewater, and it fails to include a contribution for the sur-face conductance and pore water conductance in a se-ries path.

Three-Element Network Model A third path is in-cluded in this formulation that considers flow alongparticle surfaces and through pore water in series inaddition to the paths included in the two-parallel-resistor model. The flow paths and equivalent electricalcircuit are shown in Fig. 9.15. Analysis of the electricalnetwork for determination of �T gives

a� �W s� � � b� � c� (9.50)T s W(1 � e)� � e�W s

If the surface conductivity �s is negligible, the sim-ple formulation proposed by Archie (1942) for sandsis obtained; that is, �T � constant � �W. Some of thegeometric parameters a, b, c, d, and e can be writtenas functions of porosity and degree of saturation; oth-ers are obtained through curve regression analysis of�T versus �W data.

Soil conductivity as a function of pore fluid con-ductivity is shown in Fig. 9.16 for a silty clay. Thethree-element model fits the data well over the fullrange, the two-element model gives good predictionsfor the higher values of conductivity, and the simpleformation factor relationship is a reasonable average

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Figure 9.15 Three-element network model for electrical conductivity: (a) current flow pathsand (b) equivalent electrical circuit.

for conductivity values in the range of about 0.3 to 0.6S/m.

Alternating Current Conductivity and DielectricConstant

The electrical response of a soil in an AC field is fre-quency dependent owing to the polarizability proper-ties of the system constituents. Several scale-dependentpolarization mechanisms are possible in soils, asshown in Fig. 9.17. The smaller the element size thehigher the polarization frequency. At the atomic andmolecular scales, there are polarizations of electrons[electronic resonance at ultraviolet (UV) frequencies],ions [ionic resonance at infrared (IR) frequencies], anddipolar molecules (orientational relaxation at micro-wave frequencies). A mixture of components (like wa-ter and soil particles) having different polarizabilitiesand conductivities produces spatial polarization bycharge accumulation at interfaces (called Maxwell–Wagner interfacial polarization). The ions in the Sternlayer and double layer are restrained (Chapter 6), andhence they also exhibit polarization. This polarizationresults in relaxation responses at radio frequencies.Further details of the polarization mechanisms aregiven by Santamarina et al. (2001).

The effective AC conductivity �eff is expressed as

� � � � !�"� (9.51)eff 0

where � is the conductivity, !� is the polarization loss(called the imaginary relative permittivity), " is the

frequency, and �0 is the permittivity of vacuum [8.85� 10�12 C2/(Nm2)]. The frequency-dependent effectiveconductivities of deionized water and kaolinite–watermixtures at two different water contents (0.2 and 33percent) are shown in Fig. 9.18a. The complicated in-teractions of different polarization mechanisms are re-sponsible for the variations shown.

A material is dielectric if charges are not free tomove due to their inertia. Higher frequencies areneeded to stop polarization at smaller scales. The di-electric constant (or the real relative permittivity !�5)decreases with increasing frequency; more polariza-tion mechanisms occur at lower frequencies. Thefrequency-dependent dielectric constants of deionizedwater and kaolinite–water mixtures are shown in Fig.9.18b. The value for deionized water is about 79 above10 kHz. Below this frequency, the values increase withdecrease in frequency. This is attributed to experimen-tal error caused by an electrode effect in which charges

5 To describe the out-of-phase response under oscillating excitation,the electrical properties of a material are often defined in the complexplane:

� � �� j��

where � is the complex permittivity, j is the imaginary number( ), and �� and �� are real and imaginary numbers describing the�1electrical properties. The permittivity � is often normalized by thepermittivity of vacuum �0 as

�! � � !� � j!�

�0

where ! is called the relative permittivity.

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Figure 9.16 Soil electrical conductivity as a function of porefluid conductivity and comparisons with three models.

Deionized Water

33%

0.2%

No DataAvailable

100

100

10–2

10–4

10–6

102 104 106 108 1010

Deionized Water33%

0.2% No DataAvailable

100

100

102

104

106

102 104 106 108 1010

σ eff

(S/m

)

Electrode Effect

Frequency (Hz)

Frequency (Hz)

κ�

(a)

(b)

Figure 9.18 (a) Conductivity and (b) relative permittivity asa function of frequency for deionized water and kaolinite atwater contents of 0.2 and 33 percent (from Santamarina etal., 2001).

Figure 9.17 Frequency ranges associated with different polarization mechanisms (from San-tamarina et al., 2001).

accumulate at the electrode–specimen interface (Kleinand Santamarina, 1997). Similarly to the observationsmade for the effective conductivities, the real permit-tivity values of the mixtures show complex trends offrequency dependency.

For analysis of AC conductivity and dielectric con-stant as a function of frequency in an AC field, Smithand Arulanandan (1981) modified the three-elementmodel shown in Fig. 9.15 by adding a capacitor inparallel with each resistor. The resulting equations canbe fit to experimental frequency dispersions of the con-

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Table 9.3 Self-Diffusion Coefficients for Ions atInfinite Dilution in Water

Anion(1)

D0 � 1010(m2/s)(2)

Cation(3)

D0 � 1010(m2/s)(4)

OH� 52.8 H� 93.1F� 14.7 Li� 10.3Cl� 20.3 Na� 13.3Br� 20.8 K� 19.6I� 20.4 Rb� 20.7HCO3

� 11.8 Cs� 20.5NO3

� 19.0 Be2� 5.98SO4

2� 10.6 Mg2� 7.05CO3

2� 9.22 Ca2� 7.92— — Sr2� 7.90— — Ba2� 8.46— — Pb2� 9.25— — Cu2� 7.13— — Fe2�a 7.19— — Cd2�a 7.17— — Zn2� 7.02— — Ni2�a 6.79— — Fe3�a 6.07— — Cr3�a 5.94— — Al3�a 5.95

aValues from Li and Gregory (1974). Reprinted withpermission from Geochimica et Cosmochimica Acta, Vol.38, No. 5, pp. 703–714. Copyright � 1974, PergamonPress.

ductivity and apparent dielectric constant by computeroptimization of geometrical and compositional param-eters. The resulting parameter values are useful forcharacterizing mineralogy, porosity, and fabric. Moredetailed discussions on electrical models, data inter-pretation, and correlations with soil properties aregiven by Santamarina et al. (2001).

9.7 DIFFUSION

Chemical transport through sands is dominated by ad-vection, wherein dissolved and suspended species arecarried with flowing water. However, in fine-grainedsoils, wherein the hydraulic flow rates are very small,for example, kh less than about 1 � 10�9 m/s, chemicaldiffusion plays a role and may become dominant whenkh becomes less than about 1 � 10�10 m/s. Fick’s law,Eq. (9.5), is the controlling relationship, and D(L2T�1),the diffusion coefficient, is the controlling parameter.Diffusive chemical transport is important in claybarriers for waste containment, in some geologicprocesses, and in some forms of chemical soilstabilization. Comprehensive treatments of the diffu-sion process, values of diffusion coefficients andmethods for their determination, and applications,especially in relation to chemical transport and wastecontainment barrier systems, are given by Quigley etal. (1987), Shackelford and Daniel (1991a, 1991b),Shincariol and Rowe (2001) and Rowe (2001).

Diffusive flow is driven by chemical potential gra-dients, but for most applications chemical concentra-tion gradients can be used for analysis. The diffusioncoefficient is measured and expressed in terms ofchemical gradients. Maximum values of the diffusioncoefficient D0 are found in free aqueous solution atinfinite dilution. Self-diffusion coefficients for a num-ber of ion types in water are given in Table 9.3. Usu-ally cation–anion pairs are diffusing together, therebyslowing down the faster and speeding up the slower.This may be seen in Table 9.4, which contains valuesof some limiting free solution diffusion coefficients forsome simple electrolytes.

Diffusion through soil is slower and more complexthan diffusion through a free solution, especially whenadsorptive clay particles are present. There are severalreasons for this (Quigley, 1989):

1. Reduced cross-sectional area for flow because ofthe presence of solids

2. Tortuous flow paths around particles3. The influences of electrical force fields caused by

the double-layer distributions of charges

4. Retardation of some species as a result of ionexchange and adsorption by clay minerals andorganics or precipitation

5. Biodegradation of diffusing organics6. Osmotic counterflow7. Electrical imbalance, possibly by anion exclusion

The diffusion coefficient could increase with time offlow through a soil as a result of such processes as(Quigley, 1989):

1. K� fixation by vermiculite, which would decreasethe cation exchange capacity and increase thefree water pore space

2. Electrical imbalances that act to pull cations oranions

3. The attainment of adsorption equilibrium, thuseliminating retardation of some species

In an attempt to take some of these factors, espe-cially geometric tortuosity of interconnected pores,into account, an effective diffusion coefficient D* is

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DIFFUSION 273

Table 9.4 Limiting Free Solution DiffusionCoefficients for Some Simple Electrolytes

Electrolyte(1)

D0 � 1010(m2/s)(2)

HCl 33.36HBr 34.00LiCl 13.66LiBr 13.77NaCl 16.10NaBr 16.25NaI 16.14KCl 19.93KBr 20.16KI 19.99CsCl 20.44CaCl2 13.35BaCl2 13.85

Reported by Shackelford and Daniel, 1991a after Rob-inson and Stokes, 1959. Reprinted from the Journal ofGeotechnical Engineering, Vol. 117, No. 3, pp. 467–484.Copyright � 1991. With permission of ASCE.

used. Several definitions have been proposed (Shack-elford and Daniel, 1991a) in which the different factorsare taken into account in different ways. Althoughthese relationships may be useful for analysis of theimportance of the factors themselves, it is sufficient forpractical purposes to use

D* � � D (9.52)a 0

in which �a is an ‘‘apparent tortuosity factor’’ that takesseveral of the other factors into account, and use valuesof D* measured under representative conditions. Theeffective coefficient for diffusion of different chemicalsthrough saturated soil is usually in the range of about2 � 10�10 to 2 � 10�9 m2/s, although the values canbe one or more orders of magnitude lower in highlycompacted clays and clays, such as bentonite, that canbehave as semipermeable membranes (Malusis andShackelford, 2002b). Values for compacted clays arerather insensitive to molding water content or methodof compaction (Shackelford and Daniel, 1991b), instark contrast to the hydraulic conductivity, which mayvary over a few orders of magnitude as a result ofchanges in these factors. This suggests that soil fabricdifferences have relatively minor influence on the ef-fective diffusion coefficient.

Whereas Fick’s first law, Eq. (9.5), applies forsteady-state diffusion, Fick’s second law describes

transient diffusion, that is, the time rate of change ofconcentration with distance:

2�c � c� D* (9.53)2�t �x

For transient diffusion with constant effective diffusioncoefficient D*, the solution for this equation is of ex-actly the same form as that for the Terzaghi equationfor clay consolidation and that for one-dimensionaltransient heat flow.

An error function solution for Eq. (9.53) (Ogata,1970; Freeze and Cherry, 1979), for the case of one-dimensional diffusion from a layer at a constant sourceconcentration C0 into a layer having a sufficiently lowinitial concentration that it can be taken as zero at t �0, is

C x x� erfc � 1 � erf (9.54)

C 2D*t 2D*t0

where C is the concentration at any time at distance �from the source.

Curves of relative concentration as a function ofdepth for different times after the start of chloride dif-fusion are shown in Fig. 9.19a (Quigley, 1989). Aneffective diffusion coefficient for chloride of 6.47 �10�10 m2/s was assumed. Also shown (Fig. 9.19b) isthe migration velocity of the C /C0 front within the soilas a function of time. As chloride is one of the morerapidly diffusing ionic species, Fig. 9.19 provides abasis for estimating maximum probable migration dis-tances and concentrations as a function of time thatresult solely from diffusion.

When there are adsorption–desorption reactions,chemical reactions such as precipitation–solution, ra-dioactive decay, and/or biological processes occurringduring diffusion, the analysis becomes more complexthan given by the foregoing equations. For adsorption–desorption reactions and the assumption that there islinearity between the amount adsorbed and the equi-librium concentration, Eq. (9.53) is often written as

2�c D* � c� (9.55)2�t R �xd

where Rd is termed the retardation factor, and it isdefined by

�dR � 1 � K (9.56)d d�

in which �d is the bulk dry density of the soil, � is the

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Figure 9.19 Time rate of chloride diffusion (from Quigley,1989). (a) Relative concentration as a function of depth afterdifferent times and (b) velocity of migration of the front hav-ing a concentration C /C0 of 0.5.

volumetric water content, that is, the volume of waterdivided by the total volume (porosity in the case of asaturated soil), and Kd is the distribution coefficient.The distribution coefficient defines the amount of agiven constituent that is adsorbed or desorbed by a soilfor a unit increase or decrease in the equilibrium con-centration in solution. Other reactions influencing theamount in free solution relative to that fixed in the soil(e.g., by precipitation) may be included in Kd, depend-ing on the method for measurement and the conditionsbeing modeled. Distribution coefficients are usually de-termined from adsorption isotherms, and they may beconstants for a given soil–chemical system or varywith concentration, pH, and temperature. More de-

tailed discussions of distribution coefficients and theirdetermination are given by Freeze and Cherry (1979),Quigley et al., (1987), Quigley (1989), and Shackel-ford and Daniel (1991a, b).

9.8 TYPICAL RANGES OF FLOWPARAMETERS

Usual ranges for the values of the direct flow conduc-tivities for hydraulic, thermal, electrical, and diffusivechemical flows are given in Table 9.5. These rangesare for fine-grained soils, that is, silts, silty clays,clayey silts, and clays. They are for full saturation;values for partly saturated soils can be much lower.

Also listed in Table 9.5 are values for electroosmoticconductivity, osmotic efficiency, and ionic mobility.These properties are needed for analysis of couplingof hydraulic, electrical, and chemical flows, and theyare discussed further later.

9.9 SIMULTANEOUS FLOWS OF WATER,CURRENT, AND SALTS THROUGHSOIL-COUPLED FLOWS

Usually there are simultaneous flows of different typesthrough soils and rocks, even when only one type ofdriving force is acting. For example, when pore watercontaining chemicals flows under the action of a hy-draulic gradient, there is a concurrent flow of chemicalthrough the soil. This type of chemical transport istermed advection. In addition, owing to the existenceof surface charges on soil particles, especially clays,there are nonuniform distributions of cations and ani-ons within soil pores resulting from the attraction ofcations to and repulsion of anions from the negativelycharged particle surfaces. The net negativity of clayparticles is caused primarily by isomorphous substitu-tions within the crystal structure, as discussed in Chap-ter 3, and the ionic distributions in the pore fluid aredescribed in Chapter 6. Because of the small pore sizesin fine-grained soils and the strong local electricalfields, clay layers exhibit membrane properties. Thismeans that the passage of certain ions and moleculesthrough the clay may be restricted in part or in full atboth microscopic and macroscopic levels.

Owing to these internal nonhomogeneities in iondistributions, restrictions on ion movements caused byelectrostatic attractions and repulsions, and the de-pendence of these interactions on temperature, a vari-ety of microscopic and macroscopic effects may beobserved when a wet soil mass is subjected to flow

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SIMULTANEOUS FLOWS OF WATER, CURRENT, AND SALTS THROUGH SOIL-COUPLED FLOWS 275

Table 9.5 Typical Range of Flow Parameters for Fine-Grained Soilsa

Parameter Symbol Units Minimum Maximum

Porosity n — 0.1 0.7Hydraulic

conductivitykh m s�1 1 � 10�11 1 � 10�6

Thermalconductivity

kt W m�1 K�1 0.25 2.5

Electricalconductivity

�e siemens m�1 0.01 1.0

Electro osmoticconductivity

ke m2 s�1 V�1 1 � 10�9 1 � 10�8

Diffusioncoefficient

D m2 s�1 2 � 10�10 2 � 10�9

Osmoticefficiencyb

" — 0 1.0

Ionic mobility u m2 s�1 V�1 3 � 10�9 1 � 10�8

aThe above values of flow coefficients are for saturated soil. They may bemuch less in partly saturated soil.

b0 to 1.0 is the theoretical range for the osmotic efficiency coefficient. Valuesgreater than about 0.7 are unlikely in most fine-grained materials of geotechnicalinterest.

gradients of different types. A gradient of one type Xj

can cause a flow of another type Ji, according to

J � L X (9.57)i ij j

The Lij are termed coupling coefficients. They are prop-erties that may or may not be of significant magnitudein any given soil, as discussed later. Types of coupledflow that can occur are listed in Table 9.6, along withterms commonly used to describe them.6

Of the 12 coupled flows shown in Table 9.6, severalare known to be significant in soil–water systems, atleast under some conditions. Thermoosmosis, which iswater movement under a temperature gradient, is im-portant in partly saturated soils, but of lesser impor-tance in fully saturated soils. Significant effects fromthermally driven moisture flow are found in semiaridand arid areas, in frost susceptible soils, and in expan-sive soils. An analysis of thermally driven moisture

6 Mechanical coupling also occurs in addition to the hydraulic, ther-mal, electrical, and chemical processes listed in Table 9.6. A commonmanifestation of this in geotechnical applications is the developmentof excess pore pressure and the accompanying fluid flow that resultfrom a change in applied stress. This type of coupling is usually mosteasily handled by usual soil mechanics methods. A few other typesof mechanical coupling may also exist in soils and rocks (U.S. Na-tional Committee for Rock Mechanics, 1987).

flow is developed later. Electroosmosis has been usedfor many years as a means for control of water flowand for consolidation of soils. Chemicalosmosis, theflow of water caused by a chemical gradient actingacross a clay layer, has been studied in some detailrecently, owing to its importance in waste containmentsystems.

Isothermal heat transfer, caused by heat flow alongwith water flow, has caused great difficulties in thecreation of frozen soil barriers in the presence of flow-ing groundwater. Electrically driven heat flow, the Pel-tier effect, and chemically driven heat flow, the Dufoureffect, are not known to be of significance in soils;however, they appear not to have been studied in anydetail in relation to geotechnical problems.

Streaming current, the term applied to both hydrau-lically driven electrical current and ion flows, has im-portance to both chemical flow through the ground(advection) and the development of electrical poten-tials, which may, in turn, influence both fluid and ionflows as a result of additional coupling effects. Thecomplete roles of thermoelectricity and diffusion andmembrane potentials are not yet known; however, elec-trical potentials generated by temperature and chemicalgradients are important in corrosion and in somegroundwater flow and stability problems.

Whether thermal diffusion of electrolytes, the Soreteffect, is important in soils has not been evaluated;

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Table 9.6 Direct and Coupled Flow Phenomena

Gradient X

Flow J Hydraulic Head Temperature ElectricalChemical

Concentration

Fluid HydraulicconductionDarcy’s law

Thermoosmosis Electroosmosis Chemicalosmosis

Heat Isothermal heattransfer orthermal filtration

ThermalconductionFourier’s law

Peltier effect Dufour effect

Current Streaming current ThermoelectricitySeebeck orThompson effect

ElectricconductionOhm’s law

Diffusion andmembranepotentials orsedimentationcurrent

Ion Streaming currentultrafiltration(also known ashyperfiltration)

Thermal diffusionof electrolyte orSoret effect

Electrophoresis Diffusion Fick’slaw

however, since chemical activity is highly temperaturedependent, it may be a significant process in somesystems. Finally, electrophoresis, the movement ofcharged particles in an electrical field, has been usedfor concentration of mine waste and high water contentclays.

The relative importance of chemically and electri-cally driven components of total hydraulic flow is il-lustrated in Fig. 9.20, based on data from tests onkaolinite given by Olsen (1969, 1972). The theory fordescription of coupled flows is given later. A practicalform of Eq. (9.57) for fluid flow under combined hy-draulic, chemical, and electrical gradients is

H log(C /C ) EB Aq � �k A � k A � k Ah h c eL L L(9.58)

in which kh, kc, and ke are the hydraulic, osmotic, andelectroosmotic conductivities, H is the hydraulic headdifference, E is the voltage difference, and CA and CB

are the salt concentrations on opposite sides of a claylayer of thickness L.

In the absence of an electrical gradient, the ratio ofosmotic to hydraulic flows is

q k log(C /C )hc c B A� � ( E � 0) (9.59)� �q k Hh h

and, in the absence of a chemical gradient, the ratio ofelectroosmotic flows to hydraulic flows is

q k Ehe e� ( C � 0) (9.59a)� �q k Hh h

The ratio (kc /kh) in Fig. 9.20 indicates the hydraulichead difference in centimeters of water required to givea flow rate equal to the osmotic flow caused by a 10-fold difference in salt concentration on opposite sidesof the layer. The ratio ke /kh gives the hydraulic headdifference required to balance that caused by a 1 Vdifference in electrical potentials on opposite sides ofthe layer. During consolidation, the hydraulic conduc-tivity decreases dramatically. However, the ratios kc /kh

and ke /kh increase significantly, indicating that the rel-ative importance of osmotic and electroosmotic flowsto the total flow increases. Although the data shown inFig. 9.20 are shown as a function of the consolidationpressure, the changes in the values of kc /kh and ke /kh

are really a result of the decrease in void ratio thataccompanies the increase in pressure, as may be seenin Fig. 9.20c.

These results for kaolinite provide a conservative es-timate of the importance of osmotic and electroosmoticflows because coupling effects in kaolinite are usuallysmaller than in more active clays, such as montmoril-lonite-based bentonites. In systems containing confinedclay layers acted on by chemical and/or electrical gra-dients, Darcy’s law by itself may be an insufficientbasis for prediction of hydraulic flow rates, particularlyif the clay is highly plastic and at a very low void ratio.Such conditions can be found in deeply buried clay

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QUANTIFICATION OF COUPLED FLOWS 277

Figure 9.20 Hydraulic, osmotic, and electroosmotic conductivities of kaolinite (data fromOlsen 1969, 1972): (a) consolidation curve, (b) conductivity values, and (c) conductivitiesas a function of void ratio.

and clay shale and in densely compacted clays. Formore compressible clays, the ratios kc /kh and ke /kh maybe sufficiently high to be useful for consolidation byelectrical and chemical means, as discussed later in thischapter.

9.10 QUANTIFICATION OF COUPLED FLOWS

Quantification of coupled flow processes may be doneby direct, empirical determination of the relevant pa-rameters for a particular case or by relationships de-rived from a theoretical thermodynamic analysis of thecomplete set of direct and coupled flow equations.

Each approach has advantages and limitations. It is as-sumed in the following that the soil properties remainunchanged during the flow processes, an assumptionthat may not be justified in some cases. The effects offlows of different types on the state and properties ofa soil are discussed later in this chapter. However,when properties are known to vary in a predictablemanner, their variations may be taken into account innumerical analysis methods.

Direct Observational Approach

In the general case, there may be fluid, chemical, elec-trical, and heat flows. The chemical flows can be sub-

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divided according to the particular chemical speciespresent. Each flow type may have contributions causedby gradients of another type, and their importancedepends on the values of Lij and Xj in Eq. (9.57). Acomplete and accurate description of all flows may bea formidable task.

However, in many cases, flows of only one or twotypes may be of interest, some of the gradients maynot exist, and/or some of the coupling coefficients maybe either known or assumed to be unimportant. Thematrix of flows and forces then reduces significantly,and the determination of coefficients is greatly simpli-fied. For example, if simple electroosmosis under iso-thermal conditions is considered, then Eq. (9.57) yields

q � L �(�H) � L �(�E) � L �(�C) (9.60)w HH HE HC

I � L �(�H) � L �(�E) � L �(�C) (9.61)EH EE EC

J � L �(�H) � L �(�E) � L �(�C) (9.62)C CH CE CC

where qw � water flow rateI � electrical current

Jc � chemical flow rateH � hydraulic headE � electrical potentialC � chemical concentrationLij � coupling coefficients; the first subscript

indicates the flow type and the second de-notes the type of driving force

If there are no chemical concentration differencesacross the system, then the last terms on the right-handside of Eqs. (9.60), (9.61), and (9.62) do not exist. Inthis case, Eqs. (9.60) and (9.61) become, when writtenin more familiar terms,

q � k i � k i (9.63)w h h e e

I � � i � � i (9.64)h h e e

where kh � hydraulic conductivityke � electroosmotic hydraulic conductivity�h � electrical conductivity due to hydraulic

flow�e � electrical conductivityih � hydraulic gradientie � electrical potential gradient

If permeability tests are done in the absence of anelectrical potential difference, then the hydraulic con-

ductivity coefficient kh is readily determined.7 The co-efficient of electroosmotic hydraulic conductivity isusually determined by measuring the hydraulic flowrate developed in a known DC potential field underconditions of ih � 0. The electrical conductivity �e isobtained from the same experiment through measure-ment of the electrical current.

The main advantage of this empirical, but direct, ap-proach is simplicity. It is particularly useful when onlya few of the possible couplings are likely to be im-portant and when some uncertainty in the measuredcoefficients is acceptable.

General Theory for Coupled Flows

When several flows are of interest, each resulting fromseveral gradients, a more formal methodology is nec-essary so that all relevant factors are accounted forproperly. If there are n different driving forces, thenthere will be n direct flow coefficients Lii and n(n �1) coupling coefficients Lij(i j). The determinationof these coefficients is best done within a frameworkthat provides a consistent and correct description ofeach of the flows. Irreversible thermodynamics, alsotermed nonequilibrium thermodynamics, offers a basisfor such a description. Furthermore, if the terms areproperly formulated, then Onsager’s reciprocal rela-tions apply, that is,

L � L (9.65)ij ji

and the number of coefficients to be determined is sig-nificantly reduced. In addition, the derived forms forthe coupling coefficients, when cast in terms of meas-urable and understood properties, provide a basis forrapid assessment of their importance.

The theory of irreversible thermodynamics as ap-plied to transport processes in soils is only outlinedhere. More comprehensive treatments are given byDeGroot and Mazur (1962), Fitts (1962), Katchalskyand Curran (1967), Greenberg, et al. (1973), Yeungand Mitchell (1992), and Malusis and Shackelford(2002a).

Irreversible thermodynamics is a phenomenological,macroscopic theory that provides a basis for descrip-

7 Note that unless the ends of the sample are short circuited to preventthe development of a streaming potential, there will be a small elec-troosmotic counterflow contributed by the keie term in Eq. (9.63).Streaming potentials may be up to a few tens of millivolts in soils.Streaming potential is one of four types of electrokinetic phenomenathat may exist in soils, as discussed in more detail in Section 9.16.

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SIMULTANEOUS FLOWS OF WATER, CURRENT, AND CHEMICALS 279

tion of systems that are out of equilibrium. It is basedon three postulates, namely,

1. Local equilibrium, a criterion that is satisfied iflocal perturbations are not large.

2. Linear phenomenological equations, that is,

n

J � L X ( j � 1,2, . . . , n) (9.66)�i ij jj�1

3. Validity of the Onsager reciprocal relations, acondition that is satisfied if the Ji and Xj are for-mulated properly (Onsager, 1931a, 1931b). Ex-perimental verification of the Onsager reciprocityfor many systems and processes has been ob-tained and is summarized by Miller (1960).

Both the driving forces and flows vanish in systemsthat are in equilibrium, so the deviations of thermo-dynamic variables from their equilibrium values pro-vide a suitable basis for their formulation. Thedeviations of the state parameters Ai from equilibriumare given by

0� � A � A (9.67)i i i

where is the value of the state parameter at equilib-0Ai

rium and Ai is its value in the disturbed state.Criteria for deriving the forces and flows are then

developed on the basis of the second law of thermo-dynamics, which states that at equilibrium, the entropyS is a maximum, and �i � 0. The change in entropy S that results from a change in state parameter givesthe tendency for a variable to change. Thus �S /��i isa measure of the force causing �i to change, and iscalled Xi.

The flows Ji, termed fluxes in irreversible thermo-dynamics, are given by ��i /�t, the time derivative of�i. On this basis, the resulting entropy production �per unit time becomes

ndS� � � J X (9.68)� i idt i�1

The entropy production can be related explicitly tovarious irreversible processes in terms of proper forcesand fluxes (Gray, 1966; Yeung and Mitchell, 1992). Ifthe choices satisfy Eq. (9.68), then the Onsager reci-procity relations apply.

It has been found more useful to use # � T�, thedissipation function, in which T is temperature, than �

in the formulation of the flow equations. And # is alsothe sum of products of fluxes and driving forces:

n

# � J X (9.69)� i ii�1

The units of # are energy per unit time, and it is ameasure of the rate of local free energy dissipation byirreversible processes.

Application of the thermodynamic theory of irre-versible processes requires the following steps:

1. Finding the dissipation function # for the flows2. Defining the conjugated flows Ji and driving

forces Xi from Eq. (9.69)3. Formulating the phenomenological equations in

the form of Eq. (9.66)4. Applying the Onsager reciprocal relations5. Relating the phenomenological coefficients to

measurable quantities

When the Onsager reciprocity is used, the numberof independent coefficients Lij reduces from n2 to[(n � 1)n] /2.

Application

The quantitative analysis and prediction of flowsthrough soils, for a given set of boundary conditions,depends on the values of the various phenomenologicalcoefficients in the above flow equations. Unfortunately,these are not always known with certainty, and theymay vary over wide ranges, even within an apparentlyhomogeneous soil mass. The direct flow coefficients,that is, the hydraulic, electrical, and thermal conduc-tivities, and the diffusion coefficient, exhibit thegreatest ranges of values. Thus, it is important to ex-amine these properties first before detailed analysis ofcoupled flow contributions. For many problems, it maybe sufficient to consider only the direct flows, providedthe factors influencing their values are fully appreci-ated.

9.11 SIMULTANEOUS FLOWS OF WATER,CURRENT, AND CHEMICALS

Use of irreversible thermodynamics for the descriptionof coupled flows as developed above is straightforwardin principle; however, it becomes progressively moredifficult in application as the numbers of driving forcesand different flow types increase. This is because of(1) the need for proper specification of the differentcoupling coefficients and (2) the need for independent

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Figure 9.21 Schematic diagram of system for analysis ofsimultaneous flows of water, electricity, and ions through asoil.

methods for their measurement. Thus, the analysis ofcoupled hydraulic and electrical flows or of coupledhydraulic and chemical flows is much simpler than theanalysis of a system subjected to electrical, chemical,and hydraulic gradients simultaneously. Relationshipsfor the volume flow rate of water for several cases andfor thermoelectric and thermoosmotic coupling in sat-urated soils are given by Gray (1966, 1969). The si-multaneous flows of liquid and charge in kaolinite andthe fluid volume flow rates under hydraulic, electric,and chemical gradients were studied by Olsen (1969,1972). The theory for coupled salt and water flows wasdeveloped by Greenberg (1971) and applied to flowsin a groundwater basin (Greenberg et al., 1973) and tochemicoosmotic consolidation of clay (Mitchell et al.,1973).

Equations for the simultaneous flows of water, elec-tricity, cations, and anions under hydraulic, electrical,and chemical gradients were formulated by Yeung(1990) using the formalism of irreversible thermody-namics as outlined previously. The detailed develop-ment is given by Yeung and Mitchell (1993). Theresults are given here. The chemical flow is separatedinto its anionic and cationic components in order topermit determination of their separate movements as afunction of time. This separation may be important insome problems, such as chemical transport through theground, where the fate of a particular ionic species, aheavy metal, for example, is of interest.

The analysis applies to an initially homogeneous soilmass that separates solutions of different concentra-tions of anions and cations, at different electrical po-tentials and under different hydraulic heads, as shownschematically in Fig. 9.21. Only one anion and onecation species are assumed to be present, and no ad-sorption or desorption reactions are occurring.

The driving forces are the hydraulic gradient �(�P),the electrical gradient �(�E), and the concentration-dependent parts of the chemical potential gradients ofthe cation ) and of the anion ). The fluxesc c�(� �(�c a

are the volume flow rate of the solution per unit areaJv, the electric current I, and the diffusion flow ratesof the cation and the anion per unit area relatived dJ Jc a

to the flow of water. These diffusion flows are relatedto the absolute flows according to

dJ � J � c J (9.70)i i i v

in which ci is the concentration of ion i. The set ofphenomenological equations that relates the four flowsand driving forces is

cJ � L �(�P) � L �(�E) � L �(�� )v 11 12 13 c

c� L �(�� ) (9.71)14 a

cI � L �(�P) � L �(�E) � L �(�� )21 22 23 c

c� L (�� ) (9.72)24 a

d cJ � L �(�P) � L �(�E) � L �(�� )c 31 32 33 c

c� L �(�� ) (9.73)34 a

d cJ � L �(�P) � L �(�E) � L �(�� )a 41 42 43 c

c� L �(�� ) (9.74)44 a

These equations contain 4 conductivity coefficients Lii

and 12 coupling coefficients Lij. As a result of Onsagerreciprocity, however, the number of independent cou-pling coefficients reduces because

L � L12 21

L � L13 31

L � L14 41

L � L23 32

L � L24 42

L � L34 43

Thus there are 10 independent coefficients neededfor a full description of hydraulic, electrical, anionic,

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SIMULTANEOUS FLOWS OF WATER, CURRENT, AND CHEMICALS 281

and cationic flows through a system subjected to hy-draulic, electrical, and chemical gradients. If three ofthe four forces can be set equal to zero during a mea-surement of the flow under the fourth force, then theratio of the flow rate to that force will give the valueof its corresponding Lij. However, such measurementsare not always possible or convenient. Accordingly,two forces and one flow are usually set to zero and theappropriate Lij are evaluated by solution of simultane-ous equations. For measurements of hydraulic conduc-tivity, electroosmotic hydraulic conductivity, electricalconductivity, osmotic efficiency, and effective diffusioncoefficients done in the usual manner in geotechnicaland chemical laboratories, the detailed application ofirreversible thermodynamic theory led Yeung (1990)and Yeung and Mitchell (1993) to the following defi-nitions for the Lij. It was assumed in the derivationsthat the solution is dilute and there are no interactionsbetween cations and anions.8

k L Lh 12 21L � � (9.75)11 n Lw 22

keL � L � (9.76)12 21 n

�"c k L Lc h 12 23L � L � � (9.77)13 31 n Lw 22

�"c k L La h 12 24L � L � � (9.78)14 41 n Lw 22

�eL � (9.79)22 n

L � L � c u* (9.80)23 32 c c

L � L � �c u* (9.81)24 42 a a

D* cc cL � (9.82)33 RT

L � L � 0 (9.83)34 43

D* ca aL � (9.84)44 RT

where kh � hydraulic conductivity as usually mea-sured (no electrical short circuiting)

ke � coefficient of electroosmotic hydraulicconductivity

8 The Lij coefficients in Eqs. (9.75) to (9.84) were derived in termsof the cross-sectional area of the soil voids. They may be redefinedin terms of the total cross-sectional area by multiplying each termon the right-hand side by the porosity, n.

�e � bulk electrical conductivity of the soil" � coefficient of osmotic efficiency

w � unit weight of watercc � concentration of cationca � concentration of anion

�u*c effective ionic mobility of the cation�u*a effective ionic mobility of the anion�D*c effective diffusion coefficient of the cation�D*a effective diffusion coefficient of the anion

n � soil porosityR � universal gas constant (8.314 J K�1 mol�1)T � absolute temperature (K)

Subsequently, Manassero and Dominijanni (2003)pointed out that the practical equations for diffusionL33 and L44 do not take the osmotic efficiency " (Sec-tion 9.13) into account, so Eqs. (9.82) and (9.84) moreproperly should be

2(1 � ")D* c k"c cL � c � (9.85) �33 c RT nw

2(1 � ")D* c k"a aL � c � (9.86) �44 a RT nw

This modification becomes important in clays whereinosmotic efficiency, that is, the ability of the clay torestrict the flow of ions, is high.

As the flows of ions relative to the soil are of moreinterest than relative to the water, Eq. (9.70) and Eqs.(9.73) and (9.74) can be combined to give

J � (L � c L ) �(�h) � (L � c L )�(�E)c 31 c 11 w 32 c 12

RT� (L � c L ) �(�c )33 c 13 ccc

RT� (L � c L ) �(�c )34 c 14 aca

(9.87)

J � (L � c L ) �(�h) � (L � c L )�(�E)a 41 a 11 w 42 a 12

RT� (L � c L ) �(�c )43 a 13 ccc

RT� (L � c L ) �(�c )44 a 14 aca

(9.88)

where �(�h) is the hydraulic gradient. In Eqs. (9.87)and (9.88) the gradient of the chemical potential hasbeen replaced by the gradient of the concentration ac-cording to

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RTc�(�� ) � �(�c ) (9.89)i ici

These equations reduce to the known solutions forspecial cases such as chemical diffusion, advection–dispersion, osmotic pressure according to the van’tHoff equation [see Eq. (9.98)], osmosis, and ultra-filtration. They predict reasonably well the distributionof single cations and anions as a function of time andposition in compacted clay during the simultaneous ap-plication of hydraulic, electrical, and chemical gradi-ents (Mitchell and Yeung, 1990).

The analysis of multicomponent systems is morecomplex. The use of averaged chemical properties andthe assumption of composite single species of anionsand cations may yield reasonable approximate solu-tions in some cases. Malusis and Shackelford (2002a)present a more general theory for coupled chemicaland hydraulic flow, based on an extension of the Yeungand Mitchell (1993) formulation, which accounts formulticomponent pore fluids and ion exchange proc-esses occurring during transport.9

The flow equations can be incorporated into numer-ical models for the solution of transient flow problems.Conservation of mass of species i requires that

�ci � ��J � G (9.90)i i�t

in which Gi is a source–sink term describing the ad-dition or removal rate of species i from the solution.As commonly used in groundwater flow analyses ofcontaminant transport, Gi is given by

�K �K �cd d iG � 1 � � c � (9.90a) �i i in n �t

where �i is the decay constant of species i, � is thebulk dry density of the soil, Kd is the distribution co-efficient, and n is the soil porosity. As defined previ-ously, the distribution constant is the ratio of theamount of chemical adsorbed on the soil to that insolution. The quantity in the brackets on the right-handside of Eq. (9.90) is the retardation factor Rd definedby Eq. (9.56).

Advection rather than diffusion is the dominantchemical transport mechanism in coarse-grained soils.

9 Malusis and Shackelford (2002a) defined parameters in terms of thetotal cross-sectional area for flow rather than the cross-sectional areaof voids as used in the development of Eqs. (9.75) through (9.84).

At the pore scale level, the fluid particles carrying dis-solved chemicals move at different speeds because oftortuous flow paths around the soil grains and variablevelocity distribution in the pores, ranging from zero atthe soil particle surfaces to a maximum along the cen-terline of the pore. This results in hydrodynamic dis-persion and a zone of mixing rather than a sharpboundary between two flowing solutions of differentconcentrations. Mathematically, this is accounted forby adding a dispersion term to the diffusion coefficientin the L33 and L44 terms to account for the deviationof actual motion of fluid particles from the overall oraverage movement described by Darcy’s law. More de-tails can be found in groundwater and contaminationtextbooks such as Freeze and Cherry (1979) and Dom-inico and Schwartz (1997).

Numerical models are available for groundwaterflow and contaminant transport into which the aboveflow equations can be introduced (e.g., Anderson andWoessner, 1992; Zheng and Bennett, 2002). The mostwidely used groundwater flow numerical code isMODFLOW developed by the United States Geolog-ical Survey (USGS); various updated versions areavailable (e.g., Harbaugh et al., 2000). To solvesingle-species contaminant transport problems ingroundwater, MT3DMS (Zheng and Wang, 1999) canbe used. The code utilizes the flow solutions fromMODFLOW. More complex multispecies reactions canbe simulated by RT3D (Clement, 1997). POLLUTE(Rowe and Booker, 1997) provides ‘‘one- and one-half-dimensional’’ solution to the advection–dispersionequation and is widely used in landfill design. A va-riety of public domain groundwater flow and contam-inant transport codes is available from the web sites ofthe USGS, the U.S. Environmental Protection Agency(U.S. EPA), and the U.S. Salinity Laboratory.

9.12 ELECTROKINETIC PHENOMENA

Coupling between electrical and hydraulic flows andgradients can generate four related electrokinetic phe-nomena in materials such as fine-grained soils, wherethere are charged particles balanced by mobile coun-tercharges. Each involves relative movements of elec-tricity, charged surfaces, and liquid phases, as shownschematically in Fig. 9.22.

Electroosmosis

When an electrical potential is applied across a wetsoil mass, cations are attracted to the cathode and an-ions to the anode (Fig. 9.22a). As ions migrate, they

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ELECTROKINETIC PHENOMENA 283

Figure 9.22 Electrokinetic phenomena: (a) electroosmosis, (b) streaming potential, (c) elec-trophoresis, and (d) migration or sedimentation potential.

carry their water of hydration and exert a viscous dragon the water around them. Since there are more mobilecations than anions in a soil containing negativelycharged clay particles, there is a net water flow towardthe cathode. This flow is termed electroosmosis, andits magnitude depends on ke, the coefficient of elec-troosmotic hydraulic conductivity and the voltage gra-dient, as considered in more detail later.

Streaming Potential

When water flows through a soil under a hydraulicgradient (Fig. 9.22b), double-layer charges are dis-placed in the direction of flow. This generates an elec-trical potential difference that is proportional to thehydraulic flow rate, called the streaming potential, be-tween the opposite ends of the soil mass. Streamingpotentials up to several tens of millivolts have beenmeasured in clays.

Electrophoresis

If a DC field is placed across a colloidal suspension,charged particles are attracted electrostatically to one

of the electrodes and repelled from the other. Nega-tively charged clay particles move toward the anode asshown in Fig. 9.22c. This is called electrophoresis.Electrophoresis involves discrete particle transportthrough water; electroosmosis involves water transportthrough a continuous soil particle network.

Migration or Sedimentation Potential

The movement of charged particles such as clay rela-tive to a solution, as during gravitational settling, forexample, generates a potential difference, as shown inFig. 9.22d. This is caused by the viscous drag of thewater that retards the movement of the diffuse layercations relative to the particles.

Of the four electrokinetic phenomena, electroos-mosis has been given the most attention in geotechni-cal engineering because of its practical value fortransporting water in fine-grained soils. It has beenused for dewatering, soft ground consolidation, groutinjection, and the containment and extraction of chem-icals in the ground. These applications are consideredin a later section.

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9.13 TRANSPORT COEFFICIENTS AND THEIMPORTANCE OF COUPLED FLOWS

To assess conditions where coupled chemical, electri-cal, and hydraulic flows will be significant relative todirect flows, it is necessary to know the values of theLij relative to the Lii. Estimates can be made by con-sidering the probable values of the soil state parametersand the several flow and transport coefficients given inEqs. (9.75) to (9.84). Typical ranges are given in Table9.5.

In Table 9.5 the diffusion coefficients and ionic mo-bilities for cations and anions are considered togethersince they lie within similar ranges for most species.Values of ionic mobility for specific ions in dilute so-lution are given in standard chemical references, forexample, Dean (1973), and values of diffusion coeffi-cients are given in Tables 9.3 and 9.4. Ionic mobilityis related to the diffusion coefficient according to

D �z �Fi iu � (9.91)i RT

in which zi is the ionic valence and F is Faraday’sconstant. Similarly to the diffusion coefficients, theionic mobilities are considerably less in a soil than ina free solution, especially in a fine-grained soil.

The importance of coupled flows to fluid, electricalcurrent, and chemical transport through soil under dif-ferent conditions can be examined by study of the con-tributions of the different terms in Eqs. (9.71), (9.72),(9.87), and (9.88). For this purpose, the equations havebeen rewritten in one-dimensional form and in termsof the hydraulic, electrical, and chemical concentrationgradients: ih � �dh /dx, ie � �dV /dx, and ic � �dc /dx, respectively. In addition, the chemical flows havebeen represented by a single equation. This assumesthat all dissolved species are moving together. Termsinvolving the ionic mobility u do not exist in such aformulation because the cations and anions move to-gether, with the effects of electrical fields assumed toaccelerate the slower moving ions and to retard thefaster moving ions. Thus there is no net transfer ofelectric charge due to ionic movement. The Lij coeffi-cients have been replaced by the physical and chemicalquantities that determine them, as given by Eqs. (9.74)through (9.85). The resulting equations are the follow-ing. For fluid flow:

2k k k "kh e e hJ � � i � i � RT � i � � �v w h e cn � n n ne w

(9.92)

For electrical current flow:

k �e w eI � i � i (9.93) � �h en n

For chemical flow relative to the soil:

2(1 � ")ck ck ckh e w eJ � � i � i � �c h en n� ne

"ckh� D* � RT i (9.94) � cnw

Coupling Influences on Hydraulic Flow

In the absence of applied electrical and chemical gra-dients, flow under a hydraulic gradient is given by thefirst bracketed term on the right-hand side of Eq.(9.92). It contains the quantity , which com-2k /n�e w e

pensates for the electroosmotic counterflow generatedby the streaming potential, which causes the measuredvalue of kh to be slightly less than the true value ofL11.

As it is not usual practice to short-circuit betweenthe ends of samples during hydraulic conductivity test-ing, the second bracketed term on the right-hand sideof Eq. (9.92) is not zero. This term represents an elec-troosmotic counterflow that results from the streamingpotential and acts in the direction opposite to the hy-draulically driven flow. Analysis based on the valuesof properties in Table 9.5, as well as the results ofmeasurements, for example, Michaels and Lin (1954)and Olsen (1962) show that this counterflow is negli-gible in most cases, but it may become significant rel-ative to the true hydraulic conductivity for soils of verylow hydraulic conductivity, for example, kh � 1 �10�10 m/s. For example, for a value of ke of 5 � 10�9

m2/s-V, an electrical conductivity of 0.01 mho/m, anda porosity of 35 percent, the counterflow term is 0.7� 10�10 m/s.

In the presence of an applied DC field the secondbracketed term on the right-hand side of Eq. (9.92) canbe very large relative to hydraulic flow in soils finerthan silts, as ke, which typically ranges within onlynarrow limits, is large relative to kh; that is, kh is lessthan 1 � 10�8 m/s in these soils. The relative effect-iveness of hydraulic and electrical driving forces forwater movement can be assessed by comparing gra-dients needed to give equal flow rates. They will beequal if

k i � k i (9.95)e e h h

The hydraulic gradient required to balance the elec-troosmotic flow then becomes

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TRANSPORT COEFFICIENTS AND THE IMPORTANCE OF COUPLED FLOWS 285

Figure 9.23 Theoretical values of osmotic pressure as afunction of concentration difference across a clay layer fordifferent values of osmotic efficiency coefficient, ". (T �20�C).

kei � i (9.96)h ekh

As the hydraulic conductivity of soils in which elec-troosmosis is likely to be used is usually of the orderof 1 � 10�9 m/s or less, whereas ke is in the range of1 � 10�9 to 1 � 10�8 m2/s � V, it follows that evensmall electrical gradients can balance flows caused bylarge hydraulic gradients. Because of this, and becauseke is insensitive to particle size while kh decreases rap-idly with decreasing particle size, electroosmosis is ef-fective in fine-grained soils, as discussed further inSection 9.15.

Chemically driven hydraulic flow is given by the lastterm on the right-hand side of Eq. (9.92). It dependsprimarily on the osmotic efficiency ". Osmotic effi-ciency has an important influence on the movement ofchemicals through a soil, the development of osmoticpressure, and the effectiveness of clay barriers forchemical waste containment.

Osmotic Efficiency The osmotic efficiency of clay,a slurry wall, a geosynthetic clay liner (GCL), or otherseepage and containment barrier is a measure of thematerial’s effectiveness in causing hydraulic flow un-der an osmotic pressure gradient and of its ability toact as a semipermeable membrane in preventing thepassage of ions, while allowing the passage of water.The osmotic pressure concept can be better appreciatedby rewriting the last term in Eq. (9.92):

k k RT c 1h h" RTi � " (9.97)c n n xw w

This form is analogous to Darcy’s law, with the quan-tity RT c /w being the head difference. The osmoticefficiency is a measure of the extent to which this the-oretical pressure difference actually develops. Theo-retical values of osmotic pressure, calculated using thevan’t Hoff equation, as a function of concentration dif-ference for different values of osmotic efficiency areshown in Fig. 9.23.

The van’t Hoff equation for osmotic pressure is

� � kT (n � n ) � RT(c � c ) (9.98)� iA iB iA iB

where k is the Boltzmann constant (gas constant permolecule), R is the gas constant per molecule, T is theabsolute temperature, ni is concentration in particlesper unit volume, and ci is the molar concentration. Thevan’t Hoff equation applies for ideal and relatively di-lute solution concentrations (Malusis and Shackelford,2002c). According to Fritz (1986) the error is low(�5%) for 1�1 electrolytes (e.g., NaCl, KCl) and con-centrations �1.0 M.

Values of osmotic efficiency coefficient, ", ormembrane efficiency (" expressed as a percentage),have been measured for clays and geosynthetic clayliners; for example, Kemper and Rollins (1966), Leteyet al. (1969), Olsen (1969), Kemper and Quirk (1972),Bresler (1973), Elrick et al. (1976), Barbour and Fred-lund (1989), and Malusis and Shackelford (2002b,2002c). Values of membrane efficiency from 0 to 100percent have been determined, depending on the claytype, porosity, and type and concentration of salts insolution. The results of many determinations weresummarized by Bresler (1973) as shown in Fig. 9.24.The efficiency is shown as a function of a normalizingparameter, the half distance between particles b timesthe square root of the solution concentration .c

To put these relations into more familiar terms foruse in geotechnical studies, the half spacings were con-verted to water contents on the assumption of uniformwater layer thicknesses on all particles, using specificsurface areas corresponding to different clay types andnoting that volumetric water content equals surfacearea times layer thickness. The relationship betweenspecific surface area and liquid limit (LL) obtained byFarrar and Coleman (1967) for 19 British clays

LL � 19 � 0.56A (�20%) (9.99)s

in which the specific surface area As is in square metersper gram, was then used to obtain the relationshipsshown in Fig. 9.25. The computed efficiencies shownin Fig. 9.25 should be considered upper bounds be-cause the assumption of uniform water distributionover the full surface area underestimates the effectiveparticle spacing in most cases. In most clays, espe-

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Figure 9.24 Osmotic efficiency coefficient as a function ofb where c is concentration of monovalent anion in nor-cmality and 2b is the effective spacing between particle sur-faces (from Bresler, 1973).

cially those with divalent adsorbed cations, individualclay plates associate in clusters giving an effective spe-cific surface that is less than that determined by mostmethods of measurement. This means that the curvesin Fig. 9.25 should in reality be displaced to the left.

High osmotic efficiencies are developed at low watercontents, that is, in very dense, low-porosity clays, andin dilute electrolyte systems. Malusis and Shackelford(2002a, 2002b, 2002c) found that the osmotic effi-ciency decreases with increasing solute concentrationand attribute this to compression of the diffuse doublelayers adjacent to the clay particles.

Water flow by osmosis can be significant relative tohydraulically driven water flow in heavily overconsol-idated clay and clay shale, where the void ratio is lowand the hydraulic conductivity is also very low. Suchflow may be important in geological processes (Olsen1969, 1972). Densely compacted clay barriers forwaste containment, usually composed of bentonite,possess osmotic membrane properties. As the chemical

concentrations on the inside of a lined repositoryshould be greater than on the outside, osmoticallydriven water flow should be directed from the outsidetoward the inside. The greater the osmotic efficiencythe greater the driving force for this flow. Furthermore,if the efficiency is high, then outward diffusion of con-tained chemicals is restricted (Malusis and Shack-elford, 2002b). In diffusion-dominated containmentbarriers, the effect of solute restriction on reducing sol-ute diffusion is likely substantially more significantthan the effect of osmotic flow (Shackelford et al.,2001).

Coupling Influences on Electrical Flow

Substitution of values for the parameters in Eq. (9.93)indicates, as would be expected, that electrical currentflow is dominated completely by the electrical gradientie. In the presence of an applied voltage difference, theother terms are of little importance, even if the move-ments of anions and cations are considered separatelyand the contributions due to ionic mobility are takeninto account. On the other hand, when a soil layer be-haves as an open electrical circuit, small electrical po-tentials, measured in millivolts, may exist if there arehydraulic and/or chemical flows. This may be seen bysetting I � 0 in Eq. (9.93) and solving for ie, whichmust have value if ih has value. These small potentialsand flows are important in such processes as corrosionand electroosmotic counterflow.

Coupling Influences on Chemical Flow

Equation (9.94) provides a description of chemicaltransport relative to the soil. It contains two terms thatinfluence chemical flow under a hydraulic gradient;one for chemical transport under an electrical gradient,and one for transport of chemical under a chemicalgradient. The first term in the first bracket of the right-hand side of Eq. (9.94) describes advective transport.As would be expected, the smaller the osmotic effi-ciency, the more chemical flow through the soil is pos-sible. The second term in the same bracket simplyreflects the advective flow reduction that would resultfrom electroosmotic counterflow caused by develop-ment of a streaming potential. As noted earlier, thisflow will be small, and its contribution to the total flowwill be small, except in clays of very low hydraulicand electrical conductivities. Advective transport is thedominant means for chemical flow for soils having ahydraulic conductivity greater than about 1 � 10�9

m/s.The importance of an electrical driving force for

chemical flow depends on the electrical potential gra-dient. For a unit gradient, that is, 1 V/m, chemical flow

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TRANSPORT COEFFICIENTS AND THE IMPORTANCE OF COUPLED FLOWS 287

Figure 9.25 Osmotic efficiency of clays as a function of water content.

quantities are comparable to those by advective flowunder a unit hydraulic gradient in a clay having a hy-draulic conductivity of about 1 � 10�9 m/s. Electri-cally driven chemical flow is relatively less importantin higher permeability soils and more important insoils with lower kh. In cases where the electricallydriven chemical transport is of interest, as in electro-kinetic waste containment barrier applications, anion,cation, and nonionic chemical flows must be consid-ered separately using expanded relationships such asgiven by Eqs. (9.87) and (9.88).

The last bracketed quantity of Eq. (9.94) representsdiffusive flow under chemical gradients. The quantityD*ic gives the normal diffusive flow rate. The secondterm represents a restriction on this flow that dependson the clay’s osmotic efficiency, "; that is, if the clayacts as an effective semipermeable membrane, diffu-sive flow of chemicals is restricted. However, even un-

der conditions where the value of " is low such thatthe second term in the bracket is negligible, chemicaltransport by diffusion is significant relative to advec-tive chemical transport in soils with hydraulic conduc-tivity values less than about 1 � 10�9 to 1 � 10�10

m/s for chemicals with diffusion coefficients in therange given by Table 9.7, that is, 2 � 10�10 to 2 �10�9 m2/s.

This is illustrated by Fig. 9.26 from Shackelford(1988), which shows the relative importance of advec-tive and diffusive chemical flows on the transit timethrough a 0.91-m-thick compacted clay liner having aporosity of 0.5 acted on by a hydraulic gradient of1.33. A diffusion coefficient of 6 � 10�10 m2/s wasassumed. The transit time is defined as the time re-quired for the solute concentration on the dischargeside to reach 50 percent of that on the upstream side.For hydraulic conductivity values less than about 2 �

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Figure 9.26 Transit times for chemical flow through a 0.91-m-thick compacted clay liner having a porosity of 50 percentand acted on by a hydraulic gradient of 1.33 (from Shack-elford, 1988).

10�9 m/s the transit time in the absence of diffusionwould be very long. For diffusion alone the transit timewould be about 47 years.

Most compacted clay barriers and geosynthetic clayliners are likely to have hydraulic conductivity valuesin the range of 1 � 10�11 to 1 � 10�9 m/s, with thelatter value being the upper limit allowed by the U.S.EPA for most waste containment applications. In thisrange, diffusion reduces the transit time significantlyin comparison to what it would be due to advectionalone. This is shown by the curve labeled advection–dispersion in Fig. 9.26. The calculations were doneusing the well-known advection–dispersion equation(Ogata and Banks, 1961) in which the dispersion termincludes both mechanical mixing and diffusion. Me-chanical mixing is negligible in low-permeability ma-terials such as compacted clay.

9.14 COMPATIBILITY—EFFECTS OFCHEMICAL FLOWS ON PROPERTIES

Chemical Compatibility and Hydraulic Conductivity

The compatibility between waste chemicals, especiallyliquid organics, and compacted clay liners and slurrywall barriers constructed to contain them must be con-sidered in the design of waste containment barriers.Numerous studies have been done to evaluate chemicaleffects on clay hydraulic conductivity because of fearsthat prolonged exposure may compromise the integrityof the liners and barriers and because tests have shownthat under some conditions clay can shrink and crackwhen permeated by certain classes of chemicals. Sum-maries of the results of chemical compatibility studiesare given by Mitchell and Madsen (1987) and Quigleyand Fernandez (1989), and factors controlling the long-

term stability of clay liners are discussed by Mitchelland Jaber (1990).

Rigid wall, flexible wall, and consolidometer per-meameters are used for compatibility testing in the lab-oratory. These three types of test apparatus are shownschematically in Fig. 9.27. Tests done in a rigid wallsystem overestimate hydraulic conductivity wheneverchemical–clay interactions cause shrinkage and crack-ing; however, a rigid wall system is well suited forqualitative determination of whether or not there maybe adverse interactions. In the flexible wall system thelateral confining pressure prevents cracks from open-ing; thus there is risk of underestimating the hydraulicconductivity of some soils. The consolidometer per-meameter system allows for testing clays under a rangeof overburden stress states that are representative ofthose in the field and for quantitative assessment of theeffects of chemical interactions on volume stability andhydraulic conductivity. More details of these perme-ameters are given by Daniel (1994).

The effects of chemicals on the hydraulic conduc-tivity of high water content clays such as used in slurrywalls are likely to be much greater than on lower watercontent, high-density clays as used in compacted clayliners. This is because of the greater particle mobilityand easier opportunity for fabric changes in a higherwater content system. A high compactive effort or aneffective confining stress greater than about 70 kPa canmake properly compacted clay invulnerable to attackby concentrated organic chemicals (Broderick andDaniel, 1990). However, it is not always possible toensure high-density compaction or to maintain highconfining pressures, or eliminate all construction de-fects, so it is useful to know the general effects ofdifferent types of chemicals on hydraulic conductivity.

The influences of inorganic chemicals on hydraulicconductivity are consistent with (1) their effects on thedouble-layer and interparticle forces in relation to floc-culation, dispersion, shrinkage, and swelling, (2) theireffects on surface and edge charges on particles andthe influences of these charges on flocculation and de-flocculation, and (3) their effects on pH.

Acids can dissolve carbonates, iron oxides, and thealumina octahedral layers of clay minerals. Bases candissolve silica tetrahedral layers, and to a lesser extent,alumina octahedral layers of clay minerals. Removalof dissolved material can cause increases in hydraulicconductivity, whereas precipitation can clog pores andreduce hydraulic conductivity.

The most important factors controlling the effects oforganic chemicals on hydraulic conductivity are (1)water solubility, (2) dielectric constant, (3) polarity,and (4) whether or not the soil is exposed to the pureorganic or a dilute solution. Exposure of clay barriers

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COMPATIBILITY—EFFECTS OF CHEMICAL FLOWS ON PROPERTIES 289

Figure 9.27 Three types of permeameter for compatibility testing: (a) rigid wall, (b) flexiblewall, and (c) consolidometer permeameter (from Day, 1984).

to water-insoluble pure or concentrated organics islikely only in the case of spills, leaking tanks, and withdense non-aqueous-phase liquids (DNAPLs) or ‘‘sink-ers’’ that accumulate above low spots in liners. Somegeneral conclusions about the influences of organicson the hydraulic conductivity are:

1. Solutions of organic compounds having a lowsolubility in water, such as hydrocarbons, haveno large effect on the hydraulic conductivity. Thisis in contrast to dilute solutions of inorganic com-pounds that may have significant effects as aresult of their influence on flocculation and dis-persion of the clay particles.

2. Water-soluble organics, such as simple alcoholsand ketones, have no effect on hydraulic conduc-tivity at concentrations less than about 75 to 80percent.

3. Many water-insoluble organic liquids (i.e., non-aquoues-phase liquids, NAPLs) can cause shrink-age and cracking of clays, with concurrentincreases in hydraulic conductivity.

4. Hydraulic conductivity increases caused by per-meation by organics are partly reversible whenwater is reintroduced as the permeant.

5. Concentrated hydrophobic compounds (likemany NAPLs) permeate soils through cracks andmacropores. Water remains within mini- and mi-cropores.

6. Hydrophilic compounds permeate the soil moreuniformly than NAPLs, as the polar moleculescan replace the water in hydration layers of thecations and are more readily adsorbed on particlesurfaces.

7. Organic acids can dissolve carbonates and ironoxides. Buffering of the acid can lead to precip-

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Figure 9.28 (a) Hydraulic conductivity and (b) intrinsic permeability of compacted Sarniaclay permeated with leachate–dioxane mixtures. Initial tests run using water (●) followed byleachate–chemical solution (�). (from Fernandez and Quigley, 1988). Reproduced with per-mission from the National Research Council of Canada.

itation and pore clogging downstream. However,after long time periods these precipitates may beredissolved and removed, thus leading to an in-crease in hydraulic conductivity.

8. Pure bases can cause a large increase in the hy-draulic conductivity, whereas concentrations at orbelow the solubility limit in water have no effect.

9. Organic acids do not cause large-scale dissolu-tion of clay particles.

The combined effects of confining pressure and con-centration, as well as permeant density and viscosity,are illustrated by Fig. 9.28 (Fernandez and Quigley,1988). The data are for water-compacted, brown Sarniaclay permeated by solutions of dioxane in domesticlandfill leachate. Increased hydrocarbon concentrationcaused a decrease in hydraulic conductivity up to con-centrations of about 70 percent, after which the hy-draulic conductivity increased by about three orders ofmagnitude for pure dioxane (Fig. 9.28a), for samplesthat were unconfined by a vertical stress ( � 0). On��vthe other hand, the data points for samples maintainedunder a vertical confining stress of 160 kPa indicatedno effect of the dioxane on hydraulic conductivity rel-

ative to that measured with water. The decreases inhydraulic conductivity for dioxane concentrations upto 70 percent can be accounted for in terms of fluiddensity and viscosity, as may be seen in Fig. 9.28bwhere the intrinsic values of permeability are shown.As noted earlier in this chapter, the intrinsic permea-bility is defined by K � k� /.

Although many chemicals do not have significanteffect on the hydraulic conductivity of clay barriers,this does not mean that they will not be transportedthrough clay. Unless adsorbed by the clay or by or-ganic matter, the chemicals will be transported by ad-vection and diffusion. Furthermore, the actual transittime through a barrier by advection, that is, the timefor chemicals moving with the seepage water, may befar less than estimated using the conventional seepagevelocity. The seepage velocity is usually defined as theDarcy velocity khih, divided by the total porosity n. Insystems with unequal pore sizes the flow is almost to-tally through mini- and macropores, which comprisethe effective porosity ne, which may be much less thanthe total porosity. Thus effective compaction of claybarriers must break down clods and aggregates to de-crease the effective pore size and increase the propor-

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ELECTROOSMOSIS 291

Table 9.7 Coefficients of Electroosmotic Permeability

No. MaterialWater

Content (%)ke in 10�5

(cm2/s-V)Approximate kh

(cm/s)

1. London clay 52.3 5.8 10�8

2. Boston blue clay 50.8 5.1 10�8

3. Kaolin 67.7 5.7 10�7

4. Clayey silt 31.7 5.0 10�6

5. Rock flour 27.2 4.5 10�7

6. Na-Montmorillonite 170 2.0 10�9

7. Na-Montmorillonite 2000 12.0 10�8

8. Mica powder 49.7 6.9 10�5

9. Fine sand 26.0 4.1 10�4

10. Quartz powder 23.5 4.3 10�4

11. As quick clay 31.0 20.0–2.5 2.0 � 10�8

12. Bootlegger Cove clay 30.0 2.4–5.0 2.0 � 10�8

13. Silty clay, West Branch Dam 32.0 3.0–6.0 1.2 � 10�8–6.5 � 10�8

14. Clayey silt, Little Pic River,Ontario

26.0 1.5 2 � 10�5

ke and water content data for Nos. 1 to 10 from Casagrande (1952). kh estimated by authors; no. 11from Bjerrum et al. (1967); no. 12 from Long and George (1967); no. 13 from Fetzer (1967); no. 14from Casagrande et al. (1961).

tion of the porosity that is effective porosity, therebyincreasing the transit time.

9.15 ELECTROOSMOSIS

The coefficient of electroosmotic hydraulic conductiv-ity ke defines the hydraulic flow velocity under a unitelectrical gradient. Measurement of ke is made by de-termination of the flow rate of water through a soilsample of known length and cross section under aknown electrical gradient. Alternatively, a null indicat-ing system may be used or it may be deduced from astreaming potential measurement. From experience itis known that ke is generally in the range of 1 � 10�9

to 1 � 10�8 m2/s V (m/s per V/m) and that it is ofthe same order of magnitude for most soil types, asmay be seen by the values for different soils and afreshwater permeant given in Table 9.7.

Several theories have been proposed to explain elec-troosmosis and to provide a basis for quantitative pre-diction of flow rates.

Helmholtz and Smoluchowski Theory

This theory, based on a model introduced by Helm-holtz (1879) and refined by Smoluchowski (1914), isone of the earliest and most widely used. A liquid-filled capillary is treated as an electrical condenser with

charges of one sign on or near the surface of the walland countercharges concentrated in a layer in the liquida small distance from the wall, as shown in Fig. 9.29.10

The mobile shell of counterions is assumed to dragwater through the capillary by plug flow. There is ahigh-velocity gradient between the two plates of thecondenser as shown.

The rate of water flow is controlled by the balancebetween the electrical force causing water movementand friction between the liquid and the wall. If v is theflow velocity and � is the distance between the walland the center of the plane of mobile charge, then thevelocity gradient between the wall and the center ofpositive charge is v /�; thus, the drag force per unitarea is � dv /dx � �v /�, where � is the viscosity. Theforce per unit area from the electrical field is � E / L, where � is the surface charge density and E / Lis the electrical potential gradient. At equilibrium

v E� � � (9.100)

� L

or

10 A derivation using a Poisson–Boltzmann distribution of counter-ions adjacent to the wall gives the same result.

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Figure 9.29 Helmholtz–Smoluchowski model for electrokinetic phenomena.

L�� v (9.101)

E

From electrostatics, the potential across a condenser� is given by

�� (9.102)

D

where D is the relative permittivity, or dielectric con-stant of the pore fluid. Substitution for �� in Eq.(9.102) gives

�D Ev � (9.103)� �� L

The potential � is termed the zeta potential. It is notthe same as the surface potential of the double-layer�0 discussed in Chapter 6, although conditions thatgive high values of �0 also give high values of zetapotential. A common interpretation is that the actualslip plane in electrokinetic processes is located somesmall, but unknown, distance from the surface of par-ticles; thus � should be less than �0. Values of � in therange of 0 to �50 mV are typical for clays, with thelowest values associated with high pore water salt con-centrations.

For a single capillary of area a the flow rate is

�D Eq � va � a (9.104a)a � L

and for a bundle of N capillaries within total cross-sectional area A normal to the flow direction

�D Eq � Nq � Na (9.104b)A a � L

If the porosity is n, then the cross-sectional area ofvoids is nA, which must equal Na. Thus,

�D Eq � n A (9.105)A � L

By analogy with Darcy’s law we can write Eq.(9.105) as

q � k i A (9.106)A e e

in which ie is the electrical potential gradient E / Land ke the coefficient of electroosmotic hydraulic con-ductivity is

�Dk � n (9.107)e �

According to the Helmholtz–Smoluchowski theoryand Eq. (9.107), ke should be relatively independent ofpore size, and this is borne out by the values listed inTable 9.7. This is in contrast to the hydraulic conduc-tivity kh, which varies as the square of some effectivepore size. Because of this independence of pore size,electroosmosis can be more effective in moving waterthrough fine-grained soils than flow driven by a hy-draulic gradient.

This is illustrated by the following simple example.Consider a fine sand and a clay of hydraulic conduc-tivity kh of 1 � 10�5 m/s and 1 � 10�10 m/s, respec-tively. Both have ke values of 5 � 10�9 m2/s V. Forequal hydraulic flow rates khih � keie, so

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ELECTROOSMOSIS 293

kei � i (9.108)h ekh

If an electrical potential gradient of 20 V/m is used,substitution in Eq. (9.108) shows that ih is 0.01 for thefine sand and 1000 for the clay. This means that ahydraulic gradient of only 0.01 can move water as ef-fectively as an electrical gradient of 20 V/m in finesand. However, for the clay, a hydraulic gradient of1000 would be needed to offset the electroosmoticflow.

However, it does not follow that electroosmosis willalways be an efficient means to move water in claysbecause the above analysis does not take into accountthe power requirement to develop the potential gradientof 20 V/m or energy losses in the system. These pointsare considered further later.

Schmid Theory

The Helmholtz–Smoluchowski theory is essentially alarge-pore theory because it assumes a negligible ex-tension of the counterion layer into the pore. Also, itdoes not account for an excess of ions over thoseneeded to balance the surface charge. A model thatovercomes the first of these problems was proposed bySchmid (1950, 1951). It can be considered a small-pore theory.

The counterions are assumed to be distributed uni-formly throughout the fluid phase in the soil. The elec-trical force acts uniformly over the entire pore crosssection and gives the same velocity profile as shownby Fig. 9.29. The hydraulic flow rate through a singlecapillary of radius r is given by Poiseuille’s law:

4�rq � i (9.109)w h8�

The hydraulic seepage force per unit length causingflow is

2F � �r i (9.110)H w h

so

2rq � F (9.111)H8�

The electrical force per unit length FE is equal to thecharge times the potential, that is,

E2F � A F �r (9.112)E 0 0 L

where A0 is the concentration of wall charges in ionicequivalents per unit volume of pore fluid, and F0 is theFaraday constant. Replacement of FH by FE in Eq.(9.111) gives

4�r E F A0 0 2q � A F � r i a (9.113)a 0 0 e8� L 8�

so for a total cross section of N capillaries and area A

2A F r0 0q � ni A (9.114)A e8�

This equation shows that ke should vary as r2, whereasthe Helmholtz–Smoluchowski theory leads to ke in-dependent of pore size, as previously noted. Of the twotheories, the Helmholtz gives the better results forsoils, perhaps because most clays have a cluster or ag-gregate structure with electroosmotic flow controlledmore by the larger pores than by the intracluster pores.

Spiegler Friction Model

A completely different concept for electrokinetic proc-esses takes into account the interactions of the mobilecomponents (water and ions) on each other and of thefrictional interactions of these components with porewalls (Spiegler, 1958). This theory provides insightinto conditions leading to high electroosmotic effi-ciency.

The assumptions include:

1. Exclusion of coions,11 that is, the medium be-haves as a perfect perm-selective membrane,admitting ions of only one sign

2. Complete dissociation of pore fluid ions

The following equation for electroosmotic transportof water across a fine-grained porous material contain-ing adsorbed and free ions can be derived:

C3 � (W � H) � (9.115)C � C (X /X )1 3 34 13

in which is the true electroosmotic water flow(moles/faraday), W is the measured water transport

11 Ions of the opposite sign to the charged surface are termed coun-terions. Ions of the same sign are termed coions.

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Figure 9.30 Schematic prediction of water transport by elec-troosmosis in various clays according to the Donnan concept(from Gray, 1966).

(moles/faraday), H is the water transport by ion hy-dration (moles/faraday), C3 is the concentration of freewater in the material (mol/m3), C1 is the concentrationof mobile counterions m2, X34 is the friction coefficientbetween water and the solid wall, and X13 is the frictioncoefficient between cation and water.

Concentrations C1 and C3 are hypothetical and prob-ably less than values measured by chemical analysisbecause some ions may be immobile. Evaluation of X13

and X34 requires independent measurements of diffu-sion coefficients, conductance, transference numbers,and water transport. Thus Eq. (9.115) is limited as apredictive equation. Its real value is in providing a rel-atively simple physical representation of a complexprocess.

From Eq. (9.115),

1 � (W � H) � (9.116)

(C /C � X /X )1 3 34 13

At high water contents and for large pores, X34 /X13 →0 because X34 becomes negligible. Then

� C /C (9.117)X 3 134→0

This relationship indicates that a high water-to-cationratio implies a high rate of electroosmotic flow. At lowwater contents and for small pores, X34 will not bezero, thus reducing the flow. An increase in C1 reducesthe flow of water per faraday of current passed becausethere is less water per ion. An increase in X13 increasesthe flow because there is greater frictional drag on thewater by the ions.

Ion Hydration

Water of hydration is carried along with ions in a directcurrent electric field. The ion hydration transport H isgiven by

H � t N � t N (9.118)� �

where t� and t are the transport numbers, that is, num-bers that represent the fraction of current carried by aparticular ionic species. The numbers N� and N arethe number of moles of hydration water per mole ofcation and anion, respectively.

9.16 ELECTROOSMOSIS EFFICIENCY

Electroosmotic water flow occurs if the frictional dragbetween the ions of one sign and their surroundingwater molecules exceeds that caused by ions of the

opposite sign. The greater the difference between theconcentrations of cations and anions, the greater thenet drag on the water in the direction toward the cath-ode. The efficiency and economics of the process de-pend on the volume of water transported per unitelectrical charge passed. If the volume is high, thenmore water is transported for a given expenditure ofelectrical energy than if it is low. This volume mayvary over several orders of magnitude depending onsuch factors as soil type, water content, and electrolyteconcentration.

In a low exchange capacity soil at high water contentin a low electrolyte concentration solution, there ismuch more water per cation than in a high exchangecapacity, low water content soil having the same porewater electrolyte concentration. This, combinedwith cation-to-anion ratio considerations, leads tothe predicted water transport–water content–soiltype–electrolyte concentration relationships shownschematically in Fig. 9.30, where increasing electrolyteconcentration in the pore water results in a much

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ELECTROOSMOSIS EFFICIENCY 295

Figure 9.31 Electroosmotic water transport versus concentration of external electrolyte so-lution for homoionic kaolinite and illite at various water content (from Gray, 1966).

greater decrease in efficiency for inactive clay thanmore plastic, active clay. Tests on sodium kaolinite (in-active clay) and sodium illite (more active clay) gavethe results shown in Fig. 9.31, which agree well withthe predictions in Fig. 9.30.

The slopes and locations of the curves can be ex-plained more quantitatively in the following way. Al-ternatively to the double-layer theory given in Chapter6, the Donnan (1924) theory can be used to describeequilibrium ionic distributions in fine-grained materi-als. The basis for the Donnan theory is that at equilib-rium the potentials of the internal and externalsolutions are equal and that electroneutrality is re-quired in both phases. It may be shown (Gray, 1966;Gray and Mitchell, 1967) that the ratio R of cations toanions in the internal phase for the case of a symmet-rical electrolyte (z� � z�) is given by

� 2 1 / 2C 1 � (1 � y )R � � (9.119)

� 2 1 / 2C �1 � (1 � y )

where

2C �0y � (9.120)A �0

The concentration C0 is in the external solution, isthe mean molar activity coefficient in the external so-lution, is the mean activity coefficient in the doublelayer, and A0 is the surface charge density per unit porevolume. The parameter A0 is related to the cationexchange capacity (CEC) by

(CEC)�wA � (9.121)0 w

where �w is the density of water and w is the watercontent. The higher R, the greater is the electroosmoticwater transport, all other things equal.

From Eqs. (9.119) to (9.121) it may be deduced thatexclusion of anions is favored by a high exchangecapacity (active clay), a low water content, and lowsalinity in the external solution. However, the concen-tration of anions in the double layer builds up more

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rapidly as the salinity of the external solution increasesin inactive clays than in active clays. As a result theefficiency, as measured by volume of water per unitcharge passed, decreases much more rapidly with in-creasing electrolyte concentration than in the more ac-tive clay.

The results of electroosmosis measurements on anumber of different materials are summarized in Fig.9.32, which shows water flow rate as a function ofwater content. This figure may be used as a guide forprediction of electroosmotic flow rates. The flow ratesshown are for open systems, that is, solution was ad-mitted at the anode at the same time it was extractedfrom the cathode. Electrochemical effects (Section9.18) and water content changes were minimized inthese tests. Thus, the values can be interpreted as upperbounds on the flow rates to be expected in practice.

Values of water content, electrolyte concentration inthe pore water, and type of clay are required for elec-troosmosis efficiency estimation. Water content is read-ily measured, the electrolyte concentration is easilydetermined using a conductivity cell, and the clay typecan be determined from plasticity and grain size in-formation if mineralogical data are not available. Elec-troosmotic flow rates of 0.03 to 0.06 gal/h/amp arepredicted using Fig. 9.32 for soils 11, 13, and 14 inTable 9.7. Electrical treatment for consolidation andground strengthening was effective in these soils. Forsoil 12, however, a flow rate of 0.008 to 0.012 gal/h/amp was predicted, and electroosmosis was not effec-tive.

Saxen’s Law Prediction of Electroosmosis fromStreaming Potential

Streaming potential can be measured directly during ameasurement of hydraulic conductivity by using ahigh-impedance voltmeter and reversible electrodes.Equivalence between streaming potential and elec-troosmosis may be derived. Expansion of Eq. (9.57)for coupled hydraulic and current flows gives

q � L P � L E (9.122)h HH HE

I � L P � L E (9.123)EH EE

in which qh is the hydraulic flow rate, I is the electriccurrent, LHH and LEE are the direct flow coefficients,LHE and LEH are the coupling coefficients for hydraulicflow due to an electrical gradient and electrical flowdue to a hydraulic gradient, P is the pressure drop,and E is the electrical potential drop.

In a usual hydraulic conductivity measurement,there is no electrical current flow, so I � 0, and E isthe streaming potential. Equation (9.123) then becomes

E LEH� � (9.124) P LEE

In electroosmosis P � 0, so Eq. (9.122) is

q � L E (9.125)h HE

and Eq. (9.122) becomes

I � L E (9.126)EE

so

q Lh HE� (9.127)I LEE

By Onsager’s reciprocity theorem LEH � LHE so

q Eh � � (9.128)� � � �I P P�0 I�0

This equivalence between streaming potential and elec-troosmosis was first shown experimentally by Saxen(1892) and is known as Saxen’s law. It has been ver-ified for clay–water–electrolyte systems. Care must betaken to ensure consistency in units. For example, theelectroosmotic flow rate in gallons per hour per ampereis equal to 0.0094 times the streaming potential in mil-livolts per atmosphere.

Energy Requirements

The preceding analysis leads to a prediction of theamount of water moved per unit charge passed, forexample, gallons or cubic meters of water per hour perampere or moles per faraday. If this quantity is denotedby ki, then

q � k I (9.129)h i

Unlike ke, ki varies over a wide range, as may be seenin Fig. 9.32. The power consumption P is

EqhP � E � I � (in W) (9.130)ki

for E in volts and I in amperes. The power consump-tion per unit volume of flow is

P E�3� � 10 (in kWh) (9.131)

q kh i

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297

Figure 9.32 Electroosmotic water transport as a function of water content, soil type, andelectrolyte concentration: (a) homoionic kaolinite and illite, (b) illitic clay and collodionmembrane, and (c) silty clay, illitic clay, and kaolinite.

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Relationship Between ke and ki

From Eqs. (9.108) and (9.129), the electroosmotic flowrate is given by

Eq � k I � k A (9.132)h i e L

Because E /I is resistance and L / (resistance � A) isspecific conductivity �, Eq. (9.132) becomes

kek � (9.133)i �

As ke varies within relatively narrow limits, Eq. (9.133)shows that the electroosmotic efficiency, measured byki, is a sensitive function of the electrical conductivityof the soil. For soils 11, 13, and 14 in Table 9.7, � isin the range of 0.02 to 0.03 S. For soil 12, in whichelectroosmosis was not effective, � is 0.25 S. In es-sence, a high value of electrical conductivity meansthat the current required to develop the voltage is toohigh for economical movement of water. In addition,if high current is used, the generation of gas, heat, andelectrochemical effects become excessive.

9.17 CONSOLIDATION BY ELECTROOSMOSIS

If, in a compressible soil, electroosmosis draws waterto a cathode where it is drained away and no water isallowed to enter at the anode, then consolidation of thesoil between the electrodes occurs in an amount equalto the volume of water removed. Water movementaway from the anode causes consolidation in the vi-cinity of the anode. The effective stress must increaseconcurrently. Because the total stress in the vicinity ofthe anode remains essentially unchanged, the pore wa-ter pressure must decrease. Water drains at the cathodewhere there is no consolidation. Therefore, the total,effective, and pore water pressures at the cathode re-main unchanged. As a result, hydraulic gradient de-velops that tends to cause water flow from cathode toanode. Consolidation continues until the hydraulicforce that drives water back toward the anode exactlybalances the electroosmotic force driving water towardthe cathode.

The usefulness of consolidation by electroosmosisas a means for soil stabilization was established by anumber of successful field applications, for example,Casangrande (1959) and Bjerrum et al. (1967). Twoquestions are important: (1) How much consolidationwill there be? and (2) How long will it take? Answersto these questions are obtained using the coupled flow

equations in place of Darcy’s law in consolidationtheory.

Assumptions

The following idealizing assumptions are made:

1. There is homogeneous and saturated soil.2. The physical and physicochemical properties of

the soil are uniform and constant with time.12

3. No soil particles are moved by electrophoresis.4. The velocity of water flow by electroosmosis is

directly proportional to the voltage gradient.5. All the applied voltage is effective in moving wa-

ter.13

6. The electrical field is constant with time.7. The coupling of hydraulic and electrical flows

can be formulated by Eqs. (9.63) and (9.64).8. There are no electrochemical reactions.

Governing Equations

For one-dimensional flow between plate electrodes(Fig. 9.33a), Eq. (9.63) becomes

k �u �Vhq � � � k (9.134)h e �x �xw

for the flow rate per unit area. For radial flow for theconditions shown in Fig. 9.33b and a layer of unitthickness

k �u �Vhq � � � 2�r � k � 2�r (9.135)h e �r �rw

Introduction of Eq. (9.134) in place of Darcy’s lawin the derivation of the diffusion equation governingconsolidation in one dimension leads to

2 2k � u � V �uh � k � m (9.136)e v2 2 �x �x �tw

and

12 Flow of water away from anodes toward cathodes causes a non-uniform decrease in water content along the line between electrodes.This leads to changes in hydraulic conductivity, electroosmotic hy-draulic conductivity, compressibility, and electrical conductivity withtime and position. To account for these effects, which are discussedby Mitchell and Wan (1977) and Acar et al. (1990), would greatlycomplicate the analysis because it would be highly nonlinear. Similarproblems arise in classical consolidation theory, but the simple lineartheory developed by Terzaghi is adequate for most cases.13 In most cases some of the electrical energy will be consumed bygeneration of heat and gases at the electrodes. To account for thoselosses, an effective voltage can be used (Esrig and Henkel, 1968).

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CONSOLIDATION BY ELECTROOSMOSIS 299

Figure 9.33 Electrode geometries for analysis of consoli-dation by electroosmosis: (a) one-dimensional flow and (b)radial flow.

2 2� u k � V 1 �ue� � (9.137)w2 2�x k �x c �th v

where mv is the compressibility and cv is the coefficientof consolidation. For radial flow, the use of Eq. (9.135)gives

2 2� u k � V 1 �u k �V 1 �ue e� � � �� w w2 2�r k �r r �r k �r c �th h v

(9.138)

Both V and u are functions of position, as shown inFig. 9.34; V is assumed constant with time, whereas uvaries.

Amount of Consolidation

When the hydraulic gradient that develops in responseto the differing amounts of consolidation between theanode and cathode generates a counterflow (kh /w) /(�u /�x) that exactly balances the electroosmotic flowke(�V /�x) in the opposite direction, consolidation iscomplete. As there then is no flow, qh in Eqs. (9.14)and (9.135) is zero. Thus Eq. (9.134) is

k �u �Vh � �k (9.139)e �x �xw

or

kedu � � dV (9.140)wkh

The solution of this equation is

keu � � V � C (9.141)wkh

At the cathode, V � 0 and u � 0; therefore, C � 0,and the pore pressure at equilibrium at any point isgiven by

keu � � V (9.142)wkh

where the values of u and V are those at any point ofinterest. A similar result is obtained from Eq. (9.135)for radial flow.

Equation (9.142) indicates that electroosmotic con-solidation continues at a point until a negative porepressure, relative to the initial value, develops that isproportional to the ratio ke /kh and to the voltage at thepoint. For conditions of constant total stress, there mustbe an equal and opposite increase in the effectivestress. This increase in effective stress causes the con-solidation. For the one-dimensional case, consolidationby electroosmosis is analogous to the loading shownin Fig. 9.35.

For a given voltage, the magnitude of effective stressincrease that develops depends on ke /kh. As ke onlyvaries within narrow limits for different soils, the totalconsolidation that can be achieved depends largely onkh. Thus, the potential for consolidation by electroos-mosis increases as soil grain size decreases because thefiner grained the soil, the lower is kh. However, theamount of consolidation in any case depends on thesoil compressibility as well as on the change in effec-tive stress. For linear soil compression with increase ineffective stress, the coefficient of compressibility av is

de dea � � � (9.143)v d�� du

or

de � a du � �a d�� (9.144)v v

in which d�� is the increase in effective stress.

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Figure 9.34 Assumed variation of voltage with distance during electroosmosis: (a) one-dimensional flow and (b) radial flow.

Thus, the more compressible the soil, the greaterwill be the amount of consolidation for a given stressincrease, just as in the case of consolidation under ap-plied loads. It follows, also, that electroosmosis will beof little value in an overconsolidated clay unless theeffective stress increases are large enough to bring thematerial back into the virgin compression range.

The consolidation loading of any small element ofthe soil is isotropic, as it is done by increasing theeffective stress through reduction in the pore waterpressure. The entire soil mass being treated is not con-solidated isotropically or uniformly, however, becausethe amount of consolidation varies with position, de-

pendent on the voltage at the point. Accordingly, prop-erties at the end of treatment vary along a line betweenthe anode and cathode, as shown, for example, by theposttreatment variations in shear strength and watercontent shown in Fig. 9.36. Values of these propertiesbefore treatment are also shown for comparison. Moreuniform property distributions between electrodes canbe obtained if the polarity of electrodes is reversedafter partial completion of consolidation (Wan andMitchell, 1976).

The results shown in Fig. 9.36 were obtained at asite in Norway where electroosmosis was used for theconsolidation of quick clay (Bjerrum et al., 1967). The

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CONSOLIDATION BY ELECTROOSMOSIS 301

Figure 9.35 Consolidation by electroosmosis and by direct loading, one-dimensional case:(a) electroosmosis and (b) direct loading.

variations in strength and water content after treatmentare consistent with the patterns to be expected basedon the predicted variation of pore pressure decreaseand vertical strain stress increase with voltage and po-sition shown in Fig. 9.35.

Rate of Consolidation

Solutions for Eqs. (9.137) and (9.138) have been ob-tained for several cases (Esrig, 1968, 1971). For theone-dimensional case, and assuming a freely draining(open) cathode and a closed anode (no flow), the porepressure is

k 2k Ve e w mu � V(x) �w 2k k �h h

� n(�1) (n � 1/2)�x� sin� �2(n � 1/2) Ln�0

1 2 2� exp � n � � T (9.145) � � �V2

where V(x) is the voltage at x, Vm is the maximum

voltage, and TV is the time factor, defined in terms ofthe distance between electrodes L and real time t as

c tvT � (9.146)V 2L

where cv is the coefficient of consolidation, given by

khc � (9.147)v m v w

The average degree of consolidation U as a functionof time is

2� n4 (�1) 1 2U � 1 � exp � n � � T� � � �V3 3� (n � 1/2) 2n�0

(9.148)

Solutions for Eqs. (9.145) and (9.148) are shown inFigs. 9.37 and 9.38. They are applied in the same wayas the theoretical solution for classical consolidationtheory.

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Figure 9.36 Effect of electroosmosis treatment on properties of quick clay at As, Norway(from Bjerrum et al., 1967): (a) Undrained shear strength, (b) remolded shear strength, (c)water content, and (d) Atterberg limits.

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ELECTROCHEMICAL EFFECTS 303

Figure 9.37 Dimensionless pore pressure as a function ofdimensionless time and distance for one-dimensional consol-idation by electroosmosis.

Figure 9.38 Average degree of consolidation versus dimen-sionless time for one-dimensional consolidation by electroos-mosis.

Figure 9.39 Average degree of consolidation as a functionof dimensionless time for radial consolidation by electroos-mosis (from Esrig, 1968). Reprinted with permission ofASCE.

A numerical solution to Eq. (9.138) gives the resultsshown in Fig. 9.39 (Esrig, 1968, 1971). For the caseof two pipe electrodes, a more realistic field conditionthan the radial geometry of Fig. 9.33b, Fig. 9.39 cannotbe expected to apply exactly. Along a straight line be-tween two pipe electrodes, however, the flow patternis approximately the same as for the radial case for aconsiderable distance from each electrode.

A solution for the rate of pore pressure buildup atthe cathode for the case of no drainage (closed cath-ode) is shown in Fig. 9.40. This condition is relevant

to pile driving, pile pulling, reduction of negative skinfriction, and recovery of buried objects. Special solu-tions for in situ determination of soil consolidationproperties by electroosmosis measurements have alsobeen developed (Banerjee and Mitchell, 1980).

One of the most important points to be noted fromthese solutions is that the rate of consolidation dependscompletely on the coefficient of consolidation, whichvaries directly with kh, but is completely independentof ke. Low values of kh, as is the case in highly plasticclays, mean long consolidation times. Thus, whereas alow value of kh means a high value of ke /kh and thepotential for a high effective consolidation pressure, italso means longer required consolidation times for agiven electrode spacing. The optimum situation iswhen ke /kh is high enough to generate a large porewater tension for reasonable electrode spacings (2 to 3m) and maximum voltage (50 to 150 V DC), but kh ishigh enough to enable consolidation in a reasonabletime. The soil types that best satisfy these conditionsare silts, clayey silts, and silty clays. Most successfulfield applications of electroosmosis for consolidationhave been in these types of materials. As noted earlier,the electrical conductivity of the soil is also important;if it is too high, as in the case of high-salinity porewater, adverse electrochemical effects and unfavorableeconomics may preclude use of electroosmosis forconsolidation.

9.18 ELECTROCHEMICAL EFFECTS

The measured strength increases in the quick clay atAs, Norway (Fig. 9.36), were some 80 percent greater

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Figure 9.40 Dimensionless pore pressure at the face of a cylindrical electrode as a functionof dimensionless time for the case of a closed cathode (a swelling condition) (from Esrigand Henkel, 1968).

than can be accounted for solely by reduction in watercontent. Also, the liquid and plastic limits werechanged as a result of treatment. Consolidation aloneshould have no effect on the Atterberg limits becausechanges in mineralogy, particle characteristics, and/orpore solution characteristics are needed to do this.

In addition to movement of water when a DC volt-age field is applied between metal electrodes insertedinto a wet soil, the following effects may develop: iondiffusion, ion exchange, development of osmotic andpH gradients, desiccation by heat generation at theelectrodes, mineral decomposition, precipitation ofsalts or secondary minerals, electrolysis, hydrolysis,oxidation, reduction, physical and chemical adsorption,and fabric changes. As a result, continuous changes insoil properties that are not readily accounted for by thesimplified theory developed previously must be ex-pected. Some of them, such as electrochemical hard-ening of the soil that results in permanent changes inplasticity and strength, may be beneficial; others, suchas heating and gas generation, may impair the effi-ciency of electroosmosis. For example, heat and gasgeneration were so great that a field test of consoli-dation by electroosmosis for foundation stabilization ofthe leaning Tower of Pisa was unsuccessful.

A simplified mechanism for some of the processesduring electroosmosis is as follows. Oxygen gas isevolved at the anode by hydrolysis

� �2H O � 4e → O ↑ � 4H (9.149)2 2

Anions in solution react with freed H� to form acids.

Chlorine may also form in a saline environment. Someof the exchangeable cations on the clay may be re-placed by H�. Because hydrogen clays are generallyunstable, and high acidity and oxidation cause rapiddeterioration of the anodes, the clay will soon alter tothe aluminum or iron form depending on the anodematerial. As a result, the soil is usually strengthenedin the vicinity of the anode. If gas generation at theanode causes cavitation and heat causes desiccation,cracking may occur. This will limit the negative porepressure that can develop to a value less than 1 atm,and also the electrical resistance will increase, leadingto a loss in efficiency.

Hydrogen gas is generated at the cathode

� �4H O � 4e → 2H ↑ � 4OH (9.150)2 2

Cations in solution are drawn to the cathode wherethey combine with (OH)� that is left behind to formhydroxides. The pH may rise to values as high as 12at the cathode. Some alumina and silica may go intosolution in the high pH environment.

More detailed information about electrochemical re-actions during electroosmosis can be found in Titkovet al. (1965), Esrig and Gemeinhardt (1967), Chilingarand Rieke (1967), Gray and Schlocker (1969), Gray(1970), Acar et al. (1990), and Hamed et al. (1991).

Soil strength increases resulting from consolidationby electroosmosis and the concurrent electrochemicalhardening have application for support of foundationson and in fine-grained soil. Pile capacity for a bridge

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SELF-POTENTIALS 305

Figure 9.41 Natural electroosmosis due to self-potential dif-ferences between oxidizing and reducing soil layers. The ox-idizing soil layer is positive relative to the reducing layer(redrawn from Hilbert, in Veder, 1981).

foundation in varved clay at a site in Canada was wellbelow the design value and inadequate for support ofthe structure (Soderman and Milligan, 1961; Milligan,1994). Electrokinetic treatment using the piles as an-odes resulted in sufficient strength increase to providethe needed support. Recently reported model tests byMicic et al. (2003) on the use of electrokinetics in softmarine clay to increase the load capacity of skirt foun-dations for offshore structures resulted in increases insoil strength and supporting capacity of up to a factorof 3.

9.19 ELECTROKINETIC REMEDIATION

The transport of dissolved and suspended constituentsinto and out of the ground by electroosmosis and elec-trophoresis, as well as electrochemical, reactions havebecome of increasing interest because of their potentialapplications in waste containment and removal of con-taminants from fine-grained soils. The electrolysis re-actions at the electrodes described in the precedingsection, wherein acid is produced at the anode and baseat the cathode, are of particular relevance. After a fewdays of treatment the pH in the vicinity of the anodemay drop to less than 2, and that at the cathode in-crease to more than 10 (Acar and Alshewabkeh, 1993).

Toxic heavy metals are preferentially adsorbed byclay minerals and they precipitate except at low pH.Iron or aluminum cations from decomposing anodescan replace heavy-metal ions from exchange sites, theacid generated at the anode can redissolve precipitatedmaterial, and the acid front that moves across the soilcan keep the metals in solution until removed at thecathode. Geochemical reactions in the soil pores im-pact the efficiency of the process. Among them arecomplexation effects that reverse ion charge andreverse flow directions, precipitation/dissolution,sorption, desorption and dissolution, redox, and im-mobilization or precipitation of metal hydroxides in thehigh pH zone near the cathode.

Some success has been reported in the removal oforganic pollutants from soils, at least in the laboratory,as summarized by Alshewabkeh (2001). However, it isunlikely that large quantities of non-aqueous-phase liq-uids can be effectively transported by electrokineticprocesses, except as the NAPL may be present in theform of small bubbles that move with the suspendingwater.

An in-depth treatment of the fundamentals of elec-trokinetic remediation and the practical aspects of itsimplementation are given by Alshewabkeh (2001) andthe references cited therein.

9.20 SELF-POTENTIALS

Natural DC electrical potential differences of up toseveral tens of millivolts exist in the earth. These self-potentials are generated by differing chemical condi-tions in adjacent soil layers, fluid flow, subsurfacechemical reactions, and temperature differences. Theself-potential (SP) method is one of the oldest geo-physical methods for characterization of the subsurface(National Research Council, 2000). Self-potentialsmay be the source of phenomena of importance in geo-technical problems as well.

The magnitude of self-potential between differentsoil layers depends on the contents of oxidizing andreducing substances in the layers (F. Hilbert, in Veder,1981). These potentials can cause a natural electroos-mosis in which water flows in the direction from thehigher to the lower potential, that is, toward the cath-ode. The process is shown schematically in Fig. 9.41.An oxidizing soil layer is positive relative to a reducinglayer, thus inducing an electroosmotic water flow to-ward the interface. If water accumulates at the inter-face, there can be swelling and loss of strength, leadingultimately to formation of a slip surface.

Generation of Self-Potentials in Soil Layers

Soils in an oxidizing environment are usually yellowor tan to reddish brown and are characterized by oxidesand hydrates of trivalent iron and a low pH relative toreducing soils, which are usually dark gray to blue-gray in color and contain sulfides and oxides and hy-droxides of divalent iron. The local electrical potentialof the soil � depends on the iron concentrations andcan be calculated from Nernst’s equation:

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Figure 9.42 Electrical potentials measured in a trench cut into a slide (from Veder, 1981).Reprinted with permission of Springer-Verlag.

3�RT cFe� � 0.771 � ln (9.151)� �2�F cFe

in which the concentrations are of Fe in solution inmoles/liter pore water. The difference in potentials be-tween two layers gives the driving potential for elec-troosmosis. Values calculated using the Nernstequation are too high for actual soil systems becauseit applies for conditions of no current flow, and theflowing current also generates a diffusion potential act-ing in the opposite direction. Hilbert, in Veder (1981),gives the electrical potential as a function of the in situpH, that is,

� � 0.186 � 0.059 pH (9.152)

Reasonable agreement has been obtained betweenmeasured and calculated values of � for different soillayers. The end result is that potential differences ofup to 50 mV or so are developed between differentlayers. Potentials measured in a trench excavated in aslide zone are shown in Fig. 9.42.

Excess Pore Pressure Generation by Self-Potentials

The pore pressure that may develop at an interface be-tween two different soil layers is given by Eq. (9.142)in which V is the difference in self-potentials betweenthe layers. For a given value of V, the magnitude ofpore pressure depends directly on ke /kh. For example,if ke � 5 � 10�9 m2/s V and kh � 1 � 10�10 m/s,

then ke /hh � 50 m/V. If the self-potential difference is50 mV, then from Eq. (9.142) a pore pressure value of

u � 50 � 9.81 � 0.05 � 25 kPa

is generated, which is not an insignificant value. If wa-ter that is driven toward the interface cannot escape orbe absorbed by the soil, then the effective stress willbe reduced by this amount. If the water is absorbedinto the clay layer, then softening will result. Eitherway, the resistance to sliding along the interface willbe reduced.

Landslide Stabilization Using Short-CircuitConductors

If slope instability is caused by a slip surface betweenreducing and oxidizing soil layers, then a simple meansfor stabilization can be used (Veder, 1981). Short-circuiting conductors, such as steel rods, are driveninto the soil so that they extend across the slip surfaceand about 1 to 2 m into the soil below. The mechanismthat is then established is shown in Fig. 9.43.

Electric current generated by reduction reactions inthe oxidizing soil layer and oxidizing reactions in thereducing layer flows through the conductors. Becauseof the presence of oxidizing agents such as ferric iron,oxygen, and manganese compounds, in the upper ox-idizing layer that take up electrons, electrons pass fromthe metal conductor to the soil. That is, the introduc-tion of electrons initiates reducing reactions. In the re-ducing layer, on the other hand, there is already a

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THERMALLY DRIVEN MOISTURE FLOW 307

Figure 9.43 Mechanism for slide stabilization using short-circuiting conductors (adapted from Veder, 1981).

surplus of electrons. If these pass into the conductor,then the environment becomes favorable for oxidationreactions. Thus, positive charges are generated in thereducing soil layer as the conductor carries electronsaway. The oxidizing soil layer then takes up these elec-trons.

Completion of the electrical circuit requires currentflow through the soil pore water in the manner shownin Fig. 9.43, where adsorbed cations, shown as Na�,plus the associated water, flow away from the soil layerinterface. This electroosmotic transport of water re-duces the water content in the slip zone. Thus, short-circuit conductors have three main effects (Veder,1981):

1. Natural electroosmosis is prevented because theshort-circuiting conductors eliminate the poten-tial difference between the two soil layers.

2. Electrochemical reactions produce electroos-motic flow in the opposite direction, thus helpingto drain the shear zone.

3. Corrosion of the conductors produces high va-lence cations that exchange for lower valence ad-sorbed cations, for example, iron for sodium,which leads to soil strengthening.

Several successful cases of landslide stabilizationusing short-circuiting conductors have been describedby Veder (1981) and the references cited therein. Typ-ically, steel rods about 25 mm in diameter are used,spaced a maximum of 3 to 4 m apart in grid patternscovering the area to be stabilized. Conditions favorable

for use of short-circuiting conductors are (1) intact co-hesive soils with a low hydraulic conductivity, (2)shear between oxidizing and reducing clay layers, and(3) a relatively thin, well-defined shear zone.

9.21 THERMALLY DRIVEN MOISTURE FLOW

Thermally driven flows in saturated soils are rathersmall. Gray (1969) measured thermoelectric currentson the order of 1 to 10 �A/�C cm, with the warm sidepositive relative to the cold side. Thermoosmotic pres-sures of only a few tenths of a centimeter water headper degree Celsius were measured in saturated soil. Netflows in different directions have been measured in dif-ferent investigations, evidently because of differenttemperature dependencies of chemical activity coeffi-cients. These small thermoelectric and thermoosmoticeffects in saturated soils may be of little practical sig-nificance in geotechnical problems.

On the other hand, thermally driven moisture flowsin partly saturated soils can be large, and that theseflows can be very important in subgrade stability,swelling soils, and heat transfer and storage problemsof various types. Theoretical representations of mois-ture flow through partly saturated soils based solely onthe application of irreversible thermodynamics, such asdeveloped by Taylor and Cary (1964), have not beencompletely successful. They underestimate the flowssubstantially, perhaps because of the inability to ade-quately represent all the processes and interactions.

A widely used theory for coupled heat and moistureflow through soils was developed by Philip and DeVries (1957). It accounts for both liquid- and vapor-phase flows. Vapor-phase flow depends on the thermaland isothermal vapor diffusivities and is driven by tem-perature and moisture content gradients. The liquid-phase flow depends on the thermal and isothermalliquid diffusivities and is driven by the temperaturegradient, the moisture content gradient, and gravity.The two governing equations are:

For vapor-phase flow:

qvap � �D �T � D �� (9.153)TV �V�w

and for liquid-phase flow:

qliq � �D �T � D �� k i (9.154)TL �L ��w

where qvap � vapor flux density (M /L2 /T)�w � density of water (M /L3)

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T � temperature (K)� � volumetric water content (L3 /L3)

DTV � thermal vapor diffusivity (L2 /T /K)D�V � isothermal vapor diffusivity (L2 /T)qliq � liquid flux density (M /L2 /T)

DTL � thermal liquid diffusivity (L2 /T /K)D�L � isothermal liquid diffusivity (L2 /T)

k� � unsaturated hydraulic conductivity (L /T)i � unit vector in vertical direction

The thermal vapor diffusivity is given by

D d�0 0D � v�[a � ƒ(a) � �]h� (9.155)� � � �TV � dTw

The isothermal vapor diffusivity is given by

D � hg d�0 0D � v�a (9.156)� � � �� V � RT d�w

where D0 � molecular diffusivity of water vapor in air(L2 /T)

v � mass flow factor � P / (P � p)P � total gas pressure in pore spacep � partial pressure of water vapor in pore

space� � tortuosity factora � volumetric air content (L3 /L3)h � relative humidity of air in pores� � ratio of average temperature gradient in

the air-filled pores to the overall temper-ature gradient

g � acceleration of gravity (L /T2)R � gas constant (FL /M /K)�0 � density of saturated water vapor (M /L3)� � suction head of water in the soil (negative

head) (L)ƒ(a) � a /ak for 0 � a � ak

� 1 for a � ak

ak � a at which liquid conductivity is lost orat which the hydraulic conductivity fallsbelow some arbitrary fraction of the sat-urated value

The thermal liquid diffusivity is given by

� d�D � k (9.157)� �� TL � � dT

The isothermal diffusivity is given by

d�D � k (9.158)� ��L � d�

in which � is the surface tension of water (F /L).Use of the above equations requires knowledge of

four relationships to describe the properties of the soilsin the system:

1. Hydraulic conductivity as a function of watercontent

2. Thermal conductivity as a function of water con-tent

3. Volumetric heat capacity (see Table 9.2)4. Suction head as a function of water content

The hydraulic conductivity and suction relationshipsare hysteretic; that is, they depend on whether the soilis wetting or drying. Examples of the variations of thedifferent properties needed for the analysis are shownin Fig. 9.44 as a function of degree of saturation andvolumetric water content. The data are for a crushedlimestone that is used for a trench backfill around bur-ied electrical transmission cables. This material is usedbecause of its low thermal resistivity, which makes itsuitable for effective dissipation of heat from the bur-ied cable, provided the saturation does not fall belowabout 40 percent.

The vapor flow is made up of a flow away from thehigh-temperature side that is driven by a vapor densitygradient and a return flow caused by variation in thepore vapor humidity as reflected by variations in soilsuction. At moderate soil suction values, for example,a few meters for sand and several tens of meters forclay, the thermal vapor diffusivity predominates, andmoisture is driven away from the heat source (McMil-lan, 1985).

The isothermal diffusivity term only becomes im-portant at very high suction levels. The liquid flow con-sists of a capillarity-driven flow toward the heat sourceand an outward liquid flow due to variations in watersurface tension with temperature. McMillan’s analysisshowed that for both sand and clay the isothermal liq-uid diffusivity term was 4 to 5 orders of magnitudegreater than the thermal liquid diffusivity term. Thuscapillarity-driven flow predominates for any significantgradient in the volumetric moisture content. The verysmall thermal liquid diffusivity is consistent with theobservations noted earlier for saturated soils in whichmeasured water flows under thermal gradients aresmall.

The total water flow q in an unsaturated soil underthe action of a temperature gradient and its resultingwater content gradient equals the sum of the vapor-phase and liquid-phase movements. Thus, from Eqs.(9.153) to (9.158),

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THERMALLY DRIVEN MOISTURE FLOW 309

Figure 9.44 Examples of properties used for analysis of thermally driven moisture flow ina partially saturated, compacted, crushed limestone: (a) particle size distribution, (b) suctionhead as a function of volumetric water content, (c) hydraulic conductivity as a function ofdegree of saturation and volumetric water content, (d) isothermal liquid diffusivity as afunction of degree of saturation and volumetric water content, (e) isothermal vapor diffusivityas a function of degree of saturation and volumetric water content, and (f) Thermal waterdiffusivity as a function of degree of saturation and volumetric water content. Thermal re-sistivity as a function of water content for this soil is shown in Fig. 9.14.

q� �(D � D )�T � (D � D )�� k iTV TL �V �L ��w

� �D �T � D � � k iT � � � (9.159)

in which

D � D � D � thermal water diffusivityTV TL

(9.160)

and

D � D � D � isothermal water diffusivity� �V �L

(9.161)

Equation (9.159) is the governing equation for mois-ture movement under a thermal gradient in unsaturatedsoils as proposed by Philip and De Vries (1957). Dif-ferentiation of this equation and application of thecontinuity requirement gives the general differentialequation for moisture flow:

�� k�� (D �T) � �(D ��) � (9.162)T ��t �z

The heat conduction equation for the soil is

�T kt� � �T (9.163)� ��t C

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where kt � thermal conductivityC � volumetric heat capacity

The ratio of thermal conductivity to the volumetricheat capacity is the thermal diffusivity A.

Both transient and steady-state temperature distri-butions computed using the Philip and De Vries theoryincorporated into numerical models have agreed wellwith measured values in a number of cases. The actualmoisture movements and distributions have not agreedas well, for example, Abdel-Hadi and Mitchell (1981)and Cameron (1986). The numerical simulations havebeen done using transform methods, finite differencemethods, the finite element method, and the integratedfinite difference method. Cameron (1986) reformulatedthe equations in terms of suction head rather thanmoisture content and incorporated them into the finiteelement model of Walker et al. (1981) for solution oftwo-dimensional problems.

9.22 GROUND FREEZING

Heat conduction in soils and rocks is discussed in Sec-tion 9.5, and values for thermal properties are given in

Table 9.2. Three topics are considered in this section:(1) the depth of frost penetration, which illustrates theapplication of transient heat flow analysis, (2) frost ac-tion in soils, a phenomenon of great practical impor-tance that can be understood through consideration ofinteractions of the physical and physicochemical prop-erties of the soil, and (3) some effects of freezing onthe behavior and properties of the soil after thawing.These topics are also covered in some detail by Konrad(2001) and the references therein.

Depth of Frost Penetration

Accurate estimation of the depth of ground freezingduring the winter, the depth of thawing in permafrostareas during the summer, and the refrigeration and timerequirements for artificial ground freezing for tempo-rary ground stabilization are all problems involvingtransient heat flow analysis. They differ from the con-duction analyses in the preceding sections in that thephase change of water to ice must be taken into ac-count. Prediction of the maximum depth of frost pen-etration illustrates this type of problem. Theoreticalsolutions of this problem are based on a mathematical

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GROUND FREEZING 311

Figure 9.45 Thermal energy as a function of temperaturefor a wet soil. Figure 9.46 Assumed conditions for the Stefan equation.

analysis developed by Neumann in about 1860 (Berg-gren, 1943; Aldrich, 1956; Brown, 1964; Konrad,2001).

The relationship between thermal energy u and tem-perature T for a soil mass at constant water content isshown in Fig. 9.45. In the absence of freezing or thaw-ing

�u� C (9.164)

�T

The Fourier equation for heat flow is

�Tq � �k (9.165)t t �z

In the absence of freezing or thawing, thermal conti-nuity and conservation of thermal energy require thatthe rate of change of thermal energy of an element plusthe rate of heat transfer into the element equal zero,that is, for the one-dimensional case

�u �q� � 0 (9.166)

�t �z

Using Eqs. (9.164) and (9.165), Eq. (9.166) may bewritten

2�T � TC � k (9.167)t 2�t �z

or

2�T � T� a (9.168)2�t �z

where a � kt /C is the thermal diffusivity (L2 /T). Equa-tion (9.168) is the one-dimensional, transient heat flowequation.

At the interface between frozen and unfrozen soil,z � Z, and the equation of heat continuity is

dZL � q � q (9.169)s ƒ udt

where Ls is the latent heat of fusion of water and qƒ �qu is the net rate of heat flow away from the interface.Equation (9.169) can be written

dZ �T �Tƒ uL � k � k (9.170)s ƒ udt �z �z

where the subscripts u and f pertain to unfrozen andfrozen soil, respectively. Simultaneous solution of Eqs.(9.168) and (9.170) gives the depth of frost penetra-tion.

Stefan Formula The simplest solution is to assumethat the latent heat is the only heat to be removed dur-ing freezing and neglect the heat that must be removedto cool the soil water to the freezing point, that is, thethermal energy stored as volumetric heat is neglected.This condition is shown by Fig. 9.46. For this case Eq.(9.168) does not exist, and Eq. (9.170) becomes

dZ TsL � k (9.171)s ƒdt Z

where Ts is the surface temperature. The solution ofthis equation is

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Figure 9.47 Freezing index in relation to the annual temperature cycle.

1 / 22k � T dtƒ s� �Z � (9.172)

Ls

The integral of Ts dt is a measure of freezing intensity.It can be expressed by the freezing index F, which hasunits of degrees � time. Index F is usually given indegree-days. It is shown in relation to the annual tem-perature cycle in Fig. 9.47. Freezing index values arederived from meteorological data. Methods for deter-mination of freezing index values are given by Linellet al. (1963), Straub and Wegmann (1965), McCormick(1971), and others. Maps showing mean freezing indexvalues are available for some areas. It is importantwhen using such data sources to be sure that there arenot local deviations from the average values that aregiven. Different types of ground cover, local topogra-phy and vegetation, and solar radiation all influencethe net heat flux at the ground surface.

The Stefan equation can also be used to estimate thesummer thaw depth in permafrost; that is, the thicknessof the active layer. In this case the ground thawingindex, also in degree-days and derived from meteoro-logical data, is used in Eq. (9.172) in place of thefreezing index (Konrad, 2001).

Modified Berggren Formula The Stefan formulaoverpredicts the depth of freezing because it neglectsthe removal of the volumetric heats of frozen and un-frozen soil. Simultaneous solution of Eqs. (9.168) and

(9.170) has been made for the conditions shown in Fig.9.48, assuming that the soil has a uniform initial tem-perature that is T0 degrees above freezing and that thesurface temperature drops suddenly to Ts below freez-ing (Aldrich, 1956). The solution is

1 / 22kT tsZ � � (9.173)� �Ls

where k is taken as an average thermal conductivityfor frozen and unfrozen soil. The dimensionless cor-rection coefficient � depends on the two parametersshown in Fig. 9.49. The thermal ratio � is given by

T0� � (9.174)Ts

and the fusion parameter � is

C� � T (9.175)sLs

An averaged value for the volumetric heats of frozenand unfrozen soil can be used for C in Eq. (9.175).

In application, the quantity Tst in Eq. (9.173) is re-placed by the freezing index, and Ts in (9.175) is givenby F / t, where t is the duration of the freezing period.

The coefficient � corrects the Stefan formula for ne-glect of volumetric heat. For soils with high water con-tent C is small relative to Ls; therefore, � is small and

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GROUND FREEZING 313

Figure 9.48 Thermal conditions assumed in the derivation of the modified Berggren for-mula.

the Stefan formula is reasonable. For arctic climates,where T0 is not much above the freezing point, � issmall, � is greater than 0.9, and the Stefan formula issatisfactory. However, in more temperate climates andin relatively dry or well-drained soils, the correctionbecomes important.

A comparison between theoretical freezing depthsand a design curve proposed by the Corps of Engineersis shown in Fig. 9.50 for several soil types. The the-oretical curves were developed by Brown (1964) usingthe modified Berggren equation and the thermal prop-erties given in Fig. 9.13.

Consideration should be given to the effect of dif-ferent types of surface cover on the ground surfacetemperature because air temperature and ground tem-perature are not likely to be the same, and the effectsof thermal radiation may be important. Observed

depths of frost penetration may be misleading if esti-mates for a proposed pavement or other structure areneeded because of differences in ground surface char-acteristics and because the pavement or foundationbase will be at different water content and density thanthe surrounding soil.

The solutions do not account for flow of water intoor out of the soil or the formation of ice lenses duringthe freezing period. This may be particularly importantwhen dealing with frost heave susceptible soils orwhen developing frozen soil barriers for the cutoff ofgroundwater flow. Methods for prediction of frostdepth in soils susceptible to ice lens formation and therate of heave are given by Konrad (2001). The initia-tion of freezing of flowing groundwater requires thatthe rate of volumetric and latent heat removal be highenough so that ice can form during the residence time

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Figure 9.49 Correction coefficients for use in the modified Berggren formula (from Aldrich,1956).

of an element of water moving between the boundariesof the specified zone of solidification.

Frost Heaving

Freezing of some soils is accompanied by the forma-tion of ice layers or ‘‘lenses’’ that can range from amillimeter to several centimeters in thickness. Theselenses are essentially pure ice and are free from largenumbers of contained soil particles. The ground sur-face may ‘‘heave’’ by as much as several tens of cen-timeters, and the overall volume increase can be manytimes the 9 percent expansion that occurs when waterfreezes. Heave pressures of many atmospheres arecommon. The freezing of frost-susceptible soils be-neath pavements and foundations can cause major dis-tress or failure as a result of uneven uplift duringfreezing and loss of support on thawing, owing to thepresence of large water-filled voids. Ordinarily, icelenses are oriented normal to the direction of cold-frontmovement and become thicker and more widely sep-arated with depth.

The rate of heaving may be as high as several mil-limeters per day. It depends on the rate of freezing in

a complex manner. If the cooling rate is too high, thenthe soil freezes before water can migrate to an ice lens,so the heave becomes only that due to the expansionof water on freezing.

Three conditions are necessary for ice lens forma-tion and frost heave:

1. Frost-susceptible soil2. Freezing temperature3. Availability of water

Frost heaving can occur only where there is a watertable, perched water table, or pocket of water reason-ably close to the freezing front.

Frost-Susceptible Soils Almost any soil may bemade to heave if the freezing rate and water supplyare controlled. In nature, however, the usual rates offreezing are such that only certain soil types are frostsusceptible. Clean sands, gravels, and highly plasticintact clays generally do not heave. Although the onlycompletely reliable way to evaluate frost susceptibilityis by some type of performance test during freezing,soils that contain more than 3 percent of their particlesfiner than 0.02 mm are potentially frost susceptible.

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GROUND FREEZING 315

Figure 9.50 Predicted frost penetration depths compared with the Corps of Engineers’ de-sign curve (Brown, 1964). Curve a—sandy soil: dry density 140 lb/ ft3, saturated, moisturecontent 7 percent. Curve b—silt, clay: dry density 80 lb/ ft3, unsaturated, moisture content2 percent. Curve c—sandy soil; dry density 140 lb/ ft3, unsaturated, moisture content 2percent. Curve d—silt, clay: dry density 120 lb/ ft3, moisture content 10 to 20 percent (sat-urated). Curve e—silt, clay: dry density 80 lb/ ft3 saturated, moisture content 30 percent.Curve f—Pure ice over still water.

Frost-susceptible soils have been classified by theCorps of Engineers in the following order of increasingfrost susceptibility:

Group(increasing

susceptibility) Soil Types

F1 Gravelly soils with 3 to 20 percentfiner than 0.02 mm

F2 Sands with 3 to 15 percent finerthan 0.02 mm

F3 a. Gravelly soils with more than20 percent finer than 0.02-mm sands, except fine siltsands with more than 15percent finer than 0.02 mm

b. Clays with PI greater than 12percent, except varved clays

F4 a. Silts and sandy siltsb. Fine silty sands with more than

15 percent finer than 0.02mm

c. Lean clays with PI less than 12percent

d. Varved clays

A method for the evaluation of frost susceptibilitythat takes project requirements and acceptable risksand freezing conditions into account as well as the soiltype is described by Konrad and Morgenstern (1983).

Mechanism of Frost Heave The formation of icelenses is a complex process that involves interrelation-ships between the phase change of water to ice, trans-port of water to the lens, and general unsteady heatflow in the freezing soil. The following explanation ofthe physics of frost heave is based largely on the mech-anism proposed by Martin (1959). Although the Martin(1959) model may not be correct in all details in thelight of subsequent research, it provides a logical andinstructive basis for understanding many aspects of thefrost heave process.

The ice lens formation cycle involves four stages:

1. Nucleation of ice2. Growth of the ice lens3. Termination of ice growth4. Heat and water flow between the end of stage 3

and the start of stage 1 again

In reality, heat and water flows continue through allfour stages; however, it is convenient to consider themseparately.

The temperature for nucleation of an ice crystal, Tn,is less than the freezing temperature, T0. In soils, T0 in

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Figure 9.51 Temperature versus depth relationships in afreezing soil.

pore water is less than the normal freezing point ofwater because of dissolved ions, particle surface forceeffects, and negative pore water pressures that exist inthe freezing zone. The freezing point decreases withdecreasing distance to particle surfaces and may beseveral degrees lower in the double layer than in thecenter of a pore. Thus, in a fine-grained soil, there isan unfrozen film on particle surfaces that persists untilthe temperature drops below 0�C.

The face of an ice front has a thin film of adsorbedwater. Freezing advances by incorporation of watermolecules from the film into the ice, while additionalwater molecules enter the film to maintain its thick-ness. It is energetically easier to bring water to the icefrom adjacent pores than to freeze the adsorbed wateron the particle or to propagate the ice through a poreconstriction.

The driving force for water transport to the ice is anequivalent hydrostatic pressure gradient that is gener-ated by freezing point depression, by removal of thewater from the soil at the ice front, which creates ahigher effective stress in the vicinity of the ice thanaway from it, by interfacial tension at the ice–waterinterface, and by osmotic pressure generated by thehigh concentration of ions in the water adjacent to theice front. Ice formation continues until the water ten-sion in the pores supplying water becomes greatenough to cause cavitation, or decreased upward waterflow from below leads to new ice lens formation be-neath the existing lens.

The processes of freezing and ice lens formationproceed in the following way with time according toMartin’s theory. If homogeneous soil, at uniform watercontent and temperature T0 above freezing, is subjectedto a surface temperature Ts below freezing, then thevariation of temperature with depth at some time is asshown in Fig. 9.51. The rate of heat flow at any pointis �kt(dT /dz). If dT /dz at point A is greater than atpoint B, the temperature of the element will drop.When water goes to ice, it gives up its latent heat,which flows both up and down and may slow or stopchanges in the value of dT /dz for some time period,thus halting the rate of advance of the freezing frontinto the soil.

Ground heave results from the formation of a lensat A, with water supplied according to the mechanismsindicated above. The energy needed to lift the over-lying material, which may include not only the soil andice lenses above, but also pavements and structures, isavailable because ice forms under conditions of super-cooling at a temperature TX � TFP, where TFP is thefreezing temperature. The available energy is

XL(T � T )FP F � (9.176)TFP

The quantity L is the latent heat. Supercooling of 1�Cis sufficient to lift 12.5 kg a distance of 10 mm. Al-ternatively, the energy for heave may originate fromthe thin water films at the ice surface (Kaplar, 1970).

As long as water can flow to a growing ice lens fastenough, the volumetric heat and latent heat can pro-duce a temporary steady-state condition so that (dT /dz)A � (dT /dz)B. For example, silt can supply water ata rate sufficient for heave at 1 mm/h. After some timethe ability of the soil to supply water will drop becausethe water supply in the region ahead of the ice frontbecomes depleted, and the hydraulic conductivity ofthe soil drops, owing to increased tension in the porewater. This is illustrated in Fig. 9.52, where hydraulicconductivity data as a function of negative pore waterpressure are shown for a silty sand, a silt, and a clay,all compacted using modified AASHTO effort, at awater content about 3 percent wet of optimum.

A small negative pore water pressure is sufficient tocause water to drain from the pores of the silty sand,and this causes a sharp reduction in hydraulic conduc-tivity. Because the clay can withstand large negativepore pressures without loss of saturation, the hydraulicconductivity is little affected by increasing reductionsin the pore pressure (increasing suction). The smalldecrease that is observed results from the consolidationneeded to carry the increased effective stress requiredto balance the reduction in the pore pressure. For thesilt, water drainage starts when the suction reaches

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GROUND FREEZING 317

Figure 9.52 Hydraulic conductivity as a function of negativepore water pressure (from Martin and Wissa, 1972).

about 40 kPa; however, a significant continuous waterphase remains until substantially greater values of suc-tion are reached.

In sand, the volume of water in a pore is large, andthe latent heat raises the freezing temperature to thenormal freezing point. Hence, there is no supercoolingand no heave. Negative pore pressure development atthe ice front causes the hydraulic conductivity to drop,so water cannot be supplied to form ice lenses. Thussands freeze homogeneously with depth. In clay, thehydraulic conductivity is so low that water cannot besupplied fast enough to maintain the temporary steady-state condition needed for ice lens growth. Heave inclay only develops if the freezing rate is slowed to wellbelow that in nature. Silts and silty soils have a com-bination of pore size, hydraulic conductivity, and freez-ing point depression that allow for large heave atnormal freezing rates in the field.

The freezing temperature penetrates ahead of a com-pleted ice lens, and a new lens will start to form onlyafter the temperature drops to the nucleation temper-ature. The nucleation temperature for a new lens maybe less than that for the one before because of reducedsaturation and consolidation from the previous flows,

which have now reduced the distance that water canbe from a particle surface. The temperature drop mustreach a depth where there is sufficient water availableafter nucleation to supply a growing lens. The thickerthe overlying lens, the greater the distance, thus ac-counting for the increased spacings between lenseswith depth. The greater the depth, the smaller the ther-mal gradient, as may be seen in Fig. 9.51, where(dT /dz)A � (dT /dz)A� where A� is on the temperaturedistribution curve for a later time t2. Because of this,the rate of heat extraction is slowed, and the temporarysteady-state condition for lens growth can be main-tained for a longer time, thus enabling formation of athicker lens.

More quantitative analyses of the freezing and frostheaving processes in terms of segregation potential,rates, pressures, and heave amounts are available. TheProceedings of the International Symposia on GroundFreezing, for example, Jones and Holden (1988),Nixon (1991), and Konrad (2001) provide excellentsources of information on these issues.

Thaw Consolidation and Weakening

When water in soil freezes, it expands by about 9 per-cent of its original volume. Thus a fully saturated soilincreases in volume by 9 percent of its porosity, evenin the absence of ice segregation and frost heave. Theexpansion associated with freezing disrupts the origi-nal soil structure. When thawed, the water returns toits original volume, the melting of segregated iceleaves voids, and the soil can be considerably moredeformable and weaker that before it was frozen. Un-der drained conditions and constant applied overburdenstress, the soil may consolidate to a denser state thanit had prior to freezing. The lower the density of thesoil, the greater is the amount of thaw consolidation.The total settlement of foundations and pavements as-sociated with thawing is the sum of that due to (1) thephase change, (2) melting of segregated ice, and (3)compression of the weakened soil structure.

Testing of representative samples under appropriateboundary conditions is the most reliable means forevaluating thaw consolidation. Samples of frozen soilare allowed to thaw under specified levels of appliedstress and under defined drainage conditions, and thedecrease in void ratio or thickness is determined. Anexample of the effects of freezing and thawing on thecompression and strength of initially undisturbed Bos-ton blue clay is shown in Fig. 9.53 from Swan andGreene (1998). These tests were done as part of aground freezing project for ground strengthening to en-able jacking of tunnel sections beneath operating raillines during construction of the recently completedCentral Artery/Tunnel Project in Boston. Detailed

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C4-FTe0 = 1.171

C1-UFe0 = 1.064

10 100

100

120

80

60

40

20

0

1000 10000

Effective Stress, σ�c (kPa)

UUC1-UF(σ1–σ3)max = 109.6 kPa

ε1 = 2.3%su/σ3cell = 0.36

e0 = 1.02; w = 37.5%

UUC4-FT(σ1– σ3)max = 42.4 kPa

ε1 = 12.8%su/σ3cell = 0.14

e0 = 1.13; w = 43.2%

Axial Strain. %

0 5 10 15 20 25

Dev

iato

r S

tres

s, σ

1–

σ 3 (

kPa)

Ver

tical

Str

ain,

εv

(%)

0

10

12

14

16

18

20

22

2

4

6

8

(a)

(b)

Figure 9.53 (a) Comparison between the compression behavior of unfrozen (C1-UF) andfrozen then thawed (C4-FT) samples of Boston blue clay. (b) Deviator stress vs. axial strainin unconsolidated–undrained triaxial compression of unfrozen (UUC1-UF) and frozen andthawed (UUC4-FT) Boston blue clay (from Swan and Greene, 1998).

analysis of the thaw consolidation process and its an-alytical representation is given by Nixon and Ladanyi(1978) and Andersland and Anderson (1978).

Ground Strengthening and Flow Barriers byArtificial Ground Freezing

Artificial ground freezing has applications for formationof seepage cutoff barriers in situ, excavation support,and other ground strengthening purposes. These appli-

cations are usually temporary, and they have the ad-vantage that the ground is not permanently altered,except for such property changes as may be caused bythe freeze–thaw processes. Returning the ground to itspristine state may be important for environmental rea-sons where alternative methods for stabilization couldpermanently change the state and composition of thesubsoil.

Freezing is usually accomplished by installation offreeze pipes and circulation of a refrigerant. For emer-

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Stress effect

Time, t (hr)

tf00

10

40

80

120

160

20 30

TemperatureEffect

T = –2.2 °C, σ = 0.138 MPa

T = –2.2 °C, σ = 0.55 MPa

T = 0 °C, σ = 0.55 M

Pa

FirstStage

SecondStage

ThirdStage

Nat

ural

Str

ain,

ε -

%

Figure 9.54 Creep curves for a frozen organic silty clay(from Sanger and Sayles, 1979).

gency and rapid ground freezing, expendable refrig-erants such as liquid nitrogen or carbon dioxide in anopen pipe can be used. The thermal energy removaland time requirements for freezing the ground can becalculated using the appropriate thermal conductivity,volumetric heat, and latent heat properties for theground and heat conduction theory in conjunction withthe characteristics of the refrigeration system (Sanger,1968; Shuster, 1972; Sanger and Sayles, 1979). Formany applications the energy required to freeze theground in kcal/m3 will be in the range of 2200 to 2800times the water content in percent (Shuster, 1972).However, if the rate of groundwater flow exceeds about1.5 m/day, it may be difficult to freeze the groundwithout a very high refrigeration capacity to ensurethat the necessary temperature decrease and latent heatremoval can be accomplished within the time any el-ement of water is within the zone to be frozen.

The long-term strength and stress–strain character-istics of frozen ground depend on the ice content, tem-perature, and duration of loading. The short-termstrength under rapid loading, which can be up to 20MPa at low temperature, may be 5 to 10 times greaterthan that under sustained stresses. That is, frozen soilsare susceptible to creep strength losses (Chapter 12).The deformation behavior of frozen soil is viscoplastic,and the stress and temperature have significant influ-ence on the deformation at any time. The creep curvesin Fig. 9.54 illustrate these effects. The onset of thethird stage of creep indicates the beginning of failure.The evaluation of stability of frozen soil masses, theprediction of creep deformation, and the possibility ofcreep rupture are complex problems because of het-erogeneous ground conditions, irregular geometries,and temperature and stress variations throughout thefrozen soil mass. Design and implementation consid-erations for use of ground freezing in construction aregiven by Donohoe et al. (1998).


Conductivity properties are one of the four key dimen-sions of soil behavior that must be understood andquantified for success in geoengineering. The otherthree dimensions are volume change, deformation andstrength, and the influences of time. They form thesubjects of the following three chapters of this book.

Water flows through soils and rocks under fully sat-urated conditions have been the most studied, and hy-draulic conductivity properties, their determination andapplication for seepage studies of various types, con-struction dewatering, and the like are central to geo-technical engineering. One objective of this chapter hasbeen to elucidate the fundamental factors that control

the permeability of soils to water and how this propertydepends on soil type, especially gradation, and issensitive to testing conditions, soil fabric, and en-vironmental factors. The understanding of these fun-damentals is important, not only because of theinsights provided but also because many of the sameconsiderations apply to the several other types of flowsthat are known to be important—chemical, electrical,and thermal. Knowledge of one is helpful in the un-derstanding and quantification of the other because themathematical descriptions of the flows follow similarforce-flux relationships.

At the same time it is necessary to take into accountthat the flows of fluids of different composition and theapplication of hydraulic, chemical, electrical, and ther-mal driving forces to soils can cause changes in com-positions and properties, with differing consequences,depending on the situation. Furthermore, as examinedin considerable detail in this chapter, flow coupling canbe important, especially advective and diffusive chem-ical transport, electroosmotic water and chemical flow,and thermally driven moisture flow. Considerable im-petus for research on these processes has been gener-ated by geoenvironmental needs, including enhanced

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and more economical waste containment and site re-mediation strategies.

Ground freezing, in addition to its importance in en-gineering and construction in cold regions, is seeingnew applications for temporary ground stabilizationneeded for underground construction in sensitive urbanareas.


1. A uniform sand with rounded particles has a voidratio of 0.63 and a hydraulic conductivity, k, of 2.7� 10�4 m/s. Estimate the value of k for the samesand at a void ratio of 0.75.

2. The soil profile at a site that must be dewateredconsists of three homogeneous horizontal layers ofequal thickness. The value of k for the upper andlower layers is 1 � 10�6 m/s and that of the mid-dle layer is 1 � 10�4 m/s. What is the ratio of theaverage hydraulic conductivity in the horizontaldirection to that in the vertical direction?

3. Consider a zone of undisturbed San Francisco Baymud free of sand and silt lenses. Comment on theprobable effect of disturbance on the hydraulicconductivity, if any. Would this material be ex-pected to be anisotropic with respect to hydraulicconductivity? Why?

4. Assume the specific surface of the San FranciscoBay mud in Question 3 is 50 m2/g and prepare aplot of the hydraulic conductivity in meters/sec-ond as a function of water content over the rangeof 100 percent decreased to 25 percent by consol-idation using the Kozeny–Carman equation.Would you expect the actual variation in hydraulicconductivity as a function of water content to beof this form? Why? Sketch the variation youwould expect and explain why it has this form.

5. At a Superfund site a plastic concrete slurry wallwas proposed as a vertical containment barrieragainst escape of liquid wastes and heavily con-taminated groundwater. The subsurface conditionsconsist of horizontally bedded mudstone and silt-stone above thick, very low permeability clayshale. The cutoff wall was to extend into the slayshale, which has been shown to be able to serveas a very effective bottom barrier. For the finaldesign and construction, however, a 3-ft-widegravel trench was used instead of the slurry wall.Sumps and pumps placed in the bottom of thetrench are used to collect liquids. Explain how thistrench can serve as an effective cutoff and discussthe pros and cons of the two systems.

6. How can the effects of incompatibility betweenchemicals in a waste repository and a compactedclay liner best be minimized?

7. Two parallel channels, one with flowing water andthe other with contaminated water, are 100 ft apart.The surface elevation of the contaminated channelis 99 ft, and the surface elevation of the clean wa-ter channel is at 97 ft. The soil between the twochannels is sand with a hydraulic conductivity of1 � 10�4 m/s, a dry unit weight of 100 pcf, anda specific gravity of solids of 2.65. Estimate thetime it will take for seepage from the contaminatedchannel to begin flowing into the initially cleanchannel. Make the following assumptions and sim-plifications:a. Seepage is one dimensional.b. The only subsurface reaction is adsorption onto

the soil particles.c. The soil–water partitioning coefficient is 0.4

cm3/g.d. Hydrodynamic dispersion can be ignored.

8. For the compacted clay waste containment linershown below and assuming steady-state condi-tions:a. What is the contaminant transport for pure

molecular diffusion?b. What is the contaminant transport rate for pure

advection?c. What is the contaminant transport rate for ad-

vection plus diffusion?d. Why don’t the answers to parts (a) and (b) add

up to (c)?

NOTE: Advection and diffusion are in thesame direction; therefore, J � 0, and the so-lution will be in the form

a x2c � a e � a1 3

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9. One-dimensional flow is occurring by electroos-mosis between two electrodes spaced at 3.0 m witha potential drop of 100 V (DC) between them.What should the water flow rate be if the coeffi-cient of electroosmotic permeability, ke, is 5 �10�9 m2/s V assuming an open system? If no wa-ter is resupplied at the anode, what maximum con-solidation pressure should develop at a pointmidway between electrodes if the hydraulic con-ductivity of the soil is 1 � 10�8 m/s?

10. a. A soil has a coefficient of electroosmotic per-meability equal to 0.3 � 10�8 m/s per V/mand a hydraulic conductivity of 6 � 10�9 m/s.Starting from the general relationship

J � L Xi ij j

derive an expression for the pore water tensionthat may be developed under ideal conditionsfor consolidation of the clay by electroosmosisand compute the value that should develop at apoint where the voltage is 25 V. Be sure toindicate correct units with your answers.

b. In the absence of electrochemical effects orcavitation, would you consider your answer topart (a) to represent an upper or lower boundestimate of the pore water tension? Why?(HINT: Consider the influence of consolidationon the soil properties that are used to predictthe pore water tension.)

11. In 1892 Saxen established that there is equivalencebetween electroosmosis and streaming potentialsuch that the results of a hydraulic conductivitytest in which streaming potential is measured canbe used to predict the volume flow rate duringelectroosmosis in terms of the electrical current.Starting with the general equations for coupledelectrical and hydraulic flow, derive Saxen’s law.What will be the drainage rate from a soil, inm3/h amp, if the streaming potential is 25 mV/atm? What will be the cost of electrical power percubic meter of water drained if electricity costs$0.10 per kWh and a maximum voltage of 75 Vis used?

12. It might be possible to prevent leakage of hazard-ous and toxic chemicals through waste impound-ment and landfill clay or geosynthetic-clay linersby means of an electroosmosis counterflow barrieragainst hydraulically driven seepage. Consider theimpoundment and liner system shown below.

Assume that the water pressure at the top of the leach-ate collection layer is atmospheric and that the onlyfluxes across the liner are water and electricity. Thecharacteristics of the compacted clay liner are:

Hydraulic conductivity�7k � 1 � 10 m/sh

Electroosmotic coefficients�9 2k � 2 � 10 m /s Ve

�6 3k � 0.2 � 10 m /s ampi

a. Wire mesh is proposed for use as electrodes.Where would you place the anode and cathodemeshes?

b. If the waste pond is to be filled to an averagedepth of 6 m, what voltage drop should bemaintained between the electrodes?

c. What will the power cost be per hectare of im-poundment per year? Power costs $0.09 perkWh.

d. Assume that the leachate collection layer isflushed continuously with freshwater and thatthe liquid waste contains dissolved salts. Writethe complete set of equations that would be re-quired to describe all the flows across the linerduring electroosmosis. Define all terms.

e. Will maintenance of a no hydraulic flow con-dition ensure that no leachate will escapethrough the clay liner? Why?

13. a. Estimate the minimum footing depths for struc-tures in a Midwestern city where the freezingindex is 750 degree-days and the duration ofthe freezing index is 100 days. The mean an-nual air temperature is 50�F. The soil is siltyclay with a water content of 20 percent and adry unit weight of 110 lb/ft3. Assume no icesegregation and compare values according tothe Stefan and modified Berggren formulas.

b. What will be the depth of frost penetration be-low original ground surface level if a surfaceheave of 6 inches develops due to ice lens for-

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mation? Assume a frozen ground temperatureof 32�F.

c. If a pavement is to be placed over the soil, whatthickness of granular base course should beused to prevent freezing of the subgrade? Thebase course will be compacted to a dry densityof 125 lb/ft3 at a water content of 15 percent.If the pavement structure is to contain an 8-inch-thick Portland cement concrete surfacelayer, will your result tend to overestimate orunderestimate the base thickness required?Why?

14. A compacted fine-grained soil is to be used as aliner for a chemical waste storage area. Free liquidleachate and possibly some heavier than waterfree phase nonsoluble, nonpolar organic liquids(DNAPLs) may accumulate in some areas as a re-sult of rupturing and corrosion of the drums inwhich they were stored. Two sources of soil foruse in the liner are available. They have the fol-lowing properties:

Property Soil A Soil B

Unified class (CH) (CL)Liquid limit (%) 90 45Plastic limit (%) 30 25Clay size (%) 50 30Silt size (%) 30 40Sand size (%) 20 30Predominant clay

mineralSmectite Illite

Cation exchangecapacity (meg/100 g)

60 20

a. Which of the two soils would be best suited foruse in the liner? Why?

b. What tests would you use to validate yourchoice? Why?

c. Assume that you have confirmed that it will bepossible to compact the soil to states that willhave hydraulic conductivities in the range of 1� 10�8 to 1 � 10�11 m/s. A liner thickness of0.6 m is proposed. Leachate is likely to accu-mulate to a depth of 1.0 m above the top of theliner. A leachate collection layer will underliethe liner.

d. If the concentration of dissolved salts in theleachate is 1.0 M and the average diffusion co-efficient is 5 � 10�10 m2/s, determine for thesteady state the total amount of dissolvedchemical per unit area per year that will escape

through the liner as a function of the hydraulicconductivity. Show in the same diagram theproportions of the total that are attributable todiffusion and advection.

Assume that the leachate collection layer isfully drained, but for purposes of analysis thefluid level can be considered at the bottom ofthe clay. Determine the leakage rate throughthe liner per unit area as a function of the hy-draulic conductivity and show it on a diagram.

15. The diagram below shows the cross section of atunnel and underlying borehole in which wastecanisters for spent nuclear fuel are located. Suchan arrangement is proposed for deep (e.g., severalhundred meters) burial of nuclear waste in crys-talline rock. The surrounding rock can be assumedfully saturated, and the groundwater table will bewithin a few tens of meters of the ground surface.Thermal studies have shown that the temperatureof the waste canister will rise to as high as 150�Cat its surface. A canister life of about 100 years isanticipated using either stainless steel or copperfor the material. The surrounding environmentmust be safe against leakage of radionuclides fromthe repository for a minimum of 100,000 years.

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Clay or a mix of clay with other materials such assand and crushed rock is proposed for use as thefill both around the canisters and in the tunnel.a. What are the most important properties that the

backfill should possess to ensure isolation andbuffering of the waste from the outside envi-ronment?

b. What clay material would you propose for thisapplication and under what conditions wouldyou place it?

c. Assess the probable natures and directions ofheat and fluid flows that will develop, if any.

d. What alterations might occur in the materialduring the life of the repository if any? Con-sider the effects of groundwater from the sur-rounding ground, corrosion of the canister, andthe prolonged exposure to high temperature.Would each of these alternations be likely toenhance or impair the effectiveness of the claypack?

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325

CHAPTER 10

Volume Change Behavior

10.1 INTRODUCTION

Volume changes in soils are important because theydetermine settlements due to compression, heave dueto expansion, and contribute to deformations caused byshear stresses. Changes in volume cause changes instrength and deformation properties that, in turn, influ-ence stability. Volume changes are induced by changesin applied stresses, chemical and moisture environ-ments, and temperature. The effects of stress changesare generally the most important and have been themost studied.

In this chapter, factors contributing to volumechange are discussed, and their relative importance isconsidered. Emphasis is on consolidation and swelling.Shrinkage is a special case of consolidation, whereinthe consolidation pressure is developed internally fromcapillary menisci and the surface tension of water.

Reader familiarity with the phenomenological as-pects of compression and swelling as ordinarily treatedin geotechnical engineering is assumed, as describedby the idealized void ratio–effective pressure relation-ships shown in Fig. 10.1. Unless otherwise noted, thediscussion in this chapter is based on the behavior inone-dimensional deformation conditions. Although themathematics and numerical analyses needed for quan-tification of volume changes in two or three dimen-sions are more complex, the phenomena and processesthat control the behavior are the same.

10.2 GENERAL VOLUME CHANGE BEHAVIOROF SOILS

Soil void ratio is normally in the range of about 0.5 to4.0, as shown in Fig. 10.2. Although the range of pres-sures of interest in most cases (up to a few hundredkilopascals) is relatively small on a geological scale,

the void ratios encompass virtually the full range fromfresh sediments to shale. Mechanical and chemicalchanges accompany and influence the densificationprocess. In general, the void ratio–effective pressurerelationship is related to grain size and plasticity in themanner shown by Fig. 10.2b.

Particle size and shape, which together determinespecific surface area, are the most important factorsinfluencing both the void ratio at any pressure and theeffects that physicochemical and mechanical factorshave on consolidation and swelling (Meade, 1964).Particle size and shape are direct manifestations ofcomposition, with increasing colloidal activity and ex-pansiveness associated with decreasing particle sizes.

Values of compression index, Cc, defined in Fig.10.1, from less than 0.2 to as high as 17 for speciallyprepared sodium montmorillonite under low pressurehave been measured, although values less than 2.0 areusual. The compression index for most natural clays isless than 1.0, with a value less than 0.5 in most cases.The swelling index, Cs, is less than the compressionindex, usually by a substantial amount, as a result ofparticle rearrangement during compression that doesnot recur during expansion. After one or more cyclesof recompression and unloading accompanied withsome irrecoverable volumetric strain, the reloading andswelling indices measured in the preyield region be-come nearly equal. Swelling index values for threeclay minerals, muscovite, and sand are listed in Table10.1. For undisturbed natural soils the swelling indexvalues are usually less than 0.1 for nonexpansive ma-terials to more than 0.2 for expansive soils.

The compressibility of dense sands and gravels isfar less than that of normally consolidated clays; none-theless, volume changes under high pressures may besubstantial in granular materials as shown in Fig. 10.3.At low stress levels, the compressibility of sand de-

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326 10 VOLUME CHANGE BEHAVIOR

Figure 10.1 Idealized void ratio–effective stress relationships for a compressible soil.

Figure 10.2 Compression curves for several soils (redrawn from Lambe and Whitman,1969).

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PRECONSOLIDATION PRESSURE 327

Table 10.1 Swelling Index Values for Several Minerals

Mineral(1)

Pore Fluid, Adsorbed Cations,Electrolyte Concentration, in Gram

Equivalent Weights per Liter(2)

Void Ratio at EffectiveConsolidation Pressure of

100 psf (5 kPa)(3)

Swelling Index(4)

Kaolinite Water, sodium, 1 0.95 0.08Water, sodium, 1 � 10�4 1.05 0.08Water, calcium, 1 0.94 0.07Water, calcium, 1 � 10�4 0.98 0.07Ethyl alcohol 1.10 0.06Carbon tetrachloride 1.10 0.05Dry air 1.36 0.04

Illite Water, sodium, 1 1.77 0.37Water, sodium, 1 � 10�3 2.50 0.65Water, calcium, 1 1.51 0.28Water, calcium, 1 � 10�3 1.59 0.31Ethyl alcohol 1.48 0.19Carbon tetrachloride 1.14 0.04Dry air 1.46 0.04

Smectite Water, sodium, 1 � 10�1 5.40 1.53Water, sodium, 5 � 10�4 11.15 3.60Water, calcium, 1 1.84 0.26Water, calcium, 1 � 10�3 2.18 0.34Ethyl alcohol 1.49 0.10Carbon tetrachloride 1.21 0.03

Muscovite Water 2.19 0.42Carbon tetrachloride 1.98 0.35Dry air 2.29 0.41

Sand 0.01 to 0.03

From Olson and Mesri (1970). Reprinted with permission of ASCE.

Figure 10.3 Compressibility of three sands under high pres-sure (from Pestana and Whittle, 1995).

pends on initial density. However, at higher stress lev-els, yielding is observed, and the compression curvesfor a given sand at different initial densities merge intoa unique compression line. Particle crushing is the pri-mary cause of the large volumetric strains that occuralong the normal compression line. The yield stress isrelated to particle tensile strength (McDowell and Bol-ton, 1998; Nakata et al., 2001).

Compressibility data for several sands, gravels, androckfills are shown in Fig. 10.4. At a pressure of 700kPa (100 psi) a compression of 3 percent is common,and values as high as 6.5 percent have been measured.Interestingly, the compacted shells of a rockfill damare sometimes more compressible than the compactedclay core.

10.3 PRECONSOLIDATION PRESSURE

Three different relationships between the present over-burden effective stress and the maximum past over-��v0

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Figure 10.4 Field compressibility of earth and rockfill materials (from Wilson, 1973). Re-printed with permission from John Wiley & Sons.

burden effective stress are possible for the soil at��vm

a site:

1. —Underconsolidated The soil has�� vm v0

not yet reached equilibrium under the presentoverburden owing to the time required for con-solidation. Underconsolidation can result fromsuch conditions as deposition at a rate faster thanconsolidation, rapid drop in the groundwater ta-ble, insufficient time since the placement of a fillor other loading for consolidation to be com-pleted, and disturbance that causes a structurebreakdown and decrease in effective stress.

2. —Normally Consolidated The soil is�� vm v0

in effective stress equilibrium with the presentoverburden effective stress. Surprisingly few, ifany, deposits have been encountered that are ex-actly normally consolidated. Most are at leastvery slightly overconsolidated as a result ofprocesses of the type summarized in Table 10.2.Underconsolidated soil behaves as normallyconsolidated soil until the end of primary con-

solidation, and overconsolidated clays becomenormally consolidated clays when loaded beyondtheir maximum past pressure.

3. —Overconsolidated or Preconsol-�� vm v0

idated The soil has been consolidated, or be-haves as if consolidated, under an effective stressgreater than the present overburden effectivestress. Characteristics, causes, and mechanismsof preconsolidation are summarized in Table10.2. Cemented or structured soil may behavelike an overconsolidated soil; the yield pressureis larger than the maximum past pressure eventhough the soil has not experienced a pressuregreater than the present overburden stress.

Accurate knowledge of the maximum past consoli-dation pressure is needed for reliable predictions ofsettlement and to aid in the interpretation of geologichistory. If the recompression to virgin compressioncurve does not show a well-defined break, such as atpoint B in Fig. 10.1, the preconsolidation pressure isdifficult to determine. Gentle curvature of the com-

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PRECONSOLIDATION PRESSURE 329

Table 10.2 Preconsolidation Mechanisms for Horizontal Deposits Under Geostatic Stresses

Category Description

StressHistoryProfile

In situ StressCondition Remarks/References

A. Mechanical onedimensional

1. Changes in totalvertical stress(overburden,glaciers, etc.)

Uniform withconstant�� p v0

K0, but value atgiven OCR variesfor reload versusunload

Most obvious andeasiest to identify

2. Changes in porepressure(water table,seepageconditions,etc.)

(except withseepage)

B. Desiccation 1. Drying due toevaporation,vegetation,etc.

Often highlyerratic

Can deviate fromK0, e.g., isotropiccapillary stresses

Drying crusts found atsurface of mostdeposits; can be atdepth within deltaicdeposits

2. Drying due tofreezing

C. Drained creep(aging)

1. Long-termsecondarycompression

Uniform withconstant�� /��p v0

K0, but notnecessarilynormallyconsolidatedvalue

Leonards and Altschaeffl(1964); Bjerrum(1967)

D. Physicochemical 1. Naturalcementationdue tocarbonates,silica, etc.

2. Other causes ofbonding dueto ionexchange,thixotropy,‘‘weathering’’etc.

Not uniform No information

Poorly understood andoften difficult toprove. Verypronounced in easternCanadian clays, e.g.,Sangrey (1972),Bjerrum (1973), andQuigley (1980)

After Jamiolkowski et al., 1985.

pression curve over the preconsolidation pressurerange is characteristic of sands, weathered clays, heav-ily overconsolidated clays, and disturbed clays.

The rate of loading and time have significant effectson the equilibrium void ratio–effective stress relation-ship, especially for sensitive structured clays as shownin Fig. 10.5. It is not surprising, therefore, that rate ofloading and time influence also the measured precon-solidation pressure. The preconsolidation pressure de-creases as the duration of load application increasesand as the rate of deformation decreases, as shown by

Fig. 10.6 from Leroueil et al. (1990). The higher valuesof apparent preconsolidation pressure associated withthe faster rates of loading reflect the influences of theviscous resistance of the soil structure. The rate-dependent value of preconsolidation pressure, can��pbe approximated by (e.g., Leroueil et al., 1985)

log(��) � A � B log(� ) (10.1)p a

where is the vertical strain rate in one-dimensional�a

consolidation, and A and B are fitting parameters. Typ-

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Figure 10.5 Compression curves corresponding to differenttimes after the completion of primary consolidation.

Figure 10.6 Effect of load duration increment and defor-mation rate on compression curves (Leroueil et al., 1990).(a) Ottawa clay (data from Crawford, 1964). (b) Backebolclay (data from Sallfors, 1975).

10-9 10-8 10-7 10-6 10-5 10-430

40

50

60

70

80

90100

Volumetric Strain Rate (s-1)

35 °C

25 °C

5 °C

Constant Rate of Strain Tests at 5 °CConstant Rate of Strain Tests at 25 °CConstant Rate of Strain Tests at 35 ° C

Creep Tests at 25 °C

Pre

cons

olid

atio

n P

ress

ure

(kP

a)

Conventional ConsolidationTest at 25 °C (After 24Hours of Loading)

ConventionalConsolidation Test at 25 °C (At End of PrimaryConsolidation State)

Figure 10.7 Effect of compression strain rate and tempera-ture on measured preconsolidation pressure of Berthiervilleclay (from Leroueil and Marques, 1996).

ical examples of the fitting for the results of differenttypes of compression tests on Berthierville clay areshown in Fig. 10.7 (Leroueil and Marques, 1996). Theeffect of temperature on preconsolidation pressure canalso be seen, and this is further discussed in Section10.12. The data in Figs. 10.6 and 10.7 also illustratethe difficulties and uncertainties in determining the truein situ conditions from the results of laboratory tests.

10.4 FACTORS CONTROLLING RESISTANCETO VOLUME CHANGE

Both compositional and environmental factors influ-ence volume change, so meaningful quantitative pre-

dictions of field behavior are possible only ifundisturbed samples or in situ tests are used for deter-mination of properties. The following factors, severalof which are treated in more detail in later sections,are important in determining resistance to volumechange.

Physical Interactions Between Particles Physicalinteractions include bending, sliding, rolling, andcrushing of soil particles. Physical interactions aremore important than physicochemical interactions athigh pressures and low void ratios.

Physicochemical Interactions Between ParticlesThese interactions depend on particle surface forcesthat are responsible for double-layer interactions, sur-face and ion hydration, and interparticle attractiveforces. Physicochemical interactions are most impor-tant in the formational stages of fine-grained soil de-posits when they are at low pressures and high voidratios.

Chemical and Organic Environment Chemicalprecipitates cement particles together. Organic matterinfluences surface forces and water adsorption prop-erties, which, in turn, increase the plasticity and com-pressibility. Expansion of pyrite minerals in someshales and other earth materials as a result of oxidationcaused by exposure to air and water has been thesource of significant structural damage (Bryant et al.,2003). Temperature changes may cause changes in hy-dration states of some salts leading to volume changes.

Mineralogical Detail Small differences in certaincharacteristics of expansive clay minerals can have ma-jor effects on the swelling of a soil.

Fabric and Structure Compacted expansive soilswith flocculent structures may be more expansive thanthose with dispersed structures. Figure 10.8 is an ex-

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PHYSICAL INTERACTIONS IN VOLUME CHANGE 331

Figure 10.8 Effect of structure and electrolyte concentrationof absorbed solution on swelling of compacted clay (adaptedfrom Seed et al. 1962a).

Figure 10.9 Comparison of compressibility and swell char-acteristics for normally consolidated (compression curve) andoverconsolidated (rebound and recompression curves) soil.

ample. At pressures less than the preconsolidationpressure, the soil with a flocculent structure was lesscompressible than the same soil with a dispersed struc-ture. The reverse is generally true for pressures greaterthan the preconsolidation pressure.

Stress History An overconsolidated soil is lesscompressible but more expansive than the same ma-terial initially at the same void ratio but normally con-solidated. This is illustrated in Fig. 10.9. If anisotropicstress systems have been applied to a soil in the past,then anisotropic compression and swelling character-istics usually result.

Temperature Increase in temperature usuallycauses a decrease in volume for a fully drained soil. Ifdrainage is prevented, increase in temperature causes

a decrease in effective stress. The responses of satu-rated soils to temperature change are analyzed in Sec-tion 10.12.

Pore Water Chemistry Any change in the pore so-lution chemistry that depresses the double layers orreduces the water adsorption forces at particle surfacesreduces swell or swell pressure. An example of this isshown in Fig. 10.8, where increased electrolyte con-centration in the water imbibed by a compacted clayresulted in reduced swelling. For soils containing onlynonexpansive clay minerals, the pore water chemistryhas relatively little effect on the compression behaviorafter the initial fabric has formed and the structure hasstabilized under a moderate effective stress. This is inaccordance with the principle of chemical irreversibil-ity of clay fabric, discussed in Section 8.2. The leach-ing of normally consolidated marine clay at high watercontent, however, may be sufficient to cause a smallreduction in volume owing to changes in interparticleforces (Kazi and Moum, 1973; Torrance, 1974).

Stress Path The amount of compression or swell-ing associated with a given change in stress usuallydepends on the path followed. Loading or unloadingfrom one stress to another in stages can give consid-erably different volume change behavior than if thestress change is done in one step. An example forswelling of a compacted sandy clay is shown in Fig.10.10. Each sample was placed under water after com-paction and allowed to swell under different surchargepressures. Further discussion of the stress path de-pendency on volume change is given in Section 10.11and Chapter 11.

10.5 PHYSICAL INTERACTIONS IN VOLUMECHANGE

Physical interactions between particles include bend-ing, sliding, rolling, and crushing. In general, thecoarser the gradation, the more important are physicalparticle interactions relative to chemically induced par-ticle interactions. Deformation resistance developed byparticle rolling and sliding is discussed in Chapter 11.

Particle bending is important in soils with platy par-ticles. Even small amounts of mica in coarse-grainedsoils can greatly increase the compressibility. Mixturesof a dense sand having rounded grains with mica flakescan even duplicate the form of the compression andswelling curves of clays, as shown in Fig. 10.11. Chat-tahoochie River sand with a mica content of 5 percentis twice as compressible as the same sand with no mica(Moore, 1971). On the other hand, a well-graded soilmay be little affected in terms of compressibility bythe addition of mica. Further discussion of the me-

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Figure 10.10 Effect of unloading stress path on swelling of a compacted sandy clay (Seedet al. 1962a).

Figure 10.11 Comparison of compression and swelling curves for several clays and sand–mica mixtures (from Terzaghi, 1931).

chanical behavior of mica–sand mixtures is given inChapter 11.

Cross-linking adds rigidity to soil fabric, especiallyclays containing platy particles. Particles and particlegroups act as struts whose resistance depends both ontheir bending resistance and on the strengths of thejunctions at their ends. According to van Olphen(1977), cross-linking is important even in ‘‘pure clay’’systems, where the confining pressure is sometimes in-

terpreted, probably erroneously, as balanced entirelyby interparticle repulsion.

The importance of grain crushing increases with in-creasing particle size and confining stress magnitude.Particle breakage is a progressive process that starts atrelatively low stress levels because of the wide disper-sion of the magnitudes of interparticle contact forces.The number of contacts per particle depends on gra-dation and density, and the average contact force in-

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PHYSICAL INTERACTIONS IN VOLUME CHANGE 333

Table 10.3 Contacts and Contact Forces in GranularSoils

Soil Type

GrainContacts /Particle(Range)

GrainContacts /Particle(Mean)

AverageContact

Force for�� 1 atm

(N)

Loose uniformgravel

4–10 6.1

Dense uniformgravel

4–13 7.7

Well-gradedgravel, 0.8mm � d �200 mm

5–1912 5.9

Medium sand 10�2

Gravel 10Rockfill,

� 0.7 md104

creases greatly with particle size, as summarized inTable 10.3. Statistical analyses of the probable fre-quency distribution of contact forces show large devi-ations from the mean (Marsal, 1973). An example ofthis obtained from a numerical simulation of a particleassemblage is presented in Chapter 11.

Unstressed, or idle particles, can occupy voids be-tween larger particles or particle arches associated withstrong force chains, as discussed in Chapter 7. Thepercentage of idle particles depends on gradation, fab-ric, void ratio, stress history, and stress level. In soilscontaining idle particles, particulate mechanics analy-ses of behavior that depend on such quantities as av-erage number of particles per unit area or per unitvolume, average number of contacts per particle, andthe like lose their relevance unless the analyses allowfor their existence.

The resistance to grain crushing or breakage de-pends on the strength of the particles, which, in turn,depends on mineralogy and the soundness of thegrains. Failure may be by compression, shear, or in asplit tensile mode. Quartz grains are more resistantthan feldspar, but there is greater variability in crushingand splitting resistance with changes in particle sizefor quartz than for feldspar.

The amount of grain crushing to be expected forrockfills and gravels is summarized in Table 10.4. Inthis table, Bq is the proportion of the solid phase byweight that will undergo breakage, and qi is the con-centration of solids [Vs /V � 1/(1 � e)].

Studies of compressibility and grain crushing insands and gravels under isotropic and anisotropic tri-axial stresses up to 20 MPa showed the following (Leeand Farhoomand, 1967):

1. Coarse granular soils compress more and havemore particle breakage than fine granular soils.A comparison of gradation curves before and af-ter isotropic compression is shown in Fig. 10.12.

2. Soils with angular particles compress more andundergo more particle crushing than soils withrounded particles.

3. Uniform soils compress and crush more thanwell-graded soils with the same maximum grainsize.

4. Under a given stress, compression and crushingcontinue indefinitely at a decreasing rate.

5. Volume change during compression depends pri-marily on the major principal stress and is inde-pendent of the principal stress ratio.

6. The higher the principal stress ratio (Kc � �1c /�3c) during consolidation, the greater the amountof grain crushing.

Particle crushing results in increase in fines contentwith increasing confining pressure. An example of thechange in particle size distribution curve with increas-ing confining pressure is shown in Fig. 10.13 (Fuku-moto, 1992). Particle crushing can be quantified byHardin’s (1985) relative breakage parameter Br, which

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Table 10.4 Grain Crushing in Rockfills and Gravels

SamplesGrain SizeDistribution

CrushingStrengthof Grains

ParticleBreakage

Bqqia

El infiernillosilicified con-glomerate

Well-gradedrockfills andgravels

High 0.02–0.10for 5 �

�1f � 80kg/cm2

Pinzandaran sandand gravel

San Franciscobasalt (grada-tions 1 and 2)

El infiernillodiorite

Somewhat uni-form rockfills

High 0.10–0.20for 5 �

�1f � 80kg/cm2

El granero slate(gradation A)

Well-gradedrockfills

Low

Mica granitic–gneiss(gradation X)

Mica granitic–gneiss(gradation Y)

Uniform rockfillproduced byblasting meta-morphic rocks(Cu � 5)

Low Increaseswith �1f �

maximumvalue �0.30

aBq is grain breakage parameter; qi is initial concentration of solids; �1f

is major principal stress at failure.From Marsal, 1973. Reprinted with permission of John Wiley & Sons.

Figure 10.12 Comparison of crushing of soils with different initial grain sizes for isotropiccompression under 8 MPa (from Lee and Farhoomand, 1967). Reproduced with permissionfrom the National Research Council of Canada.

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FABRIC, STRUCTURE, AND VOLUME CHANGE 335

σ'v=1000 psi (6.9MPa)

σ'v=5000 psi (34MPa)

σ'v=8000 psi (55MPa)

σ'v=14000 psi (97MPa)

Grain Size (mm)0.01 0.1 1

0

20

40

60

80

100

Isotropically consolidated to 980 kPa


20

40

60

80

100

10


0

20

40

60

80

100Ottawa Sand : Initial Grading 0.42-0.82 mm

Initial

Isotropically consolidated to 490 kPa andthen sheared in triaxial compression toaxial strain of 24%

Isotropically consolidated to 98 kPa andthen sheared in triaxial compression toaxial strain of 24%

One dimensional consolidation to

Landstejin Sand : Initial Grading 4-7 mm

Initial

(a)

(b)

Per

cent

Fin

er b

y W

eigh

tP

erce

nt F

iner

by

Wei

ght

Figure 10.13 Change in particle size distribution curve with increasing confining pressure:(a) Ottawa sand and (b) Landstejn sand (from Fukumoto, 1992).

is defined in Fig. 10.14. The increase in Br with iso-tropic compression pressure is shown in Fig. 10.15 forDog’s Bay carbonate sand (Coop and Lee, 1993). Thefigure also shows the increase in Br at critical-statefailure (discussed further in Chapter 11). A uniqueparticle breakage characteristic at failure is obtainedirrespective of shearing conditions (i.e., undrainedtriaxial, drained triaxial, or constant mean pressureshearing).

Aggregates of clay mineral particles are often ob-served in clays, and intact aggregate clusters of clayparticles can be considered as the smallest units con-trolling the macroscopic mechanical behavior. Theseaggregate clusters behave in some ways similarly togranular particles (e.g., Barden, 1973, and Collins andMcGown, 1974). It can be conceptualized that the con-

solidation of these clays is related to sequential break-age of clay aggregates into smaller aggregates as con-solidation pressure increases (Bolton, 2000).

10.6 FABRIC, STRUCTURE, AND VOLUMECHANGE

Collapse, shrinkage, and compression are due to par-ticle rearrangements from shear and sliding at inter-particle contacts, disruption of particle aggregates, andgrain crushing. Thus, both the arrangement of particlesand particle groups and the forces holding them inplace are important. Swelling depends strongly onphysicochemical interactions between particles, butfabric also plays a role.

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Figure 10.14 Definition of relative breakage parameter Br

by Hardin (1985).

Figure 10.15 Increase in Br with confining pressure underisotropic compression (NCL) and at critical state (CSL)achieved by standard triaxial compression shearing (bothdrained and undrained) and constant mean pressure shearing.

Shrinkage

Drying shrinkage of fine-grained soils is caused byparticle movements resulting from pore water tensionsdeveloped by capillary menisci. If two samples of clayare at the same initial water content but have differentfabrics, the one that is the more deflocculated and dis-persed shrinks the most. This is because the averagepore sizes are smaller in the deflocculated sample, thusallowing greater capillary stresses, and because of eas-ier relative movements of particles and particle groups.

An illustration of such differences is provided by thedata in Table 10.5, where dry void ratios of severalundisturbed and remolded clays are listed. In eachcase, the clay was dried from its natural water contenteither undisturbed or after thorough remolding. Thesubstantially lower dry void ratios for the remoldedsamples indicate greater shrinkage than in the undis-turbed samples.

Structure anisotropy on a macroscale may be re-flected by anisotropic shrinkage. For preferred orien-tation of platy particles parallel to the horizontal,vertical shrinkage on drying is greater than lateralshrinkage. For example, the vertical shrinkage ofSeven Sisters clay was three times greater than the hor-izontal shrinkage (Warkentin and Bozozuk, 1961).

Collapse

Collapse, as a result of wetting under constant totalstress, is an apparent contradiction to the principal ofeffective stress discussed in Chapter 7. The addition ofwater increases the pore water pressure and reducesthe effective stress; hence, expansion might be ex-pected. The apparent anomaly of volume decreaseunder decreased effective stress is because of theapplication of continuum concepts to a phenomenonthat is controlled by particulate behavior at contact lev-els for unsaturated soils. Collapse requires:

1. An open, low-density, partly unstable, partlysaturated fabric

2. A high enough total stress that the structure ismetastable

3. A strong enough clay binder or other cementingagent to stabilize the structure when dry

When water is added to a collapsing soil in whichthe silt and sand grains are stabilized by clay coatingsor buttresses, the effective stress in the clay is reduced,the clay swells, becomes weaker, and contacts fail inshear, thereby allowing the coarser silt and sand par-ticles to assume a denser packing. Thus, compatibilitywith the principle of effective stress is maintained ona microscale.

Compression

Sands In Chapter 8 it was shown that the volumechanges during the shear of samples of sand at thesame void ratio but with different initial fabrics can bedifferent. Different volume change tendencies for dif-ferent fabrics developed resulting from different meth-ods of sample preparation have also manifestedthemselves by differences in liquefaction behavior un-der undrained cyclic loading (see Fig. 8.22).

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FABRIC, STRUCTURE, AND VOLUME CHANGE 337

Table 10.5 Void Ratios of Several Clays After Drying in the Undisturbed andRemolded States

Clay

NaturalWater

Content(%) Sensitivity

Dry VoidRatio

Undisturbed

Dry VoidRatio

Remolded

Boston blue 35.6 6.8 0.69 0.50Boston blue 37.5 5.8 0.75 0.53Fore River, Maine 41.5 4.5 0.65 0.46Goose Bay, Labrador 29.0 2.0 0.60 0.55Chicago 39.7 3.4 0.65 0.55Beauharnois, Quebec 61.3 5.5 0.76 0.70St. Lawrence 53.6 5.4 0.79 0.66

IntactReconstitutedIntact IB

NCL

4 5 6 7 8 9 10 11 12In p�(kPa)

p� (kPa)

2.20

2.00

1.80

1.60

2.40

1.20

ν

100 1000 1000010000

Figure 10.16 Isotropic compression curves of intact and re-constituted calcarenite sand specimens (from Cuccovillo andCoop, 1997).

The compression behavior of a natural intact ce-mented calcarenite sand is shown in Fig. 10.16 (Cuc-covillo and Coop, 1997). Similarly to structured clays,the initial compressibility before yielding is stiff dueto cementation. If the cementation is stronger than theparticle crushing strength, the compression line will lieto the right of the normal compression line of the un-cemented reconstituted sand. If the cementation isweaker than the particle crushing strength, the com-pression curve will merge gradually toward that of theuncemented sand before yielding (Cuccovillo andCoop, 1999). This highlights the importance of relative

strengths of cementation bonding and particles on thecompression behavior of structured soils.

Clays Compression curves obtained by odometertests on undisturbed and remolded Leda (Champlain)clay, illite, and kaolinite are shown in Fig. 10.17. Li-quidity index is used as an ordinate, and the sensitivitycurves from Fig. 8.49 are superimposed.

Curve A is for undisturbed Leda clay at an initialwater content corresponding to a liquidity index of1.82. Because the sensitivity contours were developedfor normally consolidated clays, they cannot be usedto estimate sensitivity for stresses less than the precon-solidation pressure. After the preconsolidation stresshas been exceeded the curve cuts sharply across thesensitivity contours, indicating a large decrease in sen-sitivity as the structure is broken down by compres-sion.

Curve B is for kaolinite remolded at a liquidity indexof 2.06. The early part of the consolidation curve isnot shown in Fig. 10.17. Immediately after remoldingat high water content the effective stress is very low,and the sensitivity is equal to 1. Curve B shows thatconsolidation results in an increase in sensitivity to amaximum of about 15 to 18, at an effective consoli-dation pressure of about 20 kPa. At this point, the in-terparticle and interaggregate shear stresses caused bythe applied compressive stress begin to exceed thebond strengths, the degree of structural metastabilitydecreases, and the sensitivity decreases.

Curve D is for kaolinite remolded at a liquidity in-dex of 0.98. It differs considerably from curve B. Thisis consistent with the results of other studies that showthat the compression behavior, and therefore also thestructure, are different for a given clay remolded at

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Figure 10.17 Change in sensitivity with consolidation for various clays.

different water contents, for example, Morgenstern andTchalenko (1967b). Significantly lower sensitivity isdeveloped in the kaolinite of curve D than that of curveB. These observations show that both the concentrationof clay in suspension and the rate of sediment accu-mulation are important in determining the initial struc-ture of clay deposits. At high pressures, both curvestend to merge together, indicating that the initial fab-rics have been destroyed.

Curve E is for a well-graded illitic clay remolded ata liquidity index of 1.36. The consolidation curve in-dicates a low sensitivity at all consolidation pressures.Results of strength tests showed that the actual sensi-tivity ranged from 1.0 to 2.6.

Curve C is for Leda clay remolded at a liquidityindex of 1.82. The sensitivity increases from 1 to about8 with reconsolidation, indicating development of me-tastability after remolding and recompression. The sen-sitivity decreases at high pressures as convergence withcurve A is approached. All of the above findings areconsistent with the principles stated in Section 8.13.

Swelling

The structure influences swelling of fine-grained soilsthat is initiated by reduction of effective stress by un-loading and/or addition of water. For example, an ex-pansive soil that is compacted dry of optimum watercontent can swell more than if compacted to the samedensity wet of optimum (Seed and Chan, 1959). Thisdifference cannot be accounted for in terms of differ-ences in initial water content and, therefore, must beascribed to differences in structure.

A swell sensitivity has been observed in some clayswherein the swelling index for the remolded clay ishigher than that of the same clay undisturbed. The in-creased swelling of the disturbed material can resultboth from the rupture of interparticle bonds that inhibitswelling in the undisturbed state and from differencesin fabric. Old, unweathered, overconsolidated claysmay be particularly swell sensitive. Swell sensitivitiesas high as 20 were measured in one case (Schmert-mann, 1969).

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OSMOTIC PRESSURE AND WATER ADSORPTION INFLUENCES ON COMPRESSION AND SWELLING 339

Figure 10.18 Osmotic pressure: (a) Initial condition: noequilibrium, (b) final condition: equilibrium, and (c) osmoticpressure equilibrium.

10.7 OSMOTIC PRESSURE AND WATERADSORPTION INFLUENCES ON COMPRESSIONAND SWELLING

Adsorption of cations on clays, the formation of doublelayers, and water adsorption on soil surfaces generaterepulsive forces between particles as described inChapters 6 and 7. Calculation of interparticle repul-sions due to interacting double layers may be done inmore than one way; the osmotic pressure concept isconvenient and most widely used. By this approach,the pressure that must be applied to prevent movementof water either in or out of clay is determined as afunction of particle spacings expressed in terms of voidratio or water content.

The concept of osmotic pressure is illustrated byFig. 10.18. The two sides of the cell in Fig. 10.18a areseparated by a semipermeable membrane throughwhich solvent (water) may pass but solute (salt) can-not. Because the salt concentration in solution isgreater on the left side of the membrane than on theright side, the free energy and chemical potential ofthe water on the left are less than on the right.1 Becausesolute cannot pass to the right to equalize concentra-tions due to the presence of the membrane, solventpasses into the chamber on the left.

The effect of this is twofold as shown by Fig.10.18b. First, the solute concentration on the left isreduced and that on the right side is increased, whichreduces the concentration imbalance between the twochambers. Second, a difference in hydrostatic pressuredevelops between the two sides. Since the free energyof the water varies directly with pressure and inverselywith concentration, both effects reduce the imbalancebetween the two chambers. Flow continues through themembrane until the free energy of the water is thesame on each side.

It would be possible in a system such as that shownby Fig. 10.18a to completely prevent flow through themembrane by applying a sufficient pressure to the so-lution in the left chamber, as shown by Fig. 10.18c.The pressure needed to exactly stop flow is termed theosmotic pressure �, and it may be calculated, for dilutesolutions, by the van’t Hoff equation, which was intro-duced in Section 9.13:

� � kT (n � n ) � RT (c � c ) (10.2)� �iA iB iA iB

where k is the Boltzmann constant (gas constant permolecule), R is the gas constant per mole, T is the

1 Formal treatment of the concepts stated here and derivation of Eq.(10.1) are given in standard texts on chemical thermodynamics.

absolute temperature, ni is the concentration (particlesper unit volume), and ci is the molar concentration.Thus, the osmotic pressure difference between two so-lutions separated by a semipermeable membrane is di-rectly proportional to the concentration difference.

In a soil, there is no true semipermeable membraneseparating regions of high- and low-salt concentration.The effect of a restrictive membrane is created, how-ever, by the influence of the negatively charged claysurfaces on the adsorbed cations. Because of the at-traction of adsorbed cations to particle surfaces, thecations are not free to diffuse, and concentration dif-ferences responsible for osmotic pressures are devel-oped whenever double layers on adjacent particles

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Figure 10.19 Mechanism of osmotic swelling pressure generation in clay.

overlap. The situation is shown schematically in Fig.10.19. The difference in osmotic pressure midway be-tween particles and in the equilibrium solution sur-rounding the clay is the interparticle repulsive pressureor swelling pressure Ps. It can be expressed in termsof midplane potentials according to the followingequation (see Section 6.11):

P � p � 2n kT(cosh u � 1) (10.3)s 0

where n0 is the concentration in the external solution,and u is the midplane potential function.

In terms of midplane cation and equilibrium solutionconcentrations cc and c0 (Bolt, 1956), Eq. (10.2) be-comes

P � � � RT (c � c ) (10.4)�s ic i 0

For single cation and anion species of the same valence

� �P � RT(c � c � c � c ) (10.5)s c a 0 0

where ca is the midplane anion concentration, and �c0

and are the equilibrium solution concentrations of�c0

cations and anions. At equilibrium in dilute solutions

� � 2c � c � c � c � c (10.6)c a 0 0 0

because � . Thus Eq. (10.5) becomes� �c c0 0

c cc 0P � RTc � � 2 (10.7)� �s 0 c c0 c

Midplane concentrations can be determined usingthe relationships in Chapter 6. Equation (10.7) assumesparallel flat plates and may be written in terms of voidratio for saturated clay. The water content w, in termsof weight of water per unit weight of soil solids, di-vided by the specific surface of soil solids As gives theaverage thickness of water layer, which is half the par-ticle spacing or d. Thus,

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wd � (10.8)

Aw s

For saturated soil the void ratio is related to the watercontent by

e � G w (10.9)s

where Gs is the specific gravity of solids. SubstitutingEq. (10.9) into Eq. (10.8) gives

ed � (10.10)

G As w s

Bolt (1955, 1956) showed that the double-layer equa-tions (see Chapter 6) can be combined with Eq. (10.10)to give

1/2c01 / 2v(�c ) (x � d) � 2 � �0 0 cc

�/2 d�� (10.11)2 2 1/2

��0 (1 � (c /c ) sin �)0 c

in which v is the cation valence and distance x0 equalsapproximately 0.1/v nm for illite, 0.2/v nm for kao-linite, and 0.4/v nm for montmorillonite. The param-eter � is given by

2� � 2F /DRT (10.12)

in which F is the Faraday constant, R is the gas con-stant, and T is the temperature.

Combinations of (Ps /RTc0) and v(�c0)1/2(x0 � e /

GswAs) that satisfy Eqs. (10.7) and (10.11) are givenin Table 10.6. These values may be used to calculatetheoretical curves of void ratio versus pressure for con-solidation or swelling. For any value of log[Ps / (RTc0)]the swelling pressure may be calculated. The void ratiocan be computed from the corresponding value ofv(�c0)

1/2(x0 � e /GswAs). For a given soil, Ps dependscompletely on cc and c0 and those factors that cause cc

to be large relative to c0; for example, low c0, lowvalence of cation, and high dielectric constant, causehigh interparticle repulsions, high swelling pressures,and large physicochemical resistance to compression.It is apparent from the values in Table 10.6 that thedominating influence on swelling pressure at any givenvoid ratio is the specific surface area, which is deter-mined mainly by mineralogy and particle size.

The preceding relationships were developed for soilscontaining a single electrolyte, and they assume idealbehavior in accord with the DLVO theory as developedin Chapter 6. Approximate equations for mixed-cation

systems that cover most of the moisture suction oroverburden ranges of interest in soil mechanics or soilscience are available (Collis-George and Bozeman,1970). They are suitable for

�5�� 4 � 10� 20 (10.13)

c� 0

where �� is the swelling pressure or matric suction (seeSection 7.12) measured in centimeters of water.

Since the sum of the applied constraint �� in con-centration units and the external solution concentrationmust equal the midplane concentration, the pressure orsuction is given by

c � c� �m 0�� (10.14)

�54 � 10

For homovalent and dication/monoanion systems, �cm

is found from

e � 21/2v(�) � �� 1/2G As s 1 2–�% � c�c � �4 m� m(10.15)

where � � 1.0 � 1015 cm/mmol at 20�C and % is thedouble-layer charge in meq/cm2. For dilute concentra-tions in the external solution, Eqs. (10.14) and (10.15)reduce to

2�5�� 0.25 � 10 (10.16)2 2v �(e /G A )s s

For mixed-cation heterovalent systems, �cm is given by

e �1/2v(�) �� 1/2G As s c�� m

1/2 1/2

�1 1 2–�cos 1/a 1� c �% � c� �� m 4 m

�cm

(10.17)

The value of a in Eq. (10.17) is given by

� �� 2 1/22c� � (c � c ) � [4c� c � (c � c ) ]m m m m m m ma �2c�m

(10.18)

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Table 10.6 Relation Between the Distance Variable Expressed as aFunction of the Void Ratio and the Swelling Pressure of Pure ClaySystema

v(�c0)1/2

(x0 � e /GswAs) log Ps / (RTc0)v(�c0)1/2

(x0 � e /GswAs) log Ps / (RTc0)

0.050 3.596 0.997 0.9090.067 3.346 1.188 0.7170.100 2.993 1.419 0.5050.200 2.389 1.762 0.2120.300 2.032 2.076 �0.0460.400 1.776 2.362 �0.3010.500 1.573 2.716 �0.5730.600 1.405 3.09 �0.8990.700 1.258 3.57 �1.3010.801 1.130 4.35 �1.9550.902 1.012

av is the cation valence; � is 8�F /1000 DRT � 1015 cm/mmol for waterat normal T; c0 is the concentration in bulk solution (mmol/cm3); x0 � 4/v�T� 1/v A for illite, 2/v A for kaolinite, and 4/v A for montmorillonite; e isthe void ratio; Gsw is the density of solids, As is the specific surface area ofclay; Ps is the swelling pressure; R is the gas constant; T is the absolutetemperature; F is the Faraday constant; and D is the dielectric constant.

Adapted from Bolt (1956).

Figure 10.20 Relationship between particle spacing andpressure for montmorillonite (modified from Warkentin et al.,1957).

where is the midplane anion concentration. Sincec�mevaluation of Eq. (10.18) requires knowledge of themidplane concentrations of the different ions sepa-rately, the application of Eq. (10.17) is not as straight-forward as is the case of Eqs. (10.13) and (10.14).

Applicability of Osmotic Pressure Concepts

A reasonably clear understanding of how well the os-motic pressure concept can account for the compres-sion and swelling behavior of fine-grained soils hasbeen developed.

Homoionic Cation Systems

Early testing of the applicability of the osmotic pres-sure theory was done using ‘‘pure clays’’ consisting ofspecially prepared, very fine grained clay minerals.Good agreement between theoretical and experimentalvalues of interparticle spacing and pressure for mont-morillonite with particles finer than 0.2 �m in 10�4

NaCl solution is shown in Fig. 10.20. The first com-pression curves are above decompression and re-compression curves because of cross-linking andnonparallel particle arrangements, that is, fabric ef-fects, which are eliminated during the first compres-sion cycle. Theoretical and experimental compression

curves for sodium and calcium montmorillonite in 10�3

M electrolyte solutions are compared in Fig. 10.21.Agreement is fairly good as regards the influence ofcation valence. However, the experimental curves aresubstantially above the theoretical curves. This may becaused by ‘‘dead’’ volumes of liquid resulting fromterraced particle surfaces (Bolt, 1956).

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Figure 10.21 Compression curves of Na-montmorilloniteand Ca-montmorillonite, fraction �2 �m, in equilibrium with10�3 M NaCl and CaCl2, respectively. The dashed lines rep-resent the theoretical curves for As � 800 m2 /g (Bolt, 1956).

Figure 10.22 Predicted and measured swelling pressures forOpalinum shale (Madsen and Muller-Vonmoos, 1989).

Osmotic pressure theory was used successfully forprediction of swelling pressure developed in opalinumshale, a Jurassic clay rock (Madsen and Muller-Vonmoos, 1985, 1989). Swelling pressure was pre-dicted using Eq. (10.2) and compared with themeasured values, with the results shown in Fig. 10.22.Particle spacings were calculated from specific surfacearea and water content.

Agreement between theory and experiment has notbeen good for clays containing particles larger than afew tenths of a micrometer. The coarse fraction (0.2 to2.0 �m) of two bentonites gave swelling pressures lessthan predicted, whereas the fine fraction (�0.2 �m)gave values close to theoretical, even though thecharge densities of the two fractions were the same(Kidder and Reed, 1972).

Compression and swelling curves for three size frac-tions of sodium illite are shown in Fig. 10.23. Thediscrepancies between theory and experiment are fairlylarge for the �0.2-�m fraction; nonetheless, the ex-perimental curves are in the predicted relative positions(Fig. 10.23a). However, for samples containing coarserparticles (Figs. 10.23b and 10.23c), the curves are inreverse order to theoretical prediction. This is becausethe compression was controlled by initial particle ori-entations and physical interactions between the largerparticles rather than by osmotic repulsive pressures.The concentration of CaCl2 or MgCl2 has essentiallyno influence on the swelling of a 2-�m fraction ofillite, and the consolidation is influenced only by howthe changes in concentration change the initial struc-ture (Olson and Mitronovas, 1962).

Factors in addition to clay particle size may alsocontribute to failure of the theory in natural soils. TheDLVO theory that serves as the basis for determination

of the midplane concentrations suffers from several de-ficiencies, as discussed in Chapter 6. In addition, phys-ical particle interactions and the effects of interparticleshort- and long-range forces such as van der Waalsforces are neglected.

Mixed-Cation Systems

Most soils contain mixtures of sodium, potassium, cal-cium, and magnesium in their adsorbed cation com-plex. Therefore, modifications of the double-layer andosmotic pressure equations for homoionic clays are re-quired. The extent to which the resulting equationsmay be suitable depends on the structural status of theclay as well as on the particle size. Equations formixed-cation systems are derived on the assumptionthat ions of all species are distributed uniformly overthe clay surfaces in proportion to the amounts present.However, sodium and calcium ions may separate intodistinct regions. This is termed demixing (Glaeser andMering, 1954; McNeal et al., 1966; McNeal, 1970;Fink et al., 1971).

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Figure 10.23 Influence of NaCl concentration and particle size on compression and swellingbehavior of Fithian illite.

Observed behavior was good for several cases ex-amined using a demixed ion model (5 out of 6) forvalues of exchangeable sodium percentage (ESP) lessthan about 50 (McNeal, 1970). Based on X-ray deter-minations of interplate spacings in montmorillonite(Fink et al., 1971) it appears that for

1. ESP � 50 percent, there is random mixing ofNa� and Ca2� and unlimited swelling between allplates on addition of water.

2. 10 percent � ESP � 50 percent, there is demix-ing on interlayer exchange sites, with progres-sively more sets of plates collapsing to a 20-Arepeat spacing with decrease in ESP.

3. ESP � 10 to 15 percent the interlayer exchangecomplex is predominantly Ca saturated, with Naions on external planar and edge sites.

Summary

Osmotic pressure (double-layer) theory fails to explainthe first compression of most natural clays of the typeencountered in geotechnical practice because of phys-

ical particle interference and fabric factors related toparticle size. The behavior is consistent with the prin-ciple of chemical irreversibility of clay fabric (Bennettand Hurlbut, 1986), which is discussed in Section 8.2.Nonetheless, when the physical and chemical influ-ences of cation type on fabric and effective specificsurface are taken into account, the behavior can bebetter understood, as illustrated, for example, by DiMaio (1996). For those cases in which fabric changesand interparticle interactions are small, such as swell-ing from a precompressed state, or for clays with veryhigh specific surface area (very small particles) suchas bentonite, the theory gives a reasonable descriptionof swelling, at least qualitatively.

Water Adsorption Theory of Swelling

An alternative to the osmotic pressure theory for clayswelling is that swelling is caused by surface hydration(Low, 1987, 1992). Interaction of water with clay sur-faces reduces the chemical potential of the water,thereby generating a gradient in the chemical potentialthat causes additional water to flow into the system.

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INFLUENCES OF MINERALOGICAL DETAIL IN SOIL EXPANSION 345

The general relationships that describe the water prop-erties as a function of water layer thickness and watercontent are given in Section 6.5.

The swelling pressure � (in atmospheres) for pureclays follows the following empirical relationship(Low, 1980):

(� � 1) � B exp[� /w] � B exp[k / (t� )] (10.19)i w

in which B and � are constants characteristic of theclay, w is the water content, �w is the density of water,t is the average thickness of water layers, and ki � � /(�wAs), where As is the specific surface.

Equation (10.19) shows, as would be expected, thatthe lower the water content and, therefore, the smallerthe water layer thickness, the higher is the swellingpressure. Whereas this approach can explain the swell-ing of pure clays accurately, the osmotic pressure the-ory cannot (Low, 1987, 1992).

On the other hand, the influences of surface chargedensity, cation valence, electrolyte concentration, anddielectric constant, which have profound influences onswelling and swelling pressure, as shown in the pre-vious section, are not directly accounted for by thehydration theory unless appropriate adjustments can bemade for the influences of these factors on B, �, andki. An explanation that is consistent with both the in-fluences of the double-layer/osmotic pressure theoryand the water adsorption theory is as follows.

Charge density and cation type influence the relativeproportions of fully expandable and partially expand-able layers in swelling clay. For example, calciummontmorillonite does not swell to interplate distancesgreater than about 0.9 nm where the particles stabilizeby attractive interactions between the basal planes ofthe unit layers as influenced by exchangeable cationsand adsorbed water (Norrish, 1954; Blackmore andMiller, 1962; Sposito, 1984). In the presence of highelectrolyte concentrations or pore fluids of low dielec-tric constant, interlayer swelling is suppressed, and theeffective specific surface is greatly reduced relative tothat for the case where interlayer swelling occurs. Theamount of water required to satisfy surface hydrationis reduced greatly.

A hydration water layer thickness on smectite sur-faces of about 10 nm is needed to reach a distancebeyond which the water properties are no longer influ-enced by surface forces (see Fig. 6.9), and Low (1980)indicates that the swelling pressure of montmorilloniteis about 100 kPa for a water layer thickness of about5 nm. For a fully expanding smectite having a specificsurface area of 800 m2/g, this latter water layer thick-

ness would correspond to a water content of 400 per-cent. Thus, a material such as sodium montmorillonite(bentonite) with its very high specific surface wouldbe expected to be expansive over a wide range of watercontents, and experience shows clearly that it is. Onthe other hand, consider an illite or a smectite madeup of quasi-crystals so that interlayer swelling is neg-ligible. As both materials have surface structures thatare essentially the same, it would be expected that thehydration forces should be similar. Thus, an adsorbedwater layer of 5 nm would also be reasonable. How-ever, the specific surface areas of pure illite and non-expanded smectite are only about 100 m2/g, whichcorresponds to a water content of 50 percent. For apure kaolinite having a specific surface of 15 m2/g, thewater content would be only 7.5 percent for a 5-nm-thick adsorbed layer.

It is evident, therefore, that the specific surface dom-inates the amount of water required to satisfy forcesof hydration. Except for very heavily overconsolidatedclays and those soils that contain large amounts of ex-pandable smectite, there is sufficient water presenteven at low water contents to satisfy surface hydrationforces, and swelling is small. On the other hand, whenthe clay content is high and particle dissociation intounit layers is extensive, the effective specific surfacearea is large and swelling can be significant. The ten-dency for smectite dissociation into unit layers can beevaluated through consideration of double-layer inter-actions, with those conditions that favor the develop-ment of high repulsive forces, as discussed in Chapter6, leading to greater dissociation.

10.8 INFLUENCES OF MINERALOGICALDETAIL IN SOIL EXPANSION

In soils where swelling is attributable solely to the claycontent, smectite or vermiculite are the most likelyminerals because only these minerals have sufficientspecific surface area so that there are unsatisfied wateradsorption forces at low water contents. Details ofstructure and the presence of interlayer materials mayhave significant effects on the swelling properties ofthese minerals. In addition, the presence of certainother minerals in soils and shales, such as pyrite andgypsum, as well as geochemical and microbiologicalfactors, may lead to significant amounts of swellingand heave. Details of all the phenomena go well be-yond the scope of this book; however, a few examplesare given in this section to illustrate their nature andimportance.

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Table 10.7 Influence of Lattice Charge onExpansion

MineralNegative Charge

per Unit Cell Tendency to Expand

Margarite 4 NoneMuscovite Only with drastic

chemical treat-ment, if at all

Biotite 2ParagoniteHydrous mica

and illite�1.2

Vermiculite 1.4–0.9 ExpandingMontmorilloniteBeidellite 1.0–0.6 Readily expandingNontroniteHectoritePyrophyllite 0 None

From Brindley and MacEwen (1953).

Crystal Lattice Configuration Effects

Greatest swelling is observed for charge deficienciesin silicate layer structures of about one per unit cell asindicated in Table 10.7. Evidently, for layer silicateswith sufficient isomorphous substitution to give chargedeficiencies greater than 1.0 to 1.5 per unit cell, thebalancing cations are so strongly held and organizedin the interlayer regions that interlayer swelling is pre-vented.

Within the range of charge deficiencies where swellis observed, there is no consistent relationship betweencharge, as measured by the cation exchange capacity,and the amount of swell (Foster, 1953, 1955). Thisfinding is more consistent with the surface hydrationmodel for clay swelling than with the osmotic pressuretheory.

An inverse correlation exists between free swell andthe b dimension of the montmorillonite crystal lattice(Davidtz and Low, 1970). Differences in b dimension,which may be caused by differences in isomorphoussubstitution, evidently cause changes in water hydra-tion forces. Furthermore, as the water content in-creases, so also does the b dimension, as shown in Fig.6.5. Swelling ceases when the b dimension reaches0.9 nm.

Hydroxy Interlayering

The occurrence, formation, and properties ofhydroxyl–cation interlayers (Fe–OH, Al–OH, Mg–H)have been studied regarding their effects on physical

properties of expansive clays, for example, Rich(1968). Some aspects of interlayering between the ba-sic sheets in the expansive clay minerals are:

1. Optimum conditions for interlayer formation are:a. Supply of A13� ionsb. Moderately acid pH (�5)c. Low oxygen contentd. Frequent wetting and drying

2. Hydroxyaluminum is the principal interlayer ma-terial in acid soils, but Fe–OH layers may bepresent.

3. Mg(OH)2 is probably the principal interlayercomponent in alkaline soils.

4. Randomly distributed islands of interlayer mate-rial bind adjacent layers together. The degree ofinterlayering in soils is usually small (10 to 20percent), but this is enough to fix the basal spac-ing of montmorillonite and vermiculite at 14 A.

5. The cation exchange capacity is reduced by in-terlayer formation.

6. Swelling is reduced.

Salt Heave

Some saline soils with high contents of salts can un-dergo changes in volume associated with hydration–dehydration phenomena. One example is the swellingof some soils containing large amounts of sodium sul-fate (Na2SO4) found in and around the Las Vegas areaof Nevada. When the temperature falls from aboveabout 32�C to below about 10�C, the salt hydrates toNa2SO4 � 10H2O with accompanying increase in vol-ume. This salt heave has been responsible for damageto light structures and is described in more detail byBlaser and Scherer (1969) and Blaser and Arulanandan(1973).

Impact of Pyrite

Sulfur occurs in rock and soil as sulfide (S� or S2�),sulfate (SO4

2�), and organic sulfur. The sulfide min-erals, of which pyrite is one of the most common andeasily oxidized (Burkart et al., 1999), are of greatestconcern. The amount of sulfide sulfur is a good indi-cator of the potential for oxidation reactions andweathering that can result in expansion. Sulfide-induced heave has occurred in materials containing aslittle as 0.1 percent sulfide sulfur (Belgeri and Siegel1998). Products of pyrite oxidation include sulfateminerals, insoluble iron oxides such as goethite(FeOOH) and hematite (Fe2O3), and sulfuric acid(H2SO4). Sulfuric acid can dissolve other sulfides,heavy metals, carbonates, and the like that are presentin the oxidation zone, thus allowing the effects of ox-idation to increase as the process builds upon itself.

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INFLUENCES OF MINERALOGICAL DETAIL IN SOIL EXPANSION 347

Table 10.8 Volume Increases of Selected MineralTransformations

Mineral Transformation

OriginalMineral New Mineral

Volume Increase ofCrystalline Solids (%)

Illite Alunite 8Illite Jarosite 10Calcite Gypsum 60Pyrite Jarosite 115Pyrite Anhydrous ferrous

sulfate 350Pyrite Melanterite 536

Data from Fasiska et al. (1974), Shamburger et al.(1975), and Taylor (1988).

The relative proportion of sulfate sulfur is indicativeof the degree of weathering or oxidation that has al-ready occurred. Sulfate crystals develop in the capil-lary zone and tend to localize along discontinuities dueto reduced stress in these regions. The increase in vol-ume resulting from the growth of sulfate mineralsalong bedding planes is a dominant factor in the ver-tical heave that occurs in shales and other materialsthat have subhorizontal fissility (Kie, 1983; Hawkinsand Pinches, 1997). The production of sulfates by py-rite oxidation also increases the potential for furtherdeleterious reactions, such as the formation of gypsumand expansive sulfate minerals (e.g., ettringite). Gyp-sum (CaSO4 � 2H2O) is considered to be the primarycause of heave resulting from sulfate expansion. Vol-ume increases associated with several sulfidic chemicalweathering reactions are given in Table 10.8. For com-parative purposes, these percentages are based on theassumption that the altered rock was initially com-posed of 100 percent of the original mineral.

Sulfide oxidation reactions are usually catalyzed bymicrobial activity. Gypsum forms when sulfate ionsreact with calcium in the presence of water, resultingin very large volume increases. The products of pyriteoxidation reactions are significantly less dense than theinitial sulfide product (pyrite); for example, the specificgravity of pyrite is 4.8 to 5.1, whereas that of gypsumis only 2.3, and that of calcium is 2.6. Acidity pro-duced by pyrite oxidation can also result in significantquantities of acid mine and rock drainage.

Bacterially Generated Heave—Case History

About 1000 wooden houses founded on mudstone sed-iments in Iwaki City, Fukushima Prefecture, Japan,were damaged by heaving of their foundations (Oyama

et al., 1998; Yohta, 1999, 2000). The amount of heavewas as much as 480 mm. The cost for repairs wasestimated at 10 billion yen (Yohta, 2000). The mud-stone at the site contained 5 percent pyrite. Whereasthe pH of the sediment was initially 7 to 8 beforeheave, the pH of the heaved ground was about 3,and it contained acidophilic iron-oxidizing bacteria(Oyama et al., 1998).

Yamanaka et al. (2002) further confirmed the pres-ence and effects of sulfate-reducing, sulfur-oxidizing,and acidophilic iron-oxidizing bacteria by means ofseveral series of laboratory culture experiments. Testresults presented by Yamanaka et al. (2002), whichinclude electron photomicrographs of the bacteria,showed consistent variations of hydrogen sulfide con-centration, pH, Fe3� concentration, Fe2� � Fe3� con-centration, and SO4

2� concentration over time periodsup to 50 days for both the natural mudstone and themudstone after heat treatment to 121�C. The heat treat-ment prevented or greatly slowed the bacterial activity,whereas very significant changes in concentrations andpH were measured for tests done at 28�C. For example,the concentration of H2S increased from 0.3 to 2.2 mMin 20 days, the pH decreased from about 6.5 to 1.3in 47 days, the concentration of Fe3� increased fromabout 6 to 125 in 5 days, and the concentration ofSO4

2� increased from less than 1 to about 15 mM in25 days.

Based on their results and observations, Yamanakaet al. (2002) developed the following explanation forthe processes leading to the foundation heave. Theground temperature, which had been about 18�C atdepth, increased to about 25�C in the summer afterexcavation. Initial anaerobic, high water content con-ditions and the stimulation of sulfate-reducing bacteriagenerated H2S. As the ground dried and became per-meable to air, sulfate-oxidizing bacteria grew and stim-ulated production of H2SO4, the lowering of pH, andpyrite oxidation. The reaction of H2SO4 with the cal-cium carbonate present in the mudstone led to forma-tion of gypsum and, with potassium and ferric ions, toformation of jarosite. The foundation heave was asso-ciated with the volume increase that accompanied theformation of both gypsum and jarosite crystals.

Sulfate-Induced Swelling of Cement- and Lime-Stabilized Soils

Some fine-grained soils, especially in arid and semiaridareas, contain significant amounts of sulfate and car-bonate. Sodium sulfate, Na2SO4, and gypsum, Ca SO4

� 2H20, are the common sulfate forms, and calciumcarbonate, CaCO3, and dolomite, MgCO3, are the usualcarbonate forms. The dominant clay minerals in thesesoils are expansive smectites. Delayed expansion fol-

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lowing admixture stabilization of these soils usingPortland cement and lime has developed at several sites(Mitchell, 1986). Although test programs showed sup-pression of swelling and substantial strength increaseat short times (days) as a result of the incorporation ofthe stabilizer, subsequent heave of magnitude sufficientto destroy pavements developed after of exposure towater at some later time. The mechanism associatedwith this process appears to be as follows.

When cement or lime is mixed with soil and water,there is a pH increase to about 12.4, some calciumgoes into solution and exchanges with sodium on theexpansive clay. This ion exchange, along with lightcementation by carbonate and gypsum, if present, sup-presses the swelling tendency of the clay. The mixedand compacted soil is nonexpansive and has higherstrength than the untreated material. If sodium sulfateis present, then available lime is depleted according to

Ca(OH) � Na SO → CaSO � 2NaOH2 2 4 4

Silica (SiO2) and alumina (Al2O3) dissolve from theclay in the high pH environment and/or they may bepresent in amorphous form initially. These compoundscan then combine with calcium, carbonate, and sulfateto form ettringite, Ca6[Si(OH)6]2(SO4)3 � 26H2O, and/or thaumasite, Ca6[Si(OH)6]2(SO4)2(CO3)2 � 24H2O,which are very expansive materials (Mehta and Hu,1978). In addition, in the case of lime-treated soil, ifthe available lime is depleted, the pH will drop and thefurther dissolution of SiO2 from the clay will stop. Assilica is needed for formation of the cement (CSH) thatis the desired end product of the pozzolanic lime sta-bilization reaction, long-term strength gain is pre-vented. Consequently, when the treated material isgiven access to water, a large amount of swell mayoccur. Further details concerning lime–sulfate heavereactions in soils are given in Dermatis and Mitchell(1992).

10.9 CONSOLIDATION

Introduction and Simple One-Dimensional Theory

Terzaghi’s (1925b) quantitative description of soilcompression and its relation to effective stress and therate at which it occurs marked the beginning of modernsoil mechanics. An ideal homogeneous clay layer isassumed to follow the paths shown in Fig. 10.1 whensubjected to compression, unloading, and reloading.Key assumptions for analysis of the consolidation rateaccording to the Terzaghi theory are that the soil issaturated, the relationship between void ratio and ef-

fective stress is linear, and properties of the soil do notchange during the consolidation process. Deformationsin only one dimension, usually vertical, are consideredsince determinations of settlements caused by loadingsfrom structures or fills are common applications of thetheory. In such a case, the relationship between voidratio and vertical stress is as shown in Fig. 10.24a fora normally consolidated clay layer, and that in Fig.10.24b applies for an overconsolidated clay layer.2

As shown in any basic text on soil mechanics, theamount of vertical settlement H that a homogeneousclay layer of thickness H will undergo if subjected toa vertical stress increase at the surface is given by

e H � H (10.20)

1 � e0

in which e0 is the initial void ratio and e is the de-crease in void ratio due to the stress increase from

to . For convenience, the change in void ratio�� v0 v1

is often written in terms of compression index or co-efficient of compressibility and change in effectivestress as defined in Fig. 10.1.

The rate at which consolidation under the stress in-creases from to is determined using Terzaghi’s�� v0 v1

solution to the one-dimensional diffusion equation ap-plied to the transient state water flow from the consol-idating clay layer. It is assumed in this theory that therate of volume decrease is controlled totally by hydro-dynamic lag, that is, the time required for water to flowout of the consolidating soil under the gradients gen-erated by the applied pressures. The governing equa-tion is

2�u � u� c (10.21)v 2�t �z

in which u is the excess pore pressure, t is time, z isdistance from a drainage surface, and cv is the coeffi-cient of consolidation. The coefficient is given by

k (1 � e)hc � (10.22)v a v w

where kh is the hydraulic conductivity, av � �de /d��vis the coefficient of compressibility, and w is the unitweight of water.

2 In engineering practice compression and swelling curves are oftenplotted using settlement ratio, H /H as ordinate rather than voidratio, e, for convenience in settlement computations. Void ratio isused herein because it is more indicative of the state and propertiesof the soil.

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CONSOLIDATION 349

Figure 10.24 Idealized compression curves for clay layers: (a) normally consolidated and(b) overconsolidated.

Solutions for Eq. (10.22) for different boundary con-ditions are given in standard soil mechanics texts interms of a dimensionless depth z /H (where H is themaximum distance to a drainage boundary) and a di-mensionless time factor T � cvt /H

2 for differentboundary conditions. The solution for u � ƒ(z /H, T)for a layer of thickness 2H that is initially at equilib-rium and subjected to a rapidly applied uniform sur-face loading is shown in Fig. 10.25a. The averagedegree of consolidation U over the full depth of theclay layer as a function of T for this case is shown inFig. 10.25b.

Ranges of Compressibility and ConsolidationParameters

The curves in Fig. 10.2, as well as the fact that thevoid ratio of a soil cannot decrease without limit underincreasing pressure, mean that the assumption of a lin-ear relationship between void ratio and log of effectiveconsolidation pressure that defines the compression in-dex Cc is simply a useful engineering approximationthat applies over a range of stresses and void ratios ofpractical interest.3 Values for compression index lessthan 0.2 represent soils of slight to low compressibil-ity; values of 0.2 to 0.4 are for soils of moderate tointermediate compressibility; and a compression index

3 Compression index Cc or swelling index Cs and the coefficient ofcompressibility av are related as follows:

de C Cc sa � � � ln 10 or ln 10v d�� v v v

Hence, av is both stress level and stress history dependent.

greater than 0.4 indicates high compressibility. Corre-lations between compression index and compositionaland state parameters have been proposed by a numberof investigators. Several such relationships for cohesivesoils were summarized by Djoenaidi (1985) and quotedby Kulhawy and Mayne (1990), and these relationshipsare shown in Fig. 10.26. A simple correlation betweenthe compression ratio, defined as Cc / (1 � e0), wheree0 is the initial void ratio, and the natural water contentis shown in Fig. 10.27.

The large increase in compressibility that occurswhen sensitive clay is loaded beyond its maximumprior effective consolidation pressure is shown in Fig.8.44. Values of compression index for the steepest partof the compression curve as a function of in situ voidratio and sensitivity are shown in Fig. 10.28. The pro-found influence of structure metastability as repre-sented by high sensitivity is clearly evident.

Usual ranges of coefficient of consolidation for fine-grained soils are given in Fig. 4.19. Owing to the directdependence of the coefficient of consolidation cv onhydraulic conductivity and its inverse proportionalityto coefficient of compressibility, reliable determinationof a representative value in any case is difficult. Bothhydraulic conductivity and compressibility are changedby sample disturbance and by consolidation itself.Most settlement predictions are done using averagevalues for coefficient of consolidation.

Shortcomings of Simple Theory for PredictingVolume Change and Settlements

In many cases, predictions of the volume changes andsettlements and the rates at which they develop, which

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Figure 10.25 Solution to the one-dimensional consolidation equation: (a) distribution ofexcess pore water pressures as a function of dimensionless time and depth for a doublydrained clay layer and (b) average degree of consolidation as a function of time factor.

are based on the above simple theory, are poor. Amongthe types of deviations between the observed and pre-dicted settlement and pore pressure responses are thefollowing (Crooks et al., 1984; Becker et al., 1984;Tse, 1985; Mitchell, 1986; Duncan, 1993):

1. Differences in predicted and observed initial porepressure development upon load applications

2. Continued pore pressure buildup after completionof loading

3. Differences between field consolidation rates andthose predicted based on the results of laboratorytests

4. Changes in pore pressure dissipation rates duringand following construction

5. Apparent lack of strength gain with consolidationfollowing load application

There are two types of reasons for deviations fromthe simple theory. In the first category are those thatrelate to soil behavior and the fact that in general thesimple relationships between effective stress shown inFigs. 10.1 and 10.24 are neither unique nor time in-dependent. In the second category are those that relateto the constitutive models and their application and thefact that the simplifying assumptions that may be re-quired are not representative of the real conditions.

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CONSOLIDATION 351

Figure 10.26 Representative values of compression index Cc for cohesive soils (Djoenaidi,1985).

Figure 10.27 Compression ratio as a function of natural wa-ter content (from Lambe and Whitman, 1969). Reprintedwith permission from John Wiley & Sons.

Figure 10.28 The influence of sensitivity and in situ voidratio on compression index (from Leroueil et al., 1983). Re-produced with permission of the National Research Councilof Canada.

Soil Behavior Factors Characteristics of the realbehavior of fine-grained soils that are important in de-termining the amount and rate of consolidation in-clude:

1. Fabric and Structure Resistance to compressionis determined by both effective stress and struc-ture. Structural influences that must be consid-ered relate to the initial state, the effects ofsample disturbance, structural breakdown asso-ciated with consolidation under pressures greaterthan the maximum past consolidation pressure,and the effects of anisotropic loading.

2. Time and Rate of Loading The relationship be-tween void ratio and effective consolidation pres-sure is not unique for a fine-grained soil but isinfluenced by rate of loading and time under aconstant load as well. That is,

e � e(��, t) (10.23)

In differential form, Eq. (10.23) can be written

de �e d�� e� � (10.24)� � � �dt �� dt �tt ��

According to this relationship, the total void ratiochange at any time is the sum of two compo-nents: (1) that due to change in effective stress,or effective stress related compressibility, givenby the first term on the right-hand side of Eq.(10.24) and (2) that due to time, or time-relatedcompressibility, given by the second term on theright. The rate at which the total void ratio de-creases as a function of time after application of

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a stress increase may be controlled by either howrapidly the water can escape under a hydraulicgradient or by how fast the structure of the soilcan deform or creep under a given magnitude ofeffective stress. Component (1) compression iscommonly referred to as primary consolidation.Component (2) compression is commonly re-ferred to as secondary compression. In addition,aging phenomena during time under sustainedstress generate additional resistance to furthercompression.

3. Temperature Owing to differential thermal ex-pansions of soil solids and the pore fluid andchanges in interparticle bond strength and resis-tance to sliding that can result from changes intemperature, temperature-induced changes in ef-fective stress and volume are possible. These ef-fects are considered further in Section 10.12.

Modeling Factors The commonly used constitutivemodels for soil compression and consolidation may notgive suitable representations of actual behavior for thefollowing reasons:

1. The relationship between void ratio and effectiveconsolidation pressure is not linear, as is assumedfor the Terzaghi consolidation theory. In fact, theuse of compression index and swelling index tocharacterize soil compression and swelling rec-ognize the nonlinear nature of the void ratio–effective stress relationship.

2. Changes in void ratio, compressibility, and hy-draulic conductivity during consolidation are ne-glected or not properly taken into account.

3. Secondary compression, which is creep of thesoil skeleton, is often neglected, and models fortaking it into account are of uncertain validity.

4. Soil properties differ among the strata making upthe soil profile and within the individual stratathemselves.

5. Boundary conditions are uncertain or unknown,especially the drainage boundaries. Given that thetime for primary consolidation varies as thesquare of the distance to a drainage layer, errorsin definition and location of drainage boundarieshave a major impact on settlement rate predic-tions.

6. Although one-dimensional analyses are oftenused, two- and three-dimensional effects may beimportant.

7. The stress increments may not be known withcertainty.

Analysis of modeling factors of the type listed aboveis outside the scope of this book; however, additional

information about them and about how to account forthem can be found in Gibson et al. (1981), Tse (1985),Mesri and Castro (1987), Leroueil et al. (1990), Scott(1989), Duncan (1993), and elsewhere. Generalizationof Terzaghi’s one-dimensional consolidation theory tothree dimensions was made by Biot (1941). At present,there are finite element and finite difference codes thatsolve Biot’s consolidation equation incorporating non-linear stress–stress relationships as well as anisotropichydraulic conductivity. The hydraulic conductivity canalso be a function of void ratio or effective stress. Fur-ther details can be found in Lewis and Schrefler (1997)and Coussy (2004). Soil behavior factors are consid-ered further in the remainder of this section.

Effects of Sample Disturbance

The effects of sample disturbance on the compressioncurve of sensitive or structured clay are shown in Fig.8.44 and include:

1. A lower void ratio under any effective stress.2. Higher values of recompression index and lower

values of the compression index for a disturbedclay than for the undisturbed soil.

3. Less clearly defined stress history; determinationof the maximum past consolidation pressure maybe difficult and uncertain.

Several methods to estimate the influences of sampledisturbance on measured compression properties andstrength have been proposed. Among them, Schmert-mann’s (1955) procedure is useful for determination ofa corrected maximum past pressure and for estimationof more representative values of swelling and recom-pression indices.

The SHANSEP (stress history and normalized soilengineering properties) method (Ladd and Foott, 1974)was developed for more accurate determination of thestrength of soft clay. By this method, samples are con-solidated beyond the maximum past pressure into thevirgin compression range. Provided the structure of theconsolidated clay does not differ extensively from thatof the undisturbed clay, the relationships between theratios of shear stress divided by effective consolidationpressure versus strain and pore pressure divided by ef-fective consolidation pressure versus strain are thesame for both the original undisturbed clay and theconsolidated samples. An uncertainty in this method,however, is the extent of breakdown of a structuredsoil from its initial state when it is consolidated pastits prior maximum past pressure. Evidence indicatesthat it works well for clays of low-to-medium sensi-tivity.

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SECONDARY COMPRESSION 353

Figure 10.29 Idealized relationship between void ratio andlogarithm of time showing primary consolidation and sec-ondary compression.

10.10 SECONDARY COMPRESSION

According to the simple consolidation theory, whichassumes uniqueness between void ratio and effectivestress, consolidation ends when excess hydrostaticpressures within a clay layer are fully dissipated. Onthis basis, the relationship between degree of consoli-dation and dimensionless time is as shown in Fig.10.25b. In reality, however, most soils continue tocompress in the manner shown in Fig. 10.29. The rea-son for secondary compression is that the soil structureis susceptible to a viscous or creep deformation underthe action of sustained stress as the fabric elementsadjust slowly to more stable arrangements. The rate ofsecondary compression is controlled by the rate atwhich the structure can deform, as opposed to the rateof primary consolidation, which is controlled byDarcy’s law, which determines how rapidly water canescape from the pores under a hydraulic gradient.4

The mechanism of secondary compression involvessliding at interparticle contacts, expulsion of waterfrom microfabric elements, and rearrangement of ad-sorbed water molecules and cations into different po-sitions. The observed behavior is consistent with thatof a thermally activated rate process, which involvesmechanisms that are discussed in more detail in Sec-tion 12.4.

The relationship between void ratio and log of timeduring secondary compression is linear for most soilsover the time ranges of interest following primary con-

4 It is commonly assumed that there are no excess hydrostatic pres-sures during secondary compression. However, water is expelled dur-ing secondary compression, and water flow is driven by hydrostatichead differences, so there must be some small hydrostatic pressuredifference between the interior and a drainage boundary.

solidation.5 Thus, it is convenient to define a coefficientof secondary compression, C�e, according to

C � �de /d(log t) (10.25)�e

The value of C�e is usually related to the compressionindex Cc as shown in Table 10.9, where values arelisted for a number of different natural soils. Averagevalues for C�e /Cc are 0.04 � 0.01 for inorganic claysand silts, 0.05 � 0.01 for organic clays and silts, and0.075 � 0.01 for peats. Similar behavior for a numberof clean sands is shown in Fig. 10.30, where it maybe seen that C�e /Cc falls in the range of 0.015 to 0.03.

A general relationship between void ratio, effectiveconsolidation pressure, and time is shown in Fig.10.31, with slopes C�e and Cc indicated. When thecurves corresponding to different times after the endof primary consolidation are projected onto the voidratio–log effective stress plane, Fig. 10.5 is obtainedfor the assumption of linearity between void ratio andlog ��. Algebraic manipulation of the secondary com-pression equation and the primary compression equa-tion shows that the preconsolidation pressure is ratedependent (Soga and Mitchell, 1996), consistent withthe data presented in Fig. 10.7.

Both laboratory tests and field measurements, aswell as theoretical arguments, have been made to es-tablish whether or not (1) the relationship between theend-of-primary consolidation void ratio and effectiveconsolidation pressure is unique and independent ofload increment ratio or deformation rate, and (2)whether or not both primary consolidation and second-ary compression can occur together or if all primaryconsolidation must be completed before secondarycompression begins. The answers to these questionsare important as they impact the usefulness of labo-ratory odometer test results on thin samples with shortdrainage paths, in which consolidation times are short,for prediction of the consolidation of thick layers inthe field wherein consolidation times are often verylong. Detailed discussion of these issues is outside thescope of this book. Among the many important refer-ences on these points are Taylor (1942), Murayamaand Shibata (1961), Bjerrum (1967), Walker (1969),

5 There is no reason to believe that secondary compression shouldcontinue indefinitely because a final equilibrium of the structureshould ultimately develop under a given stress state. In nature, chem-ical, biological, and climate changes also develop over long timeperiods. These changes can accelerate the establishment of equilib-rium or create new conditions of disequilibrium. However, the as-sumption of linearity between void ratio and log of time after theend of primary consolidation is sufficiently accurate for most prac-tical cases.

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Table 10.9 Values of the Ratio of Coefficient of SecondaryCompression to Compression Index for Natural Soils

Grouping Soil Type C�e /Cc

Inorganic clays Whangamarino clay 0.03–0.04and silts Leda clay 0.025–0.06

Soft blue clay 0.026Portland sensitive clay 0.025–0.055San Francisco Bay mud 0.04–0.06New Liskeard varved clay 0.03–0.06Silty clay C 0.032Near-shore clays and silts 0.055–0.075Mexico City clay 0.03–0.035Hudson River silt 0.03–0.06

Organic clays Norfolk organic silt 0.05and silts Calcareous organic silt 0.035–0.06

Postglacial organic clay 0.05–0.07Organic clays and silts 0.04–0.06New Haven organic clay silt 0.04–0.075

Peats Amorphous and fibrous peat 0.035–0.083Canadian muskeg 0.09–0.10Peat 0.075–0.085Peat 0.05–0.08Fibrous peat 0.06–0.085

From Mesri and Godlewski (1977).

Figure 10.31 General relationship among void ratio, effec-tive stress, and time (from Mesri and Godlewski, 1977). Re-printed with permission of ASCE.

Figure 10.30 C� /Cc values for clean sands (from Mesri etal., 1990). Reprinted with permission of ASCE.

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IN SITU HORIZONTAL STRESS (K0) 355

Aboshi (1973), Mesri (1973), Mesri and Godlewski(1977), Jamiolkowski et al. (1985), Leroueil et al.(1985, 1988), Mesri and Choi (1985), Leroueil (1988),Mesri et al. (1995), Leroueil (1995), and Mesri (2003).

In spite of these uncertainties, conventional practicehas been to assume that secondary compression doesnot begin until completion of primary consolidation.This has the advantage of simplicity in that settlementestimates can be made on the basis of degree of con-solidation according to the simple theory during timesup to the end of primary consolidation. For longertimes, the total settlement is taken as the consolidationsettlement increased by an amount of secondary com-pression derived from Eq. (10.25). This is undoubtedlyan oversimplification of real behavior, as from the per-spective of the soil, there should be no difference be-tween the two types of compression. It compresses justsufficiently to withstand the applied stresses at anytime, and the rate at which it occurs in any elementdepends on whether or not the rate of water flow fromthe element at that time is controlled by a preexistinghydrostatic excess pressure gradient (primary consoli-dation) or by the time-dependent generation of smallpore pressures owing to structural readjustment (sec-ondary compression).

On this basis, it would seem most likely that withina clay layer both primary consolidation and secondarycompression may be occurring concurrently in differ-ent elements. The major difficulty has been in the for-mulation of a constitutive model to describe both thehydrodynamic and viscous components of the soil re-sponse that is both accurate and that can be readilyimplemented into analytical or numerical solutions.With recent advances in theory and programs that canbe run on personal computers, it is now possible tomore properly describe the actual soil response and tomake improved settlement rate predictions (Duncan,1993).

10.11 IN SITU HORIZONTAL STRESS (K0)

Terzaghi’s consolidation theory considers compressiononly in one dimension. The soil model relates the ver-tical strain to the change in vertical stress, and thisdefines the volume change under zero horizontal dis-placement conditions. There is no need to consider thechange in horizontal stress to calculate the deforma-tion, even though the actual horizontal stress changesduring loading and unloading. However, once soil de-formation departs from the one-dimensional condition,it is necessary to consider the state and changes of thestresses in the other directions and the associated vol-ume change behavior.

In most cases, the horizontal stress in the grounddoes not equal the vertical overburden stress. The min-imum and maximum possible values can be calculatedon the basis of plasticity theories for earth pressure.The actual value, which must fall somewhere betweenthese limiting values, is a proportion of the verticaloverburden stress that depends primarily on soil typeand stress history. It is often determined (or estimated)on the basis of these two factors using empirical cor-relations, and, sometimes the results of in situ testssuch as the self-boring pressuremeter (Mair and Wood,1987). The main limitation of in situ measurements isthat they invariably cause disturbance and allow lateraldeformations of the ground that change the stress beingmeasured. The general ranges of in situ lateral stressfor different soil types are summarized, and factors in-fluencing lateral stress are reviewed in this section.

Development of Horizontal Stress

The relationship between the horizontal effective stressand the vertical effective stress depends on the lateraldeformation that accompanies changes in verticalstress. If the vertical stress and strain increase withoutany deformation in the horizontal directions (i.e., one-dimensional compression, as would be the case for anaccumulating sediment), the soil is said to be in an at-rest state, and the horizontal stress associated with thiscondition is termed the at-rest pressure.

The ratio between the horizontal and vertical effec-tive stresses during initial compression of a soil is aconstant, defined by the coefficient of earth pressure atrest K0 (� ��h /��v). Values of K0 for normally con-solidated soils are generally in the range of 0.3 to 0.75.Jaky’s equation has been found to give a good estimatefor many soils:

K � 1 � sin �� (10.26)0

in which �� is the effective stress friction anglemeasured in triaxial compression tests. Although cor-relations have been published that suggest unique re-lationships between K0 and liquid limit or plasticityindex, a comprehensive set of data for 135 clay soilsindicates little correlation, as shown in Fig. 10.32. Thisis not surprising since the Atterberg limits depend onlyon composition, and K0 is a state parameter that isdependent on composition, structure, and stress history.

When the vertical stress on a normally consolidatedsoil is reduced, the horizontal stress does not decreasein the same proportion as the vertical stress. Thus, thevalue of at-rest earth pressure coefficient for an over-consolidated soil (K0)oc is greater than that for the nor-mally consolidated soil (K0)nc, and it varies with the

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Figure 10.32 Lack of correlation between coefficient ofearth pressure at rest and plasticity index for normally con-solidated soils (from Kulhawy and Mayne, 1990). Reprintedwith permission from EPRI.

Figure 10.34 Dependence of (K0)oc on overconsolidation ra-tio (from Kulhawy and Mayne, 1990). Reprinted with per-mission from EPRI.

Figure 10.33 Variation of horizontal effective stress withvertical effective stress for loading and unloading.

amount of overconsolidation, as shown schematicallyin Fig. 10.33, and in Fig. 10.34 for 48 clays. The datain Fig. 10.34 can be approximated by the equation

sin ��K � (1 � sin ��)(OCR) (10.27)0

Kulhawy and Mayne (1990) give additional useful cor-relations for estimation of K0.

The complicated stress paths associated with one-dimensional compression of four clays are illustratedin Fig 10.35. In the upper plot for each clay the de-viator stress is shown as a function of the mean ef-fective stress during one-dimensional compression.Before yielding, the stress path shows larger stress ra-tios than the K0 � 1 � sin �� line. As the stress stateapproaches the preconsolidation pressure, the stresspath moves to the K0 � 1 � sin �� line. The curvature

toward the K0 line coincides with the region of largestcompression index (steepest slope on the volumetricstrain versus effective mean stress diagrams), implyingstructural degradation.

Effect of Lateral Yielding on the Coefficient of EarthPressure

If an element of soil initially under an at-rest stresscondition is allowed to yield by compressing in a ver-tical direction while spreading laterally, for example,triaxial or plane strain compression, then the horizontalearth pressure coefficient decreases until a failure con-dition is reached. If, on the other hand, the element iscompressed in the horizontal direction while being al-lowed to expand in the vertical direction, triaxial orplane strain extension, then the horizontal earth pres-sure increases until failure develops. These two con-ditions and the associated variations in K are shown inFig. 10.36. The two failure conditions are termed ac-tive and passive, respectively, and the correspondingearth pressure coefficients are the coefficient of activeearth pressure Ka and the coefficient of passive earthpressure Kp.

According to classical theories of earth pressurebased on limiting equilibrium of a plastic material hav-

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IN SITU HORIZONTAL STRESS (K0) 357

150 1500200100 100050 5000

0

0

0

000

100

200

4

8

12

0

50

10

20

100

20000

500

1000

(σ�a + ��r)/2(kPa) (σ�a + ��r)/2(kPa)

(σ�a + ��r)/2(kPa)(σ�a + ��r)/2(kPa)

(σ� a

– �

� r)/

2(kP

a)(σ

� a –

�� r

)/2(

kPa)

(σ� a

– �

� r)/

2(kP

a)(σ

� a –

�� r

)/2(

kPa)

Ko(destructured

by weathering)

Ko(destructured)

Peak failure

Peak failure

e0 = 0.69e0 = 1.97

(b) Unweathered Keuper marl

50

25

025 50 75 100100 100 100 100

(d) Chalk

(a) Sensitive Canadian clay

ε v(%

)

0

5

10

15

e0 = 1.04

(c) Artificially bonded soil

ε v( %

)

0

5

10

15

e0 = 0.69

ε v(%

)ε v

(%)

Figure 10.35 Variation in lateral stress with mean stress during one-dimensional consoli-dation of four clays (from Leroueil and Vaughan, 1990).

ing a friction angle �� and a cohesion c�, the limitingminimum and maximum values of the earth pressurecoefficients are

�� 2c� ��2K � tan 45� � � tan 45� � (10.28)� � � �a 2 �� 2v

�� 2c� ��2K � tan 45� � � tan 45� � (10.29)� � � �p 2 �� 2v

These limiting values are for isotropic soil and a hor-izontal ground surface. Standard soil mechanics textsshould be consulted for further details on limiting earthpressure coefficients under sloping ground and the in-fluences of changes in applied loads on in situ lateralstress.

Under one-dimensional conditions, compression isusually plotted on the e–log �v plane, as shown in Fig.10.1. For three-dimensional stress and deformationconditions, however, the volumetric behavior is oftenplotted on the e–ln p� plane (or v–ln p� plane), wherep� is the mean effective pressure and v is the specificvolume (�1 � e). When a specimen is consolidatedisotropically, the slope of the normal compression lineis defined as � � �de /d ln p�(� �dv /d ln p�) (Scho-field and Wroth, 1968).6

Figure 10.37 shows the change in void ratio withmean effective stress (p�) for reconstituted kaolin clayspecimens consolidated isotropically at constant stress

6 The swelling (or recompression) line is often called the ! line one–ln p� plane and the slope is defined as the recompression index!(� �de /d ln p�)

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Figure 10.36 Variation of lateral earth pressure coefficientwith deformation of a soil element.

70 500100 200 300 1000

1.3

1.5

1.7

1.9

Mean Pressure p� (kPa)

p�

qStress Paths

12

3

Stress Path 3: q/p� = 0

Stress Path 2: q/p� = 0.288

Stress Path 1: q/p� = 0.375

Voi

d R

atio

Figure 10.37 Effect of stress ratio ( q /p�) on vol-�� /�� or1 3

umetric compression behavior of reconstituted kaolin clay.

ratios (��1 /��3 or q /p�) as shown by the stress pathsin the insert diagram. The compression lines are par-allel to each other and therefore they will have thesame compression index �. Similar behavior is ob-served in sands; the isotropic compression line and theone-dimensional compression line are parallel to eachother. Assuming that K0 is constant during loading, the� value of isotropically consolidated specimens will bethe same as that of one-dimensionally consolidatedspecimens.7

Examination of Fig. 10.37 indicates that the volu-metric behavior of soils can be separated into two com-ponents: (i) one due to compression or swelling by theincrease or decrease in mean effective pressure p� and(ii) the other due to dilation or contraction by shearingof the soil by the increase in q. Further discussion ofdeformation behavior under combined volumetric anddeviatoric stress loading conditions is given in Chapter11.

Anisotropy

Unless the horizontal earth pressure coefficient is equalto 1.0, which is not the usual case, the stress condition

7 In one dimensional consolidation condition, p� � (1 � 2K0) . The��vrelationship between Cc (� �de /d log ) and � (� �de /d ln p�)��vis Cc � � ln 10: Cc � �de /d log � �ln 10[de /d(ln )] � �ln�� v v10de / {d ln p� � d[ln(1 � 2K0)]} � �ln 10de /d ln p�) (K0 is constantin normally consolidated state, hence d[ln(1 � 2K0)] � 0). On theother hand, it is not possible to relate Cs obtained from the one-dimensional consolidation test to ! obtained from the isotropic un-loading test. This is because the K0 value changes as the specimenis unloaded and therefore the d[ln(1 � 2K0)] term in the above equa-tion does not become zero.

in the ground is anisotropic. Furthermore, although itis usually assumed that the in situ stresses are the samein all directions beneath level ground, there are someconditions in which this may not be true. These includesituations wherein there is a directional component tothe soil fabric that formed during deposition, as mightbe the case, for example, for an alluvial or beach de-posit. Directional variability has been measured atsome sites by means of pressure cells, pressure metersthat contain multiple sensing arms, and flat plate dil-atometers. With the development of new shear waveand tomography methods for the nondestructive andnonintrusive testing of soil layers, it is possible to ob-tain much more data on the actual lateral stress stateand its variability, thus providing new insights into ge-ologic and soil formational history, as well as quanti-tative values for use in the analysis and prediction ofbehavior.

Time Dependence of Lateral Earth Pressure at Rest

It is usually assumed in conventional geotechnicalanalyses that the coefficient of lateral earth pressure at-rest K0 is a time-invariant constant. Whether or not thisis indeed the case is not known with certainty, andthere is no clear consensus on how K0 should be ex-pected to vary with time (Schmertmann, 1983). How-ever, if a soil is assumed to remain under a constanteffective stress state following consolidation and thereare no changes in the compositional or environmentalconditions, then slow changes in lateral pressureshould occur in any material that is susceptible to creepand stress relaxation. Creep and stress relaxation areanalyzed in Section 12.7.

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TEMPERATURE–VOLUME RELATIONSHIPS 359

Figure 10.39 Volume of pore water drained from saturatedillite under an isotropic effective stress of 200 kPa as a func-tion of temperature change.

Figure 10.38 K0 as a function of time for San Francisco Baymud. The theoretical curve was developed by Kavazanjianand Mitchell (1984) using the general stress–strain–time Eq.(12.43) adapted for zero lateral strain.

As long as a deviator stress is acting K0 1.0, anda soil element will tend to distort. If the vertical stressis greater than the horizontal stress (K0 � 1.0), thenthe element will try to expand laterally, but under one-dimensional conditions it cannot, and the horizontalstress increases to restrain it. Conversely, if the hori-zontal stress is initially greater than the vertical stress(K0 � 1.0), then the element will try to compress lat-erally, but under one-dimensional conditions it cannot,so the horizontal stress decreases. Thus, over long pe-riods of time, the coefficient of horizontal earth pres-sure at rest in normally consolidated soil shouldincrease toward 1.0 and that in heavily overconsoli-dated soil should decrease toward 1.0.

Values of K0 as a function of time, as determined intriaxial cells by Lacerda (1976), for undisturbed sam-ples of soft San Francisco Bay mud, are shown in Fig.10.38. Also shown is a theoretical relationship betweenK0 and time that was developed using the generalstress–strain–time equations developed in Section12.9. Thus, both theory and experiment support theabove reasoning that K0 should increase with timewhen K0 is less than 1.0.

10.12 TEMPERATURE–VOLUMERELATIONSHIPS

Temperature changes generate volume and/or effectivestress changes in saturated soils. For example, the per-centage of the original pore water volume that isdrained from a saturated specimen of illite subjectedto a temperature increase from 18.9 to 60�C followedby cooling to 18.9�C while maintaining an isotropiceffective stress of 200 kPa is shown in Fig. 10.39. Thevariation in effective stress under the same temper-��3ature changes but with drainage prevented is shown in

Fig. 10.40. Temperature effects such as these must beconsidered relative to their influences on deformationand stability both in the laboratory and the field.

Theoretical Analysis

Drained Conditions Increase in temperature causesthermal expansion of mineral solids and pore water. Inaddition, there can be changes in soil structure. For atemperature change T, the volume change of the porewater is

( V ) � � V T (10.30)w T w w

where �w is the thermal expansion coefficient of soilwater, and Vw is the pore water volume. The change involume of mineral solids is

( V ) � � V T (10.31)s T s s

where �s is the thermal coefficient of cubical expansionof mineral solids, and Vs is the volume of solids. Thethermal coefficient of water is approximately 15 timesgreater than that of the solids (Cui et al., 2000).

If a saturated soil is free to drain due to a change intemperature while under constant effective stress, thevolume of water drained is

( V ) � ( V ) � ( V ) � ( V ) (10.32)DR T w T s T m T

in which ( Vm) T is the change in total volume due to T, with volume increases considered positive.

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Figure 10.40 Effect of temperature changes on the effective stress in saturated illite underconstant confining pressure.

In a soil mass with all grains in contact, and assum-ing the same coefficient of thermal expansion for allsoil minerals, the soil grains and the soil mass undergothe same volumetric strain �s T. In addition, thechange in temperature induces a change in interparticleforces, cohesion, and/or frictional resistance that ne-cessitates some particle reorientations to permit the soilstructure to carry the same effective stress. If the vol-ume change due to this effect is ( VST) T , then

( V ) � � V T � ( V ) (10.33)m T s m ST T

and

( V ) � � V T � � V TDR T w w s s

� [� V T � ( V ) ] (10.34)s m ST T

Undrained Conditions The governing criterion forundrained conditions is that the sum of the separatevolume changes of the soil constituents due to bothtemperature and pressure changes must equal the sumof the volume changes of the soil mass due to bothtemperature and pressure changes; that is

( V ) � ( V ) � ( V ) � ( V )w T s T w P s P

� ( V ) � ( V ) (10.35)m T m P

where the subscripts T and P refer to temperatureand pressure changes, respectively. If mw, ms, and m�s

refer to the compressibility of water, the compressibil-

ity of mineral solids under hydrostatic pressure, andthe compressibility of mineral solids under concen-trated loadings, respectively, then

( V ) � m V u (10.36)w P w w

( V ) � m V u � m�V �� (10.37)s P s s s s

where u is the change in pore water pressure and ��is the change in effective stress. The term ism�V ��s s

the change in volume of mineral solids due to a changein effective stress, which also manifests itself bychanges in forces at interparticle contacts. Also

( V ) � m V �� (10.38)m P v m

where mv is the compressibility of the soil structure.From Eqs. (10.30), (10.31), (10.36), (10.37), and

(10.38), Eq. (10.35) becomes

� V T � � V T � ( V ) � M V ��w w s s m T v m

� m V u � V (m u � m� ��)w w s s s (10.39)

For constant total stress during a temperature change

�� u (10.40)

Thus, Eq. (10.39) becomes

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� V T � � V T � ( V ) � m V ��w w s s m T v m

� m V u � u V (m � m�)w w s s s (10.41)

Since ms and m�s are not likely to be significantly dif-ferent, and both are much less than mv and mw , littleerror results from assuming ms � m�s � 0, so Eq.(10.41) can be written

� V T � � V T � ( V )w w s s m T

� �m V u � m V u (10.42)v m w w

The left side of Eq. (10.42) is equal to ( VDR) T ,and the right side is an equivalent volume changecaused entirely by a change in pore pressure. Because

V � V � V (10.43)m w s

Eq. (10.42) may be written, after substitution for( Vm) T by Eq. (10.33),

� V T � � V T � ( V ) � �m V uw w s w ST T v m

�m V uw w (10.44)

Rearrangement of Eq. (10.44) gives the pore pressurechange accompanying a temperature change:

n T(� � � ) � ( V ) /Vs w ST T m u �m � nmv w

n T(� � � ) � � Ts w ST� (10.45)m � nmv w

in which n is the porosity, and �ST is the physicochem-ical coefficient of structural volume change defined by

( V ) /VST T m� � (10.46)ST T

Thus, the factors controlling pore pressure changes arethe magnitude of T, porosity, the difference betweenthermal expansion coefficients for soil grains and wa-ter, the volumetric strain due to physicochemical ef-fects, and the compressibility of the soil structure. Formost soils (but not rocks) mv » mw , so

n(� � � ) T � � Ts w ST u � (10.47)mv

Consistency in algebraic signs is required for theapplication of the above equations. Both �s and �w arepositive and indicate volume increase with increasing

temperature. The compressibilities mv and mw are neg-ative because an increase in pressure causes a decreasein volume, and �ST is negative if an increase in tem-perature causes a decrease in volume of the soil struc-ture.

Volume Change Behavior

Permanent volume decreases occur when the temper-ature of normally consolidated clay is increased underdrained conditions, as shown by Fig. 10.41. Tempera-ture changes in the order indicated were carried out ona sample of saturated, remolded illite after initial con-solidation to an effective stress of 200 kPa. Waterdrains from the sample during increase in temperatureand is absorbed during temperature decrease. Theshape of the curves is similar to normal consolidationcurves for volume changes caused by changes in ap-plied stresses.

When the temperature is increased, two effects oc-cur. If the increase is rapid, a significant positive porepressure develops due to greater volumetric expansionof the pore water than of the mineral solids. The lowerthe hydraulic conductivity of the soil, the longer thetime required for this pore pressure to dissipate. Dis-sipation of this pressure accounts for the parts of thecurves in Fig. 10.41 that resemble primary consolida-tion.

The second effect results because increase in tem-perature causes a decrease in the shearing resistance atindividual particle contacts. As a consequence, there ispartial collapse of the soil structure and decrease invoid ratio until a sufficient number of additional bondsare formed to enable the soil to carry the stresses atthe higher temperature. This effect is analogous to sec-ondary compression under stress increase.

When the temperature drops, differential thermalcontractions between the soil solids and the pore watercause pressure reduction in the pore water. The soilthen absorbs water, as shown by the temperature de-crease curves in Fig. 10.41. No secondary volumechange effect is observed because the temperature de-crease causes a strengthening of the soil structure andno further structural adjustment is required to carry theeffective stress. On subsequent temperature increases,the secondary effect is negligible because the structurehas already been strengthened in prior cycles.

The final height changes and volumes of waterdrained associated with each temperature changeshown in Fig. 10.41 are plotted as a function of tem-perature in Fig. 10.42, and clay structure volumechanges are shown in Fig. 10.43. The forms of theseplots are similar to conventional compression curvesinvolving virgin compression, unloading, and reload-

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Figure 10.41 Volume of water drained from a saturated clay as a function of time as aresult of temperature changes.

ing. An irrecoverable volume reduction after eachtemperature cycle is noted. Again, the effect oftemperature increase is analogous to a pressure in-crease. The slope of the curves in Fig. 10.43 is thecoefficient of thermal expansion for the soil structure

�ST, defined previously by Eq. (10.46). For the casesshown, �ST has a value of about �0.5 � 10�4 �C�1.

The effect of temperature on clay compression de-pends on the pressure range (Campanella and Mitchell,1968; Plum and Esrig, 1969). Weaker structure at low

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Figure 10.42 Effect of temperature variations on the height and volume change of saturatedillite.

stresses caused by increased temperature causes con-solidation to a lower void ratio in order to carry thestress. The weakening effect of higher temperature iscompensated by the strengthening effect of lower voidratio. As shown in Fig. 10.44, the compression indexCc is found to be approximately independent of tem-perature. On the other hand, the isothermal swellingindex ! (� �de /d ln p�) of reconstituted samples ofan illitic clay measured under isotropic confining stressconditions is found to be temperature dependent asshown in Fig. 10.45.

The preconsolidation pressure of a natural soft claydepends on temperature as illustrated in Fig. 10.7. Fig-ure 10.46 shows the normalized preconsolidation pres-sure (� preconsolidation pressure at temperature T /preconsolidation pressure at 20�C) with temperature

(Leroueil and Marques, 1996). The data show thatthere is approximately 1 percent decrease in precon-solidation pressure per one 1�C temperature increasebetween 5 and 40�C and somewhat less at higher tem-peratures (Leroueil and Hight, 2002).

Stress history or overconsolidation ratio has a majorinfluence on the volume change caused by increase intemperature (Hueckel and Baldi, 1990). For normallyconsolidated to moderately overconsolidated clay, ir-recoverable volume reduction was observed by struc-ture degradation and the shear strength increased.Volume expansion was observed in heavily overcon-solidated clay, and the expansion rate increased withOCR.

The effect of heating followed by cooling at twostages in a consolidation test is shown in Fig. 10.47.

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Figure 10.43 Volume changes in clay structure caused bytemperature change.

��

�

��

10 20 40 60 80 100 200

0.08

0.06

0.04

0.02

0.00

κ T

Figure 10.45 Effect of temperature on swelling index of is-otropically consolidated illitic clay specimens. The clay con-tained small amounts of Kaolin, chlorite and quartz and hada liquid limit of 30 percent (after Graham et al., 2001).

Figure 10.46 Effect of temperature on preconsolidationpressure. The preconsolidation pressure at temperature T isnormalized by the preconsolidation pressure at 20�C (afterLeroueil and Marques, 1996).

Figure 10.44 Effect of temperature on isotropic consolida-tion behavior of saturated illite (Campanella and Mitchell,1968).

The effect is remarkably similar to the development ofan apparent precompression due to aging and creepunder a sustained stress as discussed in Chapter 12.

Pore Pressure Behavior

Pore pressure changes in saturated soils caused by tem-perature changes are reasonably well predicted by Eq.(10.47). The most important factors are the thermalexpansion of the pore water, the compressibility of thesoil structure, and the initial effective stress. The ap-propriate value of the compressibility mv depends onthe rebound and recompression characteristics of thesoil. When temperature increases, pore pressure in-creases, and effective stress decreases, which is a con-dition analogous to unloading. When temperaturedecreases, pore pressure decreases, and effective stress

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Figure 10.47 Effect of heating and cooling on void ratioversus pressure relationship of illite (Plum and Esrig, 1969).

increases. As the previous temperature history causedpermanent volume decrease at the higher temperature,the condition is analogous to recompression. Thus, theappropriate value of mv is based on the slope of therebound or recompression curves, both of which areapproximately the same, and can be defined by

V /V 0.435 Cm m s(m ) � � (10.48)v R �� (1 � e ) ��0

where Cs is the swelling index, e0 is the initial voidratio, and �� is the effective stress at which (mv)R is tobe evaluated.

A pore pressure–temperature parameter F may bedefined as the change in pore pressure per unit changein temperature per unit effective stress, or alternatively,the change in unit effective stress per unit change intemperature, that is,

u / T �� /�� e [(� � � ) � � /n]0 s w STF � � � �� T 0.435Cs

(10.49)

Some values of F are given in Table 10.10. The valueslisted for �� are averages for the indicated temperatureranges.

The influence of effective stress on change in porepressure can be seen for the data for Vicksburg buck-shot clay and for the saturated sandstone. The greaterchange in pore pressure for a given T for a higherinitial effective stress is predicted by this theory. Also,the much lower compressibility of the sandstone is re-sponsible for a much higher temperature sensitivity of

pore water pressure and effective stress than for thebuckshot clay.

The parameter F is approximately the same for dif-ferent clays (Table 10.10). Knowledge of F values al-lows determination of laboratory temperature controlto assure accurate pore pressure measurements in un-drained testing of soil samples. For example, if it weredesired to keep pore pressure fluctuations within �5kPa for one of the clays in Table 10.10, the requiredtemperature control would be about 0.5�C for a sampleat an effective stress of 500 kPa.

The preceding analyses indicate that the overall vol-ume changes that result from changes in temperaturemay not be large. However, the structural weakeningand pore pressure changes that occur may be signifi-cant in terms of their influences on shear deformationand strength.


Knowledge of volume changes to be expected in a soilmass as a result of changes in confinement, loading,exposure to water and chemicals, changes in temper-ature and the like is one of the four dimensions of soilbehavior that must be understood for success in geo-engineering, the other three being fluid and energyconduction properties, deformation and strengthproperties, and the influences of time. The nature andinfluences of different factors on volume change havebeen the subject of this chapter.

Soil compression and consolidation under appliedstress have been the most studied owing to their es-sential role in estimation of settlements, and this wasone of the first motivations for development of soilmechanics. The mechanical aspects of compressionand swelling are far better understood and quantifiedthan are those generated by physicochemical, geo-chemical, and microbiological factors, although inter-est and research on the latter is intensifying.

Although analysis of volume change is typicallydone through consideration of a soil mass as a contin-uum, the processes that determine it are at the partic-ulate level and involve discreet particle movementsrequired to produce a new equilibrium followingchanges in stress and environmental conditions. Im-portant aspects of colloidal type interactions involvinginterparticle forces, water adsorption phenomena, andsoil fabric effects were analyzed in this chapter. Dis-creet particle movements and their relationships tomacroscopic volumetric and deviatoric behavior arediscussed in more detail in Chapters 11 and 12.

Soil swelling, sometimes referred to as ‘‘the hiddendisaster’’ owing to the very large economic, but un-spectacular, damages (several billion dollars in the

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Table 10.10 Temperature-Induced Pore Pressure Changes UnderUndrained Condtions

Soil Type��

(kN/m2) T(�C)

u(kN/m2)

F( u / T)

��

(�C�1)

Illite (grundite) 200 21.1–43.4 �58 0.013San Francisco

Bay mud150 21.1–43.4 �50 0.015

Weald Claya 710 25.0–29.0 �51 0.018Kaolinite 200 21.1–43.4 �78 0.017Vicksburg

buckshotclayb

100650

20.0–36.020.0–36.0

�28�190

0.0170.018

Saturatedsandstone(porous stone)

250580

5.3–15.05.3–15.0

�190�520

0.0790.092

aFrom Henkel and Sowa (1963).bFrom Ladd (1961) Fig. VIII-6.

U.S.) to pavements, structures, and utilities each year,is attributable to both double layer repulsions and wa-ter adsorption in soils that contain significant amountsof high plasticity clay minerals. Other causes of soiland rock expansion have been identified as well, suchas pyrite related mineral transformations and sulfatereactions, often mediated by microorganisms.


1. What is the single most important property orcharacteristic controlling the consolidation andswelling behavior of a soil? Why?

2. If two samples of the same sand have the samerelative density and are confined under the sameeffective stress, can they have different volumechange properties? Why?

3. In what soil types and under what conditions dophysical particle interactions dominate in deter-mining the compression and swelling behavior? Inwhat soil types and under what conditions dophysicochemical factors dominate?

4. Provide an explanation for the differences inamount of swelling associated with expansion fol-lowing the different stress paths shown in Fig.10.10.

5. Consider the following soil profile beneath a levelground surface:

Depth Range(m) Soil Type

Unit Weight(kN/m3)

0–5 Surcharge fill 19.05–10 Rubble fill 17.0

10–18 Clean sand 18.018–30 Soft clay 16.0�30 Bedrock —

The water table is at a depth of 8 m.a. Show profiles of vertical total, effective, and

water pressure as a function of depth below theground surface before placement of the sur-charge fill. Assume that each layer is normallyconsolidated.

b. Show profiles of vertical total, effective, andwater pressure as a function of depth immedi-ately after placement of the surcharge fill.Indicate if the clay layer is normally consoli-dated, overconsolidated, or underconsolidatedat this time.

c. Show profiles of vertical total, effective, andwater pressure as a function of depth at a longtime after the placement of the surcharge fill.Are the sand and clay layers normally consol-idated, underconsolidated, or overconsolidated?

d. Show profiles of vertical total, effective, andwater pressure as a function of depth immedi-ately after removal of the surcharge fill. Are thesand and clay layers normally consolidated, un-derconsolidated, or overconsolidated?

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e. Show profiles of vertical total, effective, andwater pressure as a function of depth at a longtime after removal of the surcharge fill. Are thesand and clay layers normally consolidated,under-consolidated, or overconsolidated?

f. Show depth profiles and approximate values ofthe horizontal coefficient of earth pressure atrest for the conditions in parts (a) through (e).

6. Two near-surface strata of the same soft clay areto be consolidated. In one the consolidation is tobe done by placement of a surcharge fill at theground surface. In the other, the consolidation isto be effected by lowering the water table to thebottom of the clay layer and evaporation of waterfrom the ground surface, which will cause shrink-age of the clay. The ground water table is initiallyat the top of the clay stratum. Show profiles ofeffective stress and water pressure versus depth foreach stratum corresponding to the condition wherethe vertical effective stress is the same in each atmiddepth. Will the clay structure be the same ineach stratum at this depth at this time? Why?

7. Describe and contrast the compression, consoli-dation, and swelling potential properties of the fol-lowing soil types. Assume their initial states (wa-ter content, overburden pressure, environmentalchemistry) to be representative of the indicatedsoil type as ordinarily encountered in nature.a. Loessb. Varved clayc. Carbonate sandd. Quick claye. Tropical andisolf. Glacial moraineg. Torrential stream deposit or mudflowh. Sand hydraulic filli. Compacted clay liner of an earth dam

8. Prepare a schematic diagram of liquidity indexversus log effective consolidation pressure. Showthe positions of normally consolidated and heavilyoverconsolidated samples of a given clay on thisdiagram.

9. Discuss the strengths and weaknesses of the os-motic pressure and water adsorption theories forclay swelling in terms of their adequacy to explainthe influences of mineralogical and compositionalfactors on the swelling of fine-grained soils.

10. Calculate the equilibrium void ratios at a pressureof 1.0 atm for the following systems assuming thatthe DLVO and osmotic pressure theories are valid:

a. Sodium montmorillonite in 0.002 M NaClb. Sodium montmorillonite in 0.2 M NaClc. Sodium illite in 0.002 M NaCld. Sodium illite in 0.2 M NaClAssume any quantities needed but not stated.

11. Consider the real behavior of sediments formedfrom montmorillonite and illite in waters of theabove concentrations. Approximately what voidratios would you expect to find after normal con-solidation to a pressure of 1.0 atm? If differentthan the values you calculated in the precedingproblem, state why?

12. A normally consolidated, saturated marine clay issampled without structural disturbance from be-neath the seafloor and sealed to prevent watermovement in or out. The temperature of the clayin situ is 5�C. The effective stress at the time ofsampling is 200 kPa and the void ratio of the clayis 0.90. The sealed sample is taken immediately tothe shipboard laboratory where the original in situconfining stress is immediately reapplied.a. What will be the subsequent effective stress in

the laboratory at a temperature of 20�C? Theclay has a compression index of 0.5 and aswelling index of 0.05. Other properties are asfollows:

• Compressibility of water � �4.83 � 10�5

cm2/kg

• Coefficient of thermal expansion of solidmineral particles � 0.35 � 10�4 �C�1

• Coefficient of thermal expansion of water �2.07 � 10�4�C�1

• Coefficient of thermal expansion of the soilstructure � 0.5 � 10�4�C�1

b. How does the change in effective stress com-puted in part (a) compare with the value esti-mated on the basis of Table 10.10 in the text?

c. If the same confining stress is maintained butdrainage of the sample is then allowed, howmuch water, expressed as a percentage of theoriginal sample volume, will move in or out ofthe clay?

d. Illustrate the changes accompanying the oper-ation in parts (a) and (c) on a diagram of voidratio versus log effective consolidation pres-sure.

13. Identify and discuss some possible consequencesof seawater intrusion into a freshwater sand aqui-fer overlying a compressible clay stratum which,in turn, overlies another freshwater aquifer.

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14. What is a collapsing soil? What conditions caninitiate collapse? What factors determine the mag-nitude and rate of collapse? Is the process com-patible with the principle of effective stress? Why?

15. Volume and temperature stability over long peri-ods of time (thousands of years) is a very im-portant consideration in the utilization of earthmaterials as containment barriers for various typesof chemical and radioactive waste. What mineraltypes, gradations, and placement conditions wouldyou specify for this application? Why?

16. Suggest possible methods other than direct loadingusing surcharge fills for reducing the water content

(consolidating) a highly plastic clay slurry that isinitially at a liquidity index considerably greaterthan 1.0. Explain how each of the methods thatyou have identified works.

17. Comment on the mechanisms of primary consoli-dation and secondary compression in terms of therate-controlling factors, influences of and effectson soil structure, whether they occur sequentiallyor concurrently, and the suitability of our usualprocedures for quantifying them for geoengineer-ing analysis.

18. Suggest possible methods for preventing or reduc-ing swelling on the exposure of expansive soil towater and explain the mechanisms involved.

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369

CHAPTER 11

Strength and DeformationBehavior

11.1 INTRODUCTION

All aspects of soil stability—bearing capacity, slopestability, the supporting capacity of deep foundations,and penetration resistance, to name a few—depend onsoil strength. The stress–deformation and stress–deformation–time behavior of soils are important inany problem where ground movements are of interest.Most relationships for the characterization of thestress–deformation and strength properties of soils areempirical and based on phenomenological descriptionsof soil behavior. The Mohr–Coulomb equation is byfar the most widely used for strength. It states that

� � c � � tan � (11.1)ff ff

� � c� � �� tan �� (11.2)ff ff

where �ff is shear stress at failure on the failure plane,c is a cohesion intercept, �ff is the normal stress on thefailure plane, and � is a friction angle. Equation (11.1)applies for �ff defined as a total stress, and c and � arereferred to as total stress parameters. Equation (11.2)applies for defined as an effective stress, and c� and��ff�� are effective stress parameters. As the shear resis-tance of soil originates mainly from actions at inter-particle contacts, the second equation is the morefundamental.

In reality, the shearing resistance of a soil dependson many factors, and a complete equation might be ofthe form

Shearing resistance � F(e, c�, ��, ��, C, H, T, �, S)�,

(11.3)

in which e is the void ratio, C is the composition, His the stress history, T is the temperature, � is the strain,

is the strain rate, and S is the structure. All param-�eters in these equations may not be independent, andthe functional forms of all of them are not known.Consequently, the shear resistance values (including c�and ��) are determined using specified test type (i.e.,direct shear, triaxial compression, simple shear), drain-age conditions, rate of loading, range of confiningpressures, and stress history. As a result, different fric-tion angles and cohesion values have been defined, in-cluding parameters for total stress, effective stress,drained, undrained, peak strength, and residualstrength. The shear resistance values applicable inpractice depend on factors such as whether or not theproblem is one of loading or unloading, whether or notshort-term or long-term stability is of interest, andstress orientations.

Emphasis in this chapter is on the fundamental fac-tors controlling the strength and stress–deformationbehavior of soils. Following a review of the generalcharacteristics of strength and deformation, some re-

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370 11 STRENGTH AND DEFORMATION BEHAVIOR

(a)

Strain

Peak

Critical State

Residual

ShearStress τ

Normal effective stress σ�

φresidual

φcritical state

φpeak

Tangent PeakStrength Envelope

Critical stateStrength Envelope

Residual Strength Envelope

(b)

Peak Strength

Secant PeakStrength Envelope

At Large Strains

a

b

c

da

b

c

d

Dense orOverconsolidated

a�

d�

Loose or NormallyConsolidated

ShearStress τor StressRatio τ/σ�

b�, c�

Figure 11.1 Peak, critical, and residual strength and associated friction angle: (a) a typicalstress–strain curve and (b) stress states.

lationships among fabric, structure, and strength areexamined. The fundamentals of bonding, friction, par-ticulate behavior, and cohesion are treated in some de-tail in order to relate them to soil strength properties.Micromechanical interactions of particles in an assem-blage and the relationships between interparticle fric-tion and macroscopic friction angle are examined fromdiscrete particle simulations. Typical values of strengthparameters are listed. The concept of yielding is intro-duced, and the deformation behavior in both the pre-yield (including small strain stiffness) and post-yieldregions is summarized. Time-dependent deformationsand aging effects are discussed separately in Chapter12. The details of strength determination by means oflaboratory and in situ tests and the detailed constitutivemodeling of soil deformation and strength for use innumerical analyses are outside the scope of this book.

11.2 GENERAL CHARACTERISTICS OFSTRENGTH AND DEFORMATION

Strength

1. In the absence of chemical cementation betweengrains, the strength (stress state at failure or theultimate stress state) of sand and clay is ap-proximated by a linear relationship with stress:

� � �� tan �� (11.4)ff ff

or

(�� ) � (�� )sin �� (11.5)1ff 3ff 1ff 3ff

where the primes designate effective stressesand are the major and minor principal�� 1ff 3ff

effective stresses at failure, respectively.2. The basic contributions to soil strength are fric-

tional resistance between soil particles in con-tact and internal kinematic constraints of soilparticles associated with changes in the soil fab-ric. The magnitude of these contributions de-pends on the effective stress and the volumechange tendencies of the soil. For such materialsthe stress–strain curve from a shearing test istypically of the form shown in Fig. 11.1a. Themaximum or peak strength of a soil (point b)may be greater than the critical state strength,in which the soil deforms under sustained load-ing at constant volume (point c). For some soils,the particles align along a localized failure planeafter large shear strain or shear displacement,and the strength decreases even further to theresidual strength (point d). The correspondingthree failure envelopes can be defined as shownin Fig. 11.1b, with peak, critical, and residualfriction angles (or states) as indicated.

3. Peak failure envelopes are usually curved in themanner shown in Fig. 4.16 and schematically inFig. 11.1b. This behavior is caused by dilatancysuppression and grain crushing at higherstresses. Curved failure envelopes are also ob-served for many clays at residual state. When

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GENERAL CHARACTERISTICS OF STRENGTH AND DEFORMATION 371

Figure 11.2 Variation of residual strength with stress level (after Bishop et al., 1971): (a)Brown London clay and (b) Weald clay.

expressed in terms of the shear strength nor-malized by the effective normal stress as a func-tion of effective normal stress, curves of thetype shown in Fig. 11.2 for two clays are ob-tained.

4. The peak strength of cohesionless soils is influ-enced most by density, effective confiningpressures, test type, and sample preparationmethods. For dense sand, the secant peak fric-tion angle (point b in Fig. 11.1b) consists in part

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c�e

0Normal Effective Stress σ�

τ

eff

φ�e

φ�crit

A� A

AA�

σ�eσ�ff

σ�ff

Hvorslev Envelope

Peak Strength Envelope

Normally Consolidated

Virgin Compression

Rebound

Overconsolidated

Overconsolidated


She

ar S

tres

s τ

Voi

d R

atio

eW

ater

Con

tent

w

Figure 11.3 Effect of overconsolidation on effective stressstrength envelope.

of internal rolling and sliding friction betweengrains and in part of interlocking of particles(Taylor, 1948). The interlocking necessitateseither volume expansion (dilatancy) or grainfracture and/or crushing if there is to bedeformation. For loose sand, the peak frictionangle (point b� in Fig. 11.1b) normally coincideswith the critical-state friction angle (point c�),and there is no peak in the stress–strain curve.

5. The peak strength of saturated clay is influencedmost by overconsolidation ratio, drainage con-ditions, effective confining pressures, originalstructure, disturbance (which causes a change ineffective stress and a loss of cementation), andcreep or deformation rate effects. Overconsoli-dated clays usually have higher peak strength ata given effective stress than normally consoli-dated clays, as shown in Fig. 11.3. The differ-ences in strength result from both the differentstress histories and the different water contentsat peak. For comparisons at the same water con-tent but different effective stress, as for pointsA and A�, the Hvorslev strength parameters ce

and �e are obtained (Hvorslev, 1937, 1960).Further details are given in Section 11.9.

6. During critical state deformation a soil is com-pletely destructured. As illustrated in Fig. 11.1b,the critical state friction angle values are inde-pendent of stress history and original structure;for a given set of testing conditions the shearing

resistance depends only on composition and ef-fective stress. The basic concept of the criticalstate is that under sustained uniform shearing atfailure, there exists a unique combination ofvoid ratio e, mean pressure p�, and deviatorstress q.1 The critical states of reconstitutedWeald clay and Toyoura sand are shown in Fig.11.4. The critical state line on the p�–q plane islinear,2 whereas that on an e-ln p� (or e-log p�)plane tends to be linear for clays and nonlinearfor sands.

7. At failure, dense sands and heavily overconsol-idated clays have a greater volume after drainedshear or a higher effective stress after undrainedshear than at the start of deformation. This isdue to its dilative tendency upon shearing. Atfailure, loose sands and normally consolidatedto moderately overconsolidated clays (OCR upto about 4) have a smaller volume after drainedshear or a lower effective stress after undrainedshear than they had initially. This is due to itscontractive tendency upon shearing.

8. Under further deformation, platy clay particlesbegin to align along the failure plane and theshear resistance may further decrease from thecritical state condition. The angle of shear re-sistance at this condition is called the residualfriction angle, as illustrated in Fig. 11.1b. Thepostpeak shearing displacement required tocause a reduction in friction angle from the crit-ical state value to the residual value varies withthe soil type, normal stress on the shear plane,and test conditions. For example, for shale my-lonite3 in contact with smooth steel or other pol-ished hard surfaces, a shearing displacement ofonly 1 or 2 mm is sufficient to give residualstrength.4 For soil against soil, a slip along the

1 In three-dimensional stress space , �xy, �yz, �zx) or�� (��, ��, ��x y z

the equivalent principal stresses ( ), the mean effective��, ��, ��1 2 3

stress p�, and the deviator stress q is defined as

p� � (�� ) /3 � (�� ) /3x y z 1 2 3

q � (1 /2)

2 2 2 2 2 2(�� ) � (�� ) � (�� ) � 6� � 6� � 6�x y y z z x xy yz zx

2 2 2� (1 /2)(�� ) � (�� ) � (�� )1 2 2 3 3 1

For triaxial compression condition (�� ), p� � (�� 1 2 3 1

2��) /3, q � �� 2 1 22 The critical state failure slope on p�–q plane is related to frictionangle ��, as described in Section 11.10.3 A rock that has undergone differential movements at high temper-ature and pressure in which the mineral grains are crushed againstone another. The rock shows a series of lamination planes.4 D. U. Deere, personal communication (1974).

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(a-1) p� versus q

(a) (b)

Mean Pressure p�(kPa)

0 100 200 300 400 500 6000

100

200

300

400

500

0.7

0.6

0.5

0.4

0.3

100 200 300 400 500


0 1 2 3 40

1

2

3

4

Mean Pressure p�(MPa)

(b-1) p� versus q

Initial State


0.050.02 0.1 0.5 1 5

0.95

0.90

0.85

0.80

0.75

Overconsolidated


Overconsolidated


Isotropic NormalCompression Line

Critical State Line

Critical State Line Critical State Line

Critical State Line

Dev

iato

r S

tres

s q

(MP

a)

Voi

d ra

tio e

(a-2) e versus lnp�(b-2) e versus logp�

Dev

iato

r S

tres

s q

(kP

a)

Voi

d ra

tio e

Figure 11.4 Critical states of clay and sand: (a) Critical state of Weald clay obtained bydrained triaxial compression tests of normally consolidated (�) and overconsolidated (●)specimens: (a-1) q–p� plane and (a-2) e–ln p� plane (after Roscoe et al., 1958). (b) Criticalstate of Toyoura sand obtained by undrained triaxial compression tests of loose and densespecimens consolidated initially at different effective stresses, (b-1) q–p� plane and (b-2) e–log p� plane (after Verdugo and Ishihara, 1996).

shear plane of several tens of millimeters maybe required, as shown by Fig. 11.5. However,significant softening can be caused by strainlocalization and development of shear bands,especially for dense samples under low confine-ment.

9. Strength anisotropy may result from both stressand fabric anisotropy. In the absence of chemi-cal cementation, the differences in the strength

of two samples of the same soil at the same voidratio but with different fabrics are accountablein terms of different effective stresses as dis-cussed in Chapter 8.

10. Undrained strength in triaxial compression maydiffer significantly from the strength in triaxialextension. However, the influence of type of test(triaxial compression versus extension) on theeffective stress parameters c� and �� is relatively

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Figure 11.5 Development of residual strength with increasing shear displacement (afterBishop et al., 1971).

Figure 11.6 Effect of temperature on undrained strength ofkaolinite in unconfined compression (after Sherif and Bur-rous, 1969).

small. Effective stress friction angles measuredin plane strain are typically about 10 percentgreater than those determined by triaxial com-pression.

11. A change in temperature causes either a changein void ratio or a change in effective stress (ora combination of both) in saturated clay, as dis-cussed in Chapter 10. Thus, a change in tem-perature can cause a strength increase or astrength decrease, depending on the circum-stances, as illustrated by Fig. 11.6. For the testson kaolinite shown in Fig. 11.6, all sampleswere prepared by isotropic triaxial consolidationat 75�F. Then, with no further drainage allowed,temperatures were increased to the values indi-cated, and the samples were tested in uncon-fined compression. Substantial reductions instrength accompanied the increases in temper-ature.

Stress–Strain Behavior

1. Stress–strain behavior ranges from very brittlefor some quick clays, cemented soils, heavilyoverconsolidated clays, and dense sands to duc-tile for insensitive and remolded clays and loosesands, as illustrated by Fig. 11.7. An increase in

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Figure 11.7 Types of stress–strain behavior.10-4 10-3 10-2 10-1 100 101

Strain %Dynamic Methods

Local Gauges

Conventional Soil Testing

Retaining Walls

Foundations

TunnelsLinear Elastic

Nonlinear Elastic

Preyield Plastic

Full Plastic

(a) Typical Strain Ranges in the Field

(b) Typical Strain Ranges for Laboratory Tests

Stif

fnes

sG

or

E

Figure 11.9 Stiffness degradation curve: stiffness plottedagainst logarithm of strains. Also shown are (a) the strainlevels observed during construction of typical geotechnicalstructures (after Mair, 1993) and (b) the strain levels that canbe measured by various techniques (after Atkinson, 2000).

Figure 11.8 Effect of confining pressure on the consoli-dated-drained stress–strain behavior of soils.

confining pressure causes an increase in the de-formation modulus as well as an increase instrength, as shown by Fig. 11.8.

2. Stress–strain relationships are usually nonlin-ear; soil stiffness (often expressed in terms oftangent or secant modulus) generally decreaseswith increasing shear strain or stress level up topeak failure stress. Figure 11.9 shows a typicalstiffness degradation curve, in terms of shearmodulus G and Young’s modulus E, along withtypical strain levels developed in geotechnicalconstruction (Mair, 1993) and as associated withdifferent laboratory testing techniques used tomeasure the stiffness (Atkinson, 2000). For ex-ample, Fig. 11.10 shows the stiffness degrada-tion of sands and clay subjected to increase inshear strain. As illustrated in Fig. 11.9, the stiff-ness degradation curve can be separated into

four zones: (1) linear elastic zone, (2) nonlinearelastic zone, (3) pre-yield plastic zone, and (4)full plastic zone.

3. In the linear elastic zone, soil particles do notslide relative to each other under a small stressincrement, and the stiffness is at its maximum.The soil stiffness depends on contact interac-tions, particle packing arrangement, and elasticstiffness of the solids. Low strain stiffness val-ues can be determined using elastic wave veloc-ity measurements, resonant column testing, orlocal strain transducer measurements. The mag-nitudes of the small strain shear modulus (Gmax)and Young’s modulus (Emax) depend on appliedconfining pressure and the packing conditionsof soil particles. The following empirical equa-tions are often employed to express these de-pendencies:

nGG � A F (e)p� (11.6)max G G

nEE � A F (e)�� (11.7)i(max) E E i

where FG(e) and FE(e) are functions of voidratio, p� is the mean effective confining pres-sure, is the effective stress in the i direction,��iand the other parameters are material constants.

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Toyoura Sand

Ticino Sand

TC PSC

20

40

60

80

100

120

140

10010-110-210-310-4

Shear Strain (%)

(a)

10010-110-210-310-410-5

Shear Strain (%)

20

40

60

80

100

120

σc = 30 kPa

σc = 100 kPa

σc = 200 kPa

σc = 400 kPa

Confining Pressures

ConfiningPressure

78.4 kPa

49 kPa

(b)

Sec

ant S

hear

Mod

ulus

G (M

Pa)

Sec

ant S

hear

Mod

ulus

G (M

Pa)

Figure 11.10 Stiffness degradation curve at different confining pressures: (a) Toyoura andTicino sands (TC: triaxial compression tests, PSC: plain strain compression tests) (afterTatsuoka et al., 1997) and (b) reconstituted Kaolin clay (after Soga et al., 1996).

104103102101100100

101

102

103

104

nG = 0.13

nG = 0.65

nG = 0.63

Confining pressure, p� (kPa)

UndisturbedRemoldedRemolded with CaCO3

100 150 200 250 300

500

400

300

250

350

450

Vertical Effective Stress, σv� (kPa)

(b)(a)

nE = 0.49

At each vertical effective stress,horizontal effective stress σh� (kPa)was varied between 98 kPa and196 kPa

She

ar M

odul

us,G

max

MP

a

Ver

tical

You

ng's

Mod

ulus

Evm

ax/

FE(e

) (M

Pa)

Figure 11.11 Small strain stiffness versus confining pressure: (a) Shear modulus Gmax ofcemented silty sand measured by resonant column tests (from Stokoe et al. 1995) and (b)vertical Young’s modulus of sands measured by triaxial tests (after Tatsuoka and Kohata,1995).

Figure 11.11 shows examples of the fitting ofthe above equations to experimental data.

4. The stiffness begins to decrease from the linearelastic value as the applied strains or stressesincrease, and the deformation moves into thenonlinear elastic zone. However, a complete cy-cle of loading, unloading, and reloading withinthis zone shows full recovery of strains. Thestrain at the onset of the nonlinear elastic zoneranges from less than 5 � 10�4 percent for non-

plastic soils at low confining pressure conditionsto greater than 5 � 10�2 percent at high confin-ing pressure or in soils with high plasticity (San-tamarina et al., 2001).

5. Irrecoverable strains develop in the pre-yieldplastic zone. The initiation of plastic strains canbe determined by examining the onset of per-manent volumetric strain in drained conditionsor residual excess pore pressures in undrainedconditions after unloading. Available experi-

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1.00.80.60.40.2

q = σ�a-σ�r

0.2

0.4

0.6

0.8

0.0

-0.2

-0.4

MPa

MPa

Initial Condition

Yield State

Stress PathFailure Line

Failure Line

Yield Envelope

0.60.40.2

MPa0.0

-0.2

0.2

0.4

0.6

q = σ�a-σ�r

MPa

Yield State

Yield Envelope

Preyield Boundary

Pre-yield State

Initial State Surrounded byLinear Elastic Boundary

Linear ElasticBoundary

(a) (b)

p� = (σ�a + 2σ�r)/3 p� = (σ�a + 2σ�r)/3

Figure 11.12 Yield envelopes: (a) Aoi sand (Yasufuku et al., 1991) and (b) Bothkennar clay(from Smith et al., 1992).

mental data suggest that the strain level that in-itiates plastic strains ranges between 7 � 10�3

and 7 � 10�2 percent, with the lower limit foruncemented normally consolidated sands andthe upper limit for high plasticity clays and ce-mented sands.

6. A distinctive kink in the stress–strain relation-ship defines yielding, beyond which full plasticstrains are generated. A locus of stress statesthat initiate yielding defines the yield envelope.Typical yield envelopes for sand and naturalclay are shown in Fig. 11.12. The yield envelopeexpands, shrinks, and rotates as plastic strainsdevelop. It is usually considered that expansionis related to plastic volumetric strains; the sur-face expands when the soil compresses andshrinks when the soil dilates. The two inner en-velopes shown in Fig. 11.12b define the bound-aries between linear elastic, nonlinear elastic,and pre-yield zones. When the stress statemoves in the pre-yield zone, the inner envelopesmove with the stress state. This multienvelopeconcept allows modeling of complex deforma-tions observed for different stress paths (Mroz,1967; Prevost, 1977; Dafalias and Herrman,1982; Atkinson et al., 1990; Jardine, 1992).

7. Plastic irrecoverable shear deformations ofsaturated soils are accompanied by volume

changes when drainage is allowed or changes inpore water pressure and effective stress whendrainage is prevented. The general nature of thisbehavior is shown in Figs. 11.13a and 11.13bfor drained and undrained conditions, respec-tively. The volume and pore water pressurechanges depend on interactions between fabricand stress state and the ease with which sheardeformations can develop without overallchanges in volume or transfer of normal stressfrom the soil structure to the pore water.

8. The stress–strain relation of clays dependslargely on overconsolidation ratio, effectiveconfining pressures, and drainage conditions.Figure 11.14 shows triaxial compression behav-ior of clay specimens that are first normally con-solidated and then isotropically unloaded todifferent overconsolidation ratios before shear-ing. The specimens are consolidated at the sameconfining pressure but have different voidp�,0

ratios due to the different stress history (Fig.11.14a). Drained tests on normally consolidatedclays and lightly overconsolidated clays showductile behavior with volume contraction (Fig.11.14b). Heavily overconsolidated clays exhibita stiff response initially until the stress statereaches the yield envelope giving the peakstrength and volume dilation. The state of the

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Same Initial Confining Pressure

Loose Soil

Dense Soil

Critical State

DeviatorStress

Metastable Fabric

Loose Soil

Dense Soil

Metastable Fabric

0

+ΔV/V0

-ΔV/V0

Axial or Deviator Strain

(a)

Same Initial Confining Pressure

Loose Soil

Dense Soil

Critical State

DeviatorStress

Metastable Fabric

Loose soil

Dense Soil

Metastable Fabric

0

-Δu

+Δu

Axial or Deviator Strain

(b)

Critical State

Cavitation

Cavitation

Figure 11.13 Volume and pore pressure changes during shear: (a) drained conditions and(b) undrained conditions.

1 Normally consolidated

2 Lightly Overconsolidated

3 HeavilyOverconsolidated

U1

U2

U3D

Virgin Compression Line

CriticalState Line

1 Normally Consolidated

2 LightlyOverconsolidated

3 HeavilyOverconsolidated



3 Heavily Overconsolidated

Axial or Deviatoric Strain

DeviatorStress

+ΔV/V0

-ΔV/V0







Axial or Deviatoric Strain

DeviatorStress

-Δu

+Δu

VoidRatio

log p�

D Critical State

(a) (b) (c)

U1

U2

U3

p0�

Initial StateFailure at Critical State(D: Drained, U: Undrained)

Figure 11.14 Stress–strain relationship of normally consolidated, lightly overconsolidated,and heavily overconsolidated clays: (a) void ratio versus mean effective stress, (b) drainedtests, and (c) undrained tests.

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FABRIC, STRUCTURE, AND STRENGTH 379

Figure 11.16 Effect of temperature on the stiffness of Osakaclay in undrained triaxial compression (Murayama, 1969).

0.00.40.30.20.1

0.1

0.2

0.3

-0.1

-0.2

-0.3

(MPa)

(MPa)

Mean Pressurep� = (σ�a+ 2σ�r)/3

σ�r/σ�a = 0.54

σ�r/σ�a = 1.84

Failure Line inTriaxial Extension

Failure Line inTriaxial Compression

Initial At Failure

Anisotropically Consolidated σ�r/ σ�a = 0.54

Isotropically Consolidated

Dev

iato

r S

tres

s q

= σ

� a+

σ�rσ

Anisotropically Consolidated σ�r/σ�a = 1.84

Figure 11.15 Undrained effective stress paths of anisotrop-ically and isotropically consolidated specimens (after Laddand Varallyay, 1965).

soil then progressively moves toward the criticalstate exhibiting softening behavior. Undrainedshearing of normally consolidated and lightlyoverconsolidated clays generates positive excesspore pressures, whereas shear of heavily over-consolidated clays generates negative excesspore pressures (Fig. 11.14c).

9. The magnitudes of pore pressure that are de-veloped in undrained loading depend on initialconsolidation stresses, overconsolidation ratio,density, and soil fabric. Figure 11.15 shows theundrained effective stress paths of anisotropi-cally and isotropically consolidated specimens(Ladd and Varallyay, 1965). The difference inundrained shear strength is primarily due to dif-ferent excess pore pressure development asso-ciated with the change in soil fabric. At largestrains, the stress paths correspond to the samefriction angle.

10. A temperature increase causes a decrease in un-drained modulus; that is, a softening of the soil.As an example, initial strain as a function ofstress is shown in Fig. 11.16 for Osaka clay

tested in undrained triaxial compression at dif-ferent temperatures. Increase in temperaturecauses consolidation under drained conditionsand softening under undrained conditions.

11.3 FABRIC, STRUCTURE, AND STRENGTH

Fabric Changes During Shear of CohesionlessMaterials

The deformation of sands, gravels, and rockfills is in-fluenced by the initial fabric, as discussed and illus-trated in Chapter 8. As an illustration, fabric changesassociated with the sliding and rolling of grains duringtriaxial compression were determined using a uniformsand composed of rounded to subrounded grains withsizes in the range of 0.84 to 1.19 mm and a mean axiallength ratio of 1.45 (Oda, 1972, 1972a, 1972b, 1972c).Samples were prepared to a void ratio of 0.64 by tamp-ing and by tapping the side of the forming mold. Adelayed setting water–resin solution was used as thepore fluid. Samples prepared by each method weretested to successively higher strains. The resin wasthen allowed to set, and thin sections were prepared.The differences in initial fabrics gave the markedly dif-ferent stress–strain and volumetric strain curves shownin Fig. 11.17, where the plunging method refers to

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Figure 11.17 Stress–strain and volumetric strain relationships for sand at a void ratio of0.64 but with different initial fabrics (after Oda, 1972a). (a) Sample saturated with waterand (b) sample saturated with water–resin solution.

tamping. There is similarity between these curves andthose for Monterey No. 0 sand shown in Fig. 8.23. Astatistical analysis of the changes in particle orientationwith increase in axial strain showed:

1. For samples prepared by tapping, the initial fab-ric tended toward some preferred orientation oflong axes parallel to the horizontal plane, and theintensity of orientation increased slightly duringdeformation.

2. For samples prepared by tamping, there was veryweak preferred orientation in the vertical direc-tion initially, but this disappeared with deforma-tion.

Shear deformations break down particle and aggre-gate assemblages. Shear planes or zones did not appearuntil after peak stress had been reached; however, thedistribution of normals to the interparticle contactplanes E(�) (a measure of fabric anisotropy) didchange with strain, as may be seen in Fig. 11.18. Thisfigure shows different initial distributions for samplesprepared by the two methods and a concentration ofcontact plane normals within 50� of the vertical as de-formation progresses. Thus, the fabric tended towardgreater anisotropy in each case in terms of contactplane orientations. There was little additional changein E(�) after the peak stress had been reached, whichimplies that particle rearrangement was proceedingwithout significant change in the overall fabric.

As the stress state approaches failure, a direct shear-induced fabric forms that is generally composed ofregions of homogeneous fabric separated by discon-tinuities. No discontinuities develop before peakstrength is reached, although there is some particle ro-tation in the direction of motion. Near-perfect preferredorientation develops during yield after peak strength isreached, but large deformations may be required toreach this state.

Compaction Versus Overconsolidation of Sand

Specimens at the same void ratio and stress state be-fore shearing, but having different fabrics, can exhibitdifferent stress–strain behavior. For example, considera case in which one specimen is overconsolidated,whereas the other is compacted. The two specimensare prepared in such a way that the initial void ratio isthe same for a given initial isotropic confining pres-sure. Coop (1990) performed undrained triaxial com-pression tests of carbonate sand specimens that wereeither overconsolidated or compacted, as illustrated inFig. 11.19a. The undrained stress paths and stress–strain curves for the two specimens are shown in Figs.11.19b and 11.19c, respectively. The overconsolidatedsample was initially stiffer than the compacted speci-men. The difference can be attributed to (i) differentsoil fabrics developed by different stress paths prior toshearing and (ii) different degrees of particle crushingprior to shearing (i.e., some breakage has occurred dur-

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FABRIC, STRUCTURE, AND STRENGTH 381

Figure 11.18 Distribution of interparticle contact normals as a function of axial strain forsand samples prepared in two ways (after Oda, 1972a): (a) specimens prepared by tappingand (b) specimens prepared by tamping.

ing the preconsolidation stage for the overconsolidatedspecimen). Therefore, overconsolidation and compac-tion produced materials with different mechanicalproperties. However, at large deformations, both spec-imens exhibited similar strengths because the initialfabrics were destroyed.

Effect of Clay Structure on Deformations

The high sensitivity of quick clays illustrates the prin-ciple that flocculated, open microfabrics are more rigidbut more unstable than deflocculated fabrics. Similarbehavior may be observed in compacted fine-grainedsoils, and the results of a series of tests on structure-sensitive kaolinite are illustrative of the differences(Mitchell and McConnell, 1965). Compaction condi-tions and stress–strain curves for samples of kaolinitecompacted using kneading and static methods areshown in Fig. 11.20. The high shear strain associatedwith kneading compaction wet of optimum breaksdown flocculated structures, and this accounts for the

much lower peak strength for the sample prepared bykneading compaction.

The recoverable deformation of compacted kaolinitewith flocculent structure ranges between 60 and 90percent, whereas the recovery of samples with dis-persed structures is only of the order of 15 to 30 per-cent of the total deformation, as may be seen in Fig.11.21. This illustrates the much greater ability of thebraced-box type of fabric that remains after static com-paction to withstand stress without permanent defor-mation than is possible with the broken-down fabricassociated with kneading compaction.

Different macrofabric features can affect the defor-mation behavior as illustrated in Fig. 11.22 for the un-drained triaxial compression testing of Bothkennarclay, Scotland (Paul et al., 1992; Clayton et al., 1992).Samples with mottled facies, in which the bedding fea-tures had been disrupted and mixed by burrowingmollusks and worms (bioturbation), gave the stiffestresponse, whereas samples with distinct laminated fea-tures showed the softest response.

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2

1.5

1

0.1 1Mean Pressure p�

VoidRatio

Compacted Sample

OverconsolidatedSample

Normal Compression Line

(MPa)

0.60.40.200

0.2

0.4

0.6

0.8

1.0

p� (MPa)

Overconsolidated

Compacted

0 4 8 12 16 20

1.0

0.75

0.5

0.25

0

q (MPa)

Axial strain εa(%)

Compacted

Overconsolidated

(a)

(b)

(c)

q (M

Pa)

Figure 11.19 Undrained response of compacted specimen and overconsolidated specimenof carbonate sand: (a) stress path before shearing, (b) undrained stress paths during shearing,and (c) stress–strain relationships (after Coop, 1990).

If slip planes develop at failure, platy and elongatedparticles align with their long axes in the direction ofslip. By then, the basal planes of the platy clay parti-cles are enclosed between two highly oriented bandsof particles on opposite sides of the shear plane. Thedominant mechanism of deformation in the displace-ment shear zone is basal plane slip, and the overallthickness of the shear zone is on the order of 50 �m.Fabrics associated with shear planes and zones havebeen studied using thin sections and the polarizing mi-croscope and by using the electron microscope (Mor-genstern and Tchalenko, 1967a, b and c; Tchalenko,1968; McKyes and Yong, 1971). The residual strengthassociated with these fabrics is treated in more detailin Section 11.11.

Structure, Effective Stresses, and Strength

The effective stress strength parameters such as c� and�� are isotropic properties, with anisotropy in un-drained strength explainable in terms of excess porepressures developed during shear. The undrainedstrength loss associated with remolding undisturbed

clay can also be accounted for in terms of differencesin effective stress, provided part of the undisturbedstrength does not result from cementation. Remoldingbreaks down the structure and causes a transfer of ef-fective stress to the pore water.

An example of this is shown in Fig. 11.23, whichshows the results of incremental loading triaxial com-pression tests on two samples of undisturbed and re-molded San Francisco Bay mud. In these tests, theundisturbed sample was first brought to equilibriumunder an isotropic consolidation pressure of 80 kPa.After undrained loading to failure, the triaxial cell wasdisassembled, and the sample was remolded in place.The apparatus was reassembled, and pore pressure wasmeasured. Thus, the effective stress at the start of com-pression of the remolded clay at the same water con-tent as the original undisturbed clay was known.Stress–strain and pore pressure–strain curves for twosamples are shown in Figs. 11.23a and 11.23b, andstress paths for test 1 are shown in Fig. 11.23c.

Differences in strength that result from fabric dif-ferences caused by thixotropic hardening or by differ-ent compaction methods can be explained in the same

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FRICTION BETWEEN SOLID SURFACES 383

Figure 11.20 Stress–strain behavior of kaolinite compactedby two methods.

Figure 11.21 Ratio of recoverable to total strain for samplesof kaolinite with different structure.

0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

Axial Strain (%)0 2 4

0.0

0.2

0.4

0.6

Stress-Strain Relationships Stress Paths

MottledFacies

BeddedLaminated

MottledFacies

BeddedLaminated

(σ�a + σ�r)/2σ�ao

(σ� a

– σ

� r)/

2σ�

ao

(σ� a

– σ

� r)/

2σ�

ao

Figure 11.22 Effect of macrofabric on undrained responseof Bothkennar clay in Scotland (after Hight and Leroueil,2003).

way. Thus, in the absence of chemical or mineralogicalchanges, different strengths in two samples of the samesoil at the same void ratio can be accounted for interms of different effective stress.

11.4 FRICTION BETWEEN SOLID SURFACES

The friction angle used in equations such as (11.1),(11.2), (11.4), and (11.5) contains resistance contri-butions from several sources, including sliding ofgrains in contact, resistance to volume change (dila-tancy), grain rearrangement, and grain crushing. The

true friction coefficient is shown in Fig. 11.24 and isrepresented by

T� � � tan � (11.8)�N

where N is the normal load on the shear surface, T isthe shear force, and ��, the intergrain sliding frictionangle, is a compositional property that is determinedby the type of soil minerals.

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Figure 11.23 (a) and (b) Effect of remolding on undrained strength and pore water pressurein San Francisco Bay mud. (c) Stress paths for triaxial compression tests on undisturbed andremolded samples of San Francisco Bay mud.

Basic ‘‘Laws’’ of Friction

Two laws of friction are recognized, beginning withLeonardo da Vinci in about 1500. They were restatedby Amontons in 1699 and are frequently referred to asAmontons’ laws. They are:

1. The frictional force is directly proportional to thenormal force, as illustrated by Eq. (11.8) and Fig.11.24.

2. The frictional resistance between two bodies isindependent of the size of the bodies. In Fig.

11.24, the value of T is the same for a given valueof N regardless of the size of the sliding block.

Although these principles of frictional resistancehave long been known, suitable explanations camemuch later. It was at one time thought that interlockingbetween irregular surfaces could account for the be-havior. On this basis, � would be given by the tangentof the average inclination of surface irregularities onthe sliding plane. This cannot be the case, however,because such an explanation would require that � de-

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Figure 11.23(Continued )

Figure 11.24 Coefficient of friction for surfaces in contact.

crease as surfaces become smoother and be zero forperfectly smooth surfaces. In fact, the coefficient offriction can be constant over a range of surface rough-ness. Hardy (1936) suggested instead that staticfriction originates from cohesive forces between

contacting surfaces. He observed that the actual areaof contact is very small because of surface irregulari-ties, and thus the cohesive forces must be large.

The foundation for the present understanding of themobilization of friction between surfaces in contactwas laid by Terzaghi (1920). He hypothesized that thenormal load N acting between two bodies in contactcauses yielding at asperities, which are local ‘‘hills’’on the surface, where the actual interbody solid contactdevelops. The actual contact area Ac is given by

NA � (11.9)c �y

where �y is the yield strength of the material. Theshearing strength of the material in the yielded zone isassumed to have a value �m. The maximum shearingforce that can be resisted by the contact is then

T � A � (11.10)c m

The coefficient of friction is given by T /N,

T A � �c m m� � � � (11.11)N A � �c y y

This concept of frictional resistance was subse-quently further developed by Bowden and Tabor (1950,

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Figure 11.25 Contact between two smooth surfaces.Figure 11.26 Monolayer formation time as a function of at-mospheric pressure.

1964). The Terzaghi–Bowden and Tabor hypothesis,commonly referred to as the adhesion theory of fric-tion, is the basis for most modern studies of friction.Two characteristics of surfaces play key roles in theadhesion theory of friction: roughness and surface ad-sorption.

Surface Roughness

The surfaces of most solids are rough on a molecularscale, with successions of asperities and depressionsranging from 10 nm to over 100 nm in height. Theslopes of the nanoscale asperities are rather flat, withindividual angles ranging from about 120� to 175� asshown in Fig. 11.25. The average slope of asperitieson metal surfaces is an included angle of 150�; onrough quartz it may be over 175� (Bromwell, 1966).When two surfaces are brought together, contact is es-tablished at the asperities, and the actual contact areais only a small fraction of the total surface area.

Quartz surfaces polished to mirror smoothness mayconsist of peaks and valleys with an average height ofabout 500 nm. The asperities on rougher quartz sur-faces may be about 10 times higher (Lambe and Whit-man, 1969). Even these surfaces are probably smootherthan most soil particles composed of bulky minerals.The actual surface texture of sand particles depends ongeologic history as well as mineralogy, as shown inFig. 2.12.

The cleavage faces of mica flakes are among thesmoothest naturally occurring mineral surfaces. Evenin mica, however, there is some waviness due to ro-tation of tetrahedra in the silica layer, and surfaces usu-ally contain steps ranging in height from 1 to 100 nm,reflecting different numbers of unit layers across theparticle.

Thus, large areas of solid contact between grains arenot probable in soils. Solid-to-solid contact is throughasperities, and the corresponding interparticle contactstresses are high. The molecular structure and com-position in the contacting asperities determine the mag-nitude of �m in Eq. (11.11).

Surface Adsorption

Because of unsatisfied force fields at the surfaces ofsolids, the surface structure may differ from that in theinterior, and material may be adsorbed from adjacentphases. Even ‘‘clean’’ surfaces, prepared by fracture ofa solid or by evacuation at high temperature, are rap-idly contaminated when reexposed to normal atmos-pheric conditions.

According to the kinetic theory of gases, the timefor adsorption of a monolayer tm is given by

1t � (11.12)m �SZ

where � is the area occupied per molecule, S is thefraction of molecules striking the surface that stick toit, and Z is the number of molecules per second strik-ing a square centimeter of surface. For a value of Sequal to 1, which is reasonable for a high-energy sur-face, the relationship between tm and gas pressure isshown in Fig. 11.26. The conclusion to be drawn fromthis figure is that adsorbed layers are present on thesurface of soil particles in the terrestrial environment,

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Figure 11.27 Plastic junction between asperities with ad-sorbed surface films.

and contacts through asperities involve adsorbed ma-terial, unless it is extruded under the high pressure.5

Adhesion Theory of Friction

The basis for the adhesion theory of friction is in Eq.(11.10), that is, the tangential force that causes slid-ing depends on the solid contact area and the shearstrength of the contact. Plastic and/or elastic defor-mations determine the contact area at asperities.

Plastic Junctions If asperities yield and undergoplastic deformation, then the contact area is propor-tional to the normal load on the asperity as shown byEq. (11.9). Because surfaces are not clean, but are cov-ered by adsorbed films, actual solid contact may de-velop only over a fraction � of the contact area asshown in Fig. 11.27. If the contaminant film strengthis �c, the strength of the contact will be

T � A [�� (1 � �)� ] (11.13)c m c

Equation (11.13) cannot be applied in practice be-cause � and �c are unknown. However, it does providea possible explanation for why measured values of fric-tion angle for bulky minerals such as quartz and feld-spar are greater than values for the clay minerals andother platy minerals such as mica, even though thesurface structure is similar for all the silicate minerals.The small particle size of clays means that the loadper particle, for a given effective stress, will be smallrelative to that in silts and sands composed of the bulkyminerals. The surfaces of platy silt and sand size par-ticles are smoother than those of bulky mineral parti-

5 Conditions may be different on the Moon, where ultrahigh vacuumexists. This vacuum produces cleaner surfaces. In the absence ofsuitable adsorbate, clean surfaces can reduce their surface energy bycohering with like surfaces. This could account for the higher co-hesion of lunar soils than terrestrial soils of comparable gradation.

cles. The asperities, caused by surface waviness, aremore regular but not as high as those for the bulkyminerals.

Thus, it can be postulated that for a given numberof contacts per particle, the load per asperity decreaseswith decreasing particle size and, for particles of thesame size, is less for platy minerals than for bulkyminerals. Because � should increase as the normal loadper asperity increases, and it is reasonable to assumethat the adsorbed film strength is less than the strengthof the solid material (�c � �m), it follows that the truefriction angle (��) is less for small and platy particlesthan for large and bulky particles. In the event that twoplaty particles are in face-to-face contact and the sur-face waviness is insufficient to cause direct solid-to-solid contact, shear will be through the adsorbed films,and the effective value of � will be zero, again givinga lower value of ��.

In reality, the behavior of plastic junctions is morecomplex. Under combined compression and shearstresses, deformation follows the von Mises–Henkycriterion, which, for two dimensions, is

2 2 2� � 3� � � (11.14)y

For asperities loaded initially to � � �y, the appli-cation of a shear stress requires that � become lessthan �y. The only way that this can happen is for thecontact area to increase. Continued increase in � leadsto continued increase in contact area. This phenome-non is called junction growth and is responsible forcold welding in some materials (Bowden and Tabor,1964). If the shear strength of the junction equals thatof the bulk solid, then gross seizure occurs. For thecase where the ratio of junction strength to bulk ma-terial strength is less than 0.9, the amount of junctiongrowth is small. This is the probable situation in soils.

Elastic Junctions The contact area between parti-cles of a perfectly elastic material is not defined interms of plastic yield. For two smooth spheres in con-tact, application of the Hertz theory leads to

1 / 3d � (�NR) (11.15)

where d is the diameter of a plane circular area ofcontact; � is a function of geometry, Poisson’s ratio,and Young’s modulus6; and R is the sphere radius. Thecontact area is

6 For a sphere in contact with a plane surface � � 12(1 � � 2) /E.

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� 2 / 3A � (�NR) (11.16)c 4

If the shear strength of the contact is �i, then

T � � A (11.17)i c

and

T � 2 / 3 �1 / 3� � � � (�R) N (11.18)iN 4

According to these relationships, the friction coef-ficient for two elastic asperities in contact should de-crease with increasing load. Nonetheless, the adhesiontheory would still apply to the strength of the junction,with the frictional force proportional to the area of realcontact.

If it is assumed that the number of contacting as-perities in a soil mass is independent of particle sizeand effective stress, then the influences of particle sizeand effective stress on the frictional resistance of a soilwith asperities deforming elastically may be analyzed.For uniform spheres arranged in a regular packing, thegross area covered by one sphere along a potentialplane of sliding is 4R2. The normal load per contactingasperity, assuming one asperity per contact, is

2N � 4R �� (11.19)

Using Eq. (11.16), the area per contact becomes

� 3 2 / 3A � (4�R ��) (11.20)c 4

and the total contact area per unit gross area is

1 � �2 2 / 3 2 / 3(A ) � R (4��) � (4��)� �c T 24R 4 16 (11.21)

The total shearing resistance of �� is equal to thecontact area times �i, so

� �i2 / 3 �1 / 3� � (4��) � � K(��) (11.22)i16 ��

where K � �(4�)2 / 3 /16. On this basis, the coefficientof friction should decrease with increasing ��, but itshould be independent of sphere radius (particle size).

Data have been obtained that both support and con-tradict these predictions. A 50-fold variation in the nor-mal load on assemblages of quartz particles in contactwith a quartz block was found to have no effect on

frictional resistance (Rowe, 1962). The residual fric-tion angles of quartz, feldspar, and calcite are indepen-dent of normal stress as shown in Fig. 11.28.

On the other hand, a decreasing friction angle withincreasing normal load up to some limiting value ofnormal stress is evident for mica and the clay mineralsin Fig. 11.28 and has been found also for several claysand clay shales (Bishop et al., 1971), for diamond(Bowden and Tabor, 1964), and for solid lubricantssuch as graphite and molybdenum disulfide (Campbell,1969). Additional data for clay minerals show that fric-tional resistance varies as (��)�1 / 3 as predicted by Eq.(11.22) up to a normal stress of the order of 200 kPa(30 psi), that is, the friction angle decreases with in-creasing normal stress (Chattopadhyay, 1972).

There are at least two possible explanations of thenormal stress independence of the frictional resistanceof quartz, feldspar, and calcite:

1. As the load per particle increases, the number ofasperities in contact increases proportionally, andthe deformation of each asperity remains essen-tially constant. In this case, the assumption of oneasperity per contact for the development of Eq.(11.22) is not valid. Some theoretical considera-tions of multiple asperities in contact are availa-ble (Johnson, 1985). They show that the area ofcontact is approximately proportional to the ap-plied load and hence the coefficient of friction isconstant with load.

2. As the load per asperity increases, the value of �in Eq. (11.13) increases, reflecting a greater pro-portion of solid contact relative to adsorbed filmcontact. Thus, the average strength per contactincreases more than proportionally with the load,while the contact area increases less than pro-portionally, with the net result being an essen-tially constant frictional resistance.

Quartz is a hard, brittle material that can exhibit bothelastic and plastic deformation. A normal pressure of11 GPa (1,500,000 psi) is required to produce plasticdeformation, and brittle failure usually occurs beforeplastic deformation. Plastic deformations are evidentlyrestricted to small, highly confined asperities, and elas-tic deformations control at least part of the behavior(Bromwell, 1965). Either of the previous two expla-nations might be applicable, depending on details ofsurface texture on a microscale and characteristics ofthe adsorbed films.

With the exception of some data for quartz, thereappears to be little information concerning possiblevariations of the true friction angle with particle size.Rowe (1962) found that the value of �� for assem-blages of quartz particles on a flat quartz surface de-

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FRICTIONAL BEHAVIOR OF MINERALS 389

Figure 11.28 Variation in friction angle with normal stress for different minerals (afterKenney, 1967).

creased from 31� for coarse silt to 22� for coarse sand.This is an apparent contradiction to the independenceof particle size on frictional resistance predicted by Eq.(11.22). On the other hand, the assumption of one as-perity per contact may not have been valid for all par-ticle sizes, and additionally, particle surface textures ona microscale could have been size dependent. Further-more, there could have been different amounts of par-ticle rearrangement and rolling in the tests on thedifferent size fractions.

Sliding Friction

The frictional resistance, once sliding has been initi-ated, may be equal to or less than the resistance thathad to be overcome to initiate movement; that is, thecoefficient of sliding friction can be less than the co-efficient of static friction. A higher value of staticfriction than sliding friction is explainable by time-dependent bond formations at asperity junctions.Stick–slip motion, wherein � varies more or less er-ratically as two surfaces in contact are displaced, ap-pears common to all friction measurements of mineralsinvolving single contacts (Procter and Barton, 1974).Stick–slip is not observed during shear of assemblagesof large numbers of particles because the slip of indi-vidual contacts is masked by the behavior of the massas a whole. However, it may be an important mecha-nism of energy dissipation for cyclic loading at verysmall strains when particles are not moving relative toeach other.

11.5 FRICTIONAL BEHAVIOR OF MINERALS

Evaluation of the true coefficient of friction � and fric-tion angle �� is difficult because it is very difficult to

do tests on two very small particles that are slidingrelative to each other, and test results for particle as-semblages are influenced by particle rearrangements,volume changes, surface preparation factors, and thelike. Some values are available, however, and they arepresented and discussed in this section.

Nonclay Minerals

Values of the true friction angle �� for several mineralsare listed in Table 11.1, along with the type of test andconditions used for their determination. A pronouncedantilubricating effect of water is evident for polishedsurfaces of the bulky minerals quartz, feldspar, and cal-cite. This apparently results from a disruptive effect ofwater on adsorbed films that may have acted as a lu-bricant for dry surfaces. Evidence for this is shown inFig. 11.29, where it may be seen that the presence ofwater had no effect on the frictional resistance ofquartz surfaces that had been chemically cleaned priorto the measurement of the friction coefficient. Thesamples tested by Horn and Deere (1962) in Table 11.1had not been chemically cleaned.

An apparent antilubrication effect by water mightalso arise from attack of the silica surface (quartz andfeldspar) or carbonate surface (calcite) and the for-mation of silica and carbonate cement at interparticlecontacts. Many sand deposits exhibit ‘‘aging’’ effectswherein their strength and stiffness increase noticeablywithin periods of weeks to months after deposition,disturbance, or densification, as described, for exam-ple, by Mitchell and Solymar (1984), Mitchell (1986),Mesri et al. (1990), and Schmertmann (1991). In-creases in penetration resistance of up to 100 percenthave been measured in some cases. The relative im-portance of chemical factors, such as precipitation at

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Table 11.1 Values of Friction Angle (��) Between Mineral Surfaces

Mineral Type of Test Conditions �� (deg) Comments Reference

Quartz Block over particleset in mortar

Dry 6 Dried over CaCl2 beforetesting

Tschebotarioff andWelch (1948)

Moist 24.5Water saturated 24.5

Quartz Three fixed particlesover block

Water saturated 21.7 Normal load per particleincreasing from 1 to100 g

Hafiz (1950)

Quartz Block on block Dry 7.4 Polished surfaces Horn and Deere (1962)Water saturated 24.2

Quartz Particles onpolished block

Water saturated 22–31 � decreasing with in-creasing particle size

Rowe (1962)

Quartz Block on block Variable 0–45 Depends on roughnessand cleanliness

Bromwell (1966)

Quartz Particle–particle Saturated 26 Single-point contact Procter and Barton(1974)

Particle–plane Saturated 22.2Particle–plane Dry 17.4

Feldspar Block on block Dry 6.8 Polished surfaces Horn and Deere (1962)Water saturated 37.6

Feldspar Free particles on flatsurface

Water saturated 37 25–500 sieve Lee (1966)

Feldspar Particle–plane Saturated 28.9 Single-point contact Procter and Barton(1974)

Calcite Block on block Dry 8.0 Polished surfaces Horn and Deere (1962)Water saturated 34.2

Muscovite Along cleavagefaces

Dry 23.3 Oven dry Horn and Deere (1962)

Dry 16.7 Air equilibratedSaturated 13.0

Phlogopite Along cleavagefaces



Biotite Along cleavagefaces



Chlorite Along cleavagefaces



interparticle contacts, changes in surface characteris-tics, and mechanical factors, such as time-dependentstress redistribution and particle reorientations, in caus-ing the observed behavior is not known. Further detailsof aging effects are given in Chapter 12.

As surface roughness increases, the apparent anti-lubricating effect of water decreases. This is shownin Fig. 11.29 for quartz surfaces that had not beencleaned. Chemically cleaned quartz surfaces, whichgive the same value of friction when both dry and wet,

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FRICTIONAL BEHAVIOR OF MINERALS 391

Figure 11.29 Friction of quartz (data from Bromwell, 1966 and Dickey, 1966).

show a loss in frictional resistance with increasing sur-face roughness. Evidently, increased roughness makesit easier for asperities to break through surface films,resulting in an increase in � [Eq. (11.13) and Fig.11.27]. The decrease in friction with increased rough-ness is not readily explainable. One possibility is thatthe cleaning process was not effective on the roughsurfaces.

For soils in nature, the surfaces of bulky mineralparticles are most probably rough relative to the scalein Fig. 11.29, and they will not be chemically clean.Thus, values of � � 0.5 and �� 26� are reasonablefor quartz, both wet and dry.

On the other hand, water apparently acts as a lubri-cant in sheet minerals, as shown by the values for mus-covite, phlogopite, biotite, and chlorite in Table 11.1.This is because in air the adsorbed film is thin, andsurface ions are not fully hydrated. Thus, the adsorbedlayer is not easily disrupted. Observations have shownthat the surfaces of the sheet minerals are scratchedwhen tested in air (Horn and Deere, 1962). When thesurfaces of the layer silicates are wetted, the mobilityof the surface films is increased because of their in-creased thickness and because of greater surface ionhydration and dissociation. Thus, the values of ��

listed in Table 11.1 for the sheet minerals under satu-rated conditions (7�–13�) are probably appropriate forsheet mineral particles in soils.

Clay Minerals

Few, if any, directly measured values of �� for the clayminerals are available. However, because their surfacestructures are similar to those of the layer silicates dis-cussed previously, approximately the same valueswould be anticipated, and the ranges of residual fric-tion angles measured for highly plastic clays and clayminerals support this. In very active colloidal pureclays, such as montmorillonite, even lower friction an-gles have been measured. Residual values as low as 4�for sodium montmorillonite are indicated by the datain Fig. 11.28.

The effective stress failure envelopes for calciumand sodium montmorillonite are different, as shown byFig. 11.30, and the friction angles are stress dependent.For each material the effective stress failure envelopewas the same in drained and undrained triaxial com-pression and unaffected by electrolyte concentrationover the range investigated, which was 0.001 N to 0.1N. The water content at any effective stress was inde-pendent of electrolyte concentration for calcium mont-morillonite, but varied in the manner shown in Fig.11.31 for sodium montmorillonite.

This consolidation behavior is consistent with thatdescribed in Chapter 10. Interlayer expansion in cal-cium montmorillonite is restricted to a c-axis spacingof 1.9 nm, leading to formation of domains or layeraggregates of several unit layers. The interlayer spac-

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Figure 11.30 Effective stress failure diagrams for calcium and sodium montmorillonite (af-ter Mesri and Olson, 1970).

Figure 11.31 Shear and consolidation behavior of sodiummontmorillonite (after Mesri and Olson, 1970).

ing of sodium montmorillonite is sensitive to double-layer repulsions, which, in turn, depend on theelectrolyte concentration. The influence of the electro-lyte concentration on the behavior of sodium mont-morillonite is to change the water content, but not thestrength, at any effective consolidation pressure. Thissuggests that the strength generating mechanism is in-dependent of the system chemistry.

The platelets of sodium montmorillonite act as thinfilms held apart by high repulsive forces that carry theeffective stress. For this case, if it is assumed that thereis essentially no intergranular contact, then Eq. (7.29)becomes

�� A � u � R � 0 (11.23)i 0

Since � � u0 is the conventionally defined effectivestress ��, and assuming negligible long-range attrac-tions, Eq. (11.23) becomes

�� R (11.24)

This accounts for the increase in consolidation pres-sure required to decrease the water content, while at

the same time there is little increase in shear strengthbecause the shearing strength of water and solutions isessentially independent of hydrostatic pressure. Thesmall friction angle that is observed for sodium mont-morillonite at low effective stresses can be ascribedmainly to the few interparticle contacts that resist par-ticle rearrangement. Resistance from this source evi-dently approaches a constant value at the highereffective stresses, as evidenced by the nearly horizontalfailure envelope at values of average effective stressgreater than about 50 psi (350 kPa), as shown in Fig.11.30. The viscous resistance of the pore fluid maycontribute a small proportion of the strength at all ef-fective stresses.

An hypothesis of friction between fine-grained par-ticles in the absence of interparticle contacts is givenby Santamarina et al. (2001) using the concept of‘‘electrical’’ surface roughness as shown in Fig. 11.32.Consider two clay surfaces with interparticle fluid asshown in Fig. 11.32b. The clay surfaces have a numberof discrete charges, so a series of potential energywells exists along the clay surfaces. Two cases can beconsidered:

1. When the particle separation is less than severalnanometers, there are multiple wells of minimumenergy between nearby surfaces and a force isrequired to overcome the energy barrier betweenthe wells when the particles move relative to eachother. Shearing involves interaction of the mole-cules of the interparticle fluid. Due to the multi-ple energy wells, the interparticle fluid moleculesgo through successive solidlike pinned states.This stick–slip motion contributes to frictionalresistance and energy dissipation.

2. When the particle separation is more than severalnanometers, the two clay surfaces interact onlyby the hydrodynamic viscous effects of the in-terparticle fluid, and the frictional force may beestimated using fluid dynamics.

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PHYSICAL INTERACTIONS AMONG PARTICLES 393

Figure 11.32 Concept of ‘‘electrical’’ surface roughness ac-cording to Santamarina et al., (2001): (a) electrical roughnessand (b) conceptual picture of friction in fine-grained particles.

The aggregation of clay plates in calcium montmo-rillonite produces particle groups that behave more likeequidimensional particles than platy particles. There ismore physical interference and more intergrain contactthan in sodium montmorillonite since the water contentrange for the strength data shown in Fig. 11.30 wasonly about 50 to 97 percent, whereas it was about 125to 450 percent for the sodium montmorillonite. At aconsolidation pressure of about 500 kPa, the slope ofthe failure envelope for calcium montmorillonite wasabout 10�, which is in the middle of the range for non-clay sheet minerals (Table 11.1).

11.6 PHYSICAL INTERACTIONS AMONGPARTICLES

Continuum mechanics assumes that applied forces aretransmitted uniformly through a homogenized granularsystem. In reality, however, the interparticle force dis-tributions are strongly inhomogeneous, as discussed inChapter 7, and the applied load is transferred througha network of interparticle force chains. The generic

disorder of particles, (i.e., local spatial fluctuations ofcoordination number, and positions of neighboring par-ticles) produce packing constraints and disorder. Thisleads to inhomogeneous but structured force distribu-tions within the granular system. Deformation is as-sociated with buckling of these force chains, andenergy is dissipated by sliding at the clusters of par-ticles between the force chains.

Discrete particle numerical simulations, such as thediscrete (distinct) element method (Cundall and Strack,1979) and the contact dynamics method (Moreau,1994), offer physical insights into particle interactionsand load transfers that are difficult to deduce fromphysical experiments. Typical inputs for the simula-tions are particle packing conditions and interparticlecontact characteristics such as the interparticle frictionangle ��. Complete details of these numerical methodsare beyond the scope of this book; additional infor-mation can be found in Oda and Iwashita (1999).However, some of the main findings are useful fordeveloping an improved understanding of how stressesare carried through discrete particle systems such assoils and how these distributions influence the defor-mation and strength properties.

Strong Force Networks and Weak Clusters

Examples of the computed normal contact force dis-tribution in a granular system are shown in Figs.11.33a for an isotropically loaded condition and11.33b for a biaxial loaded condition (Thornton andBarnes, 1986). The thickness of the lines in the figureis proportional to the magnitude of the contact force.The external loads are transmitted through a networkof interparticle contact forces represented by thickerlines. This is called the strong force network and is thekey microscopic feature of load transfer through thegranular system. The scale of statistical homogeneityin a two-dimensional particle assembly is found to bea few tens of particle diameters (Radjai et al., 1996).Forces averaged over this distance could therefore beexpected to give a stress that is representative of themacroscopic stress state. The particles not forming apart of the strong force network are floating like a fluidwith small loads at the interparticle contacts. This canbe called the weak cluster, which has a width of 3 to10 particle diameters.

Both normal and tangential forces exist at interpar-ticle contacts. Figure 11.34 shows the probability dis-tributions (PN and PT) of normal contact forces N andtangential contact forces T for a given biaxial loadingcondition. The horizontal axis is the forces normalizedby their mean force value (�N� or �T�), which de-pend on particle size distribution (Radjai et al., 1996).The individual normal contact forces can be as great

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Figure 11.33 Normal force distributions of a two-dimensional disk particle assembly: (a) isotropic stress con-dition and (b) biaxial stress condition with maximum load inthe vertical direction (after Thornton and Barnes, 1986).

as six times the mean normal contact force, butapproximately 60 percent of contacts carry normalcontact forces below the mean (i.e., weak clusterparticles). When normal contact forces are larger thantheir mean, the distribution law of forces can be ap-proximated by an exponentially decreasing function;Radjai et al. (1996) show that PN(� � N /�N�) �ke1.4(1�� ) fits the computed data well for both two-andthree-dimensional simulations. The exponent wasfound to change very slightly with the coefficient ofinterparticle friction and to be independent of particlesize distributions.

Simulations show that applied deviator load is trans-ferred exclusively by the normal contact forces in thestrong force networks, and the contribution by theweak clusters is negligible. This is illustrated in Fig.11.35, which shows that the normal contact forces con-tribute greater than the tangential contact forces to thedevelopment of the deviator stress during axisymme-

tric compression of a dense granular assembly (Thorn-ton, 2000). The strong force network carries most ofthe whole deviator load as shown in Fig. 11.36 and isthe load-bearing part of the structure. For particles inthe strong force networks, the tangential contact forcesare much smaller than the interparticle frictional resis-tance because of the large normal contact forces. Incontrast, the numerical analysis results show that thetangential contact forces in the weak clusters are closeto the interparticle frictional resistance. Hence, the fric-tional resistance is almost fully mobilized between par-ticles in the weak clusters, and the particles are perhapsbehaving like a viscous fluid.

Buckling, Sliding, and Rolling

As particles begin to move relative to each other duringshear, particles in the strong force network do not slide,but columns of particles buckle (Cundall and Strack,1979). Particles in the strong force network collapseupon buckling, and new force chains are formed.Hence, the spatial distributions of the strong force net-work are neither static nor persistent features.

At a given time of biaxial compression loading, par-ticle sliding is occurring at almost 10 percent of thecontacts (Kuhn, 1999) and approximately 96 percentof the sliding particles are in the weak clusters (Radjaiet al., 1996). Over 90 percent of the energy dissipationoccurs at just a small percentage of the contacts (Kuhn,1999). This small number of sliding particles is asso-ciated with the ability of particles to roll rather than toslide. Particle rotations reduce contact sliding and dis-sipation rate in the granular system. If all particlescould roll upon one another, a granular assemblywould deform without energy dissipation.7 However,this is not possible owing to restrictions on particlerotations. It is impossible for all particles to move byrotation, and sliding at some contacts is inevitable dueto the random position of particles (Radjai and Roux,1995).8 Some frictional energy dissipation can there-fore be considered a consequence of disorder of par-ticle positions.

As deformation progresses, the number of particlesin the strong force network decreases, with fewer par-ticles sharing the increased loads (Kuhn, 1999). Figure

7 This assumes that the particles are rigid and rolling with a single-point contact. In reality, particles deform and exhibit rolling resis-tance. Iwashita and Oda (1998) state that the incorporation of rollingresistance is necessary in discrete particle simulations to generaterealistic localized shear bands.8 For instance, consider a chain loop of an odd number of particles.Particle rotation will involve at least one sliding contact.

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Figure 11.34 Probability distributions of interparticle contact forces: (a) normal forces and(b) tangential forces. The distributions were obtained for contact dynamic simulations of500, 1024, 1200 and 4025 particles. The effect of number of particles in the simulation onprobability distribution appears to be small (after Radjai et al., 1996).

Figure 11.35 Contributions of normal and tangential contactforces to the evolution of the deviator stress during axisym-metric compression of a dense granular assembly (afterThornton, 2000).

Figure 11.36 Contributions of strong and weak contactforces to the evolution of the deviator stress during axisym-metric compression of a dense granular assembly (afterThornton, 2000).

11.37 shows the spatial distribution of residual defor-mation, in which the computed deformation of eachparticle is subtracted from the average overall defor-mation (Williams and Rege, 1997). A group of inter-locked particles that instantaneously moves as a rigidbody in a circular manner can be observed. The outer

boundary of the group shows large residual deforma-tion, whereas the center shows very small residual de-formation. The rotating group of interlocked particles,which can be considered as a weak cluster, becomesmore apparent as applied strains increase toward fail-ure. The bands of large residual deformation [termed

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Figure 11.37 Spatial distribution of residual deformation ob-served in an elliptic particle assembly at an axial strain levelof (a) 1.1%, (b) 3.3%, (c) 5.5%, (d) 7.7%, (e) 9.8%, and(ƒ) 12.0% (after Williams and Rege, 1997).

2 4 6 8 10-2-4-6-8

0.5

1.0

1.5

-0.5

-1.0

Stress Ratio q/p�

Axial Strain (%)

2 4 6 8 10-2-4-6-8

0.10.2

Fabric Anisotropy A

Axial Strain (%)

0.30.4

-0.1-0.2

-0.3-0.4-0.5

Triaxial Compression

Triaxial Extension

More in Vertical Direction

Contact Plane Normalsin Initial State:

Same in All Directions

More in Horizontal Direction

More in Vertical Direction

Contact Plane Normalsin Initial State:

Same in All Directions

More in Horizontal Direction

(a)

(b)

A

BC

A

BC

Figure 11.38 Discrete element simulations of drained tri-axial compression and extension tests of particle assembliesprepared at different initial contact fabrics: (a) stress–strainrelationships and (b) evolution of fabric anisotropy parameterA (after Yimsiri, 2001).

microbands by Kuhn (1999)] are where particle trans-lations and rotations are intense as part of the strongforce network. Kuhn (1999) reports that their thick-nesses are 1.5D50 to 2.5D50 in the early stages of shear-ing and increase to between 1.5D50 and 4D50 asdeformation proceeds. This microband slip zone mayeventually become a localized shear band.

Fabric Anisotropy

The ability of a granular assemblage of particles tocarry deviatoric loads is attributed to its capability todevelop anisotropy in contact orientations. An initialisotropic packing of particles develops an anisotropiccontact network during compression loading. This isbecause new contacts form in the direction of com-pression loading and contacts that orient along the di-rection perpendicular to loading direction are lost.

The initial state of contact anisotropy (or fabric)plays an important role in the subsequent deformationas illustrated in Fig. 11.18. Figure 11.38 shows results

of discrete particle simulations of particle assembliesprepared at different states of initial contact anisotropyunder an isotropic stress condition (Yimsiri, 2001). Theinitial void ratios are similar (e0 � 0.75 to 0.76) andboth drained triaxial compression and extension testswere simulated. Although all specimens are initiallyisotropically loaded, the directional distributions ofcontact forces are different due to different orientationsof contact plane normals (sample A: more in the ver-tical direction; sample B: similar in all directions; sam-ple C: more in the horizontal direction). As shown inFig. 11.38a, both samples A and C showed stiffer re-sponse when the compression loading was applied inthe preferred direction of contact forces, but softer re-sponse when the loading was perpendicular to the pre-ferred direction of contact forces. The response ofsample B, which had an isotropic fabric, was in be-tween the two. Dilation was most intensive when thecontact forces were oriented preferentially in the di-

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0.1

0.05

0.0

-0.05

-0.1

1 2 3 4 5 6N/<N>

Fab

ric A

niso

trop

y P

aram

eter

A

Figure 11.39 Fabric anisotropy parameter A for differentlevels of contact force when the specimen is under biaxialcompression loading conditions (after Radjai et al., 1996).

Figure 11.40 Evolution of the fabric anisotropy parametersof strong forces and weak clusters when the specimen is un-der biaxial compression loading conditions (after Thorntonand Antony, 1998).

rection of applied compression; and experimental datapresented by Konishi et al. (1982) shows a similartrend.

Figure 11.38b shows the development of fabric an-isotropy with increasing strain. The degree of fabricanisotropy is expressed by a fabric anisotropy param-eter A; the value of A increases with more verticallyoriented contact plane normals and is negative whenthere are more horizontally oriented contact plane nor-mals.9 The fabric parameter gradually changes with in-creasing strains and reaches a steady-state value as thespecimens fail. The final steady-state value is indepen-dent of the initial fabric, indicating that the inherentanisotropy is destroyed by the shearing process. Thefinal fabric anisotropy after triaxial extension is largerthan that after triaxial compression because the addi-tional confinement by a larger intermediate stress inthe extension tests created a higher degree of fabricanisotropy.

Close examination of the contact force distributionfor the strong force network and weak clusters givesinteresting microscopic features. Figure 11.39 showsthe values of A determined for the subgroups of contact

9 The density of contact plane normals E(�) with direction � is fittedwith the following expression (Radjai, 1999):

cE(�) � {1 � A cos 2(� � � )}c�

where c is the total number of contacts, �c is the direction for whichthe maximum E is reached, and the magnitude of A indicates theamplitude of anisotropy. When the directional distribution of contactforces is independent of �, the system has an isotropic fabric andA � 0.

forces categorized by their magnitudes when the spec-imen is under a biaxial compression loading condition(Radjai, 1999). The direction of contact anisotropy ofthe weak clusters (N /�N� less than 1) is orthogonalto the direction of compression loading, whereas thatof the strong force network (N /�N� more than 2) isparallel. Figure 11.40 shows an example of fabric ev-olution with strains in biaxial loading (Thornton andAntony, 1998). The fabric anisotropy is separated intothat in the strong force networks (N /�N� of morethan 1) and that in the weak clusters (N /�N� less than1). Again the directional evolution of the fabric in theweak clusters is opposite to the direction of loading.Therefore, the stability of the strong force chainsaligned in the vertical loading direction is obtained bythe lateral forces in the surrounding weak clusters.

Changes in Number of Contacts and MicroscopicVoids

At the beginning of biaxial loading of a dense granularassembly, more contacts are created from the increasein the hydrostatic stress, and the local voids becomesmaller. As the axial stress increases, however, the lo-cal voids tend to elongate in the direction of loadingas shown in Fig. 11.41. Consequently particle contactsare lost. As loading progresses, vertically elongated lo-cal voids become more apparent, leading to dilation in

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Figure 11.41 Simulated spatial distribution of local microvoids under biaxial loading (afterIwashita and Oda, 2000): (a) 11 � 1.1% (before failure), (b) 11 � 2.2% (at failure), (c)� �

11 � 4.4% (after failure), and (d ) 11 � 5.5% (after failure).� �

terms of overall sample volume (Iwashita and Oda,2000).

Void reduction is partly associated with particlebreakage. Thus, there is a need to incorporate graincrushing in discrete particle simulations to model thecontractive behavior of soils (Cheng et al., 2003). Nor-mal contact forces in the strong force network are quitehigh, and, therefore, particle asperities, and even par-ticles themselves, are likely to break, causing the forcechains to collapse.

Local voids tend to change size even after the ap-plied stress reaches the failure stress state (Kuhn,1999). This suggests that the degrees of shearing re-quired for the stresses and void ratio to reach the crit-ical state are different. Numerical simulations byThornton (2000) show that at least 50 percent axial

strain is required to reach the critical state void ratio.Practical implication of this is discussed further in Sec-tion 11.7.

Macroscopic Friction Angle Versus InterparticleFriction Angle

Discrete particle simulations show that an increase inthe interparticle friction angle �� results in an increasein shear modulus and shear strength, in higher rates ofdilation, and in greater fabric anisotropy. Figure 11.42shows the effect of assumed interparticle friction angle�� on the mobilized macroscopic friction angle of theparticle assembly (Thornton, 2000; Yimsiri, 2001). Themacroscopic friction angle is larger than the interpar-ticle friction angle if the interparticle friction angle issmaller than 20�. As the interparticle friction becomes

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Drained (Thornton, 2000)

Drained Triaxial Compression (Yimsiri, 2001)

Undrained Triaxial Compression (Yimsiri, 2001)

Drained Triaxial Extension (Yimsiri, 2001)

Undrained Triaxial Extension (Yimsiri, 2001)

Experiment (Skinner, 1969)

10 20 30 40 50 60 70 80 9000

10

20

30

40

50

Interparticle Friction Angle (degrees)

Mac

rosc

opic

Fric

tion

Ang

le (

degr

ees)

Figure 11.42 Relationships between interparticle friction angle and macroscopic frictionangle from discrete element simulations. The macroscopic friction angle was determinedfrom simulations of drained and undrained triaxial compression (TC) and extension (TE)tests. The experimental data by Skinner (1969) is also presented (after Thornton, 2000, andYimsiri, 2001).

more than 20�, the contribution of increasing interpar-ticle friction to the macroscopic friction angle becomesrelatively small; the macroscopic friction angle rangesbetween 30� and 40�, when the interparticle frictionangle increases from 30� to 90�.10

The nonproportional relationship between macro-scopic friction angle of the particle assembly and in-terparticle friction angle results because deviatoric loadis carried by the strong force networks of normalforces and not by tangential forces, whose magnitudeis governed by interparticle friction angle. Increase ininterparticle friction results in a decrease in the per-centage of sliding contacts (Thornton, 2000). The in-terparticle friction therefore acts as a kinematicconstraint of the strong force network and not as thedirect source of macroscopic resistance to shear. If theinterparticle friction were zero, strong force chainscould not develop, and the particle assembly will be-

10 Reference to Table 11.1 shows that actually measured values of ��

for geomaterials are all less than 45�. Thus, numerical simulationsdone assuming larger values of �� appear to give unrealistic results.

have like a fluid. Increased friction at the contacts in-creases the stability of the system and reduces thenumber of contacts required to achieve a stable con-dition. As long as the strong force network can beformed, however, the magnitude of the interparticlefriction becomes of secondary importance.

The above findings from discrete particle simula-tions are partially supported by the experimental datagiven by Skinner (1969), which are also shown in Fig.11.42. He performed shear box tests on spherical par-ticles with different coefficients of interparticle frictionangle. The tested materials included glass ballotini,steel ball bearings, and lead shot. Use of glass ballotiniwas particularly attractive since the coefficient of in-terparticle friction increases by a factor of between 3.5and 30 merely by flooding the dry sample. Skinner’sdata shown in Fig. 11.42 indicate that the macroscopicfriction angle is nearly independent of interparticlefriction angle.

Effects of Particle Shape and Angularity

A lower porosity and a larger coordination number areachieved for ellipsoidal particles compared to spherical

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DeviatorStress

q = σ�a – σ�r

Mean Pressure p�

M (triaxialcompression)

ln p�

SpecificVolume v

1

Γ

λcs

CriticalState Line

IsotropicCompressionLine

λ

CriticalState Line

M (triaxialextension)

CriticalState Line

σ�a

σ�r σ�r

Compression Lines ofConstant Stress Ratio q/p�

(a)

(b)

Figure 11.43 Critical state concept: (a) p�–q plane and (b)v–ln p� plane.

particles (Lin and Ng, 1997). Hence, a denser packingcan be achieved for ellipsoidal particles. Ellipsoid par-ticles rotate less than spherical particles. An assemblyof ellipsoid particles gives larger values of shearstrength and initial modulus than an assemblage ofspherical particles, primarily because of the larger co-ordination number for ellipsoidal particles. Similarfindings result for two-dimensional particle assemblies.Circular disks give the highest dilation for a givenstress ratio and the lowest coordination number com-pared to elliptical or diamond shapes (Williams andRege, 1997). An assembly of rounded particles exhib-its greater softening behavior with fabric anisotropychange with strain, whereas an assembly of elongatedparticles requires more shearing to modify its initialfabric anisotropy to the critical state condition(Nouguier-Lehon et al., 2003).

11.7 CRITICAL STATE: A USEFUL REFERENCECONDITION

After large shear-induced volume change, a soil undera given effective confining stress will arrive ultimatelyat a unique final water content or void ratio that isindependent of its initial state. At this stage, the inter-locking achieved by densification or overconsolidationis gone in the case of dense soils, the metastable struc-ture of loose soils has collapsed, and the soil is fullydestructured. A well-defined strength value is reachedat this state, and this is often referred to as the criticalstate strength. Under undrained conditions, the criticalstate is reached when the pore pressure and the effec-tive stress remain constant during continued deforma-tion. The critical state can be considered a fundamentalstate, and it can be used as a reference state to explainthe effect of overconsolidation ratios, relative density,and different stress paths on strength properties of soils(Schofield and Wroth, 1968).

Clays

The basic concept of the critical state is that, undersustained uniform shearing, there exists a unique re-lationships among void ratio ecs (or specific volumevcs � 1 � ecs), mean effective pressure , and deviatorp�cs

stress qcs as shown in Fig. 11.43. An example of thecritical state of clay was shown in Fig. 11.4a. The crit-ical state of clay can be expressed as

q � Mp� (11.25)cs cs

v � 1 � e � % � � ln p� (11.26)cs cs cs cs

where qcs is the deviator stress at failure, is thep�cs

mean effective stress at failure, and M is the critical

state stress ratio. The critical state on the void ratio (orspecific volume)–mean pressure plane is defined bytwo material parameters: �cs, the critical state com-pression index and %, the specific volume intercept atunit pressure (p� � 1). The compression lines underconstant stress ratios are often parallel to each other,as shown in Fig. 11.43b.

Parameter M in Equation (11.25) defines the criticalstate stress ratio at failure and is similar to �� for theMohr–Coulomb failure line. However, Equation(11.25) includes the effect of intermediate principalstress because p� � � � , whereas the�� 2 1 2 3

Mohr–Coulomb failure criterion of Eq. (11.4) or (11.5)does not take the intermediate effective stress into ac-count. In triaxial conditions, and�� a r r r

for compression and extension, respectively�� r a

(see Fig. 11.43).11 Hence, Eqs. (11.4) and (11.25) canbe related to each other for these two cases as follows:

11 is the axial effective stress and is the radial effective stress.�� a r

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CRITICAL STATE: A USEFUL REFERENCE CONDITION 401

DeviatorStress q

Mean pressure p�

M

ln p�

SpecificVolume v

1

Γ

λcs

Critical State Line


λ

CriticalState Line

A

A

B

B

C

C

3

1

DeviatorStress q

Mean pressure p�

M

ln p�

SpecificVolume v

1

Γ

λcs

Critical State Line


λ

CriticalState Line

D

E

F

D

F

E

31

(a)

Drained Strength

Drained Strength

UndrainedStrength

Undrained Strength

D�

D�

G

G

Drained Peak Strength

(b)

Figure 11.44 Drained and undrained stress–strain response using the critical state concept:(a) normally consolidated clay and (b) overconsolidated clay.

6 sin ��critM � for triaxial compression (11.27)3 � sin ��crit

6 sin ��critM � for triaxial extension (11.28)3 � sin ��crit

These equations indicate that the correlation be-tween M and is not unique but depends on the��crit

stress conditions. Neither is a fundamental property ofthe soil, as discussed further in Section 11.12. None-theless, both are widely used in engineering practice,and, if interpreted properly, they can provide usefuland simple phenomenological representations of com-plex behavior.

The drained and undrained critical state strengths areillustrated in Figs. 11.44a and 11.44b for normallyconsolidated clay and heavily overconsolidated clay,respectively. The initial mean pressure–void ratio stateof the normally consolidated clay is above the criticalstate line, whereas that of the heavily overconsolidatedclay is below the critical state line. When the initialstate of the soil is normally consolidated at A (Fig.11.44a), the critical state is B for undrained loading

and C for drained triaxial compression. Hence, the de-viator stress at critical state is smaller for the undrainedcase than for the drained case. On the other hand, whenthe initial state of the soil is overconsolidated fromD� (Fig. 11.44b), the critical state becomes E for un-drained loading and F for drained triaxial compression.The deviator stress at critical state is smaller for thedrained case compared to the undrained case. It is im-portant to note that the soil state needs to satisfy bothstate equations [Eqs. (11.25) and (11.26)] to be at crit-ical state. For example, point G in Fig. 11.44b satisfies

and qcs, but not ecs; therefore, it is not at the criticalp�cs

state.Converting the void ratio in Eq. (11.26) to water

content, a normalized critical state line can be writtenusing the liquidity index (see Fig. 11.45).

w � w ln(p� /p�)cs PL PLLI � � (11.29)cs w � w ln(p� /p� )LL PL PL LL

where wcs is the water content at critical state whenthe effective mean pressure is p�. and are thep� p�LL PL

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wLL

wPL

ln(p�PL)ln(p�LL)

LI = 1

LI = 0

ln(p�PL)ln(p�LL) ln(p�)

LiquidityIndex

WaterContent

Liquid Limit

Plastic Limit

(ln(p’), LI)

ln(p�)

wLI

LICS

LIeq-1wcs

CriticalState Line

IsotropicCompression Line

CriticalState Line

Meanpressure

MeanPressure

(a) (b)

(ln(p�), w)

Figure 11.45 Normalization of the critical state line: (a) water content versus mean pressureand (b) liquidity index versus mean pressure.

mean effective pressure at liquid limit (wLL) and plasticlimit (wPL), respectively; � 1.5 to 6 kPa andp� p�LL PL

� 150 to 600 kPa are expected considering the un-drained shear strengths at liquid and plastic limits arein the ranges suLL � 1 to 3 kPa and suPL � 100 to 300kPa, respectively12 (see Fig. 8.48).

Using Eq. (11.29), a relative state in relation to thecritical state for a given effective mean pressure (i.e.,above or below the critical state line) can be definedas (see Fig. 11.45)

log(p� /p� )LLLI � LI � LI � 1 � LI � (11.30)eq cs log(p� /p� )PL LL

where LIeq is the equivalent liquidity index defined bySchofield (1980). When LIeq � 1 (i.e., LI � LIcs) andq/p� � M, the clay has reached the critical state. Figure11.46 gives the stress ratio when plastic failure (orfracture) initiates at a given water content. When LIeq

� 1 (the state is above the critical state line), and thesoil in a plastic state exhibits uniform contractive be-havior. When LIeq � 1 (the state is below the criticalstate line), and the soil in a plastic state exhibits lo-calized dilatant rupture, or possibly fracture, if thestress ratio reaches the tensile limit (q/p� � 3 for tri-axial compression and �1.5 for triaxial extension; seeFig. 11.46b). Hence, the critical state line can be usedas a reference to characterize possible soil behaviorunder plastic deformation.

12 A review by Sharma and Bora (2003) gives average values ofsuLL � 1.7 kPa and suPL � 170 kPa.

Sands

The critical state strength and relative density of sandcan be expressed as

q � Mp� (11.31)cs cs

e � e 1max csD � � (11.32)R,cs e � e ln(� /p�)max min c

where ecs is the void ratio at critical state, emax and emin

are the maximum and minimum void ratios, and �c isthe crushing strength of the particles.13 The criticalstate line based on Eq. (11.32) is plotted in Fig. 11.47.The plotted critical state lines are nonlinear in the e–ln p� plane in contrast to the linear relationship foundfor clays. This nonlinearity is confirmed by experi-mental data as shown in Fig. 11.4b.

At high confining pressure, when the effective meanpressure becomes larger than the crushing strength,many particles begin to break and the lines becomemore or less linear in the e–ln p� plane, similar to the

13 Equation (11.32) is derived from Eq. 11.36 proposed by Bolton(1986) with IR � 0 (zero dilation). Bolton’s equation is discussedfurther in Section 11.8. Other mathematical expressions to fit theexperimentally determined critical state line are possible. For exam-ple, Li et al. (1999) propose the following equation for the criticalstate line (ecs versus p�):

�p�e � e � � � �cs 0 s pa

where e0 is the void ratio at p � 0, pa is atmospheric pressure, and�s and � are material constants.

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CRITICAL STATE: A USEFUL REFERENCE CONDITION 403

q/p�

0.5 LIeq1.0

3

-1.5

MTC

MTE

DilatantRupture

Fracture

Ductile Plasticand Contractive

DilatantRuptureFracture


Triaxial Extension

(a)

p�

qTriaxial Compression

Triaxial Extension

1

3

2

3

MTC

MTE

TensileFracture

TensileFracture

(b)

Ductile Plasticand Contractive

Figure 11.46 Plastic state of clay in relation to normalized liquidity index: (a) stress ratiowhen plastic state initiates for a given LIeq and (b) definition of stress ratios used in (a) (afterSchofield, 1980).

0

0.2

0.4

0.6

0.8

1

1.20.001 0.01 0.1 1

p�/σc p�/σc

Rel

ativ

e D

ensi

ty D

r

0

0.2

0.4

0.6

0.8

1

1.20 0.1 0.2 0.3 0.4 0.5

Rel

ativ

e D

ensi

ty D

r

emax

emin

emax

emax

emin

(a) (b)

DR,cs =––

ecs

emax emin=

In (σc/p�)1

Figure 11.47 Critical state line derived from Eq. (11.32): (a) e–log p� plane and (b) e–p�plane.

behavior of clays. Coop and Lee (1993) found thatthere is a unique relationship between the amount ofparticle breakage that occurred on shearing to a criticalstate and the value of the mean normal effective stress.This implies that sand at the critical state would reacha stable grading at which the particle contact stresses

would not be sufficient to cause further breakage. Coopet al. (2004) performed ring shear tests (see Section11.11) on a carbonate sand to find a shear strain re-quired to reach the true critical state (i.e., constantparticle grading). They found that particle breakagecontinues to very large strains, far beyond those

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reached in triaxial tests. Figure 11.48a shows the vol-umetric strains measured for a selection of their tests,which were carried out at vertical stress levels in therange of 650 to 860 kPa. A constant volumetric strainis reached at a shear strain of around 2000 percent. Forspecimens at lower stress levels, more shear strains(20,000 percent or more) were required. Similar find-ings were made for quartz sand (Luzzani and Coop,2002). Figure 11.48b shows the degree of particlebreakage with shear strains in the logarithmic scale.The amount of breakage is quantified by Hardin’s(1985) relative breakage parameter Br defined in Fig.10.14. At very large strains, the value of Br finallystabilizes. The strain required for stabilization dependson applied stress level. Interestingly, less shear strainwas needed for the mobilized friction angle to reachthe steady-state value (Fig. 11.48c) than for attainmentof the constant volume condition, (Fig. 11.48a). Thecritical state friction angle was unaffected by the par-ticle breakage.

In summary, the critical state concept is very usefulto characterize the strength and deformation propertiesof soils when it is used as a reference state. That is, asoil has a tendency to contract upon shearing when itsstate is above the critical state line, whereas it has atendency to dilate when it is below the critical stateline. Various normalized state parameters have beenproposed to characterize the difference between the ac-tual state and the critical state line, as illustrated in Fig.11.49. These parameters have been used to character-ize the stiffness and strength properties of soils. Someof them are introduced later in this chapter.

11.8 STRENGTH PARAMETERS FOR SANDS

Many factors and phenomena act together to deter-mined the shearing resistance of sands, for example,mineralogy, grain size, grain shape, grain size distri-bution, (relative) density, stress state, type of tests andstress path, drainage, and the like [see Eq. (11.3)]. Inthis section, the ways in which these factors have be-come understood and have been quantified over the lastseveral decades are summarized. Several correlationsare given to provide an overview and reference fortypical values and ranges of strength parameters forsands and the influences of various factors on theseparameters.14

14 A number of additional useful correlations are given by Kulhawyand Mayne (1990).

Early Studies

The important role of volume change during shear, es-pecially dilatancy, was recognized by Taylor (1948).From direct shear box testing of dense sand specimens,he calculated the work at peak shear stress state andshowed that the energy input is dissipated by the fric-tion using the following equation:

� dx � �� dy � �� dx (11.33)peak n n

where �peak is the applied shear stress at peak, is the��nconfining normal (effective) stress on the shear plane,dx is the incremental horizontal displacement at peak,dy is the incremental vertical displacement (expansionpositive) at peak stress, and � is the friction coefficient.The energy dissipated by friction (the component inthe right-hand side) is equal to the sum of the workdone by shearing (first component in the left-handside) and that needed to increase the volume (the sec-ond component in the left-hand side). The latter com-ponent is referred to as dilatancy.

Rearranging Eq. (11.33),

� dypeak � tan �� (11.34)� �m�� dx

Thus, the peak shear stress ratio or the peak mobilizedfriction angle consists of both interlocking (dy/dx)��mand sliding friction between grains (�). This equationthat relates stress to dilation is called the stress–dilatancy rule, and it is an important relationship forcharacterizing the plastic deformation of soils, as fur-ther discussed in Section 11.20.

Rowe (1962) recognized that the mobilized frictionangle must take into account particle rearrange-��mments as well as the sliding resistance at contacts anddilation. Particle crushing, which increases in impor-tance as confining pressure increases and void ratiodecreases, should also be added to these components.The general interrelationships among the strength con-tributing factors and porosity can be represented asshown in Fig. 11.50. In this figure, is the friction��fangle corrected for the work of dilation. It is influencedby particle packing arrangements and the number ofsliding contacts. The denser the packing, the more im-portant is dilation. As the void ratio increases, the mo-bilized friction angle decreases. The critical state isdefined as the condition when there is no volumechange by shearing [i.e., (dy/dx) � 0 in Eq. (11.34)].The corresponding mobilized friction angle is .�� m crit

The ‘‘true friction’’ in the figure is associated with theresistance to interparticle sliding.

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STRENGTH PARAMETERS FOR SANDS 405

0

0

20

40

0.0

0.2

0.4

0.6

0.8

1.0

?

0

10

20

30

40

50

(a)

(b)

(c)

Shear Strain (%)

50,000 100,000 150,000

Vol

umet

ric s

trai

n (%

) RS3

RS5

RS7

RS8

RS13

RS15

RS3

RS7

RS8

RS9

RS10

RS15

RS7

800 kPaunsheared

RS8

Luzzani & Coop, 805 kPa

650-930 kPa

248-386 kPa

60-97 kPa

Shear Strain

Shear Strain (%)

10

101

100

100

1000

1000

10,000

10,000

100,000

100,000

1,000,000

Rel

ativ

e B

reak

age

Mob

ilize

d F

rictio

n A

ngle

(de

gree

s)

Figure 11.48 Ring shear test results of carbonate sand: (a) volumetric strain versus shearstrain, (b) the degree of particle breakage with shear strains, and (c) mobilized friction angleversus shear strains (after Coop et al., 2004).

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Log (Mean pressure p�)

Void ratioe

Critical stateline (p�c , e c)

LooseSand

Densesand

(p�L, eL)

ecL

1. State parameter (Been and Jefferies, 1985)

Ψ = e – ec

Loose sand Ψ = eL – ecL (>0)

Dense sand Ψ = eD – ecD (<0)

2. State index (Ishihara et al., 1998)

Is = (e0 – ec )/(e0 – e)

Loose sand Is = (e0 – ecL)/(e0 – eL) (>1)

Dense sand Is = (e0 – e cD)/(e0 – e0) (<1)

3. State pressure index (Wang et al., 2002)

Ψ>0

ecD

(p�D, eD)

Ψ<0

p�cDp�cL Loose sand Ip = p�L/p�cL (>1)

Dense sand Ip = p�D/p�cD (<1)

Ip = p�/p�c

Figure 11.49 Various parameters that relate the current state to the critical state.

Porosity n (%)

26 30 34 38 42

26

46

42

38

34

30

φ

DensestPacking

CriticalVoid Ratio

φ�crit

φ�m

φ�f

True Friction

To Zero

Crushing (estimated)Rearrangement, Fabric Development

DilationInterlocking

Figure 11.50 Contributions to shear strength of granularsoils (modified from Rowe, 1962).

Critical State Friction Angle

The specific value of the critical state angle of internalfriction depends on the uniformity of particle��crit

sizes, their shape, and mineralogy and is developed atlarge shear strains irrespective of initial conditions.Typical values are 40� for well-graded, angular quartzor feldspar sands, 36� for uniform subangular quartzsand, and 32� for uniform rounded quartz sand. Particlecrushing appears to have little effect on (Coop,��crit

1990; Yasufuku et al., 1991). This is demonstrated inthe ring shear test results shown in Figs. 11.48b and11.48c; with increasing shear strains, the critical statestrength is reached well before particle crushingceases.

Peak Friction Angle

The peak friction angle can be considered as the sumof interparticle friction, rearrangement, crushing, andthe dilation contribution. For plane strain conditions,Bolton (1986) proposed the following empirical equa-tion that relates the mobilized friction angle �� at agiven stress state to the critical state friction angle

and dilation angle � :��crit

�� 0.8� (11.35)crit

where dilation angle � is the ratio of volumetric strainincrement d�v to the axial strain d�a at the stress stateof interest. This is similar to Taylor’s equation (Eq.(11.34)). However, � in Eq. (11.34) changes withshear, whereas is a constant material property.��crit

The relative density Dr is a convenient index to char-acterize the interlocking characteristics packing struc-ture. The effects of relative density, grain size, andgradation on the peak friction angle of cohesionlesssoils are illustrated by Fig. 11.51. Similar informationin terms of void ratio, unit weight, and Unified SoilClassification is given in Fig. 11.52. The peak valuesof friction angle for quartz sands range from about 30�to more than 50�, depending on gradation, relative den-sity, and confining pressure.

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Figure 11.51 Dependence of the friction angle of cohesion-less soils on relative density and gradation (after Schmert-mann, 1978).

Figure 11.52 Dependence of friction angle of cohesionlesssoils on unit weight and relative density (after NAVFAC,1982).

0.1 0.2 0.5 1 2 5 10 20 50 100Effective Mean Pressure at Peak Failure (kPa)

20

25

30

35

40

45

50 Uniformly Graded Cambria SandInitial Relative Density = 89.5%

Triaxial Extension

Contraction at Peak FailureDilation at Peak Failure


Sec

ant F

rictio

n A

ngle

at P

eak

Fai

lure

(deg

ree)

Figure 11.53 Effect of confining pressure on peak frictionangle (after Yamamuro and Lade, 1996).

Although the values of interparticle friction angleand the critical state friction angle are essen-�� crit

tially constant for a given mineral, the magnitudes ofthe dilation angle � in Eq. (11.35) vary with effectiveconfining pressure; that is, Figs. 11.51 and 11.52 applyfor a particular value of confining pressure. In general,the contribution of dilation increases with increasingdensity and decreases with increasing confining pres-sure. The effect of confining pressure on peak frictionangle is shown in Fig. 11.53 (Yamamuro and Lade,1996). Up to confining pressures of 5 to 10 MPa, thepeak friction angle decreases with increasing confiningpressure due to suppressed dilation and particle crush-ing. At pressures greater than about 10 MPa, the fric-tion angle remains approximately constant, but thevalues in triaxial extension are smaller than those intriaxial compression.

To take effective confining pressure into account,Bolton (1986) proposed the normalized dilatancy indexIR, defined as

�cI � D (Q � ln p�) � R � D ln � R (11.36)� �R r r p�

where Dr is the relative density, and p� is the meaneffective confining pressure. The empirical parameterQ is related to the crushing strength of the soil parti-cles; that is, Q � ln �c, where �c is the crushingstrength (same dimensions as p�). The Q values (usingkPa) are 10 for quartz and feldspar, 8 for limestones,7 for anthracite, and 5.5 for chalk. Bolton (1986) foundthat R � 1 fits the available data well. The critical stateis achieved when IR � 0, and this is given as Eq.(11.32). Index IR increases as the soil density increases.The parameter characterizes the state of the soil in re-lation to the critical state, similarly to the ones illus-trated in Fig.11.49.

Using IR (between 0 and 4), Bolton (1986) deducedthe following correlations for the peak friction angleand critical state friction angle (in degrees) from theplots shown in Fig. 11.54.

for triaxial compression conditions�� 3Im crit R

(11.37)

for plane strain conditions�� 5Im crit R

(11.38)

The dilatancy contribution to sand strength, repre-sented by the difference between the peak triaxial com-pression friction angle and the critical state friction

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Eq.(11.37)

Eq.(11.38)

0.0 0.2 0.4 0.6 0.8 1.00

4

8

12

16

20Plane Strain TestsTriaxial Compression Tests

Data for p� ≈ 300 kPa

Relative Density Dr

φ�m

ax–

φ�cr

it (d

egre

es)

Figure 11.54 Difference between peak friction angle andcritical state friction angle for triaxial compression and plainstrain compression data on sands (after Bolton, 1986).

Figure 11.55 Dilatancy component as a function of meaneffective stress at critical state and relative density (modifiedfrom Bolton, 1986).

angle , as determined by Bolton (1986), is shown��crit

in Fig. 11.55. The values shown are appropriate forquartz sands (Q � 10).

Other forms to characterize the peak friction anglein relation to the initial state of a sand are available.For example, Been and Jefferies (1986) relate the peakfriction angle to the state parameter � defined in Fig.11.49, as shown in Fig. 11.56.

As shown in Fig. 11.54 and by Eqs. (11.37) and(11.38), the critical state and peak friction angles varydepending on test conditions. The difference is relatedto the magnitude of the intermediate principal stress inrelation to the major and minor principal stresses. Fur-ther details are given in Section 11.12.

Undrained Strengths

In most cases, the deformation of sands occurs underdrained conditions. However, the undrained behaviorof sands is important when flow slides or earthquakesare of concern. These events are very rapid, and rapiddeformation of loose to medium dense cohesionlesssoils can generate excess pore water pressures resultingin loss of strength or liquefaction. The stress-strain re-lationship in undrained triaxial tests of Toyoura sandat different densities are shown in Fig. 11.57a, and thecorresponding effective stress paths are shown in Fig.11.57b (Yoshimine et al., 1998). A sudden flow failurecan occur in loose sand deposits by the drop in strengthwith increase in shear strain. Typical undrained re-sponses of sand specimens at different densities areillustrated in Fig. 11.58a.

Loose sand exhibits peak strength and then softens.The peak state on the p�–q plane is termed the collapsesurface (Sladen et al., 1985),15 and the slope increaseswith increase in initial density and decrease in confin-ing pressure, as illustrated in Fig. 11.58b. In triaxialcompression, the slope for many sandy soils rangesfrom 0.62 to 0.90 with an upper bound of 1.0 (Olsonand Stark, 2003). Once the soil softens, large sheardeformation is generated by moderate shear stresses.The softened soil eventually leads to the steady state,in which there is no further contraction tendency. Thepore pressures and stresses remain constant as the soilcontinues to shear in a steady state of deformation(Castro, 1975; Poulos, 1981). The steady state occurswhen the soil continuously deforms at constant vol-ume, constant stress, and constant velocity.16 It devel-ops under stress-controlled conditions because of theflowing nature of softened soil. When the soil is veryloose, the effective stress becomes zero, indicating astatic liquefaction condition, which is the transforma-tion of a granular material from a solid to a liquefiedstate (Youd et al., 2001).

15 Similar concepts are proposed by others. For example, the criticalstress ratio (Vaid and Chern, 1985), the instability line (Lade, 1992),and the yield strength ratio (Olson and Stark, 2003).16 The basic concept of the steady state is essentially the same as thecritical state defined for clay by Schofield and Wroth (1969).

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Figure 11.56 Peak friction angle versus state parameter � (after Been and Jefferies, 1986).

Even dense sands exhibit positive excess pore pres-sures at the beginning of deformation up to smallstrain. However, after a certain stress ratio is reached,the undrained stress path reverses its direction indicat-ing contractive to dilative behavior as shown in Fig.11.58c, and the stress reversal is called the state ofphase transformation (Ishihara et al., 1975). Thestress–strain response thereafter is strain hardening anddoes not exhibit any peak. The soil eventually reachesthe ultimate steady state or the critical state as long asthe pore water does not cavitate.

Medium dense specimens initially soften after thestress state passes the collapse line as illustrated in Fig.11.58c. The stress state then reaches a point of mini-mum strength, which is called the quasi-steady state(Alarcon-Guzman et al., 1988) or flow with limited liq-uefaction (Ishihara, 1993). At this stage, the soil is inthe state of phase transformation, and the mobilizedstrength then increases gradually with further shearstrain due to increase in effective stress by negativepore water pressure development. As shearing contin-ues, the soil shows a strain-hardening behavior, climb-ing along the critical state line, and the stress statefinally reaches the critical or ultimate steady state atvery large strains. Reported data indicate that the slopeof the critical state on the p�–q plane is approximatelythe same as that of the phase transformation line (Beenet al., 1991; Ishihara, 1993; Zhang and Garga, 1997;Vaid and Sivathayalan, 2000); at least, these lines aredifficult to distinguish from each other.

For loose sand, the steady state is the minimum un-drained shear strength associated with a rapid collaps-ing of soil structure. As discussed in Section 11.7, ithas been suggested that the stress state of the steadystate is a function of void ratio, so a unique criticalstate line exists on the e–log p� plane as shown in Fig.11.4b (Castro, 1975; Poulos et al., 1985, and others).The shape depends on grain angularity and fines con-tent (Zlatovic and Ishihara, 1995). At a given initialvoid ratio, the steady state strength can be determinedfrom the critical state line. For a relatively small con-fining pressure, a small change in void ratio can givedramatic difference in undrained shear strength be-cause the critical state line on e–log p� plane is veryflat at this stress level.

For medium dense sand, the quasi-steady state canbe considered as the minimum undrained shearstrength. As the soil continues to deform, the shearingresistance increases. Although the stress ratios atquasi-steady state, and critical state are similar on thep�–q plane, the quasi-steady state on e–log p� planelies below the critical state line as shown in Fig. 11.59.For a given initial void ratio, therefore, the stress stateof quasi-steady state is smaller than that of the criticalstate.

The location of the quasi-steady state line on e–logp� plane is influenced by shear mode and sample prep-aration method (i.e., soil fabric) (Konrad, 1990; Ishi-hara, 1993; Yoshimine and Ishihara, 1998). Figure11.60 shows the undrained shear behavior of Toyoura

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Figure 11.57 Undrained stress–strain response of Toyoura sand specimens prepared at dif-ferent densities by dry pluviation (after Yoshimine et al., 1998).

sand in triaxial compression, triaxial extension, andsimple shear (Yoshimine et al., 1999). The specimenswere prepared to similar void ratios, and an initial con-fining pressure of 100 kPa was applied. The minimumundrained shear strength and the quasi-steady statevary significantly depending on the mode of shearing,which in turn leads to different quasi-steady state lineson the e–p� plane as shown in Fig. 11.61. Hence, largevariation of minimum undrained shear strengths is of-ten observed depending on shear mode, which is pri-

marily due to the anisotropic soil fabric. Further detailsare given in Section 11.12.

The slope of the collapsing surface and the mini-mum undrained strength are related to both initialdensity and confining pressure. Typical values of thecollapse surface stress ratio obtained from triaxialcompression tests are plotted against state parameter �in Fig. 11.62 (Olson and Stark, 2003). Although thedata are scattered, a general trend for a given sand isthat the slope decreases with decreasing state param-

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STRENGTH PARAMETERS FOR CLAYS 411

Deviator Strain

Phase Transformation

Dense

Quasi-steadyState

Steady State

Liquefaction (σ�3 = 0)

Dilative

Medium Dense

Loose

Very Loose

Very Loose

Loose

Medium Dense

Dense


Critical State

Critical State

(a)

DenseMedium Dense

Collapse Surface forMedium Dense Sand

Phase TransformationLines

Critical State LineCritical State

Mean Pressure p�

Loose

Very Loose

Collapse Surfacefor Loose Sand

Critical State Line

Steady State

Collapse Surface forVery Loose SandLiquefaction

(c)

(b)Dev

iato

r S

tres

s (σ

� 1–

σ�3)

Dev

iato

r S

tres

s (σ

� 1–

σ�3)

Dev

iato

r S

tres

s (σ

� 1–

σ�3)

Exc

ess

Por

e P

ress

ure

Δu

Mean Pressure p�

Figure 11.58 Typical undrained responses of sand specimens with different densities: (a)stress–strain–pore pressure response, (b) stress paths for loose and very loose specimens,and (c) stress paths for medium dense and dense specimens.

Critical State Linefrom Fig.11.4(b)

0.95

0.90

0.85

0.80

0.75

0.02 0.05 0.1 0.2 0.5 1.0 2.0

Quasi-steady StateInitial State

Quasi-steadyState Line

Toyoura Sand

Effective Mean Pressure p� (kPa)

Voi

d R

atio

e

Figure 11.59 Quasi-steady state line and critical state lineon e–log p� plane (after Ishihara, 1993).

eter. Similarly, the minimum undrained strength nor-malized by the initial confining pressure can be relatedto state parameter as shown in Fig. 11.63 (Olson andStark, 2003). For a given soil, the strength ratio de-creases with increasing state parameter and is larger intriaxial compression than in triaxial extension.

11.9 STRENGTH PARAMETERS FOR CLAYS

Friction Angles

The peak value of �� for clays decreases with increas-ing plasticity index and activity as shown in Fig. 11.64.Similarly, the critical state friction angle of normallyconsolidated kaolin clays ranges from 20� to 25�,whereas that of montmorillonite clays is approximately20�. However, as the shearing continues, the frictionangle of normally consolidated montmorillonite claysdecreases to a value between 5� and 10�. This is calledthe residual state and further details are given in Sec-

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Figure 11.60 Undrained shear behavior of Toyoura sand intriaxial compression, triaxial extension, and simple shear (af-ter Yoshimine et al., 1999).

Figure 11.61 Quasi-steady state line in triaxial compression,triaxial extension, and simple shear on e–p� plane (afterYoshimine et al., 1999).

tion 11.11. The friction angle of kaolin clays tends toremain near the above values even at large strains.

Failure Envelope for Overconsolidated Clays

The differences in effective stress failure envelopes be-tween normally consolidated and overconsolidatedclays were illustrated in Fig. 11.3, and Hvorslev (1960)proposed the following relationship to model thestrength characteristics of overconsolidated clays:

� � c� � �� tan �� (11.39)ff e ff e

where is an equivalent friction angle and is the�� c�e e

cohesion intercept. These are called the Hvorslev pa-rameters. If is constant, becomes a linear function�� c�e e

of , which is the equivalent consolidation pressure��eas determined from the void ratio at failure eff as shownin Fig. 11.3.

c� � h �� (11.40)e c e

where hc is a material constant.Substituting Eq. (11.40) into Eq. (11.39) gives

� ��ff ff� h � tan �� (11.41)c e�� e e

Reported values of hc and range from 0.034 to��e0.145, and from 9.9� to 18.8�, respectively (Wood,1990).17

Rearranging Eq. (11.41) gives

� ��ff etan �� h � tan �� (11.42)m c e�� ff ff

17 For general stress conditions, Schofield and Wroth (1968) modifiedthe Hvorslev equation to the following:

q 6 sin �� p�e� c� cot �� for triaxial compression� �pep� 3 � sin �� p�e e e

q 6 sin �� p�e� c� cot �� for triaxial extension� �pep� 3 � sin �� p�e e e

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STRENGTH PARAMETERS FOR CLAYS 413

Figure 11.62 Relationship between the slope of the instability line and state parameter �(after Olson and Stark, 2003).

Figure 11.63 Relationship between the undrained shear strength ratio and state parameter� (after Olson and Stark, 2003).

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Figure 11.64 Relationship between sin �� and plasticity index for normally consolidatedsoils (adapted from Kenny, 1959). Data for pure clays from Olsen, 1974.

where is the mobilized friction angle at failure. For��mnormally consolidated clay, ( ) � 1 and tan �� /�� e ff m

tan . Substituting this into Eq.�� h � tan ��crit c e

(11.42) gives

��etan �� h � 1 � tan �� (11.43)� �m c crit��ff

Hence the peak friction angle for overconsolidated��mclays depends on the overconsolidation ( ) (the�� /��e ff

first term in the right-hand side) and the critical statefriction angle . The form of this equation is similar��crit

to Eqs. (11.34) and (11.35) derived for sands.The Hvorslev parameters, and , have been�� c�e e

termed true friction angle and true cohesion, and areconsidered by some to reflect the mechanism of shearstrength in terms of interparticle forces and friction.Such an interpretation is questionable, however, be-cause, as shown in Chapter 8, two samples at the samewater content but different effective stresses must havedifferent structures. Thus, during deformation, therewill be differences in volume change under drainedconditions or differences in pore water pressure for de-formation under undrained conditions. Furthermore,Eq. (11.40) shows that is an effective stress-c�edependent property. Present evidence is that true co-hesion is negligible in the absence of chemical bondingbetween particles caused by cementation.

Undrained Shear Strength

Undrained shear strength su coupled with total stressanalysis [c � su and � � 0 in Eq. (11.1)] is often usedto examine the failure state of geotechnical structuresunder undrained conditions. The undrained shearstrength of saturated normally consolidated clay deter-mined using isotropically consolidated specimens as afunction of liquidity index is shown in Fig. 8.43.

The undrained strength for a given initial void ratioeini can be obtained using the critical state Eqs. (11.25)and (11.26):

M % � 1 � einis � exp (11.44)� �u 2 �

The above equation applies to both normally consoli-dated and overconsolidated clays.

For a given soil, the initial void ratio eini can berelated to the current stress state and the overconsoli-dation ratio. The relationship between undrainedstrength normalized by the effective overburden stressafter isotropic consolidation has been deduced from��icritical state soil mechanics by Wroth and Houlsby(1985) as

s /�� 0.129 � 0.00435PI (11.45)u i

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BEHAVIOR AFTER PEAK AND STRAIN LOCALIZATION 415

Figure 11.66 Normalized undrained strength ratio as a func-tion of overconsolidation ratio (after Ladd et al., 1977).

Figure 11.65 Effect of overconsolidation on the normalizedundrained shear strength of several clays (after Ladd et al.,1977).

Figure 11.67 Effect of shear modes on undrained shearstrength ratios of different plasticity soils (after Ladd, 1991).

in which PI is the plasticity index. Alternatively, thefollowing relationship can be used for normally con-solidated to slightly overconsolidated clays with low-to-moderate plasticity (Jamiolkowski et al., 1985):

s /�� 0.23 � 0.04 (11.46)u vp

where is the vertical preconsolidation stress, and su��vp

is for direct simple shear.The influence of overconsolidation on the undrained

strength of clays is shown by Figs. 11.65 and 11.66.In Fig. 11.65, the undrained strength is normalized by

the initial effective overburden pressure. In Fig. 11.66,the normalized strength of the overconsolidated clay isfurther normalized to the normalized strength of thenormally consolidated clay. That normalization of un-drained shear strength leads to unique relationships,such as those in these figures, forms the basis of theSHANSEP (stress history and normalized soil engi-neering properties) method of design in soft clays(Ladd and Foott, 1974) that is widely used in practice:

s su u m� (OCR) (11.47)� �� v0 v0 NC

where (su / )NC is the strength ratio of normally con-��v0

solidated clay, m is a material constant, and OCR isthe overconsolidation ratio, defined as the ratio of thevertical preconsolidation stress to the current ver-��vp

tical stress . Typical values of m range between 0.7��vand 0.9. This method is particularly well suited for usewith clays of low-to-medium sensitivity, that is, claysthat do not suffer large structural breakdown whenconsolidated beyond their preconsolidation pressure. Itis also important to note that the strength ratio dependslargely on the mode of shearing as shown in Fig. 11.67(Ladd, 1991) and the values given in Eqs. (11.45) and(11.46) are at the lower range (or the conservative side)in the figure. Further details of the effect of shearingmode on undrained strength are given in Section 11.12.

11.10 BEHAVIOR AFTER PEAK AND STRAINLOCALIZATION

When laboratory tests are done on soils exhibitingpeak strength, strains at a certain location in a soilspecimen often localize after the peak, leading to

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(a) (b)

Figure 11.68 Shear bands observed in plane strain compression tests: axial strain of (a) 9.6percent and (b) 19 percent (after Alshibli and Sture, 2000).

Figure 11.69 Thickness of shear band as a function of par-ticle size (after Oda and Iwashita, 1999).

‘‘shear band’’ formation in a direction diagonal to theprincipal stress directions. Examples of shear bandsobserved in the laboratory are shown in Fig. 11.68 (Al-shibli and Sture, 2000). The deformation is localized,and the two soil bodies on opposite sides of the shearband act as rigid bodies. Strain localization tends tooccur in soils that exhibit strain-softening behavior,such as overconsolidated clay and dense sand underlow confining pressure. This observation illustrates thedifficulty in obtaining the material behavior from ex-perimental measurements at the specimen boundaries,as these strains are different from the strains in theshear band where the actual shearing is occurring. Thepeak strength and the associated strain are specimensize dependent because of the progressive nature ofshear band development.

The direction of shear banding is influenced by par-ticle size (Arthur et al., 1982; Vermeer, 1990). In planestrain conditions, the direction of shear band with re-spect to the loading direction is bounded by � /4 �� /2 and � /4 � /2, where � is the dilation angle��crit

at the peak stress and is the critical state friction��crit

angle. Experimental data indicate that the shear banddirection is close to � /4 � /2 for small diameter��crit

particles (D50 � 0.2 mm), but the inclination decreasestoward � /4 � � /2 for larger diameter particles (Odaand Iwashita, 1999).

The thickness of the shear band depends on particlesize as shown in Fig. 11.69. It increases with increas-ing displacement, but then reaches a constant valuebetween 7 to 10 particle diameters when the displace-

ment is more than 20 particle diameters (Scarpelli andWood, 1982; Oda and Kazama, 1998). However, thisdoes not mean that more particles are involved in theshear band. It is more likely that the local void ratioin the shear band is growing. Examination of resin-impregnated specimens with shear bands shows thatthis local void ratio is larger than the maximum voidratio for a stable load-carrying structure (Oda and Ka-zama, 1998, Frost and Jang, 2000) and the very loosestructure in the shear band is shown in Fig. 11.70 usingX-ray CT. Discrete particle simulations by Iwashitaand Oda (1998) show that the very large void ratios

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RESIDUAL STATE AND RESIDUAL STRENGTH 417

Figure 11.70 Large local voids observed along the shearzone using microfocus X-ray computed tomography (afterOda et al., 2004).

inside the shear band (see Fig. 11. 41d) are associatedwith particle rotation inside and near the shear band.The particles inside the shear band tend to rotate,whereas the particles outside the shear band remainedin their original positions. A high gradient of particlerotation is developed at the boundary of shear bands,and the rotational resistance at this high rotational gra-dient zone was able to transfer loads even at void ratioslarger than the maximum void ratio.

Possible situations where strain localization is likelyto occur are listed in Table 11.2.

Distinct failure planes are often observed in both thelaboratory and the field. Figure 11.72 is an X-ray pho-tograph of shear bands observed in a model of a re-taining wall failure (Milligan, 1974 and interpretationby Lesniewska and Mroz, 2000). Shear bands are ob-served in the field as slip planes. The practical impli-cation of strain localization is that there can besignificant differences between the continuum-basedassumptions and analyses used in common geotech-nical design (such as friction angle and critical state)and the actual conditions. Accordingly, careful inter-pretation of experimental and field data, as well as therelevance of analytical and numerical models is nec-essary. More detailed theoretical considerations ofstrain localization and shear band formation are outsidethe scope of this book; however, other references areavailable (Chambon et al., 1994; Vardoulakis and Su-lem, 1995).

11.11 RESIDUAL STATE AND RESIDUALSTRENGTH

The drop in drained strength after peak is reached inintact overconsolidated clay can be attributed to (1) an

increase in water content owing to dilatancy and (2)reorientation of clay particles along the shear plane.These processes transform the material to its residualstate. A postpeak drop in strength also occurs in nor-mally consolidated clays if the strength loss due tobreakdown of structure and particle reorientation ex-ceeds the strength gain due to consolidation duringshear.

The strength of the soil once the residual state hasbeen reached is a minimum and is termed the residualstrength. The deformation at this stage becomes local-ized, and the residual state is developed within a shearband, as described in the previous section. The residualstrength-determining factors for a given test type andstrain rate are reduced to the effective stress, compo-sition, and friction angle. The friction angle corre-sponding to this strength is the residual friction angle

. Its value depends on the mineralogy, gradation,��rbulky particle characteristics, and rate of shear. Therelationships between stress and shear displacement forsoils with low and high clay fractions sheared underconstant effective stress on the failure plane are shownin Fig. 11.73. A residual condition can also be devel-oped under undrained conditions. In this case, the ef-fective stress on the shear plane at the residual statewill differ from that initially or at peak stress.

As a result of the rearrangement contributions to theresidual strength of soils with low clay contents, as inFig. 11.73b, the loss of strength, under drained con-ditions, between peak and residual is small. This isillustrated by Fig. 11.74, which shows the critical andresidual friction angles for sand–bentonite mixturestested in ring shear. Three zones are identified in Fig.11.74 and termed rolling shear, transitional shear, andsliding shear.

The shear displacements required to reach the resid-ual strength can be large, as indicated by the values inTable 11.3. Because the shear displacements requiredto reach the residual state are large, the stability ofembankments and slopes is only controlled by residualstrength when there are preexisting slide surfaces. Forfirst-time slides the stability is controlled by an averagestrength that lies between the peak and residual with avalue that is influenced by the amount of progressivefailure along the shear surface.

Owing to the large displacements required to de-velop a full residual condition, special testing methodshave been developed. For example, a ring shear devicewas developed by Bishop et al. (1971), which can beused to shear specimens through large displacementsthat are always in the same direction. The values ofresidual friction angle shown in Fig. 11.28 were ob-tained by shearing samples in direct shear back and

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Table 11.2 Possible Occurrences of Strain Localization

1. Dilative Material Subjected to Drained Shear Localization occurs after the deviator stress reaches its peak as thesoil dilates. This type of localization occurs in dense sand under low confinement and in heavily overconsolidatedclay. Some examples are given in Desrues et al. (1996) and Saada et al. (1999).

2. Contractive Material Subjected to Undrained Shear Shear of loose sand at high confinement causes softeningafter the effective stress state passes the collapse line (see Section 11.8) due to generation of excess pore pressures.In some cases, shear bands are hidden by bulging (Santamarina and Cho, 2003). Some examples are given in Finnoet al. (1998) and Mokni and Desrues (1999).

3. Dilative Material Subjected to Undrained Shear Cavitation Shear of dense sand at low confinement generateslarge reductions in pore pressure. If the pore pressure becomes less than the vapor pressure (�100 kPa) of water,cavitation occurs. The effective stress drops at locations where cavitation occurs, and, therefore, the soil softens. Someexamples are given in Schrefler et al. (1996), Roger et al. (1998), and Mokni and Desrues (1999).

4. Alignment of Platy Particles If soil particles are platy, they align at a certain angle and this reduces the shearingresistance. The residual friction angle discussed in Section 11.11 is a good example of this type of strain localizationbehavior.

5. Lightly Cemented Soils When cemented sands are sheared under low confinement, interparticle cementation breaksat low strain levels, and the shear resistance drops. Examples are given in Santamarina and Cho (2003) for artificiallycemented soils and Cuccovillo and Coop (1999) for naturally structured sands.

6. Unsaturated Soils For soils at low degree of saturation, menisci form at the particle contacts, and this increasesinterparticle attractions by surface tension. When the soil is sheared, some of the menisci break, and this additionalcontribution to strength is lost, at least temporarily, until new menisci are formed. The loss of menisci causes localdecrease in interparticle attraction, and, therefore, the soil may undergo softening.

7. Particle Breakage When particle breakage occurs, there is a change in particle size distribution, particle shape, andtextures. The collapse of soil structure by particle breakage leads to contractive behavior upon shearing.

8. Heterogeneous Soil If a soil has a layer of loose material sandwiched between denser materials, strain localizes inthe loose layer. Microlayering is observed in many natural soils due to their depositional conditions. For moist tampedcompacted soil, thin looser zones exist between tamping layers, and these can initiate localized failure.

9. Other Cases The degree of localization can be influenced significantly by experimental conditions. Influencingfactors include nonuniform specimen shape, friction at end platens, high length-to-diameter specimens, and tiltedplatens. The occurrence of localization also depends on applied loading rate. Figure 11.71 shows failed samples ofkaolin clay after unconfined compression tests at two different loading rates (Atkinson, 2000). Sample A, which wasloaded slowly, exhibited strain localization due to local fluid migration in the dilating shear zone. Sample B, whichwas loaded more rapidly, did not show distinct shear bands, as the pore fluid did not have time to migrate within thespecimen.

Modified from Santamarina and Cho (2003).

forth through displacements of 2 to 2.5 mm each sideof center until minimum values were obtained. As Ta-ble 11.3 indicates that many tens of millimeters in thesame direction may be required, some of the values inFig. 11.28 may be high, especially for the layer sili-cates, where the protrusion of particle edges across theshear surface could give increased resistance. A pre-ferred method of testing, if a ring shear device is notavailable, is to separate and reset the two halves of a

direct shear box to enable continued deformation al-ways in the same direction.

Nonclay Minerals

The residual strength of nonclay minerals is not muchdifferent than the critical state strength, as noted above.Quartz, feldspar, and calcite all have the same value of

� 35�, as shown in Fig. 11.28, even though the��r

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Figure 11.71 Samples of kaolin clay after unconfined com-pression tests: (a) slower loading and (b) faster loading (cour-tesy of J. H. Atkinson, 2000). Figure 11.73 Stress–shear displacement curves under con-

stant effective normal stress on the shear plane (Skempton,1985): (a) high clay fraction (�40 percent and (b) low clayfraction (�20 percent).

(a) (b)

Figure 11.72 Shear bands observed in centrifuge modeling of retaining wall failure: (a) X-ray photograph (after Milligan, 1974) and (b) interpretation of the photography by Les-niewska and Mroz (2000).

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Figure 11.74 Influence of clay fraction on the peak and re-sidual friction angles for sand–bentonite mixtures as deter-mined by ring shear tests (after Lupini et al., 1981).

Table 11.3 Displacements Corresponding to VariousStages of Shear in Clays with a Clay Size FractionGreater Than 30 Percenta

Stage

Displacement (mm)

OverconsolidatedNormally

Consolidated

Peak 0.5–3 3–6Volume change rate � 0 4–10At � 1��r 30–200Residual ��r 100–500

aIntact clays with �� 600 kPa.Data from Skempton (1985).

Figure 11.75 Composite relationship showing dependenceof residual friction angle on soil composition as representedby activity and clay size fraction.

interparticle friction angles are different (see Table11.1). This is because the critical state friction anglebecomes approximately independent of interparticlefriction when the interparticle friction angle becomesmore than 25� (� � 0.47), as illustrated in Fig. 11.42.The shape and roughness of particles are importantfeatures that influence the critical state friction angle.

Influence of Increasing Clay Content

As the proportion of clay increases, the residual fric-tion angle decreases as a result of the reduced contri-bution from silt and sand particle rearrangement andthe lower sliding friction angle of the clay minerals incomparison to the nonclay minerals. The influence ofclay fraction is indicated through the transition fromrolling shear for soils composed mainly of bulky grains

to sliding shear at high contents of clay size particles.The more active the clay fraction, the lower the resid-ual friction angle at a given clay size fraction percent-age.

A composite relationship showing the residual fric-tion angle as a function of clay size fraction, derivedfrom Kenney (1967), Lupini et al. (1981), Skempton(1985), and others is shown in Fig. 11.75. There is asharp drop in the residual friction angle when PI ex-ceeds 30 percent. This is attributed to a transition fromturbulant shear to sliding shear. Other correlations areavailable for certain soil types (Mesri and Cepeda-Diaz, 1986; Colotta et al., 1989; Stark and Edit, 1994).

Highly plastic soils of volcanic origin are an excep-tion to the general relationship shown in Fig. 11.75.These soils, which may have clay size fractions wellabove 50 percent, exhibit residual friction angles thatare several degrees higher than those shown in the fig-ure. Both particle morphology and structural factorshave been suggested as possible causes (Sitar, 1991;Wesley, 1992). As volcanic clays often contain largeamounts of allophane, which consists of bulky shapedparticles rather than platy particles, rolling shear maycontinue to make a major contribution. Alternatively,or in addition, physicochemical attractive forces be-tween particles may be sufficiently strong to preventthe development of parallel orientations of platy par-ticles and basal plane shear. For soils with liquid limitsmore than 50, Wesley (2003) shows that the positionon the plasticity chart in relation to the A-line [i.e., PI � PI � 0.73(LL � 20)] is a good indicator to givegood correlations for residual friction angle for bothclays and volcanic ashes as shown in Fig. 11.76.

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Figure 11.76 Residual friction angle of volcanic clays andclays in relation to their location on the plasticity chart rel-ative to the A-line (from Wesley, 2003).

Table 11.4 Bonding Along Cleavage Planes, Cleavage Mode, and Residual Strength

Mineral Mode of Cleavage Bonding Along Cleavage Planes��r

(deg) Particle Shape

Quartz No definite cleavage 35 BulkyAttapulgite Along (110) plane Si–O–Si, weak 30 Fibrous and

needle-shapedMica Good basal (001) Secondary valence (0.5–5 kcal /mol)

� K linkages17–24 Sheet

Kaolinite Basal (001) Secondary valence (0.5–5 kcal /mol)� H bonds (5–10 kcal /mol)

12 Platy

Illite Basal (001) Secondary valence (0.5–5 kcal /mol)� K linkages

10.2 Platy

Montmorillonite Excellent basal (001) Secondary valence (0.5–5 kcal /mol)� exchangeable ion linkages

4–10 Platy–filmy

Talc Basal (001) Secondary valence (0.5–5 kcal /mol) 6 PlatyGraphite Basal (001) van der Waal’s 3–6 SheetMoS2 Basal (001) Weak interlayer 2 Sheet

Adapted from Chattopadhyay (1972).

Clay Minerals

Basal plane slip is the dominant deformation mecha-nism at large strain in the clay minerals and other layersilicates. Compression textures with basal planes ap-proximately perpendicular to the normal load directionare formed in the shear zone, and most of the defor-mation takes place in this zone as well as in zones ofhigh particle orientation that enclose it. The behavior

of the layer silicates and solid lubricants such as graph-ite and molybdenum disulfide (MoS2) is similar.

The type and number of bonds along the cleavageplanes are important for basal plane slip, as may beseen by the values in Table 11.4. Of the materialslisted, only attapulgite does not fit the pattern of de-creased with decreased interlayer bond strength.��rThe high residual strength of attapulgite is becausethe lathlike particles occur as intermeshed aggregates,and the crystal structure gives a stair-step mode ofcleavage. As a result, attapulgite behaves more likea massive mineral than a platy mineral in shear(Chattopadhyay, 1972).

For many clays, the residual friction angle decreaseswith increasing confining pressure, that is, the failureenvelopes are curved. The values in Fig. 11.28 for sev-eral clay minerals, as well as the data for brown Lon-don clay and Weald clay in Fig. 11.2, show significantstress dependency of the residual friction angle, thatis, the failure envelope is curved. One possible reasonfor this curvature is that under low normal stresses lesswork is required to shear the clay in the absence ofperfect orientation of clay particles in the shear zonethan would be required to develop parallelism duringshear.

An alternative explanation of the stress dependencyof for clays can be based on the elastic junction��rtheory developed in Section 11.4. If deformations atparticle contacts are elastic, then the area of real con-tact between sliding surfaces increases less than pro-

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Figure 11.77 Residual friction angle as a function of normal effective stress on the shearplane raised to the minus one-third power (replotted from data in Chattopadhyay, 1972).

portionally with increase in normal effective stress;and according to Eq. (11.22), tan should vary as��r(�n)

�1 / 3. Data for several clays are shown in Fig. 11.77,which show agreement with this theory in the low-pressure range (up to 200 kPa), but at higher stresses,

is independent of stress, indicating that the solid��rcontact area varies in direct proportion to effective nor-mal stress.

Both hypotheses appear tenable, and evidence is notavailable to favor one over the other. Nonetheless, forpractical purposes it is clear that determinations of val-ues of residual strength to be used for analysis of spe-cific problems should be made under stress conditionsapproximating those in the field.

Other important considerations include the structuralfeatures and lithological details in the field. Examplesof the former are presheared surfaces generated byold landslides and tectonic and glacial deformation,whereas those for the latter are horizontal beddingplanes, laminations, and weak seams (Mesri and Shah-ien, 2003). They all can contribute in dropping to theresidual condition after relatively small displacements.

11.12 INTERMEDIATE STRESS EFFECTS ANDANISOTROPY

The friction angles shown in Fig. 11.51 and Fig. 11.52are for triaxial compression. Kulhawy and Mayne

(1990) show from their database of past studies thatthe friction angle deduced from triaxial extension testsis 10 to 20 percent larger than that from triaxial com-pression tests. Similar differences have been observedbetween plane strain friction angle and triaxial com-pression friction angle for both sands and clays. Thepeak friction angles of sands determined from planestrain tests are 0.5� to 4� larger than those from triaxialcompression tests (Cornforth, 1964). The Mohr–Coulomb friction angle is based only on the major andminor principal stresses [i.e., Eq. (11.5)]. Under tri-axial compression conditions, the intermediate prin-cipal stress, �2, equals the minor principal stress,whereas under plane strain loading it is greater. Thehigher confinement under plane strain loading can ac-count for the higher measured friction angle.

The stress states at failure in the field differ fromtriaxial compression/extension and plane strain con-ditions. The effect of intermediate principal stress canbe expressed by a b value, defined by

�� 2 3b � (11.48)�� 1 3

where are maximum, intermediate, and��, ��, and ��1 2 3

minor principal stresses, respectively; b � 0 for triaxialcompression conditions ( ), whereas b �� 1 2 3

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INTERMEDIATE STRESS EFFECTS AND ANISOTROPY 423

Figure 11.78 Effect of intermediate principal stress on fric-tion angle (from Kulhawy and Mayne, 1990). Reprinted withpermission from EPRI.

Figure 11.79 Comparative values of effective stress frictionangle of normally consolidated clays in triaxial compressionand plane strain compression (from Kulhawy and Mayne,1990). Reprinted with permission from EPRI.

1 for triaxial extension conditions ( ). The�� 1 2 3

value of b for plane strain conditions depends on ma-terial properties but is approximately 0.3 to 0.4.

Sands

The intermediate stress effect can be measured usingtrue triaxial apparatus or hollow cylinder torsionalshear apparatus. The influence of intermediate princi-pal stress ( ) on measured friction angle of sands is��2illustrated by Fig. 11.78. In general, the peak frictionangle increases 10 to 15 percent from b � 0 (triaxialcompression) to b � 0.3 to 0.4 (plane strain), and itstays constant or slightly decreases as b reaches 1 (tri-axial extension).

The variation of measured friction angle withchanges in intermediate principal stress can be attrib-uted to the effects of different mean stress and stressanisotropy on the dilatancy and particle rearrangementcontributions to the total strength. For given maximumand minimum principal stresses, the triaxial extensionconditions have the largest mean effective stress,whereas the triaxial compression conditions have thesmallest mean effective stress. The higher confinementfor triaxial extension and plane strain conditions con-tributes to the increasing friction angle for these con-ditions.

Fabric anisotropy also contributes to differences be-tween triaxial and plane strain strengths. Discrete par-ticle simulations by Thornton (2000) show that theaverage ratio of sliding contacts to the coordinationnumber at failure were both independent of b. How-ever, a larger degree of fabric anisotropy was observed

in triaxial extension than in triaxial compression, asobserved in Fig. 11.38b. Greater shear resistance is ex-pected for conditions that give a larger degree of fabricanisotropy.

Clays

Effective stress friction angles for normally consoli-dated clays measured in plane strain compression arecompared with those determined in triaxial compres-sion in Fig. 11.79. The added confinement in planestrain yields a friction angle that is about 10 percenthigher than measured in triaxial compression. Themeasured friction angle in triaxial extension is about20 percent greater than in triaxial compression, asshown in Fig. 11.80. These results are consistent withthe data presented in Fig. 11.78 for sands.

The undrained shear strength su in triaxial compres-sion is approximately twice as large as that of triaxialextension for normally consolidated clay as shown inFig. 11.67. This large variation is primarily due to thedifference in the excess pore pressures generated andis very much related to the initial bedding structure, asdiscussed later.

Failure Envelopes

Various models fit the experimental data showing theintermediate stress effect. Among them are

I I1 2 � const. (Matsuoka and Nakai, 1985)I3

(11.49)

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Figure 11.80 Comparative values of effective stress frictionangle of normally consolidated clays in triaxial extension andtriaxial compression (from Kulhawy and Mayne, 1990). Re-printed with permission from EPRI.

0

10

20

30

40

50

60

0

TriaxialCompression

TriaxialExtension

Lade and Duncan (1975)

Triaxial compression 40°



Plane Strain

Matsuoka and Nakai (1985)

b-Value

Fric

tion

Ang

le

0.2 0.4 0.6 0.8 1

Figure 11.81 Failure criterion models that include the inter-mediate stress effect.

3I1 � const. (Lade and Duncan, 1975) (11.50)I3

where I1, I2, and I3 are the first, second and third stressinvariants.18 The models are plotted in Fig. 11.81. Mat-suoka and Nakai’s model gives the same friction anglefor compression and extension, whereas Lade andDuncan’s model gives the ratio of the triaxial extensionfriction angle ( ) to the triaxial compression friction��TE

angle ( ) to be 1.08 at � 20� to 1.15 at �� TC TC TC

40�. Given the large scatter in the published experi-mental data (see Fig. 11.78), it is not possible to con-clude that one model is better than the other.

Fabric Anisotropy

The soil fabric created during depositional and post-depositional processes contributes to mechanical ani-sotropy. For example, nonspherical particles tend to

18 The three stress invariants are defined as

I1 � � � I2 � � � I3 �� 1 2 3 1 2 2 3 3 1 1 2 3

where , and are the principal stresses.��, �� 1 2 3

deposit with their long axis in the direction perpendic-ular to gravity, and, therefore, the assembly will beinherently stiffer in the depositional (vertical) directionthan in the horizontal direction. This is inherent orfabric anisotropy. The effect of inherent anisotropyon strength is controlled by how rapidly the fabricchanges during shearing (called induced anisotropy). Ifthe fabric created by deformation-induced anisotropydestroys the inherent anisotropy, the strength will notbe affected by the inherent anisotropy (even though thedeformations prior to failure will be affected). Detailsof the effects of fabric on mechanical property aniso-tropy were given in Section 8.9.

Positive loading in triaxial compression tests is usu-ally in the direction perpendicular to the bedding plane,whereas that in triaxial extension tests tends to be ra-dially inward in the bedding plane direction. Figure11.82 shows the undrained shearing responses of Toy-oura sand specimens in triaxial compression and ex-tension tests (Yoshimine et al., 1998). The specimenssheared in extension showed 100 percent excess porepressure development leading to static liquefaction,whereas the specimens sheared in compression showedsmall softening at the beginning but then hardening atlarge strains due to large dilative behavior. Similar var-iations in undrained shear strength of clays were shownin Fig. 11.67. From these data, it is not clear whetherthe difference is due to the intermediate stress (b value)effect or to the initial anisotropic fabric generated dur-ing dry pluviation.

Figure 11.83 shows different cases of variation in bvalue and the major principal stress direction in rela-tion to initial cross-anisotropic soil fabric. A direc-

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RESISTANCE TO CYCLIC LOADING AND LIQUEFACTION 425

Figure 11.82 Undrained response of dry plluviated Toyourasand specimens in triaxial compression and extension: (a)stress–strain relationships and (b) undrained stress paths (af-ter Yoshimine et al., 1998).

tional parameter � is defined as the angle between thedirection perpendicular to the bedding plane and themajor principal stress direction. The conventional tri-axial compression will be case A (b � 0 and � � 0�)in Fig. 11.83, whereas the triaxial extension will becase B (b � 1 and � � 90�) in Fig. 11.83. Ideally,therefore, the investigation of b-value effects onstrength should be performed with the same � valueor vice versa (e.g., cases A, C, and D or cases C, E,and F in Fig. 11.83).

Using a hollow cylinder torsional shear apparatus,Yoshimine et al. (1998) examined the effects of b valueand the loading direction � separately on undrainedbehavior of Toyoura sand, and some test results areshown in Fig. 11.84. For sands with relative densitybetween 30 and 41 percent, the effect of inherent an-isotropy appears to be more significant than the effectof b. When the loading direction was in parallel to the

bedding plane, more sand particles had to move to pro-vide more stable soil fabric, and a larger magnitude ofexcess pore pressure was therefore developed. Exam-ination of Figs. 11.82 and 11.84 indicates that conven-tional triaxial compression can give higher undrainedshear strength with less softening compared to othershear modes. Similar data were presented by Kirkgardand Lade (1993) for normally consolidated San Fran-cisco Bay mud. These findings have practical signifi-cance since the use of triaxial compression data mayresult in unconservative evaluation of flow liquefactionpotential or undrained shear strength.

11.13 RESISTANCE TO CYCLIC LOADING ANDLIQUEFACTION

Repeated or cyclic loading of soils can be caused bya number of natural phenomena or human activities,including earthquakes, wind, waves, vehicular traffic,and reciprocating machinery. Cyclic loads causestresses and deformations in much the same manner asdo slowly applied loads; however, their relatively shortduration and repetitive and dynamic nature are respon-sible for several unique aspects of soil behavior. At-tention is given in this section primarily to saturatedcohesionless soils and clays because these materialsare particularly susceptible to strength degradationand/or failure during earthquakes. Soils of the typeencountered as pavement subgrades or as used in pave-ment subbases and bases are usually relatively denseand not susceptible to large strength and stiffnesslosses if properly prepared and compacted.

Drained Behavior

Repeated cyclic shear straining of sand under drainedconditions is shown in Figs. 11.85a and 11.85b forloose and dense Toyoura sand specimens, respectively.The cyclic loading usually causes densification. Fig-ures 11.85(a-2) and 11.85(b-2) show development ofvolumetric strain with increasing number of loadingcycles. For the loose sand specimen (Fig. 11.85a), thevolumetric strain increases more or less monotonically.Although there is a decreasing trend of void ratio withincreasing number of cycles, it is also interesting tonote that, for a given cyclic shear application on thedense sand specimen, the volumetric strain does notincrease monotonically but fluctuates with cyclic load-ing, as illustrated in Fig. 11.85(b-2). Shear-induced di-lation is observed as the applied shear displacementreaches its maximum in the loading stage. During un-loading, there is shear-induced volume contraction.The combination of dilation during loading and con-traction during unloading leads to overall contraction.

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σh2

b - Value0 1

Loading Directionof Major PrincipalStress in Relationto the BeddingPlane

σh1σ

σh1σh2

v

α

α = 0°

TriaxialCompression

TriaxialExtension

Parallel to theBedding Plane

Perpendicular tothe Bedding Plane

A

B

v

σh2

1

σ 2

σ

σv σv

C D

F

α

α

α = 90°

σvv= σh1 > σh2σvv> σh1 = σh2 σvv> σh1 > σh2

σ1v> σ2 > σ3

σh1v> σh2 > σv σh1v= σh2 > σv

σv σvσv

σh1 σh1

σh2σh2

σh1σh1

σ1

σ3σ2E

Figure 11.83 Effects of inherent anisotropy and the intermediate stress.

The influences of shear strain magnitude and num-ber of load cycles are shown in Fig. 11.86. The den-sification results from the disruption of the initial soilfabric caused by the repeated shear strains followed byrepositioning of the soil grains into more efficientpacking. The higher the initial void ratio and thegreater the number of cycles, the greater the effect.

Undrained Behavior

When saturated soil is subjected to repeated cycles ofloading, and provided the shear stresses are of suffi-cient magnitude, the structure begins to break down,and part of the confining stress is transferred to thepore water, with a concurrent reduction of effectivestress and strength. This, in turn, leads to increase inshear strain under constant stress cyclic loading or adecrease in the cyclic stress required to cause a givenvalue of cyclic strain. The deformation and failure be-havior of sands in undrained cyclic loading depends oninitial void ratio, initial effective stress state, and thecyclic shear stress amplitude.

The results of an undrained cyclic simple shear teston Monterey sand are shown in Fig. 11.87. Develop-

ment of shear strains with cyclic loading is called cy-clic mobility. Liquefaction is said to have occurredwhen the pore water pressure has increased to the mag-nitude of the initial effective confining pressure, atwhich point the strains become very large. Similar tothe undrained response in monotonic loading, the un-drained response of sand under cyclic loading dependson density, confining pressure, and soil fabric. The ef-fect of density on cyclic behavior of Toyoura sand un-der triaxial loading conditions is shown in Fig. 11.88.All sands exhibit increase in pore pressure with in-crease in number of loading cycles, but the shear straindevelopment for a given number of cycle is smaller fordenser specimens. In the loose sand (Fig. 11.88a),when the stress state reaches the collapse surface, thesoil softens leading to sudden liquefaction. The me-dium dense sand (Fig. 11.88b) exhibits quasi-steadystate as the stress state reaches the phase transforma-tion line. Some cycles with large stress–strain loopsare observed and the specimen finally reaches lique-faction. The dense sand (Fig. 11.88c) never liquefies.Once the stress state reaches the phase transformationline, the stress–strain curve moves back and forth

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Figure 11.84 Effect of � and b values on undrained response of dry plluviated Toyourasand: (a) effect of � when b � 0.5 and (b) effect of b when � � 45� (after Yoshimine etal., 1998).

along and below the steady-state line and shear straindevelops gradually.

Beneath gently sloping to flat ground, liquefactionmay lead to ground oscillation or lateral spread as aconsequence of either flow deformation or cyclic mo-bility (Youd et al., 2001). The liquefaction suscepti-bility of different types of natural and artificialsedimentary soil deposits is summarized in Table 11.5.As the excess pore pressure developed during lique-faction dissipates, ground settlement is observed. Sandboils can develop through overlying less permeablesoils in order to dissipate the excess pore pressuresfrom liquefied soil below.

The magnitude of the cyclic shear strains that de-velop following initial liquefaction decreases with in-creasing initial relative density and increases withincreasing cyclic shear stress. The general relationship

between cyclic shear stress and number of load cyclesto initial liquefaction depends on the relative density,and is of the form shown in Fig. 11.89. In this figurethe cyclic shear stress � applied by a simple shear ap-paratus is normalized by dividing by the initial effec-tive confining pressure , and the ratio is often called��0the cyclic resistance ratio (CRR). Methods for deter-mination of the liquefaction susceptibility of a specificsite are given by Kramer (1996) and by Youd et al.(2001).

In reality, generation of pore pressure is a result ofthe breakdown of soil structure and a tendency for thesoil to densify, and this is caused by shear deforma-tions, so liquefaction is more fundamentally controlledby shear strain than by shear stress. Furthermore, thereis a level of shear strain, or threshold shear strain be-low which no pore pressure is generated. This is illus-

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(a-1) Stress Ratio – Shear Strain Relation

(a-2) Volumetric Strain – Shear Strain Relation

Stress Ratio q/p�

2

_1.2

2_2Shear Strain γ (%)

Toyoura SandAir PluviatedInitial Void Ratio = 0.845p� = 98 kPa = constant

Stress Ratio q/p�

2

_1.2


Toyoura SandAir PluviatedInitial Void Ratio = 0.653p� = 98 kPa = constant


0

3

Volumetric Strain εv

(b-1) Stress Ratio – Shear Strain Relation

(b-2) Volumetric Strain – Shear Strain Relation

2_2

Shear Strain γ (%)

0

0.6

_0.6

Volumetric Strain εv

(a) (b)

Figure 11.85 Cyclic behavior of Toyoura sand in drained conditions: (a) loose sand and (b)dense sand (after Pradhan and Tatsuoka, 1989).

Figure 11.86 Effect of shear strain and number of load cy-cles on the reduction in void ratio of Ottawa sand (fromYoud, 1972). Reprinted with permission of ASCE.

trated by Fig. 11.90 in which the pore pressure ratioas a function of cyclic shear strain is shown for Mon-terey No. 0 sand at three relative densities.

The mechanics of pore pressure generation duringcyclic loading can be understood by reference to Fig.11.91 from Seed and Idriss (1982) and by Fig. 8.20.In Fig. 11.91, point A represents a soil specimen in itsinitial state. Under cyclic loading it would, if allowedto drain and compress, decrease in void ratio to pointB in order to be able to continue to sustain effectivepressure . However, since the soil cannot drain, the��0collapsing soil structure generates a pore pressure de-noted in Fig. 11.91 by u. The magnitude of the porepressure depends on the slope of the rebound curve B–C, as discussed below.

From laboratory cyclic simple shear tests on severalsands, the general relationship between pore pressureratio (i.e., the generated pore pressure divided by theinitial effective confining pressure) and the cycle ratioas shown in Fig. 11.92 has been determined. The cycleratio is defined by the number of load cycles Ne dividedby the number of load cycles to cause liquefaction Nl.

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Figure 11.87 Results of an undrained cyclic simple sheartest on loose Monterey sand (Seed and Idriss, 1982): (a) porewater pressure response, (b) shear strain response, and (c)applied cyclic shear stress.

Using the slope of the rebound curve (Fig. 11.91) andthe densification that would occur if drainage was per-mitted, it is possible to compute the induced pore pres-sure by

u � E � (11.51)r rd

where is the rebound modulus and �rd is the vol-Er

umetric strain that would occur if drainage were per-mitted. Martin et al. (1975) give procedures to evaluatethese two parameters from the results of static reboundtests in a consolidation ring and cyclic load tests ondry sand, respectively. Finn (1981) reported goodagreement between predicted and measured values us-ing the proposed method.

The liquefaction resistance depends not only on cy-clic stress amplitude and density but also on the initialeffective stress state. For example, Fig. 11.89 is deter-

mined from testing at different densities under thesame confining stress condition, whereas the constantdensity contour lines move downward if the confiningpressure increases, as illustrated in Fig. 11.93 for Aiosand samples prepared at the same relative density.This is because a soil at a given void ratio behaves asif relatively looser or more compressible at higher con-fining pressure. There are many other factors that im-pact the actual value of CRR to use in practice; themajor ones are the confining pressure, the initial shearstresses under static condition, sample preparationmethods, and the mode of shearing (Seed, 1979; Seedand Harder, 1990). Additional information and datacan be found in Youd et al. (2001), Vaid et al. (2001),Boulanger (2003), and Hosono and Yoshimine (2004).

Residual Strength after Liquefaction

The residual strength of sands, silty sands, and siltsfollowing liquefaction is a subject of continuing studyowing to its importance in the analysis of postearth-quake stability and deformation of embankments,dams, and structures. Detailed discussion of this topicis outside the scope of this book; however, two ap-proaches have been used to estimate the residualstrength, one based on steady state strength determinedby laboratory tests as described in Section 11.8 and theother on the Standard Penetration Test (SPT) N value(Seed, 1987; Seed and Harder, 1990). A correlationbetween the residual strength and the preearthquakeSPT N value is shown in Fig. 11.94. The strength val-ues shown in this figure were determined by back anal-ysis of liquefaction-induced slides; thus, they avoidproblems related to sampling disturbance effects onstrength and are representative of known field behavior.However, there is some uncertainty relating to howwell the measured N values are representative of thezone in which the failure developed. The selection ofa particular value within the range of strengths shownfor any given N value, and variability in the N valuesthat are measured, add additional uncertainty.

Excess pore pressures can be generated either in-ternally as described above or externally by transientseepage flow from an adjacent liquefied region. Forexample, if there is a less permeable layer above a sandlayer, excess pore pressures can develop under theimpermeable layer leading to softening of the soil.Hence, local heterogeneity plays an important role inliquefaction-induced soil deformation and failure,which requires careful site investigation to identify anylow permeable layers.

The strength degradation of clays due to cyclic load-ing follows similar patterns to that of sand, but it ismuch less for clays than for cohesionless and slightly

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30

40

50

-15 -10 -5 0 5 10 15

Reaching Collapse Surfaceafter Several Cycles

Initial StateLiquefactionReaching CollapseSurface after SeveralCycles

Liquefaction Failure

Dr = 30%Initial p� = 200 kPaCyclic Stress Δq = 40 kPa

Initial Cyclic LoopsBefore Failure

Initial State

Reaching Collapse Surfaceafter Several Cycles


Reaching CollapseSurface afterSeveral Cycles

Phase Transformation Phase Transformation

Liquefaction



Initial State


IncreasingCycles

IncreasingCycles



Dev

iato

r S

tres

s q

(MP

a)

Dev

iato

r S

tres

s q

(MP

a)

Dev

iato

r S

tres

s q

(MP

a)

Dev

iato

r S

tres

s q

(MP

a)

Dev

iato

r S

tres

s q

(MP

a)

Dev

iato

r S

tres

s q

(MP

a)

Axial Strain (%)

Axial Strain (%)

Axial Strain (%)




(a)

(b)

(c)

Figure 11.88 Cyclic behavior of Toyoura sand in undrained conditions: (a) loose sand, (b)medium dense sand, and (c) dense sand (after Yamamoto, 1998).

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Table 11.5 Liquefaction Susceptibility of Soil Deposits

Type of Deposit(1)

General Distribution ofCohesionless

Sediments in Deposits(2)

Likelihood That Cohesionless Sediments, When Saturated,Would Be Susceptible to Liquefaction (by Age of Deposit)

�500 yr(3)

Holocene(4)

Pleistocene(5)

Prepleistocene(6)

a. Continental DepositsRiver channel Locally variable Very High High Low Very lowFloodplain Locally variable High Moderate Low Very lowAlluvial fan and plain Widespread Moderate Low Low Very lowMarine terraces and

plainsWidespread — Low Very low Very low

Delta and fan-delta Widespread High Moderate Low Very lowLacustrine and playa Variable High Moderate Low Very lowColluvium Variable High Moderate Low Very lowTalus Widespread Low Low Very low Very lowDunes Widespread High Moderate Low Very lowLoess Variable High High High UnknownGlacial till Variable Low Low Very low Very lowTuff Rare Low Low Very low Very lowTephra Widespread High High ? ?Residual soils Rare Low Low Very low Very lowSabka Locally variable High Moderate Low Very low

b. Coastal Zone

Delta Widespread Very high High Low Very lowEsturine Locally variable High Moderate Low Very lowBeach high wave energy Widespread Moderate Low Very low Very lowLow wave energy Widespread High Moderate Low Very lowLagoonal Locally variable High Moderate Low Very lowFore shore Locally variable High Moderate Low Very low

c. Artificial

Uncompacted fill Variable Very high — — —Compacted fill Variable Low — — —

(From Youd and Perkins (1978); reprinted from the Journal of Geotechnical Engineering, ASCE, Vol. 104, No. 4,pp. 433–446. Copyright � 1978. With permission of ASCE.

cohesive soils that are susceptible to liquefaction asshown in Fig. 11.95 (Hyodo et al., 1994). An assump-tion of a strength loss of about 20 percent is sometimesused in practice. Figure 11.96 shows the undrained cy-clic shear stress ratio �cy /su that brings normally con-solidated clays to failure after 10 loading cycles(Andersen, 2004). The data include eight clays withdifferent plasticity indices. In the direct shear tests(Fig. 11.96a), the undrained cyclic shear stress ratio atfailure decreases with increase in initial static shearstress �a /su and increases with plasticity index. In the

triaxial tests (Fig. 11.96b), the initial static shear isdefined as �a /su � ( , where and�� ) /2s �� ac rc u ac rc

are the axial and radial consolidation stresses, respec-tively. The values of �cy /su � ( ) /2su show�� a r

peaks at �a /su � 0.2 to 0.3, indicating that the smallinitial anisotropy gave increased cyclic resistance.However, the undrained cyclic shear stress ratio at fail-ure decreases when the initial static shear stress ishigher or in triaxial extension conditions. Evidently innormal clays the magnitude of cyclic shear strain isless than that required to cause complete remolding.

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Figure 11.89 Cyclic stress ratio and number of load cycles to cause initial liquefaction ofa sand at different initial relative densities (from De Alba et al., 1976). Reprinted withpermission of ASCE.

Figure 11.90 Pore pressure as a function of cyclic shearstrain illustrating a threshold strain of about 0.01 percent,below which no excess pore pressures are developed (fromDobry et al., 1981). Reprinted with permission of ASCE.

Figure 11.91 Mechanism of pore pressure generation duringcyclic loading (Seed and Idriss, 1982).

Complete remolding would define an absolute lowerbound, and its value is defined by the clay sensitivity.Cyclic stresses could cause sufficient deformations inquick clay to initiate a liquefaction-type flow failure.Some examples are given in Andersen et al. (1988).

11.14 STRENGTH OF MIXED SOILS

The presence of fines in sands can significantly influ-ence the strength behavior. Differing effects can be ob-tained depending on particle size, shapes, and sample

preparation methods. Figure 11.97 shows different sce-narios of intergranular matrix of two different size par-ticles (Thevanayangam and Martin, 2002). Initially themaximum and minimum void ratios of a sand–silt mix-ture decrease with increase in silt content, but then the

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STRENGTH OF MIXED SOILS 433

Figure 11.92 Rate of pore pressure buildup in cyclic simpleshear tests (from Seed et al., 1976). Reprinted with permis-sion of ASCE.

Figure 11.93 Effect of confining pressure on cyclic resis-tance ratio (Hyodo et al., 2002).

Figure 11.95 Comparison of the cyclic resistance ratios ofItukaichi clay and Toyoura sand (Hyodo et al., 1994).

Figure 11.94 Postliquefaction residual strength as a functionof Standard Penetration Test N values (Seed and Harder,1990).

North Sea GC, PI=16-27%

Drammen, PI=27%

Troll II, PI=20%

Troll I, PI=37%

Marlin IIa, PI=50%

Offshore Africa, PI=80 -100%

1.00.80.60.40.20.00.0

0.2

0.4

0.6

0.8

1.0

1.2C

yclic

She

ar S

tren

gth

/ Sta

tic U

ndra

ined

She

ar S

tren

gth

( τcy

/su

DS

S)

OCR = 1

Initial Shear Stress / Static Undrained Shear Strength

1.00.80.60.0-0.60.0

0.2

0.4

0.6

0.8

1.0

Initial Shear Stress / Static Undrained Shear Strength-0.4 -0.2 0.40.2

Offshore Africa, PI=80-100%

Marlin IIa, PI=50%

Marlin IIb+, PI=45%Troll II, PI=20%

Troll I, PI=37%

Drammen, PI=27%

Triaxial Tests - Strength at 10 CyclesOCR = 1

(τa / suDSS)

(τa / su)

Cyc

lic S

hear

Str

engt

h /

Sta

tic U

ndra

ined

She

ar S

tren

gth

(τcy

/su)

Direct Simple Shear Tests - Strength at 10 Cycles

Marlin IIb+, PI=45%

Storebælt, PI=7-12%

Storebælt, PI=7-10%

Figure 11.96 Normalized shear stresses that give undrainedfailure after 10 cycles in (a) direct shear tests and (b) triaxialtests (Andersen, 2004).

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Figure 11.97 Granular mix classification (Thevanayangam and Martin, 2002).

void ratios increase when the silt becomes the host soilas shown in Fig. 4.4. In case (i), the fine particles fitin the void space formed by the coarse particles. Themechanical behavior is little affected by the presenceof fines because the external forces are transferredthrough the contacts between coarse particles. In cases(ii) and (iii), the fine particles start to fully occupysome void space and separate the coarse particles andprevent them from touching each other. These fine par-ticles may reinforce the skeleton of coarse particles orthey may make the skeleton unstable. As the propor-tion of fine particles increases, the coarse particles floatinside the matrix of fine particles as illustrated as case(iv). The fine grains then dominate the mechanical be-havior of the mixed soils, and the coarse grains mayor may not contribute to shear resistance as a reinforc-ing element. Once the mixing scenario reaches case(iv), the void ratio increases with increasing fines con-tent due to increasing specific surface of the mixture.The threshold value to become case (iv) depends onthe specific mixture but is usually in the range of 25to 45 percent fines in most cases (Polito and Martin,2001).

For cases (i) to (iii), the granular void ratio eG de-fined in Chapter 4 is a useful index for considerationof the effect of fines. If two mixed soils with different

fines content have the same granular void ratio and thesame mechanical properties, the fines are just occu-pying the void space and are not influencing shear re-sistance.

Most reported cases show that, for a given granularvoid ratio, the undrained strength and cyclic shear re-sistance are either independent of or increase with siltcontent (Shen et al., 1977; Vaid, 1994; Polito andMartin, 2001; Carraro et al., 2003). The undrainedresponse of sand mixed with equidimensional siltparticles is shown in Fig. 11.98 (Kuerbis et al., 1988).Specimens of the mixture were created by slurry dep-osition, and the density was controlled in such a waythat all specimens had relatively similar granular voidratios eG, even though the actual void ratio decreasedwith increasing silt content. Both undrained triaxialcompression and extension tests were performed fol-lowing isotropic consolidation. Increased silt contentgave stiffer response in triaxial compression. Appar-ently, the silts filled the void space and stabilized thesoil as shown in Fig. 11.99a. However, the effect wassmall in triaxial extension.

Liquefaction resistance increases with relative den-sity as shown in Fig. 11.89. However, increasing siltcontent gives scattered relationships between relativedensity and the CRR at 20 loading cycles, as shown in

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STRENGTH OF MIXED SOILS 435

–100

100

200

200100 300 400

(σ�a + ��r)/2 (kPa)

(σ� a

–�

� r)/

2 (k

Pa)

0

0.7640.7280.6690.5470.448

0.7640.8020.8050.7840.863

Silt Content%

e eG

04

7.513.322.3

Figure 11.98 Undrained triaxial compression and extensiontests on silty sand with different mixing ratios (Kuerbis etal., 1988).

(b)(a)

(d)(c)

Figure 11.99 Schematic diagrams of how fine particles areplaced inside coarse-grain matrix: (a) sand–silt mixture withsilt filling the void, (b) sand–silt mixture with silts betweensands and granular void ratio larger than emax, (c) sand–claymixture, and (d ) sand–mica mixture.

1.00.80.60.40.20.0Relative Density

0.0

0.2

0.4

0.6

0.80% fines5% fines10% fines15% fines

(a)

0.30.40.50.60.70.8Void Ratio

0.0

0.2

0.4

0.6


(b)

0.40.50.60.70.8Granular Void Ratio

0.0

0.2

0.4

0.6


(c )

Cyc

lic R

esis

tanc

e R

atio

Cyc

lic R

esis

tanc

e R

atio

Cyc

lic R

esis

tanc

e R

atio

Figure 11.100 Cyclic resistance ratios of silty sands plottedagainst (a) relative density, (b) void ratio, and (c) granularvoid ratio (from Carraro et al., 2003).

Fig. 11.100a due to variations in maximum and mini-mum void ratios with increasing silt content. If theCRR values are plotted in terms of void ratio and cy-clic resistance as shown in Fig. 11.100b, the liquefac-tion resistance at a given void ratio decreases with

increasing silt content. If the CRR values are plottedas a function of the granular void ratio eG, as shownin Fig. 11.100c, the sand–silt mixtures give higher liq-uefaction resistance than clean sand, but the resistanceof these mixtures was independent of silt content.

The above results are applicable when the granularvoid ratio eG is smaller than the maximum void ratioemax of the host medium (without fines). When finesare added, it is possible to create specimens that haveeG larger than emax even though the overall void ratiois smaller than emax (Lade and Yamamuro, 1997; Thev-anayagam and Mohan, 2000). This condition can be

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Triaxial Compression Tests

Clay Content = 0%, eG = 0.77

Clay Content = 4.6%, eG = 0.80


Triaxial Extension Tests

Clay Content = 0%, eG = 0.77



0.50.40.30.20.1

-0.1

0.0

0.1

0.2

0.3

Initial StressState

(σ’a+ σ’r)/2

(σ’ a+

σ’r)

/2

(MPa)

(MPa)

Figure 11.101 Undrained triaxial compression and exten-sion test stress paths of clay–sand mixtures with differentmixing ratios but at similar granular void ratios (Georgiannouet al., 1991).

Figure 11.102 Effect of fines (mica, silt, and kaolin) on voidratio of a sand (Hight et al. 1998).

achieved if some fines are placed between the coarserparticles as shown in Fig. 11.99b. In this case, thestructure is metastable, and the strength of the mixedsoil is reduced due to fewer sand grain contacts.

When smaller particles such as clays are added in-stead of silt-size particles, the clay fines act as a lu-bricator at sand particle contacts as shown in Fig.11.99c and make the soil unstable. Undrained re-sponses of Ham river sand mixed with different kaolincontents are shown in Fig. 11.101 (Georgiannou et al.,1991). Samples were prepared by pluviating the sandinto distilled water with suspended kaolin particles sothat similar granular void ratios were achieved. Bothundrained triaxial compression and triaxial extensiontests were performed after consolidating the samplesunder K0 stress conditions. In triaxial compression, theincrease in clay content did not affect the peak stress,but the strain-softening behavior was more pro-nounced. After the specimen passed the phase trans-formation line, the stress increased toward the criticalstate. In triaxial extension, addition of clay led to totalliquefaction. The friction angle did not change for clayfractions up to 20 percent. This delayed the develop-ment of anisotropic fabric needed to resist the increas-ing load.

The shape of fine particles also influences the sta-bility of the mixed soil. Hight et al. (1998) report thebehavior of micaceous sands in connection with flowslides that occurred during construction of the JamunaBridge in Bangladesh. The large and platy mica flakes

bridged between the host sand particles (Fig. 11.99d),and increased the overall void ratio as shown in Fig.11.102. On the other hand, inclusion of smaller silt andclay particles decreased the overall void ratio, as alsoshown in Fig. 4.4. The open fabric of a sand–micamixture can give complicated soil deformation andstrength properties depending on mica particle orien-tation and shear mode (Hight et al., 1998).

Further increase in fines content leads to sand par-ticles floating in clay or silt as shown by case (iv) inFig. 11.97. The mixed soil then behaves more like pureclay or silt. The deformation behavior then becomesmore clay/silt dominated, and the coarser particlesmay or may not contribute to the strength properties.For example, Fig. 11.103 shows that the liquefactionresistance of mixtures with fines content greater than35 percent was independent of silt content and granularvoid ratio (Polito and Martin, 2001).

11.15 COHESION

True cohesion is shear strength in excess of that gen-erated by frictional resistance to sliding between par-ticles, the rearrangement of particles, and particlecrushing. That is, true cohesion must result from ad-herence between particles in the absence of any exter-nally applied or self-weight forces. The existence oftensile or shear strength in the absence of effectivecompressive stress in the soil skeleton or on the failureplane might be considered true cohesion. However, theparticulate nature of soil and the fact that most inter-particle contacts are not oriented in the plane of shearmean that the application of directional shear stresswill induce normal forces at most interparticle con-tacts. These forces will, in turn, generate a resistance

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COHESION 437

��

�

�

�

�

�

�

�

�

�

× ×

×

×

×

MontereySand with 35%SiltMontereySand with 50%SiltMontereySand with 75%Silt

YatesvilleSand with 50%SiltYatesvilleSand with 75%Silt100% Silt

0.800.00

0.05

0.10

0.15

0.20

0.25

0.30

1.00 1.40 1.60 1.80 2.00 2.201.20

Granular Void Ratio eG

Cyc

lic R

esis

tanc

e R

atio

CR

R

Figure 11.103 Variation of cyclic resistance ratio with granular void ratio with silt contentabove the threshold value (Polito and Martin, 2001).

to sliding at the contact provided the value of �� isgreater than zero.

Confirmation of the existence of a true cohesion anddetermination of its value from strength tests is diffi-cult because projection of the failure envelope back to�� 0 is uncertain, owing to the curvature of mostfailure envelopes, unless tests are done at very loweffective stresses. Tensile tests cannot be made on mostsoils. Harison et al. (1994) performed various types oftensile tests on compacted clay specimens but foundthat the tensile strengths decreased with increase inspecimen size due to increase in the number of internalflaws. There is no convenient way to run a triaxialcompression test while maintaining the effective stressequal to zero on the potential failure plane. Strengthcan be measured by direct shear with no applied nor-mal stress �. Some examples are given in Bishop andGarga (1969), Graham and Au (1985), and Morris etal. (1992); however, for the reason given in the previ-ous paragraph, the measured strength cannot be attrib-uted specifically to true cohesion.

Possible Sources of True Cohesion

Three possible sources for true cohesion between soilparticles have been proposed:

1. Cementation Chemical bonding between par-ticles by cementation by carbonates, silica,alumina, iron oxide, and organic compounds ispossible. Cementing materials may be derivedfrom the soil minerals themselves as a result of

solution–redeposition processes, or they may betaken from solution. An analysis of the strengthof cemented bonds was given by Ingles (1962)and is summarized in Section 7.4 and Eqs. (7.2)to (7.8). Cohesive strengths of as much as severalhundred kilopascals (several tens of pounds persquare inch) may result from cementation.Stress–strain curves and peak failure envelopesfor cemented sands are shown in Fig. 11.104.These curves show that even relatively smallamounts of cement can have very large effects onthe deformation properties. Small values of co-hesion have a large effect on the stability of asoil and its ability to stand unsupported on steepslopes. However, at large strains when the ce-mentation breaks down, the strengths becomesimilar irrespective of the degree of cementationas shown in Fig. 11.104a.

2. Electrostatic and Electromagnetic AttractionsElectrostatic and electromagnetic attractions be-tween small particles are discussed in Sections6.12 and 7.4. Electrostatic attractions becomesignificant (� 7 kPa or 1 psi) for separation dis-tances �2.5 mm. Electromagnetic attractions orvan der Waals forces are a source of tensilestrength only between closely spaced particles ofvery small size (�1 �m).

3. Primary Valence Bonding and AdhesionWhen normally consolidated clay is unloaded,thus becoming overconsolidated, the strengthdoes not decrease in proportion to the effective

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Figure 11.104 Stress–strain curves and failure envelopes for cemented and uncemented sandat a relative density of 74 percent: (a) stress–strain curves and (b) failure envelopes basedon peak strength (from Clough et al., 1981). Reprinted with permission of ASCE.

stress reduction, but a part is retained as shownin Fig. 11.3. Whether or not the higher strengthin the overconsolidated clay is because of thelower void ratio or due to the formation of inter-particle bonds is not known. However, a ‘‘coldwelding’’ or adhesion may be responsible forsome of it. This could result from the formationof primary valence bonds at interparticle con-tacts.

Apparent Cohesion

An apparent cohesion can be generated by capillarystresses. Water attraction to particle surfaces combinedwith surface tension causes an apparent attraction be-tween particles in a partly saturated soil. Equation (7.9)can be used to estimate the magnitude of tensilestrength that can be developed by capillary stresses ina soil. This is not a true cohesion; instead, it is a fric-tional strength generated by the positive effective stresscreated by the negative pore water pressure.

Summary

Several contributions to cohesion are summarized inFig. 11.105 in terms of the potential tensile strengthsthat can be generated by each mechanism as a functionof particle size. For all the mechanisms except chem-ical cementation, cohesion is a consequence of normal

stresses between particles generated by internal attrac-tive forces. The mechanism of shear resistance result-ing from these attractions should be the same as if thecontact normal stresses were derived from effectivecompression stresses carried by the soil. It is conven-ient, therefore, to think of cohesion (except for cemen-tation) as due to interparticle friction derived frominterparticle attractions, whereas the friction term inthe Mohr–Coulomb equation is developed by interpar-ticle friction caused by applied stresses. Essentially thesame concept was suggested by Taylor (1948) wherecohesion was attributed to an ‘‘intrinsic pressure.’’Similarly, Trollope (1960) attributed shear strength tothe Terzaghi and Bowden–Tabor adhesion theory, withboth applied stresses and interparticle forces contrib-uting to the effective stress that developed the frictionalresistance. Present evidence indicates that cohesiondue to interparticle attractive forces is quite small inalmost all cases, whereas that due to chemical cemen-tation can be significant.

11.16 FRACTURING OF SOILS

Soil fracturing is often observed in geotechnical prac-tice. Tensile cracks develop when there is external ten-sion stress such as at the crest of a landslide or verticalcuttings. In some cases, water can fill the cracks, lead-

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FRACTURING OF SOILS 439

Figure 11.105 Potential contributions of several bonding mechanisms to soil strength(Ingles, 1962).

ing to further instability. Soil piping can occur in a damfrom water flow through cracks causing internal ero-sion. Hydraulic fracturing results from increase in thepressure at the crack tips. Hydraulic fractures can becreated by injecting fluids, grouts, or chemicals andused to control settlements caused by undergroundconstruction, to determine the in situ horizontal stressstate, to create an impermeable hydraulic barrier, or toinject ground treatment chemicals for soil reinforce-ment and contaminated ground remediation. Desicca-tion also causes the development of tensile cracks asthe suction in the soil increases by evaporation andcauses shrinkage of the soil by increase in effectivestresses.

Resistance to fracturing depends on tensile strength(or true cohesion) of the material, which is often smallin geomaterials except when they are cemented. Frac-turing can occur in clays in undrained conditions byrapid increase in external pressure or in sands andclays by fluid permeation. Various mechanisms forfracture initiation are described below.

Fracture under Undrained Conditions

If particle contacts cannot carry tension, it is often as-sumed that the tensile cracking occurs when the minorprincipal effective stress becomes zero. If the soil��3is cemented, cracking is generated when the minor

principal effective stress is equal to the negative valueof the tensile strength ( ).19 This criterion can be writ-��tten as

�� (11.52)3 t

When a tensile force is applied to a saturated soil inthe direction of minor principal stress, it will besheared in undrained conditions and the soil cracks ifEq. (11.52) is satisfied. The tensile total stress �3 thenbecomes

� � u � u � �� u3 0 t 0

� ( � � A( � � � )) � �� (11.53)3 1 3 t

where u0 is the initial pore pressure, u is the excesspore pressure generated during the shearing processleading to fracture, A is Skempton’s pore pressure pa-rameter (Section 8.9), and �1 and �3 are the changes

19 Note that the tensile strength of a soil is defined in terms of effec-tive stress. Unfortunately, many tensile strength values are written intotal stress since pore pressure is not measured.

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Pf

CavityDisplacement

σθ

σθ

(a)

−σ

σr= Pf

σθ

σ0

σ’0

σ�r

σ�θ

Pf

CavityDisplacement

σθ

σθ

σr= Pf

σθ

σ0

σ�0

σ�r

σ�θ

Dotted Line: Effective Stresses

Pf

(b)

Tension crack

2su

PlasticDeformation

Crack

Plastic Instability

-σθ= σt

Solid Line: Total Stresses

Dotted Line: Effective StressesSolid Line: Total Stresses

t

2su

Figure 11.106 Fracture mechanisms of injection fluids into a cavity: (a) tensile fracture inundrained conditions and (b) shear failure in undrained conditions.

in major and minor principal total stresses, respec-tively.20

Rearrangement of Eq. (11.53) gives

1 � � � (�� ) � � (11.54)3 3i t 1A

where is the initial minor principal effective stress��3i

prior to applying the tensile force.Injection of fluid into a cylindrical cavity surrounded

by a clay formation can lead to fracture by increase incavity pressure. Examples of this mechanism are frac-ture grouting and soil fracturing around driven piezom-eters (Lefebvre et al., 1981, 1991). According to cavityexpansion theory, the radial total stress at the cavity

20 A more general case can be written as �3 � u0 � ( p � a q) ��t, where p and q are the changes in mean pressure and deviatorstress, and a is the modified pore pressure parameter defined byWood (1990).

increases, but the circumferential stress initially de-creases as long as the soil behaves linear elasticallyand does not fail in shear (see Fig. 11.106a). Cracksdevelop in the radial direction when the effective cir-cumferential stress becomes zero for uncemented soilsand equal to the negative value of the tensile strengthfor cemented soils. Assuming that the clay behaveslinear elastically,21 the change in the radial total stress �r (� �1) at the cavity is equal to the negative ofthe change in the circumferential stress ��(� �3); �r � � ��. Substituting this condition in Eq. (11.54)under plane strain conditions (A � )22 gives1–2

P � � � � � �� orf 3i r 3i t

P � 2� � u � �� (11.55)f 3i 0 t

21 For simplicity, the undrained behavior of clays is assumed to belinear elastic-perfectly plastic.22 No change of intermediate principal stress ( �2 � 0) is assumed.

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where Pf is the injection pressure that causes the clayto fracture. The above mechanism assumes that thetensile fracture occurs when Eq. (11.53) is satisfied ina uniform displacement field at the injection cavity.The fracture pressure Pf increases linearly with the in-itial total confining pressure �3i with a slope of 2. Inreality, deformation around the cavity is not uniformand fracture can initiate at a localized zone at a pres-sure smaller than the prediction. This leads the slopebetween Pf and �3i to be smaller than 2. Other consid-erations for this fracture mechanism include the effectof shear-induced pore pressure and a nonlinear stress–strain relationship (Andersen et al., 1994).

As injection pressure increases, the clay at the sur-face of the cavity may reach undrained shear failurebefore the circumferential effective stress becomeszero in uncemented soils or reaches the tensile strengthin cemented soils. In such cases, the changes in thestress state at the cavity boundary with increasing cav-ity strain are shown in Fig. 11.106b). Upon shearfailure, the difference between the radial and circum-ferential stresses (both total and effective) remainsequal to 2su, and, therefore, the minimum principal ef-fective stress never reaches zero. In such circumstance,it is difficult to see how plastic yielding initiates a frac-ture. However, there is much field and experimentalevidence suggesting that fracture has indeed occurredeven though plastic deformation was observed at thecavity due to the low undrained shear strength of thesoil (Mori and Tamura, 1987; Panah and Yanagisawa,1989; Au et al., 2003). A possible explanation is thatthe increase in plastic shear failure zone created shearbands or an unstable state around the cavity. This leadsto a localized microscale crack and the injected fluidcan penetrate into the crack to produce local tensilestresses at the crack tips, as illustrated in Fig. 11.106b.A simple cylindrical cavity expansion analysis showsthat the cavity pressure required for the cavity bound-ary to reach the plastic state is

P � � � s (11.56)f 3i u

where �3i is the initial total stress prior to shearing andsu is the undrained shear strength. The fracture pressurePf increases with initial confining pressure in directproportion (i.e., slope of 1). If the plastic zone aroundthe expanding cavity increases before fracture initiatesor su increases with initial confining pressure, the frac-ture pressure Pf would increase from the value givenin Eq. (11.56) and, therefore, the linear proportion be-tween Pf and �3i is expected to be larger than 1.

Empirical equations to estimate soil fracture underundrained conditions are available (Jaworski et al.,

1981; Yanagisawa and Panah, 1989), and they can begeneralized by the following equation:

P � m� � n (11.57)f 3i

where m and n are material constants. Experimentaldata give values of m varying between 1.5 and 1.8(Jaworski et al., 1981), whereas data indicating shear-induced fracture give values of m � 1.05 to 1.085(Panah and Yanagisawa, 1989). Reported values offracture pressure as a function of confining pressurefor various soils are plotted in Fig. 11.107. The m val-ues of individual data sets are in general bounded byEqs. (11.55) and (11.56).

Fracture under Drained Conditions

Forced seepage flow into a cavity in permeable soilleads to soil fracture if the effective stress reduces tothe negative sign of the tensile strength of the soil.Practical applications of this situation are in situ per-meability testing and bore hole stability.

To interpret the fracture conditions around a drivenpiezometer, Bjerrum et al. (1972) developed the fol-lowing conditions for the initiation of fracture in soilsusing the equilibrium equation with the assumptions ofsteady state pore fluid flow from a cylindrical cavityand elastic soil material. Horizontal cracks may de-velop if the injection pressure exceeds the initial totalvertical stress:

P � u � �� (11.58)inj 0 v0

where Pinj is the injection pressure, u0 is the initial porepressure, and is the initial vertical effective stress.��v0

Vertical cracks in the radial direction from the pie-zometer develop when the circumferential effectivestress becomes smaller than the tensile strength of thematerial. Bjerrum et al. (1972) consider two cases: (i)the piezometer is in contact with the surrounding soiland (ii) the piezometer moves away from the surround-ing soil (called ‘‘blow off’’). For the former case,cracks develop when the following condition is satis-fied:

1P � u � � 1 [� � (1 � �)�� ] (11.59)� �inj 0 t h0�

where � is Poisson’s ratio, �t is the tensile strength,is the initial horizontal effective stresses; � is a��h0

disturbance factor that considers the change in circum-ferential effective stress due to piezometer installation.Typical values of � are given in Table 11.6.

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Figure 11.107 Increase in fracture pressure with initial confining pressure of different soils.

Table 11.6 Typical Values of Disturbance Factors � and �

Soil Type

Range ofCompressibility Ratio

E /� (1 � v)�h0 � �

High compressibility 1–3 0.4–0.2 0.5–1.1Medium compressibility 3–10 0.2 to �0.2 1.1–2.0Low compressibility 10–70 �0.2 to �1.1 2.0–4.2

From Bjerrum et al. (1972).

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Figure 11.108 Photos of desiccation cracks (Konrad andAyad, 1997).

(a)

(b)

Figure 11.109 Different fracture patterns observed in labo-ratory: (a) vertical and radial fractures hardened by epoxyand (b) horizontal fracture by cement bentonite mixture in-jection.

In some cases, the radial effective stress in the soilnext to the piezometer becomes zero and the soil sep-arates from the piezometer. This occurs when the in-jection pressure becomes larger than the total radialeffective stress:

P � u � �� (1 � �) (11.60)inj 0 h0

where � is a disturbance factor that considers thechange in radial effective stress during piezometer in-stallation. Typical values of � are given in Table 11.6.Further increase in injection pressure leads to devel-opment of vertical cracks in the radial direction, whichoccurs when the following condition is satisfied:

P � u � (1 � �)[� � (2 � � � �)�� ] (11.61)inj 0 t h0

Desiccation Cracks

Reduction in moisture by surface evaporation fromclays leads to increase in interparticle contact forcesby suction. Soil then shrinks and desiccation cracksmay develop. The generation of cracks changes thehydraulic properties from Darcy’s-type homogeneousflow to fracture-dominated flow. This can cause someenvironmental problems, such as unexpected poor per-formance of contaminant barrier systems. Figure11.108 shows the crack patterns observed after desic-cation of sensitive clays (Konrad and Ayad, 1997). Thecracks can be pentagonal and heptagonal in shape, andtheir size appears to be uniform. Morris et al. (1992)report that crack depths from 0.5 to 6.0 m are observedin natural soils in Australia and Canada. Unfortunately,the available knowledge for prediction of crack depthand spacing is limited.

The decrease in matrix suction resulting from evap-oration leads to two counteracting effects (Morris et

al., 1992). Soil shrinks by the decrease in pore pressureand increase in effective stress. This decrease in vol-ume generates vertical cracks. On the other hand, thetensile strength that provides the resistance to crackformation increases with increased negativity of porewater pressure.

Fracture Propagation

Limited knowledge is available concerning fractureorientation and propagation. Some examples of frac-tures developed by injection of different fluids areshown in Fig. 11.109. When fluid is injected into the

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Localized Shearingwith Dilation andRate EffectPermeation

Fluid PenetrationInto Crack

Cavitation?Injection Fluid

Figure 11.110 Possible fracture propagation mechanisms insoils.

γ2γ1

G1 G2

Shear Strain

Monotonicloading curve

Cyclic loadingcurves

Secant Stiffness

τ1

τ 2

Monotonicloading curve

She

ar S

tres

s

Figure 11.111 Monotonic and cyclic load stress–strain re-lationships at different strain amplitudes.

soil to create hydraulic fracture, a rule of thumb is thatvertical fractures are formed when K0 is less than 1 [asgiven Eq. (11.59)] and horizontal fractures developwhen K0 is more than 1 [as given in Eq. (11.60) with� � 0]. However, this assumes injection into a linearelastic infinite soil medium. When multiple grout in-jections are performed at close distance, horizontalfractures can be observed even though K0 is less than1 (Soga et al., 2004). Natural bedding also affects frac-ture orientation. In shallow formations, fractures areoften horizontally oriented or gradually dipped (Mur-doch and Slack, 2002).

Simple criteria presented as Eqs. (11.56) to (11.61)are applied for global stress conditions, where micro-scale cracks often develop by local tensile stresses atthe crack tips. Fracture mechanics have been used withsome success to characterize the cracking resistance ofthe soils and to examine possible crack propagation(Morris et al., 1992; Harison et al., 1994; Murdoch andSlack, 2002). The actual mechanisms of fracture de-velopment in a fluid–soil system are more complicatedthan in the above analyses, as illustrated in Fig. 11.110.They may involve plastic deformation at the crack tip,soil rate effects, penetration of injection fluid into thecracks, and permeation of injection fluid from cracksinto the soil medium. If the clay is overconsolidatedand saturated, the negative pore pressure generated byshearing in front of the crack could possibly lead tocavitation and dry cracks may develop in front of pen-etrating injection fluid.

11.17 DEFORMATION CHARACTERISTICS

Strains are often decomposed into elastic (recoverable)and plastic (irrecoverable) parts. Conventional soil me-chanics assumes that plastic strains develop only whenthe stress state satisfies some failure criterion (e.g., theMohr–Coloumb criterion). Otherwise, the soil behaveselastically. However, plastic strains usually develop

well before failure. A good example is the one-dimensional compression behavior discussed in Chap-ter 10. After the stress state becomes larger than thepreconsolidation pressure, the soil has yielded andplastic strains develop. This leads to the concept ofyield envelope (sometimes referred as yield surface orlimit state curve), which differentiates the state of thesoil between elastic and plastic. Examples of the yieldenvelope of sands and clays were shown in Fig. 11.12.When the stress state reaches the yield envelope, thetotal strain is governed by the development of plasticstrain increments.

Unfortunately, for soils, there is no distinct transitionfrom elastic to plastic behavior. Plastic strains do de-velop inside the yield envelope and the stiffness de-grades even at very small strain levels. Figure 11.111shows a schematic nonlinear stress–strain relationshipfor a soil subjected to monotonic and cyclic deviatorloads. Some experimental data are shown in Figs.11.85 and 11.88. Under cyclic loading, the relation-ships are hysteretic, which indicates energy absorption,or damping, during each complete cycle of stress re-versal. The shear modulus G and damping ratio � areused to characterize the curves in Fig. 11.111, and theyare defined by

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DEFORMATION CHARACTERISTICS 445

’

IV

p�

p�

IV

III

Y1 Envelope

Y2 Envelope

Y3 Envelope

q

I

II

Critical-State Line

Initial State

(c) State B

(d) State C

O

III

IV

Y1 Envelope

Y2 Envelope

Expanded Y3 Envelope

q

I

II

Critical State Line

Initial StateO

III

Y1 Envelope

Y2 Envelope

Y3 Envelope

q

I II

Critical State Line

(b) State A

I II III IV

(a)

State A State B

State C

0

1

dεp Plastic Strain Incrementdεt Total Strain Increment

Strain

Strain

Stif

fnes

sG

or

Ed

εp /d

εt

p�

Figure 11.112 Four zones of deformation characterization: (a) stiffness degradation andplastic strain development, (b), (c), and (d) are the stress conditions and the location of thefour zones associated with three successive states (modified from Jardine, 1992).

�cG � (11.62)c

in which �c is the applied shear stress and c is thecorresponding shear strain, and

1 E� � (11.63)22� G c

in which E is the energy dissipated per cycle per unitvolume, given by the area within the hysteresis loop.

Understanding this pre-yield deformation behavior isvery important, as most strains observed in geotech-nical construction practice are indeed small (less than0.1 percent) (Burland, 1989). Site response underearthquake loading is influenced by stiffness degrada-tion and damping characteristics that are associatedwith relatively small strain levels (Seed and Idriss,1982). This was illustrated in Fig. 11.9, which showstypical strains observed in various types of geotech-nical construction and shows that the necessary defor-

mation parameters usually cannot be determinedaccurately by conventional triaxial testing. With theuse of local strain measurement systems (Jardine et al.,1984; Goto et al., 1991; Scholey et al., 1995; Cuccov-illo and Coop, 1997; Lo Presti et al., 2001; Yimsiri andSoga, 2002), however, it is now possible to measurethe development of stresses from very small strains,which can then be used for accurate prediction of de-formations in the field.

To characterize nonlinear deformation inside theyield envelope, it is convenient to define four zones inthe p�–q plane as shown in Figs. 11.112b, 112c and112d. The initial stress state is considered to be at pointO, and the boundaries of the zones are determined bystress probe testing in different stress path directions.The boundaries often associated with strain levels (ax-ial or shear strains), and the corresponding secant stiff-ness values are illustrated in Fig. 11.112a.

1. Zone 1 (True Elastic Region) Soil particles donot slide relative to each other under a small

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Table 11.7 Elastic Limit Strain for Various Geomaterials from Triaxial Tests

Material Elastic Limit Axial Strain Soil Description

Dogs Bay sand �1 � 10�5 Uniform, angular biogenetic carbonate sandLeighton Buzzard sand 2 � 10�5 Uniform, subround, quzartz sandKaolinite �2 � 10�5 Reconstituted clayBerthieville clay �2 � 10�5 Soft silty clayBothkennar clay �2 � 10�5–3 � 10�5 Soft marine clayQueenborough clay �2 � 10�5 Soft silty clayOsaka Bay clay 1 � 10�5 Overconsolidated marine clayLondon clay 2 � 10�5 Stiff overconsolidated, fissured clayVallericca clay �1 � 10�4 Weakly cemented overconsolidated clayCalcarenite 1 � 10�4 Weak rock, carbonate sand cemented with calciteSandstone 2 � 10�4 Weak rock, quartz grain weakly bonded bny iron oxideHigh-density chalk 5 � 10�5 Dry density � 1.94 g/cm3

Low-density chalk 2 � 10�5–4 � 10�4 Dry density � 1.35 g/cm3

Cement-treated sandy soil 1 � 10�4 Hard soil /weak rockSamamihara mudstone 2 � 10�4 Weak rock

After Matthews et al. (2000).

stress increment, and the stiffness is at its maxi-mum. The soil stiffness is determined from con-tact interactions, particle packing arrangement,and elastic stiffness of the solids. The soil stiff-ness values can be obtained from elastic wavevelocity measurements, resonant column testing,and very accurate local strain transducers. Cyclicloading produces only very small hysteresis bystick–slip motions at particle contacts and othermechanisms, producing very small energy dissi-pation less than 1 percent. The strains at whichthe stress state reaches the outer boundary ofzone 1 (called Y1 envelope) are usually describedas elastic limit strains or elastic threshold strains.This state is illustrated as state A in Fig. 11.112b.The elastic limit axial strain depends on soil type,solid stiffness, and confining pressure as shownin Table 11.7 for different geomaterials. Micro-mechanics analysis by Santamarina et al. (2001)shows that it increases from less than 5 � 10�6

strain, for nonplastic soils at low confining pres-sure conditions, to greater than 5 � 10�4 strainat high confining pressure conditions or in soilswith high plasticity.

2. Zone 2 (Nonlinear Elastic Region) Soil parti-cles start to slide or roll relative to each other inthis zone. The stress–strain behavior becomesnonlinear, and the stiffness begins to decreasefrom the true elastic value as the applied strainsor stresses increase. However, a complete cyclicloading (unloading and reloading) shows full re-covery of strains and therefore the zone is called

elastic even though microscopically soil particlesmay not be back to their original locations afterthe cyclic loading. When the stress state reachesthe outer boundary of zone 2 (called the Y2 en-velope), plastic strains start to develop. The ini-tiation of plastic strains can be determined byexamining the onset of permanent volumetricstrain in drained conditions or residual excesspore pressures in undrained conditions after un-loading. Hence the strain level that defines the Y2

envelope is called volumetric threshold strain.23

The value of the volumetric threshold strain isgenerally one order of magnitude higher than thatof the elastic threshold strains. The available ex-perimental data suggest that it ranges between7 � 10�5 and 7 � 10�4 (the lower limit for un-cemented normally consolidated sands and theupper limit for high plasticity clays and cementedsands). At this strain level, the stiffness degradesto 60 to 85 percent of the true elastic value(Ishihara, 1996).

23 Other definitions of the Y2 surface are available. For example, (a)perform undrained cyclic loading test and find the linear relationshipbetween �max and �p /� max, where �max is the maximum strain for eachcycle and �p is the residual strain (Smith et al., 1992); (b) the strainlevel when excess pore pressures start to accumulate in a sequenceof undrained cyclic tests at different strain levels (Vucetic, 1994); (c)change in the direction of strain path in the �vol–�s space in drainedtests (Kuwano, 1999); and (d) change in the slope of the excess porepressure–vertical effective stress in undrained triaxial compressiontest (Kuwano, 1999).

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LINEAR ELASTIC STIFFNESS 447

0.40.30.20.1

0.1

0.2

0.3

0.0

-0.1

-0.2

-0.3

Y3 Envelope

Y3 Envelope

Y2 Envelope

Y1 EnvelopeInitial StressState

Stress Path toInitial State

p� = (σ�a + 2σ�r)/3q =

σ� a

–σ�

r

Figure 11.113 Y1, Y2, and Y3 envelopes for Ham River sand(Jardine et al., 2001).

3. Zone 3 (Preyield Plastic Region) As the stressstate approaches the yield envelope (Y3 enve-lope), the ratio of plastic to total strain increases,approaching values close to 1.0 at the yield en-velope. This state is illustrated as state B in Figs.11.112a and 11.112c. Soil particles slide relativeto one another, with strong force chains breakingand reforming continuously to accommodate thechanging stress conditions.

4. Zone 4 (Full Plastic Region) Once the stressstate reaches the Y3 yield envelope, there is a dis-tinct kink in the stress–strain relationship andplastic strains develop fully. This state is illus-trated as state C in Figs. 11.112a and 11.112d.The yield envelope expands or shrinks dependingon the plastic increments; in general, the yieldenvelope expands if positive plastic volumetricstrain (contraction) develops, whereas it shrinksif negative plastic volumetric strain (dilation)develops. The sizes of Y1 and Y2 surfaces maychange with the enlargement or shrinkage of Y3

surface. If the stress state reaches the criticalstate, the soil is considered to have reached fail-ure.

Examples of experimentally determined boundariesare shown in Fig. 11.12b for Bothkennar clay and Fig.11.113 for Ham River sand. These zones are not fixedin space when the stress state moves inside the Y3 yield

envelope as illustrated in Figs. 11.112c and 11.112d.If a stress state is probed in a certain direction withinzone 2, the Y1 envelope is dragged with the stress state.When the stress path is reversed inside the Y1 envelope,the soil behaves as truly elastic. Once the stress statereaches the other side of the Y1 envelope, the Y1 en-velope is again dragged with the stress state. When thestress state is in zone 3, both Y1 and Y2 envelopes aredragged with the stress state. The movement of thesesurfaces is therefore kinematic. The stiffness and itsdegradation are controlled by the new stress path di-rection in relation to the previous stress path direction(Atkinson et al., 1990). If the soil is allowed to age ata fixed effective stress point, the Y1 and Y2 envelopesmay grow in size.

11.18 LINEAR ELASTIC STIFFNESS

Knowledge of soil stiffness in the linear elastic regionis important for evaluating soil response under dy-namic loadings such as earthquakes, mechanical vibra-tion, and vehicle vibration. It also provides indirectinformation regarding the state and natural soil struc-ture, and, therefore, stiffness values can be used to as-sess the quality of soil samples (i.e., the degree of soildisturbance). The linear elastic stiffness of soils is eval-uated from measurements of elastic wave velocities oruse of local displacement transducers. Theoreticalanalysis of elastic waves in a particulate assembly isoutside the scope of this book, but details can be foundin Richart et al. (1970) and Santamarina et al. (2001),among others.

The small strain shear modulus (Gmax) depends onthe applied confining pressure and packing conditionsof soil particles. The following empirical equation(Hardin and Black, 1966) is often used for isotropicstress conditions24:

nG � AF(e)p� (11.64)max

where F(e) is a void ratio function, p� is the meaneffective stress, and A and n are material constants. Anexample of the fitting was shown in Fig. 11.11, andTable 11.8 summarizes some experimental data for dif-ferent types of soils.

Equation (11.64) is dimensionally inconsistent, ex-cept when n � 1. Various theoretical solutions such asthe Hertz–Mindlin contact theory are available to re-

24 In practice, Gmax and p�are often normalized by pa (reference pres-sure such as atmospheric pressure) so that the equation appears tobe dimensionally consistent. However, there is no physical meaningto this.

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Table 11.8 Coefficients Used in Eq. (11.64)

Soil Type A F(e) nVoid Ratio

RangeTest

Methoda Reference

Sand

Round-grain Ottawasand

6,900 2(2.174 � e)1 � e

0.5 0.3–0.8 RC Hardin and Richart(1963)

Angular-grain crushedquartz

3,270 2(2.973 � e)1 � e

0.5 0.6–1.3 RC Hardin and Richart(1963)

Several sands 9,000 2(2.17 � e)1 � e

0.4 0.6–0.9 RC Iwasaki et al. (1978)

Toyoura sand 8,000 2(2.17 � e)1 � e

0.5 0.6–0.8 Cyclic TX Kokusho (1980)

Several cohesionlessand cohesive soils

4,500–140,000

120.3 � 0.7e

0.5 NA RC Hardin and Blandford(1989)

Ticino sand 7,100 2(2.27 � e)1 � e

0.43 0.6–0.9 RC andTS

Lo Presi et al. (1993)

Clays

Reconstituted NCkaoline

3,270 2(2.973 � e)1 � e

0.5 0.5–1.5 RC Hardin and Black(1968)

Several undisturbedNC clays

3,270 2(2.973 � e)1 � e

0.5 0.5–1.7 RC Hardin and Black(1968)

Reconstituted NCkaolin

4,500 2(2.973 � e)1 � e

0.5 1.1–1.3 RC Marcuson and Wahls(1972)

Reconstituted NCbentonite

450 2(4.4 � e)1 � e

0.5 1.6–2.5 RC Marcuson and Wahls(1972)

Several undisturbedsilts and clays

893–1,726 2(2.973 � e)1 � e

0.46–0.61 0.4–1.1 RC Kim and Novak(1981)

Undisturbed NC clay 90 2(7.32 � e)1 � e

0.6 1.7–3.8 Cyclic TX Kokusho et al.(1982)

Undisturbed Italianclays

4,400–8,100 e�1.3(averagefrom e�x: x� 1.11–1.43)

0.40–0.58 0.6–1.8 RC andBE

Jamiolkowski et al.(1995)b

Several soft clays 5,000 e�1.5 0.5 1–5 SCPT Shibuya and Tanaka(1996)c

Several soft clays 18,000–30,000

12.4(1 � e)

0.5 1–6 SCPT Shibuya et al. (1997)c

aRC: resonant column test, TX: triaxial test, TS: torsional shear test, BE: bender element test, SCPT: seismic cone test.bFrom anisotropic stress condition.cUsing instead of p�.��vAfter Yimsiri (2001).

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Table 11.9 Some Analytical Solutions for Shear Modulus Under Isotropic Loading of p�

PackingCoordination

Number Shear Modulus

Simple cubic 6 1 / 3 1 / 31 / 3(1 � � )G 3 p�gmax � � � � �G 2 2 � � Gg g g

Body-centered cubic 8 1 / 3 1 / 31 / 3(1 � � )G 1 p�gmax � 9� � � �G 6 6 � 5� Gg g g

Face-centered cubic 12 1 / 3 1 / 3(4 � 3� )G 1 3 p�gmax � � � � �2 / 3G 2 2 (2 � � )(1 � � ) Gg g g g

Random packing Cn2 / 3 1 / 33c (5 � 4� )G 1 p�n gmax � � � � �2 / 3G 5 (2 � � )(1 � � ) G2�(1 � e)g g g g

After Santamarina and Cascante (1996).

20 40 60 80 100 200 300

300

200

400

Vs-xy

Vs-yz

Vs-zx

Vs-zx

Vs-xy

Vs-yz

Direction of Wave PropagationParticle Motion

σ�z Change in Vertical Effective Stress

Vertical Effective Stress, σ�z (kPa)

S-w

ave

Vel

ocity

, Vs

(m/s

)

Figure 11.114 Variation of shear wave velocities in differentdirections as a function of anisotropic stresses (Stokoe et al.,1995).

late the global elastic stiffness to microscopic proper-ties such as particle stiffness and Poisson’s ratio,number of contacts, void ratio, and contact force di-rections (see Table 11.9). These solutions suggest thatthe pressure p� and Gmax could be normalized by theshear modulus of the particle itself (Gg).

It is noted from Table 11.8 that the values of theexponent n range from 0.4 to 0.6. As shown in Table11.9, however, classical contact mechanics solutionsusing the Hertz–Mindlin contact theory predict n �

This is because the soil particles are assumed to be1–.3

smooth elastic spheres. If the contacts are consideredto be an interaction of rough surfaces, the modificationof theory leads to increases in the exponent to valuesthat are closer to the experimental observations givenin Table 11.8 (Yimsiri and Soga, 2000).

By comparing Eq. (11.64) with the micromechanicalmodel listed at the bottom of Table 11.9, it is possibleto relate the void ratio function F(e) to number of con-tacts per particle (i.e., coordination number) and A tothe elastic properties of particle itself. From the anal-ysis of uniform grain fabrics, the coordination numberCn can be related to the porosity n by Eq. (5.1) or tothe void ratio e by the following equation. (Chang etal., 1991).

C � 13.28 � 8e (11.65)n

By varying compaction effort, sand samples can beprepared to different densities for a given applied con-fining stress. In this case, a smaller void ratio impliesthat the number of particle contacts is larger, and,therefore, the small strain stiffness increases. This ef-fect is taken into account in the void ratio function

F(e). Several expressions are available for the void ra-tio function as listed in Table 11.8. These functions areempirical and apply for specific ranges of void ratiosand, therefore, should be used with caution.

Equation (11.64) is derived assuming isotropic stressconditions. Anisotropic stress conditions as well as an-isotropic soil fabric give stiffness values that dependon the direction of loading. The shear modulus is afunction of the principal effective stresses in the direc-tions of wave propagation and particle motion and isrelatively independent of the out-of-plane principalstress. This is shown in Fig. 11.114, in which the var-iations of measured shear wave velocities propagatingin three different directions (Vsxy, Vsyz, and Vszx) areshown as the vertical effective stress was increased��z

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20 40 60 80 100 200 300

400

300

600

Vp-zzVp-xx

Vp-yy

Vp-zz

Vp-xx

Vp-yy

Direction of Wave Propagation

σ�z Change in Vertical Effective Stress

Vertical Effective Stress, σ�z (kPa)

500

Particle Motion

P-w

ave

Vel

ocity

, Vp

(m/s

)

Figure 11.115 Variation of P-wave velocities in different di-rections as a function of anisotropic stresses (Stokoe et al.,1995).

with the horizontal effective stresses and being�� x y

held constant (Stokoe et al., 1995). The shear waveVsxy, which propagates and has the particle motion inthe out-of-plane directions, shows no change in its ve-locity. This leads to the following empirical equationfor stiffness under anisotropic stress conditions (Roes-ler, 1979; Yu and Richart, 1984; Stokoe et al., 1985,1991; Hardin and Blandford, 1989):

r s kG GG � A F �� OCR (11.66)ij(max) G G i j

where is the effective normal stress in the direction��iof wave propagation, is the effective normal stress��jin the direction of particle motion, and AG, rG, sG, andk are material constants. Experimental evidence sug-gests that rG � sG. Hence, an alternative equation thatrelates the stiffness to the mean state of stress on theplane of particle motion is also available:

nG�� i j kG � A F OCR (11.67)� �ij(max) G G 2

Equations (11.66) and (11.67) include the effect ofoverconsolidation ratio (OCR). Hardin and Black(1968) found that k is a function of plasticity index (kincreasing from 0 to 0.5 as PI increases from 0 to morethan 100). Viggiani and Atkinson (1995) report k �0.3 for reconstituted kaolin and k � 0.35 for reconsti-tuted and undisturbed London clay. It can be arguedthat the void ratio function is a redundant factor sincethe void ratio is a unique function of present effectivestress, stress history (OCR), and soil compressibility.However, this argument should be restricted to recon-stituted clays and not applied to natural clays.

Similar empirical equations are proposed for otherelastic constants. P-wave velocity is a function only ofthe effective stress in the coaxial direction as shown inFig. 11.115 (Stokoe et al., 1995). Hence, the smallstrain constrained modulus Mi(max) in the i direction canbe expressed as

nMM � A F(e)�� (11.68)i(max) M i

where AM and nM are material constants.Similarly to the constrained modulus, the small

strain Young’s modulus Ei(max) in the i direction (e.g.,vertical or horizontal) is a function of the effectivestress in the coaxial direction (i direction) only. Theincrease in Young’s modulus with stress in the coaxialdirection is shown in Fig. 11.116a, whereas no changein the modulus with the increase in the stresses in or-thogonal direction is shown in Fig. 11.116b (Hoque

and Tatsuoka, 1998). This leads to the following em-pirical equation for small strain Young’s modulus:

nEE � A F(e)�� (11.69)i(max) E i

where AE and nE are material constants. Micro-mechanics analysis by Yimsiri and Soga (2000) sup-ports this relation when the change in contact fabricanisotropy with applied stress is considered.

Limited data are available with respect to Poisson’sratio, and it is often assumed to be a constant value.The data by Hoque and Tatsuoka (1998) shown in Fig.11.117 indicate that Poisson’s ratio �vh (i.e., horizontalexpansion by vertical load) increases with vertical ef-fective stress and decreases with increase in horizontalstress. The following empirical equations are proposedby Horque and Tatsuoka (1998) for Poisson’s ratios:

nvh� � A F(e)(�� /��) (11.70)vh vh v h

nhv� � A F(e)(�� /��) (11.71)hv hv h v

where Avh, Ahv, nvh, and nhv are material constants.Hoque and Tatsuoka (1998) report the values of nvh

and nhv can be assumed to be half of nE given in Eq.(11.69).

Small strain stiffness anisotropy originates from (i)anisotropic stress conditions and (ii) anisotropic soilfabric. The former is considered in Eqs. (11.66) to(11.71). For the latter, the material constant A shouldbe directionally dependent reflecting a given aniso-tropic fabric. The effect of soil fabric on small strainstiffness of reconstituted London clay specimens isshown in Fig. 11.118 where the shear wave velocitiesin different directions are measured under the sameconfining pressures, and three different values of stiff-ness (Gvh, Ghv, and Ghh) are obtained. Results indicate

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Ev Toyoura sand

σ�v/Pa or σ�h/Pa

1.0 1.5 2.0

5000

4000

3000

2000

1000

Ev Ev SLB Sand

Eh SLB Sand

For Ev (or Eh) measurement, σ�v/Pa (or σ�h/Pa) isvaried between 1.0 and 2.0 at each σ�v (or σ�h)

Eh Toyoura Sand

Toyoura Sand

1.0 2.0 3.0 4.00.0

1.0

1.2

0.8

σ’h/Pa

Eh SLB Sand Eh Toyoura Sand

(b) Ev versus σ�h

Ev/

(F(e

)Pa)

or

Eh/(

F(e

)Pa)

(a) Ev versus σ�v and Eh versus σ�h

Ev/

(AE

F(e

)σ� v

)

Figure 11.116 Vertical and horizontal Young’s modulus asa function of anisotropic stresses for Toyoura sand (Hoqueand Tatsuoka, 1998).

Figure 11.117 Poission’s ratio as a function of anisotropicstresses (Hoque and Tatsuoka, 1998).

Figure 11.118 Stiffness anisotropy of undisturbed Londonclay under isotropic stress conditions (Jovicic and Coop,1998).

that, for a given confining pressure, the values of Ghh

are larger than those of Gvh � Ghv. Hence, the soil isinherently stiffer horizontally than vertically due to itssoil fabric.

The reported data on clay under isotropic stress con-ditions consistently show that Ghh is approximately 50percent larger than Gvh, indicating inherent anisotropiccharacteristics caused by orientation of platy clays(Pennington et al., 1997; Jovicic and Coop, 1998). Theratios of Ghh/Gvh for six Italian clays measured in one-dimensional consolidation tests were between 1.3 and2.0, and the ratio increased with overconsolidation ra-tio (Jamiolkowski et al., 1995).

For sands, most studies show that the ratio Ghh/Gvh

is greater than 1 (e.g., Lo Presti and O’Neill, 1991;Stokoe et al., 1991; Bellotti et al., 1996). However,reported values for the ratio of Ev /Eh are inconclusive;some sands are stiffer in the vertical direction (Hoqueand Tatsuoka, 1998), whereas the others are stiffer inthe horizontal direction (Stokoe et al., 1991). Aniso-tropic properties are related to fabric (contact) aniso-tropy, and therefore the mixed results obtained may bedue to the differences in sample preparation proce-dures.

The experimental data show that the small strainstiffness is rather insensitive to the strain rate and num-ber of loading cycles as long as the loading is within

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Monotonic TriaxialMonotonic Torsional ShearCyclic TriaxialCyclic Torsional shearResonant Column

Shear Strain γ (%)

100

80

60

40

20

010010-110-210-310-4

Ticino Sandσ’0 = 49 kPae = 0.640S

ecan

t She

ar M

odul

us G

G

Figure 11.119 Stiffness degradation of Ticino sand obtainedby monotonic and cyclic loadings using various testing ap-paratus (Tatsuoka et al., 1997).

the true elastic range but that the elastic limit strainincreases with strain rate (Shibuya et al., 1992; Tat-suoka et al., 1997). Resonant column tests on clays andsands show that the small strain shear modulus is in-dependent of frequency in the range of 0.05 to 2500Hz (e.g., Hardin and Richart, 1963; Hardin and Drnev-ich, 1972; Stokoe et al., 1995).

Although conservation of energy may be an issuefor true elastic response, experimental evidence indi-cates that energy is dissipated even at this strain leveland damping values are typically 0.35 to 1 percent forsands and 1.0 to 1.5 percent for clays. Similar to thesmall strain stiffness, the damping at very small strainalso depends on confining pressure and the followingempirical form is proposed (Hardin, 1965):

m� � Bp� (11.72)

where B and m are material constants. The reportedvalues of the exponent m range from �0.05 to �0.22(Santamarina and Cascante, 1996; Stokoe et al., 1999).Although the particles in contact are not moving rel-ative to each other, some microscopic proportion of thecontact area can slide or slip, which is known as thestick–slip frictional contact loss. Micromechanicalanalysis considering the energy dissipation by thisbehavior gives m � � . Santamarina and Cascante2–3(1996) attribute the difference to other attenuationmechanisms available in soils. These include chemicalinteraction of adsorbed layers at contacts, wave scat-tering, thermal relaxation, and other forms of energycoupling (e.g., mechanoelectromagnetic, mechano-acoustic). The damping is also affected by loading fre-quency, which is further described in Chapter 12.

It has been argued that the use of the empirical equa-tions presented above may produce nonconservative‘‘elastic’’ response in terms of energy conservation(i.e., it may generate energy during a closed stressloop) (Zytynski et al., 1978). To be thermomechani-cally consistent, theoretical models for the pressure-dependent stiffness of soils are available (e.g.,Houlsby, 1985; Hueckel et al., 1992; Borja et al., 1997;Einav and Puzrin, 2004). They show that, if both shearand bulk moduli are to be mean pressure dependent,the stiffness needs to be anisotropic and stress induced.This is important in deformation analysis since the an-isotropic stiffness in turn leads to cross dependencebetween shear behavior and volumetric behavior (Gra-ham and Houlsby, 1983).

11.19 TRANSITION FROM ELASTIC TOPLASTIC STATES

In some cases, accurate evaluation of stiffness valuesat very small strains may not be crucial in geotechnical

analysis. For instance, assume that the true elastic axialstiffness of a soil is 100 MPa. Considering that theelastic threshold axial strain is of the order of 10�5,the axial stress increment required to reach to thisstrain level is only 1 kPa. Hence, errors in stiffness of�100 percent result in small differences in the asso-ciated stress increments (a few kilopascals). Typicalstrain levels under working loads are usually in an in-termediate level between linear elastic and plastic de-formation, and, therefore, the knowledge of nonlinear(zone 2) and irreversible (zone 3) deformation char-acteristics is more important for evaluating groundmovements accurately.

Stiffness degradation from small strains to interme-diate strains has been recognized in resonant columntesting since the 1960s when the soil was subjected tocyclic loading (Hardin and Drnevich, 1972). Nowa-days, detailed characterization of deformation proper-ties at intermediate strain levels is possible with theuse of local strain measurement systems, as describedpreviously.

The shear modulus decreases and the damping in-creases as the shear strain increases because of struc-tural breakdown that results in a decreasing proportionof elastic deformation and an increasing proportion ofplastic strain with increasing shear strain. The shearmodulus degradation curves of Ticino sand, obtainedby monotonic and cyclic loadings using various testingapparatus (triaxial compression, torsional shear, andresonant column) are shown in Fig. 11.119 (Tastuokaet al., 1997). The small strain stiffness is nearly inde-pendent of the test type, but at larger strains, the cyclicloading gives consistently larger shear modulus com-

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TRANSITION FROM ELASTIC TO PLASTIC STATES 453

40

30

20

10

010-2 10-1 100 101

Deviator strain γ (%)

-100

100

0

Mean Pressure p� (kPa)100 200 400

C

B

O

D

X

A

(B➝)O➝X

(C➝)O➝X

(A➝)O➝X

(D➝)O➝X

(a)

(b)

She

ar M

odul

us G

(M

Pa)

Dev

iato

r st

ress

q(k

Pa)

Figure 11.120 Recent stress history effect on stiffness deg-radation: (a) stress paths and (b) stiffness degradation on OXstress path (from Atkinson et al., 1990).

0.010-4 10-3 10-2 10-1 100

Shear Strain γ (%)

0.5

1.0

Clay, 100 kPa

Sand, 50 kPa

Gravel, 50 ~ 830 kPa

She

ar M

odul

us R

atio

G/

Gm

ax

Figure 11.121 Normalized stiffness degradation curves ofvarious types of soils (Kokusho, 1987).

pared to the monotonic loading at a given strain level.This is because the soil densifies during cyclic loadingand the number of loading cycles has an effect on stiff-ness. As noted earlier, the shear strain level that givesan onset of permanent volumetric strain in drained con-ditions or residual excess pore pressures in undrainedconditions after unloading is called the volumetricthreshold strain.

The stiffness degradation curve is influenced bymany factors such as stress state, stress path, soil type,and soil fabric (i.e., anisotropy). For example, Fig.11.10 shows the stiffness degradation of sands andclays subjected to increase in shear stress at differentconfining pressures. The effect of stress path directionson the stiffness degradation curve is shown in Fig.11.120 (Atkinson et al., 1990). Triaxial tests were per-formed on reconstituted overconsolidated London clayspecimens in such a way as to maintain a constantmean pressure. Different stiffness degradation curveswere obtained even though they were sheared alongthe same stress path (OX in Fig. 11.120a). This is be-

cause the specimens had different stress path historiesprior to shearing (AO, BO, CO, and DO) [termed re-cent stress history by Atkinson et al. (1990)], andstiffer response was obtained when the stress path wasreversed (D → O → X). The use of the multisurfaceconcept described in Section 11.17 conveniently ex-plains this complex deformation behavior.

Since the small strain elastic stiffness is also influ-enced by the same factors, the stiffness degradationcurves are sometimes normalized by the small strainstiffness; G/Gmax versus log or E/Emax versus log �a.A summary of normalized shear modulus degradationcurves for a variety of soils are shown in Fig. 11.121(Kokusho, 1987). The curve for modulus degradationwith increasing strain may be somewhat flatter forgravels than that for sands and clays. The curves tendto move to the right as the confining pressure in-creases; it is possible that the degradation curve at veryhigh confining pressure (in the megapascal range) maylie beyond the bands given in Fig. 11.121 (Laird andStokoe, 1993).

Sands and Gravels

The following relationship can be used for the dynamicshear modulus of sands and gravels at different strainlevels (Seed et al., 1984):

1 / 2G p�� 22.1K (11.73)� �2p pa a

where p� is the mean effective principle stress, pa isthe atmospheric pressure, and K2 is a coefficient thatdepends primarily on grain size, relative density, andshear strain. The coefficient K2 is generally greater bya factor from about 1.35 to 2.5 for gravels than forsands. Values of K2 vary with relative density and shear

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Figure 11.122 Shear modulus factor K2 for sands as a function of relative density and shearstrain (Seed et al., 1984).

strain approximately as shown in Fig. 11.122 and withvoid ratio and shear strain as shown in Fig. 11.123.Equation (11.73) assumes that the exponent is . Ex-1–2perimental evidence suggests that the exponent in-creases with strain level as shown in Fig. 11.124 andreaches 0.8 to 0.9 at a strain level of 1 percent (Jovicicand Coop, 1998; Yamashita et al., 2000).

Values of the damping ratio for sands and gravelsare about the same, and they are only slightly influ-enced by grain size and density. The ranges of valuesas a function of cyclic shear strain are shown in Fig.11.125. The damping value decreases with increasingnumber of loading cycles and confining pressure, andmuch of the decrease occurs in the first 10 cycles (Sto-koe et al., 1999).

Clays

Although the variation of shear moduli and dampingratio with shear strain is relatively independent of com-position for sands and gravels, the same is not the casefor cohesive soils. Curves of the type shown in Figs.11.121 and 11.125 are displaced to the right for clayswith increasing plasticity, as shown by Fig. 11.126.These relationships were developed by Vucetic and

Dobry (1991) based on the results of a review of avail-able cyclic load data from 16 different studies. Theinfluences of various compositional and environmentalfactors on shear modulus and damping ratio of nor-mally consolidated and moderately overconsolidatedclays are listed in Table 11.10.

Vucetic and Dobry (1991) hypothesized that increas-ing plasticity influences the degradation curves in thefollowing manner. Increasing plasticity index reflectsdecreasing particle size and increasing specific surfacearea. The number of interparticle contacts becomeslarge, and interparticle electrical and chemical bondingand repulsive forces become large relative to the par-ticle weights in comparison with sands. The manybonds within the microstructure act as a system of rel-atively flexible linear springs that can resist largershear strains (up to 0.1 percent before they are broken)than is the case for sands, wherein particle elasticity ispractically the only source of linear behavior, and in-terparticle sliding at contacts may start at strains as lowas percent with the onset of plastic deformations.

To these ideas might be added the fact that the thin,platy morphology of most clay particles make themable to deform elastically to considerably greater levels

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TRANSITION FROM ELASTIC TO PLASTIC STATES 455

Figure 11.123 Shear modulus factor K2 for sands as a function of void ratio and shear strain(Seed et al., 1984).

Figure 11.125 Damping ratios for sands and gravels (Seedet al., 1984).

Figure 11.124 Variation of the shear modulus n exponentvalue with strains on Dogs Bay sand (Jovicic and Coop,1997).

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Figure 11.126 Normalized modulus and damping ratio as afunction of cyclic shear strain showing the influence of soilcomposition as measured by plasticity index (from Vuceticand Dobry, 1991). Reprinted with permission of ASCE.

of strain than is possible for the bulky, stiff granularparticles. Furthermore, the several orders-of-magnitudesmaller size and greater number of interparticle con-tacts per unit volume for the cohesive materials meanthat even minute elastic distortions at interparticle con-tacts can give a cumulative strain that is large. For acohesionless soil to develop such large shear defor-mations would require much greater displacements atintergrain contacts than could be accommodated with-out sliding.

11.20 PLASTIC DEFORMATION

Irrecoverable plastic strain initiates at a shear strainlevel of approximately 10�2 percent, and the amountof plastic strain increases with further deformation. A

fully plastic state is obtained when the stress statereaches the yield envelope as discussed in Section11.17. As long as the stress state during and after geo-technical construction is within the yield envelope, thestrain generated is elastic dominated. Hence, in orderto control ground deformation in overconsolidatedclays, it is useful to keep the construction-inducedstress paths within the yield envelope.

Once the stress state reaches the yield envelope, thegenerated strain will be plastic dominated. Generationof plastic strains is often unavoidable in normally andlightly overconsolidated clays because the initial stressstate is either already on or near the yield envelope.The most important mechanical feature of soil in theplastic state is dilatancy, in which there is couplingbetween shear and volumetric deformations. That is,dense sands and heavily overconsolidated clays exhibitvolume dilation in drained conditions and negative ex-cess pore pressure generation in undrained conditions,whereas loose sands and normally consolidated andlightly overconsolidated clays exhibit volume contrac-tion in drained conditions and positive excess porepressure generation in undrained conditions. The rulethat governs the generation of plastic volumetric strainassociated with plastic deviator strain is called the di-latancy (or flow) rule. Some examples of this for densesands were already presented in Eqs. (11.34) and(11.35), in which the degree of dilatancy [dy/dx in Eq.(11.34) and � in Eq. (11.35)] is related to the appliedprincipal stress ratio (or the mobilized friction angle)and the internal friction angle. These observations areimportant because the incorporation of stress–dilatancyinto plasticity theory can lead to a useful form of con-stitutive modeling for soils.

The development of plastic strains is often charac-terized by the following three aspects of soil behavior:(a) yield envelope, (b) dilatancy rule, and (c) hardeningrule, which relates the change in the size of yield en-velope to plastic strain increments. By assigning math-ematical functions to these three aspects of soilbehavior, a plastic constitutive model can be devel-oped. Detailed review and development of all recentplasticity theories and proposed constitutive soil mod-els are beyond the scope of this book. However, someessential aspects of soil behavior observed during plas-tic deformation are summarized here.

Yield Envelope and Hardening

The yield envelope defines the stress state when thereis full development of plastic strains. Typical yield en-velopes measured for a natural clay consolidated atdifferent confining pressures are shown in Fig. 11.127.

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PLASTIC DEFORMATION 457

Table 11.10 Effect of Various Compositional and Environmental Factors on Maximum Shear Modulus Gmax,Modulus Ratio G /Gmax, and Damping Ratio of Normally Consolidated and Moderately Overconsolidated Clays

Increasing Factor(1)

Gmax

(2)G /Gmax

(3)�

(4)

Confining pressure, �0

(or � )vc

Increases with �0 Stays constant orincreases with �0

Stays constant ordecreases with �0

Void ratio, e Decreases with e Increases with e Decreases with eGeologic age, tg Increases with tg May increase with tg Decreases with tg

Cementation, c Increases with c May increase with c May decrease with cOverconsolidation,

OCRIncreases with OCR Not affected Not affected

Plasticity index, PI Increases with PI ifOCR � 1; staysabout constant ifOCR � 1

Increases with PI Decreases with PI

Cyclic strain, c — Decreases with c Increases with c

Strain rate, (frequency of cyclicloading)

Increases with G increases with ;G /Gmax probably notaffected if G andGmax are measured atsame

Stays constant or mayincrease with

Number of loadingcycles, N

Decreases after Ncycles of large c butrecovers later withtime

Decreases after N cyclesof large c (Gmax

measured before Ncycles)

Not significant formoderate c and N

From Dobry and Vucetic (1987).

Figure 11.127 Yield surfaces of Winnipeg clay at differentconfining pressures (Graham et al., 1983b).

Some observations can be made from this figure asfollows:

1. The yield envelope is a function of stress and itssize is controlled by stress history variables suchas preconsolidation pressure. This is often ex-pressed mathematically as

F(��, p , �) � 0 (11.74)c

where �� is the effective stresses, pc is the pre-consolidation pressure, and � is the rotation angleof the yield envelope with respect to the meanpressure axis. The yield envelopes of intact sam-ples are larger than those of remolded (or de-structured) samples; geological aging processesand cementation produce large yield envelopesfor intact clays as shown in Fig. 11.128. Whenthe cementation bonding breaks down and thesoil becomes destructured, the yield envelope canbecome smaller.

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0.2 0.4 0.6 0.8 1.000

0.2

0.4

0.6 Intact State

Destructured State

(σ�a+σ�r)/2σ�p

(σ� a

–σ�

r)/2

σ�p

(σ� a

–σ�

r)/2

σ�p

0.2 0.4 0.6 0.8 1.000

0.2

0.4

0.6 Intact State

Destructured State

(σ�a+σ�r)/2σ�p

(b)

(a)

Figure 11.128 Yield surfaces of intact and destructured softclays: (a) Saint Alban clay and (b) Backebol clay (Leroueiland Vaughan, 1990).

2. The yield envelope increases in size with increas-ing preconsolidation pressure pc, which is oftenassociated with the generation of plastic volu-metric strain. The size increases as the soil ismore densely packed along the normal consoli-dation line. A mathematical form that describesthe change in pc with generation of plastic strainsis called the hardening rule.

3. The shape of the yield envelope is often an in-clined ellipse in the p�–q plane. The inclinationis related to the anisotropic consolidation historyas well as the anisotropic fabrics. Some yield en-velopes of sands are shown in Fig. 11.129 (Yas-ufuku et al., 1991). The yield envelopes weredetermined by applying different stress paths andconnecting the stress state when the plasticstrains initiate for a given stress path. The shapeof the yield envelopes resembles a tear drop, andthe inclinations of the yield envelopes are clearlyaffected by the initial anisotropic stress condi-

tions [i.e., (a) triaxial compression, (b) isotropic,and (c) triaxial extension]. A mathematical formthat describes the change in � with generation ofplastic strains is called the rotational hardeningrule.

Magnitude of Plastic Strains and Stress–Dilatancy

Once the stress state is on the yield envelope, the soilis in the fully plastic state. The arrows in Fig. 11.129show the vector magnitude of plastic strains measuredfor a given stress increment. The vertical componentof the arrows is the deviator plastic strain increment

(or ), whereas the horizontal component is thep pd� ds

volumetric plastic strain increment .25 Similarly, thepd�v

plastic strain vectors measured in Winnipeg clay areshown in Fig. 11.130 (Graham et al., 1983b). The vec-tor of the plastic strain increment appears to be a func-tion of the current stress state. This observation leadsto the concept of stress–dilatancy.

Dilatancy during plastic deformation can be ex-pressed as the ratio of plastic volumetric strain incre-ment to plastic deviatoric increment ; D �p pd� d�v s

. For clays, the value of D can be expressed asp pd� /d�v s

a function of stress ratio and material constants. Forinstance, the following stress–dilatancy equation canbe proposed based on Taylor’s equation (11.34)26:

pd� qv � M � � � (11.75)0pd� p�s

where �0 is the initial anisotropy (e.g., Sekiguchi andOhta, 1977). When �0 � 0, the equation becomes thestress–dilatancy rule used in the Cam-clay model (Ros-coe and Schofield, 1963). Soil exhibits contractive be-havior when the dilation angle is negative and q/p� isless than M � �0, whereas the soil exhibits dilativebehavior when the dilation angle is positive and q/p�is more than M � �0. Figure 11.131 shows the stress–dilatancy relationship for the data presented in Fig.11.130. The data follow a similar trend to Eq. (11.75).Other stress–dilatancy rules that are used to deriveconstitutive models for clays are available.

Experimental evidence suggests that the stress–dilatancy relationship for sand depends on confiningpressure and density as well as soil fabric, comparedto a simpler form used in clays such as Eq. (11.75).Rowe (1962) derived the following stress–dilatancy

25 In triaxial condition, � ( )( ), andp p p p 2 p p–d� � d� � 2d� , d� d� � d�v a r s 3 a r

d p � , where is the axial plastic strain and is thep p p pd� � d� d� d�a r a r

radial plastic strain.26 Note that Taylor’s expression was for the peak state only. Thisequation is applied to all stress state conditions under plastic defor-mation for both loose and dense cases.

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PLASTIC DEFORMATION 459

0.2

0.4

0.6

0.8

0.0

-0.2

-0.4

q(MPa)

p’0.2 0.4 0.6 0.8 1.0

(MPa)0.2

0.4

0.6

0.8

0.0

-0.2

-0.4

q(MPa)

p’0.2 0.4 0.6 0.8 1.0

(MPa)0.2

0.4

0.6

0.8

0.0

-0.2

-0.4

q(MPa)

p’0.2 0.4 0.6 0.8 1.0

(MPa)

InitialState

InitialState

InitialState

(a) (b) (c)

Figure 11.129 Yield surfaces of sands with different initial stress histories. Initial states (a)compression, (b) isotropic, and (c) extension (Yasufuku et al., 1991).

0.2 0.4 0.6 0.8 1.000

0.2

0.4

0.6

dεvp

dεsp

dε p

q/σ�

p

p�/σ�p

Figure 11.130 Plastic strain vectors at yielding of naturalWinnipeg clay (Graham et al., 1983b).

1

-2.5 -2 -1.5 -1 -0.5 00

0.5 1 1.5 2 2.5

Str

ess

Rat

io q

/p'

Plastic Strain Ratio (-dεpv/dεp

s)

dεpv/dε p

s = [M2 - (q/p�)2]/2(q/p�)

Modified Cam-clay(Roscoe and Burland, 1968)

Cam-clay(Roscoe and Schofield, 1963)dεp

v/dε ps = M - q/p�

Data from Graham et al. (1983).See Fig 11.130

1.4

1.2

0.8

0.6

0.4

0.2

Modified Cam-clay

Cam-clay

Figure 11.131 Stress dilatancy relations of natural Winnipegclay (Wood, 1991).

rule for sand in triaxial loading based on his experi-mental data as well as theoretical analysis:

p�� 2d� � �a r c2� tan �� p�� d� 4 2r a

in triaxial compression (11.76)

p�� d� � �r a c2� tan �� p�� 2d� 4 2a r

in triaxial extension (11.77)

where and are the axial and radial strainp pd� d�a r

increments, �c is the ‘‘characteristic friction angle’’and and are the axial and radial effective stresses,�� a r

respectively. Equations (11.76) and (11.77) have a sim-ilar form to Eq. (11.75), in which the dilation dependson stress ratio and material constants.27 However,Rowe (1962) noted that the material constant �c usedin Eqs. (11.76) and (11.77) is influenced by the density.Different initial anisotropic stress states give different

27 Equations (11.76) and (11.77) can be rewritten in terms of p�, q,, and d p (Pradhan and Tatsuoka, 1989):pd� v

p pq 3 (2K � 1)(�d� /d ) � 2(K � 1)v p� for d� � 0 � ap pp� 2 (K � 1)(�d� /d ) � (K � 2)v

p pq 3 (K � 2)(�d� /d ) � 2(K � 1)v p� for d� � 0 � ap pp� 2 (1 � K)(�d� /d ) � (2K � 1)v

where K � (1 � sin �c) / (1 � sin �c).

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?

?

0.5

1.0

-0.5

-1.0

1.5

2.0

1 2 3 4-1-2-3-4 0

Strain Increment

Case (a)

Case (b)

Case (c)

in Fig.11.129

Extension

Compression

ratio -dεvp/dγ p

Stress Ratio q/p�

Figure 11.132 Stress dilatancy relations of sands with dif-ferent initial anisotropic stress conditions (Yasufuku et al.,1991).

stress–dilatancy curves as shown in Fig. 11.132. Thecurves were derived from the data presented in Fig.11.129 and are presented in terms of stress ratio q /p�and plastic strain increment ratio /dp. Hence, thepd�v

stress–dilatancy relationship of a sand depends notonly on stress ratio but also on density, confining pres-sure and initial anisotropic stress conditions.

As noted in Eqs. (11.75) to (11.77) and Figs. 11.131and 11.132, the development of plastic increments isgoverned by the current stress state. This is in contrastto elastic deformation, which is related directly tostress increments. For example, for an isotropic elasticmodel,

ed� dp� Gv � 3 (11.78)ed� dq Ks

where G is the shear modulus, K is the bulk modulusand and are the elastic volumetric and devia-e ed� d�v s

toric strains, respectively.The physical mechanisms of elastic deformation and

plastic deformation are fundamentally different, that is,stress increment dependent versus stress dependent.Because of this, the same stress increment may givevery different strain increments. Careful selection ofelastic and/or plastic models is therefore necessary inground deformation analysis.

11.21 TEMPERATURE EFFECTS

The average ground temperature varies between 7� and10�, whereas laboratory conditions are between 18� and23�. In some situations, the soil can undergo large tem-perature change, for example, ground freezing, heatingof nuclear waste repositories, underground storage res-ervoirs, and the like. It can be important to recog-nize the significance of temperature when evaluatingstrength and model parameters. In general, increase intemperature will result in thermal expansion of soilgrains as well as pore fluid. The particle contact prop-erties will also be modified. A change in temperature,therefore, causes either a change in void ratio or achange in effective stress (or a combination of both)in a saturated clay, as described in Section 10.12. Inthis section some effects of temperature on shear re-sistance of soils are considered.

A change in temperature can cause a strength in-crease or a strength decrease depending on the circum-stances (e.g., temperature variation during initialconsolidation or during shearing in drained or un-drained conditions), as illustrated by Fig. 11.133.

The higher the consolidation temperature, thegreater the shear strength at any given test temperaturebecause of the greater decrease in void ratio at thehigher consolidation temperatures.28 In Fig. 11.133, Tc

represents the temperature at consolidation and Ts thetemperature of shear for consolidated undrained directshear tests on highly plastic alluvial clay. For a givenconsolidation temperature Tc, the undrained strengthdecreases in a regular manner with the increasing testtemperature. From tests such as these, it has been es-tablished that for given initial conditions the undrainedstrength of normally consolidated saturated clay maydecrease by about 10 percent for a temperature in-crease from 0 to 40�C. For overconsolidated clays, theundrained shear strength is less influenced by temper-ature (Marques et al., 2004). The relative insensitivityof overconsolidated clay to temperature may be due tothe compensating effects of increase stiffness and soft-ening of soil structure by volume expansion as de-scribed in Section 10.12.

Similar to the strain rate effect, the preconsolidationpressure, and hence the size of the yield envelope, de-creases with increase in temperature, as illustrated inFig. 10.46 and Fig. 11.134 for natural clay specimenstested between 10� and 50�. Hence, the weakening of

28 For all tests, Ts � Tc to prevent further consolidation under a highertemperature, which would result in the strength being about the sameas if it had been consolidated under the higher temperature initially.

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TEMPERATURE EFFECTS 461

Figure 11.133 Effect of consolidation and test temperatures on the strength of alluvial clayin direct shear (Noble and Demirel, 1969).

Figure 11.134 Influence of temperature on yield surface of a St-Roch-de-l’Achigan clay,Quebec (Marques et al., 2004).

soil structure by increase in temperature is apparent.On the other hand, the critical state friction angle isfound to be independent of temperature (Hueckel andBaldi, 1990; Graham et al., 2001; Marques et al.,2004).

Drainage conditions during heating prior to shear areimportant, as illustrated in Fig. 11.133. If drainage isprevented, the expansion of water controls the expan-

sion of soil volume because thermal expansion of wa-ter is much larger than that of soil particles. Thisresults in generation of positive excess pore pressureand, as a consequence, undrained stiffness and shearstrength decrease as shown in Fig. 11.16.

If drainage is allowed, the expanding water is freeto drain and hence the volume change of the soil isgoverned by the expansion of soil particles and the

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change in particle contact conditions. Normally con-solidated clays often result in decrease in void ratio,and hence the initial stiffness generally increases withtemperature. However, it has been reported that the de-crease in void ratio in normally consolidated clays can-not be solely accounted for the increase in stiffness(Tsuchida et al., 1991; Kuntiwattanakul et al., 1995).This observation is similar to the aging effect discussedin Chapter 12. Hence, it can be considered that tem-perature is one of the driving forces in time-dependentdeformation of soils, and the rate process theory de-scribed in the next chapter conveniently explains muchof the observed temperature–time–effective stress be-havior of soils.


Limit equilibrium and plasticity analyses, as done, forexample, in studies of slope stability, lateral pressure,and bearing capacity, depend on accurate representa-tion of soil strength. So also does soil resistanceagainst failure due to earthquakes or other cyclic load-ings. The stresses and deformations under subfailureloading conditions depend on stress–strain properties.The factors responsible for and influencing strengthhave been identified and analyzed.

The strength of most uncemented soils is providedby interparticle sliding, dilatancy, particle rearrange-ments, particle crushing, and true cohesion. Frictionalresistance is developed by adhesion between contact-ing asperities on opposing particle surfaces. Values oftrue friction angle (��) range from less than 4� forsodium montmorillonite to more than 30� for feldsparand calcite. In the absence of cementation, true cohe-sion in soils is small. Results from discrete particlesimulations indicate that the deviatoric load applied toa particle assembly is transferred exclusively by thenormal contact forces in the strong force networks. Theinterparticle friction therefore acts as a kinematic con-straint of the strong force network and not as the directsource of macroscopic resistance to shear.

The residual friction angle depends on gradation,mineralogical composition, and effective stress. Thevalue of residual friction angle for clay may decreaseby several degrees for increases in effective stress onthe shear surface from 0 to 400 kPa (0 to 60 psi). Theshear displacements in one direction required to de-velop residual strength may be several tens of milli-meters. These factors should be taken into accountwhen analyzing stability problems.

Loose sands behave like normally consolidatedclays. The behavior of dense sand appears to be similarto that of overconsolidated clays. However, for clays,

a dense state (below critical state) can only be achievedby unloading, and, therefore, the preconsolidation pres-sure can be used to characterize the peak strength anddeformation. For sands, on the other hand, the differ-ence in strength and deformation behavior of normallyconsolidated dense sand and overconsolidated sand isnoted even when they are at the same void ratio andconfining pressure. This is because of possible differ-ent soil fabrics. The critical friction angle of cohesion-less soils contains contributions from particle crushing,particle rearrangement by rolling, as well as from in-terparticle sliding. The critical state concept can beused to characterize the density effect on peak strengthfor normally consolidated sand. Rearrangement androlling are unimportant when the clay content is highenough to prevent granular particle interference. Ide-ally, the critical state strength or friction angle shouldbe used for design of simple geotechnical structures.Otherwise, a careful selection of safety factor is neededwhen the peak strength or peak friction angle is used.However, whether it is possible to find the true criticalstate from conventional triaxial and torsional sheartests is questionable, especially for sands.

Because of the great diversity of soil types and therange of environmental conditions to which they maybe subjected, evaluations of deformation and strength,their characterization for analyses, and prediction offuture behavior will continue as major components ofany project. In the majority of geotechnical engineer-ing projects and problems, correct site characterizationand property evaluation are the two most critical ele-ments. If they are not done reasonably and reliably,then there cannot be understanding or confidence fromsubsequent soil mechanics analyses, no matter how so-phisticated they may be or how powerful the computerthat provides the numerical solutions.


1. Based on the descriptions given in Section 11.3and 11.6, summarize microscopic interpretation ofoverconsolidation, compaction, dilation, peak fric-tion angle, and critical state friction angle.

2. A clay has liquid and plastic limits of 80 and 25,respectively. For the following conditions, findpossible plastic failure mechanisms at differentconfining pressures using Eq. (11.30) and Fig.11.46. Discuss any practical implications.a. The clay is consolidated to a water content of

65 percent.b. The clay is heavy compacted to a water content

of 25 percent.

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3. A quartz sand has minimum and maximum voidratios of 0.35 and 0.75, respectively. The criticalstate friction angle is 35�.a. Using Eqs. (11.31) and (11.32), plot the critical

state line on the p�–q plane and on the e–logp� plane.

b. Find the undrained shear strengths at criticalstate when the void ratios are 0.4 and 0.7. Doesthe initial effective stress state matter to thecomputed values? How about the values of ex-cess pore pressure generated during undrainedtests?

c. Draw the effective stress path of a drained tri-axial compression test on the p�–q plane. Theinitial effective isotropic confining pressure is100 kPa. Find the drained strength and void ra-tio at critical state.

d. Sketch possible stress–axial strain and axialstrain–void ratio curves of the drained triaxialcompression test considered in part (c). Con-sider two different initial void ratios: (i) e �0.4 and (ii) e � 0.7. Comment on the results.

e. Repeat the calculations of parts (c) and (d)when the initial confining pressure is 1 MPa.Comment on the results.

4. Using the critical state of the sand defined inQuestion 3, plot void ratio versus peak friction an-gle at three different confining pressures: (i) 5 kPa,(ii) 500 kPa, and (iii) 5 MPa. To develop the plot,try (i) Eq. (11.37) or (ii) Fig. 11.56. Comment onthe results by discussing the relative importance ofconfining pressure and void ratio on friction angleof soils.

5. A clay was isotropically normally consolidatedand the isotropic compression line was found tobe e � 1.5 � 0.35 ln p�. The clay was then un-loaded isotropically and the slope of unloadingline on a e–ln p� diagram was found to be ! �0.05. A series of undrained triaxial compressiontests were performed on the clay, and the criticalstate was found to be q � 0.8p� and ecs � 1.3 �0.35 ln p�. Plot the stress and state paths on thep�–q plane and the e–ln p� plane for the followingconditions:a. The clay is isotropically consolidated to 400

kPa along the isotropic compression line.b. The clay at state (a) is sheared in undrained

conditions to the critical state. Also, sketch apossible stress–strain relationship.

c. The clay at state (a) is unloaded isotropicallyto 200 kPa (OCR � 2).

d. The clay at state (c) is sheared in undrainedconditions to the critical state. Also, sketch apossible stress–strain relationship.

e. Repeat parts (c) and (d) for other OCR condi-tions. Comment on the results.

6. The virgin compression curve of a clay was foundto be e � 1.3 � 0.6 log from one-dimensional��vconsolidation tests. The swelling index Cs was 0.1.The clay was preconsolidated to �� 100 kPav

prior to shearing.a. Using the Hvorslev parameters of hc � 0.1 and

� 15�, plot the failure envelope on the �–��eplane.

b. Plot shear strength �f / as a function of OCR��vand compare the results to the data shown inFig. 11.65.

7. Why does a sample with shear bands give differentstrengths depending on sample size?

8. Find a case study that describes the importance ofknowing the residual friction angle of clay. Ex-plain (a) the geologic and hydrogeologic condi-tions, (b) the possible peak, critical, and residualfriction angles, and (c) microscopic interpretationof decrease in friction angle at residual state.

9. Consider two saturated samples of the same soilhaving exactly the same water content, density,temperature, and structure are initially at equilib-rium under the same effective stress states. Com-pare and explain differences in strength, if any,that you would expect ifa. One is loaded in triaxial compression and the

other in plane strain.b. One is tested in triaxial compression and the

other is tested in plane stress.c. One is tested as is and the other is tested after

heating with (i) no drainage allowed and (ii)full drainage is allowed.

d. One is tested in triaxial compression and theother is tested in triaxial extension.

10. An embankment is to be constructed on a soft clay,and a potential failure surface is shown in the fig-ure below. The clay possesses anisotropic fabric.Considering the intermediate stress effect and an-isotropy effects described in Section 11.12, con-sider possible stress paths from the stress beforethe construction and discuss what strength valuesshould be used in design for the following loca-tions in the clay: (i) location A, which is locatedunderneath the embankment, (ii) location B, whichis at some depth near the toe of the embankment,

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and (iii) location C, which is located some dis-tance away from the embankment.

11. Find a paper that describes the effects of soil fabricon liquefaction resistance of sands. Give the mi-croscopic interpretation of why a sample with acertain soil fabric generates more excess pore pres-sures than others.

12. Provide physical explanations of how and why thefollowing factors can affect the cyclic resistanceratio (CRR) of sands:a. Confining pressureb. Initial K0 stress conditionc. Static shear stress along the sloping groundd. Shear modes (triaxial compression and exten-

sion, simple shear, etc.)e. Sample preparation and soil fabricf. Silt fines and clay fines

13. Water is injected into overconsolidated clay withan OCR of approximately 3. Using the correlationsand data presented throughout the book, estimatethe injection pressure required to fracture the clay

at a depth of 20 m. Consider both fracturing in (i)undrained conditions assuming that the injectedfluid has not permeated into the ground and (ii)drained conditions assuming the injection is in asteady state seepage state.

14. Convert some of the stiffness degradation curvesplotted in Figs. 11.10 and 11.119 to shear stressversus logarithm of strain. Identify the shearstresses required to reach the boundaries of differ-ent zones described in Section 11.17. Discusswhich zones are important for what type of geo-technical activities.

15. Give physical microscopic explanations of differ-ent stiffness degradation curves presented in Fig.11.120. Why can the multisurface concept pre-sented in Section 11.17 be used to model this com-plex behavior?

16. Discuss the differences between elastic and plasticdeformations of soils as microscopic behavior andmacroscopic behavior.

17. The data showing volume reduction with increas-ing temperature at a given pressure were presentedin Fig. 10.44 (Campanella and Mitchell, 1968). Ifwe consider the normal compression curve at76.5�F to be the reference state, the compressioncurves at the other temperatures can be interpretedto have exhibited temperature-induced creep be-havior and hence reached the quasioverconsoli-dated state. Can the data presented in Fig. 11.133be explained in such a way using the Hvoslevstrength concept for overconsolidated clays?

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465

CHAPTER 12

Time Effects on Strength andDeformation

12.1 INTRODUCTION

Virtually every soil ‘‘lives’’ in that all of its propertiesundergo changes with time–some insignificant, butothers very important. Time-dependent chemical,geomicrobiological, and mechanical processes mayresult in compositional and structural changes thatlead to softening, stiffening, strength loss, strengthgain, or altered conductivity properties. The need topredict what the properties and behavior will bemonths to hundreds or thousands of years from nowbased on what we know today is a major challenge ingeoengineering. Some time-dependent changes andtheir effects as they relate to soil formation, composi-tion, weathering, postdepositional changes in sedi-ments, the evolution of soil structure, and the like areconsidered in earlier chapters of this book. Emphasisin this chapter is on how time under stress changes thestructural, deformation, and strength properties ofsoils, what can be learned from knowledge of thesechanges, and their quantification for predictive pur-poses.

When soil is subjected to a constant load, it deformsover time, and this is usually called creep. The inversephenomenon, usually termed stress relaxation, is adrop in stress over time after a soil is subjected to aparticular constant strain level. Creep and relaxationare two consequences of the same phenomenon, thatis, time-dependent changes in structure. The rate andmagnitude of these time-dependent deformations aredetermined by these changes.

Time-dependent deformations and stress relaxationare important in geotechnical problems wherein long-term behavior is of interest. These include long-termsettlement of structures on compressible ground, de-formations of earth structures, movements of naturaland excavated slopes, squeezing of soft ground aroundtunnels, and time- and stress-dependent changes in soilproperties. The time-dependent deformation responseof a soil may assume a variety of forms owing to thecomplex interplays among soil structure, stress history,drainage conditions, and changes in temperature, pres-sure, and biochemical environment with time. Time-dependent deformations and stress relaxations usuallyfollow logical and often predictable patterns, at leastfor simple stress and deformation states such as uni-axial and triaxial compression, and they are describedin this chapter. Incorporation of the observed behav-ior into simple constitutive models for analytical de-scription of time-dependent deformations and stresschanges is also considered.

Time-dependent deformation and stress phenomenain soils are important not only because of the imme-diate direct application of the results to analyses ofpractical problems, but also because the results can beused to obtain fundamental information about soilstructure, interparticle bonding, and the mechanismscontrolling the strength and deformation behavior.Both microscale and macroscale phenomena are dis-cussed because understanding of microscale processescan provide a rational basis for prediction of macro-scale responses.

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466 12 TIME EFFECTS ON STRENGTH AND DEFORMATION

Figure 12.1 Creep and stress relaxation: (a) Creep underconstant stress and (b) stress relaxation under constant strain.

12.2 GENERAL CHARACTERISTICS

1. As noted in the previous section soils exhibitboth creep1 and stress relaxation (Fig. 12.1).Creep is the development of time-dependentshear and/or volumetric strains that proceedat a rate controlled by the viscouslike resistanceof soil structure. Stress relaxation is a time-dependent decrease in stress at constant defor-mation. The relationship between creep strainand the logarithm of time may be linear, con-cave upward, or concave downward as shownby the examples in Fig. 12.2.

2. The magnitude of these effects increases withincreasing plasticity, activity, and water content

1 The term creep is used herein to refer to time-dependent shearstrains and /or volumetric strains that develop at a rate controlled bythe viscous resistance of the soil structure. Secondary compressionrefers to the special case of volumetric strain that follows primaryconsolidation. The rate of secondary compression is controlled bythe viscous resistance of the soil structure, whereas, the rate of pri-mary consolidation is controlled by hydrodynamic lag, that is, howfast water can escape from the soil.

of the soil. The most active clays usually exhibitthe greatest time-dependent responses (i.e.,smectite � illite � kaolinite). This is becausethe smaller the particle size, the greater is thespecific surface, and the greater the water ad-sorption. Thus, under a given consolidationstress or deviatoric stress, the more active andplastic clays (smectites) will be at higher watercontent and lower density than the inactive clays(kaolinites). Normally consolidated soils exhibitlarger magnitude of creep than overconsolidatedsoils. However, the basic form of behavior isessentially the same for all soils, that is, undis-turbed and remolded clay, wet clay, dry clay,normally and overconsolidated soil, and wet anddry sand.

3. An increase in deviatoric stress level results inan increased rate of creep as shown in Fig. 12.1.Some soils may fail under a sustained creepstress significantly less (as little as 50 percent)than the peak stress measured in a shear test,wherein a sample is loaded to failure in a fewminutes or hours. This is termed creep rupture,and an early illustration of its importance wasthe development of slope failures in the Cucar-acha clay shale, which began some years afterthe excavation of the Panama Canal (Casa-grande and Wilson, 1951).

4. The creep response shown by the upper curvein Fig. 12.1 is often divided into three stages.Following application of a stress, there is first aperiod of transient creep during which the strainrate decreases with time, followed by creep atnearly a constant rate for some period. For ma-terials susceptible to creep rupture, the creeprate then accelerates leading to failure. Thesethree stages are termed primary, secondary, andtertiary creep.

5. An example of strain rates as a function of stressfor undrained creep of remolded illite is shownin Fig. 12.3. At low deviator stress, creep ratesare very small and of little practical importance.The curve shapes for deviator stresses up toabout 1.0 kg/cm2 are compatible with the pre-dictions of rate process theory, discussed in Sec-tion 12.4. At deviator stress approaching thestrength of the material, the strain rates becomevery large and signal the onset of failure.

6. A characteristic relationship between strain rateand time exists for most soils, as shown, forexample, in Fig. 12.4 for drained triaxial com-pression creep of London clay (Bishop, 1966)

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GENERAL CHARACTERISTICS 467

Figure 12.2 Sustained stress creep curves illustrating different forms of strain vs. logarithmof time behavior.

and Fig. 12.5 for undrained triaxial compressioncreep of soft Osaka clay (Murayama and Shi-bata, 1958). At any stress level (shown as a per-centage of the strength before creep in Fig. 12.4and in kg/cm2 in Fig. 12.5), the logarithm of thestrain rate decreases linearly with increase in the

logarithm of time. The slope of this relationshipis essentially independent of the creep stress;increases in stress level shift the line verticallyupward. The slope of the log strain rate versuslog time line for drained creep is approximately�1. Undrained creep often results in a slope be-

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Figure 12.3 Variation of creep strain rate with deviator stress for undrained creep of re-molded illite.

tween �0.8 and �1 for this relationship. Theonset of failure under higher stresses is signaledby a reversal in slope, as shown by the topmostcurve in Fig. 12.5.

7. Pore pressure may increase, decrease, or remainconstant during creep, depending on the volumechange tendencies of the soil structure andwhether or not drainage occurs during the de-formation process. In general, saturated softsensitive clays under undrained conditions aremost susceptible to strength loss during creepdue to reduction in effective stress caused byincrease in pore water pressure with time. Heav-ily overconsolidated clays under drained con-

ditions are also susceptible to creep rupture dueto softening associated with the increase in wa-ter content by dilation and swelling.

8. Although stress relaxation has been less studiedthan creep, it appears that equally regular pat-terns of deformation behavior are observed, forexample, Larcerda and Houston (1973).

9. Deformation under sustained stress ordinarilyproduces an increase in stiffness under the ac-tion of subsequent stress increase, as shownschematically in Fig. 12.6. This reflects thetime-dependent structural readjustment or ‘‘ag-ing’’ that follows changes in stress state. It isanalogous to the quasi-preconsolidation effect

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GENERAL CHARACTERISTICS 469

Figure 12.4 Strain rate vs. time relationships during drained creep of London clay (datafrom Bishop, 1966).

due to secondary compression discussed in Sec-tion 8.11; however, it may develop under un-drained as well as drained conditions.

10. As shown in Fig. 12.7, the locations of both thevirgin compression line and the value of the pre-consolidation pressure, determined in the��,p

laboratory are influenced by the rate of loadingduring one-dimensional consolidation (Grahamet al., 1983a; Leroueil et al., 1985). Thus, esti-mations of the overconsolidation ratio of claydeposits in the field are dependent on the load-ing rates and paths used in laboratory tests fordetermination of the preconsolidation pressure.If it is assumed that the relationship betweenstrain and logarithm of time during compressionis linear over the time ranges of interest and thatthe secondary compression index C�e is constantregardless of load, the rate-dependent precon-solidation pressure at can be related to the�� p 1

axial strain rate as follows (Silvestri et al, 1986;Soga and Mitchell, 1996; Leroueil and Marques,1996):

C�e / (Cc�Cr) �� p 1 1� � (12.1)� � � �� p(ref) 1(ref) 1(ref)

where Cc is the virgin compression index, Cr isthe recompression index and is the pre-��p(ref)

consolidation pressure at a reference strain rateIn this equation, the rate effect increases� .1(ref)

with the value of � � C�e / (Cc � Cr). The var-iation of preconsolidation pressure with strainrate is shown in Fig. 12.8 (Soga and Mitchell,1996). The data define straight lines, and theslope of the lines gives the parameter �. In gen-eral, the value of � ranges between 0.011 and0.094. Leroueil and Marques (1996) report val-ues between 0.029 and 0.059 for inorganicclays.

11. The undrained strength of saturated clay in-creases with increase in rate of strain, as shownin Figs. 12.9 and 12.10. The magnitude of theeffect is about 10 percent for each order of mag-nitude increase in the strain rate. The strain rate

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Figure 12.5 Strain rate vs. time relationships during undrained creep of Osaka alluvial clay(Murayama and Shibata, 1958).

Figure 12.6 Effect of sustained loading on (a) stress–strainand strength behavior and (b) one-dimensional compressionbehavior.

effect is considerably smaller for sands. In amanner similar to Eq. (12.1), a rate parameter� can be defined as the slope of a log–log plotof deviator stress at failure qƒ at a particularstrain rate relative to qƒ(ref), the strength at a�1

reference strain rate versus strain rate.� ,1(ref)

This gives the following equation:

�q �ƒ 1� (12.2)� �q �ƒ(ref) 1(ref)

The value of � ranges between 0.018 and 0.087,similar to the � rate parameter values used todefine the rate effect on consolidation pressurein Eq. (12.1). Higher values of � are associatedwith more metastable soil structures (Soga andMitchell, 1996). Rate dependency decreaseswith increasing sample disturbance, which isconsistent with this finding.

12.3 TIME-DEPENDENTDEFORMATION–STRUCTURE INTERACTION

In reality, completely smooth curves of the type shownin the preceding figures for strain and strain rate as afunction of time may not exist at all. Rather, as dis-

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TIME-DEPENDENT DEFORMATION–STRUCTURE INTERACTION 471

Figure 12.7 Rate dependency on one-dimensional compression characteristics of Batiscanclay: (a) compression curves and (b) preconsolidation pressure (Leroueil et al., 1985).

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Figure 12.8 Strain rate dependence on preconsolidation pressure determined from one-dimensional constant strain rate tests (Soga and Mitchell, 1996).

Figure 12.9 Effect of strain rate on undrained strength (Kulhawy and Mayne 1990). Re-printed with permission from EPRI.

cussed by Ter-Stepanian (1992), a ‘‘jump-like structurereorganization’’ may occur, reflecting a stochastic char-acter for the deformation, as shown in Fig. 12.11 forcreep of an undisturbed diatomaceous, lacustrine, ov-erconsolidated clay. Ter-Stepanian (1992) suggests thatthere are four levels of deformation: (1) the molecularlevel, which consists of displacement of flow units by

surmounting energy barriers, (2) mutual displacementof particles as a result of bond failures, but withoutrearrangement, (3) the structural level of soil defor-mation involving mutual rearrangements of particles,and (4) deformation at the aggregate level. Behavior atlevels 3 and 4 is discussed below; that at levels 1 and2 is treated in more detail in Section 12.4.

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Figure 12.10 Strain rate dependence on undrained shear strength determined using constantstrain rate CU tests (Soga and Mitchell, 1996).

Figure 12.11 Nonuniformity of creep in an undisturbed, di-atomaceous, lacustrine, overconsolidated clay (from Ter-Stepanian, 1992).

Time-Dependent Process of Particle Rearrangement

Creep can lead to rearrangement of particles into morestable configurations. Forces at interparticle contactshave both normal and tangential components, even ifthe macroscopic applied stress is isotropic. If, duringthe creep process, there is an increase in the proportionof applied deviator stress that is carried by interparticlenormal forces relative to interparticle tangential forces,then the creep rate will decrease. Hence, the rate atwhich deformation level 3 occurs need not be uniformowing to the particulate nature of soils. Instead it willreflect a series of structural readjustments as particlesmove up, over, and around each other, thus leading to

the somewhat irregular sequence of data points shownin Fig. 12.11.

Microscopically, creep is likely to occur in the weakclusters discussed in Section 11.6 because the contactsin them are at limiting frictional equilibrium. Anysmall perturbation in applied load at the contacts ortime-dependent loss in material strength can lead tosliding, breakage or yield at asperities. As particlesslip, propped strong-force network columns are dis-turbed, and these buckle via particle rolling as dis-cussed in Section 11.6.

To examine the effects of particle rearrangement,Kuhn (1987) developed a discrete element model thatconsiders sliding at interparticle contacts to be visco-frictional. The rate at which sliding of two particlesrelative to each other occurs depends on the ratio ofshear to normal force at their contact. The relationshipbetween rate and force is formulated in terms of rateprocess theory (see Section 12.4), and the mechanisticrepresentations of the contact normal and shear forcesare shown in Fig. 12.12. The time-dependent compo-nent in the tangential forces model is given as a ‘‘sinh-dashpot’’.2 The average magnitudes of both normal and

2 Kuhn (1987) used the following equation for rate of sliding at acontact:

t2kT F � ƒX � � exp � sinh� � � �nh RT 2kTn ƒ1

where n1 is the number of bonds per unit of normal force, ƒt is thetangential force and ƒn is the normal force. The others are parametersrelated to rate process theory as described in Section 12.4.

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Figure 12.12 Normal and tangential interparticle force mod-els according to Kuhn (1987).

Figure 12.13 Creep curves developed by numerical analysisof an irregular packing of circular disks (from Kuhn andMitchell, 1993).

tangential forces at individual contacts can change dur-ing deformation even though the applied boundarystresses are constant. Small changes in the tangentialand normal force ratio at a contact can have a verylarge influence on the sliding rate at that contact. Thesechanges, when summed over all contacts in the shearzone, result in a decrease or increase in the overallcreep rate.

A numerical analysis of an irregular packing of cir-cular disks using the sinh-dashpot representation givescreep behavior comparable to that of many soils asshown in Fig. 12.13 (Kuhn and Mitchell, 1993). Thecreep rate slows if the average ratio of tangential tonormal force decreases, whereas it accelerates and mayultimately lead to failure if the ratio increases. In somecases, the structural changes that are responsible forthe decreasing strain rate and increased stiffness maycause the overall soil structure to become more meta-stable. Then, after the strain reaches some limitingvalue, the process of contact force transfer from de-creasing tangential to increasing normal force reverses.This marks the onset of creep rupture as the structurebegins to collapse. A similar result was obtained byRothenburg (1992) who performed discrete particlesimulations in which smooth elliptical particles werecemented with a model exhibiting viscous character-istics in both normal and tangential directions.

Particle Breakage During Creep

Particle breakage can contribute to time-dependent de-formation of sands (Leung et al., 1996; Takei et al.,2001; McDowell, 2003). Leung et al. (1996) performedone-dimensional compression tests on sands, and Fig.

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After5 days After

290 sBefore Test

Sieve Size (μm)0

0

20

40

60

80

100

100 200 300 400

Dry sandRD = 75%Pressure = 15.4 MPa

� ��

�

Per

cent

age

Pas

sing

(%

)

Figure 12.14 Changes in particle size distribution of sandbefore loading and after two different load durations (fromLeung, et al., 1996).

12.14 shows the particle size distribution curves forsamples before loading and after two different load du-rations. The amount of particle breakage increasedwith load duration. Microscopic observations revealedthat angular protrusions of the grains were ground off,producing fines. The fines fill the voids between largerparticles and crushed particles progressively rear-ranged themselves with time.

Aging—Time-Dependent Strengthening of SoilStructure

The structural changes that occur during creep that iscontinuing at a decreasing rate cause an increase insoil stiffness when the soil is subjected to further stressincrease as shown in Fig. 12.6. Leonards and Alt-schaeffl (1964) showed that this increase in preconso-lidation pressure cannot be accounted for in terms ofthe void ratio decrease during the sustained compres-sion period. Time-dependent changes of these types area consequence of ‘‘aging’’ effects, which alter thestructural state of the soil. The fabric obtained by creepmay be different from that caused by increase in stress,even though both samples arrive at the same void ratio.Leroueil et al. (1996) report a similar result for an ar-tificially sedimented clay from Quebec, as shown inFig. 12.15a. They also measured the shear wave ve-locities after different times during the tests usingbender elements and computed the small strain elasticshear modulus. Figure 12.15b shows the change inshear modulus with void ratio.

Additional insight into the structural changes ac-companying the aging of clays is provided by the re-sults of studies by Anderson and Stokoe (1978) andNakagawa et al. (1995). Figure 12.16 shows changesin shear modulus with time under a constant confiningpressure for kaolinite clay during consolidation (An-derson and Stokoe, 1978). Two distinct phases of shearmodulus–time response are evident. During primaryconsolidation, values of the shear modulus increaserapidly at the beginning and begin to level off as theexcess pore pressure dissipates. After the end of pri-mary consolidation, the modulus increases linearlywith the logarithm of time during secondary compres-sion.

The expected change in shear modulus due to voidratio change during secondary compression can be es-timated using the following empirical formula forshear modulus as a function of void ratio and confiningpressure (Hardin and Black, 1968):

2(2.97 � e) 0.5G � A p� (12.3)1 � e

where A is a unit dependant material constant, e is thevoid ratio, and p� is the mean effective stress. Thedashed line in Fig. 12.16 shows the calculated in-creases in the shear modulus due to void ratio decreaseusing Eq. (12.3). It is evident that the change in voidratio alone does not provide an explanation for the sec-ondary time-dependent increase in shear modulus. Thisaging effect has been recorded for a variety of mate-rials, ranging from clean sands to natural clays (Afifiand Richart, 1973; Kokusho, 1987; Mesri et al., 1990,and many others). Further discussion of aging phenom-ena is given in Section 12.11.

Time-Dependent Changes in Soil Fabric

Changes in soil fabric with time under stress influencethe stability of soil structure. Changes in sand fabricwith time after load application in one-dimensionalcompression were measured by Bowman and Soga(2003). Resin was used to fix sand particles after var-ious loading times. Pluviation of the sand produced ahorizontal preferred particle orientation of soil grains,and increased vertical loading resulted in a greater ori-entation of particle long axes parallel to the horizontal,which is in agreement with the findings of Oda (1972a,b, c), Mitchell et al. (1976), and Jang and Frost (1998).Over time, however, the loading of sand caused parti-cle long axes to rotate toward the vertical direction(i.e., more isotropic fabric).

Experimental evidence (Bowman and Soga, 2003)showed that large voids became larger, whereas smallvoids became smaller, and particles group or cluster

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2.6

2.4

2.2

2.0

1.84 6 8 10 20

Vertical Effective Stress σ�v (kPa)

1

Small-strain Stiffness G0 (MPa)

0.5 2

A A

B B

C C

D D

E

F

E

F

Stiffness ChangeDuring the PrimaryConsolidationBetween B and C

NormalConsolidation Line

Creep for120 days

Increase in Stiffnessduring Creep (C-D)

Quasi-preconsolidationPressure

DestructuringState

(a ) (b )

5

Voi

d R

atio

e

Figure 12.15 (a) Compression curve and (b) variation of the maximum shear modulus G0

with void ratio for artificially sedimented Jonquiere clay (from Leroueil et al., 1996).

together with time. Based on these particulate levelfindings, it appears that the movements of particleslead to interlocking zones of greater local density. Theinterlocked state may be regarded as the final state ofany one particle under a particular applied load, due tokinematic restraint. The result, with time, is a stiffer,more efficient, load-bearing structure, with areas of rel-atively large voids and neighboring areas of tightlypacked particles. The increase in stiffness is achievedby shear connections obtained by the clustering. Then,when load is applied, the increased stiffness andstrength of the granular structure provides greater re-sistance to the load and the observed aging effect isseen. The numerical analysis in Kuhn and Mitchell(1993) led to a similar hypothesis for how a more‘‘braced’’ structure develops with time. For load appli-cation in a direction different to that during the agingperiod, however, the strengthening effect of aging maybe less, as the load-bearing particle column directiondiffers from the load direction.

Time-Dependent Changes in PhysicochemicalInteraction of Clay and Pore Fluid

A portion of the shear modulus increase during sec-ondary compression of clays is believed to result from

a strengthening of physicochemical bonds betweenparticles. To illustrate this, Nakagawa et al. (1995) ex-amined the physicochemical interactions between claysand pore fluid using a special consolidometer in whichthe sample resistivity and pore fluid conductivity couldbe measured. Shear wave velocities were obtained us-ing bender elements to determine changes in the stiff-ness characteristics of the clay during consolidation.Kaolinite clay mixed with saltwater was used for theexperiment, and changes in shear wave velocities andelectrical properties were monitored during the tests.

The test results showed that the pore fluid compo-sition and ion mobility changed with time. At eachload increment, as the effective stress increased withpore pressure dissipation, the shear wave velocities,and therefore the shear modulus, generally increasedwith time as shown in Fig. 12.17. It may be seen, how-ever, that in some cases, the shear wave velocities atthe beginning of primary consolidation decreasedslightly from the velocities obtained immediately be-fore application of the incremental load, probably as aresult of soil structure breakdown. During the subse-quent secondary compression stage, the shear wave ve-locity again increased. As was the case for the resultsin Fig.12.16, the increases in shear wave velocity dur-

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10

20

30

40

50

0

0.5

1.0

1.5

2.0

Primary Consolidation Secondary Compression

Sam

ple

Hei

ght C

hang

e (m

m)

100 101 102 103 104

Time (min)

101 102 103 104

Time (min)

Ball Kaolinite

Possible Change in Gby Void Ratio DecreaseOnly Estimated UsingEq. (12.3)

Initial Consolidation Pressure = 70 kPaInitial Void Ratio e0 = 1.1

IG = ΔG per log time= 6.2 MPa

She

ar M

odul

us o

f les

s th

an γ

= 1

0-3 %

(M

Pa)

Figure 12.16 Modulus and height changes as a function oftime under constant confining pressure for kaolinite: (a) shearmodulus and (b) height change (from Anderson and Stokoe,1978).

Figure 12.17 Changes in shear wave velocity during pri-mary consolidation and secondary compression of kaolinite.Consolidation pressures: (a) 11.8 kPa and (b) 190 kPa (fromNakagawa et al., 1995).

ing secondary compression are greater than can be ac-counted for by increase in density.

The electrical conductivity of the sample measuredby filter electrodes increased during the early stages ofconsolidation, but then decreased continuously there-after as shown in Fig. 12.18. The electrical conductiv-ity is dominated by flow through the electrolytesolution in the pores. During the initial compression, abreakdown of structure releases ions into the pore wa-ter, increasing the electrical conductivity. With time,the conductivity decreased, suggesting that the releasedions are accumulating near particle surfaces. Some ofthese released ions are expelled from the specimen asconsolidation progressed as shown in Fig. 12.18b. Aslow equilibrium under a new state of effective stressis hypothesized to develop that involves both smallparticle rearrangements, associated with decrease invoid ratio during secondary compression, and devel-opment of increased contact strength as a result of pre-

cipitation of salts from the pore water and/or otherprocesses.

Primary consolidation can be considered a result ofdrainage of pore water fluid from the macropores,whereas secondary compression is related to the de-layed deformation of micropores in the clay aggregates(Berry and Poskitt, 1972; Matsuo and Kamon, 1977;Sills, 1995). The mobility of water in the microporesis restricted due to small pore size and physicochem-ical interactions close to the clay particle surfaces. Ak-agi (1994) did compression tests on specially preparedclay containing primarily Ca in the micropores and Nain the macropores. Concentrations of the two ions inthe expelled water at different times after the start ofconsolidation were consistent with this hypothesis.

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Figure 12.18 Changes in electrical conductivity of the porewater during primary consolidation and secondary compres-sion of kaolinite. Consolidation pressures: (a) 95 kPa and (b)190 kPa (from Nakagawa et al., 1995).

Figure 12.19 Energy barriers and activation energy.

12.4 SOIL DEFORMATION AS A RATEPROCESS

Deformation and shear failure of soil involve time-dependent rearrangement of matter. As such, thesephenomena are amenable for study as rate processesthrough application of the theory of absolute reactionrates (Glasstone et al., 1941). This theory providesboth insights into the fundamental nature of soilstrength and functional forms for the influences of sev-eral factors on soil behavior.

Detailed development of the theory, which is basedon statistical mechanics, may be found in Eyring(1936), Glasstone et al. (1941), and elsewhere in thephysical chemistry literature. Adaptations to the studyof soil behavior include those by Abdel-Hady and Her-rin (1966), Andersland and Douglas (1970), Christen-

sen and Wu (1964), Mitchell (1964), Mitchell et al.(1968, 1969), Murayama and Shibata (1958, 1961,1964), Noble and Demirel (1969), Wu et al. (1966),Keedwell (1984), Feda (1989, 1992), and Kuhn andMitchell (1993).

Concept of Activation

The basis of rate process theory is that atoms, mole-cules, and/or particles participating in a time-dependent flow or deformation process, termed flowunits, are constrained from movement relative to eachother by energy barriers separating adjacent equilib-rium positions, as shown schematically by Fig. 12.19.The displacement of flow units to new positions re-quires the acquisition of an activation energy F ofsufficient magnitude to surmount the barrier. The po-tential energy of a flow unit may be the same followingthe activation process, or higher or lower than it wasinitially. These conditions are shown by analogy withthe rotation of three blocks in Fig. 12.20. In each case,an energy barrier must be crossed. The assumption ofa steady-state condition is implicit in most applicationsto soils concerning the at-rest barrier height betweensuccessive equilibrium positions.

The magnitude of the activation energy depends onthe material and the type of process. For example, val-ues of F for viscous flow of water, chemical reac-tions, and solid-state diffusion of atoms in silicates areabout 12 to 17, 40 to 400, and 100 to 150 kJ/mol offlow units, respectively.

Activation Frequency

The energy to enable a flow unit to cross a barrier maybe provided by thermal energy and by various appliedpotentials. For a material at rest, the potential energy–displacement relationship is represented by curve A inFig. 12.21. From statistical mechanics it is known that

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SOIL DEFORMATION AS A RATE PROCESS 479

Figure 12.20 Examples of activated processes: (a) steady-state, (b) increased stability, and(c) decreased stability.

Figure 12.21 Effect of a shear force on energy barriers.

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the average thermal energy per flow unit is kT, wherek is Boltzmann’s constant (1.38 � 10�23 J K�1) and Tis the absolute temperature (K). Even in a material atrest, thermal vibrations occur at a frequency given bykT /h, where h is Planck’s constant (6.624 � 10�34 Js�1). The actual thermal energies are divided amongthe flow units according to a Boltzmann distribution.

It may be shown that the probability of a given unitbecoming activated, or the proportion of flow units thatare activated during any one oscillation is given by

Fp( F) � exp � (12.4)� �NkT

where N is Avogadro’s number (6.02 � 1023), and Nkis equal to R, the universal gas constant (8.3144 J K�1

mol�1). The frequency of activation � then is

kT � F� � exp (12.5)� �h NkT

In the absence of directional potentials, energy bar-riers are crossed with equal frequency in all directions,and no consequences of thermal activations are ob-served unless the temperature is sufficiently high thatsoftening, melting, or evaporation occurs. If, however,a directed potential, such as a shear stress, is applied,then the barrier heights become distorted as shown bycurve B in Fig. 12.21. If ƒ represents the force actingon a flow unit, then the barrier height is reduced by anamount (ƒ� /2) in the direction of the force and in-creased by a like amount in the opposite direction,where � represents the distance between successiveequilibrium positions.3 Minimums in the energy curveare displaced a distance � from their original positions,representing an elastic distortion of the material struc-ture.

The reduced barrier height in the direction of forceƒ increases the activation frequency in that direction to

kT F /N � ƒ� /2� → � exp � (12.6)� �h kT

and in the opposite direction, the increased barrierheight decreases the activation frequency to

kT F /N � ƒ� /2� ← � exp � (12.7)� �h kT

3 Work (ƒ� / 2) done by the force ƒ as the flow unit drops from thepeak of the energy barrier to a new equilibrium position is assumedto be given up as heat.

The net frequency of activation in the direction ofthe force then becomes

kT F ƒ�(� →) � (� ←) � 2 exp � sinh� � � �h RT 2kT

(12.8)

Strain Rate Equation

At any instant, some of the activated flow units maysuccessfully cross the barrier; others may fall back intotheir original positions. For each unit that is successfulin crossing the barrier, there will be a displacement ��.The component of �� in a given direction times thenumber of successful jumps per unit time gives the rateof movement per unit time. If this rate of movementis expressed on a per unit length basis, then the strainrate is obtained.�

Let X � F (proportion of successful barrier cross-ings and ��) such that

� � X[(� →) � (� ←)] (12.9)

Then from Eq. (12.8)

kT F ƒ�� 2X exp � sinh (12.10)� � � �h RT 2kT

The parameter X may be both time and structure de-pendent.

If (ƒ� /2kT) � 1, then sinh(ƒ� /2kT) � (ƒ� /2kT), andthe rate is directly proportional to ƒ. This is the casefor ordinary Newtonian fluid flow and diffusion where

1 � � (12.11)

�

where is the shear strain rate, � is dynamic viscosity,and � is shear stress.

For most solid deformation problems, however,(ƒ� /2kT) � 1 (Mitchell et al., 1968), so

ƒ� 1 ƒ�sinh � exp (12.12)� � � �2kT 2 2kT

and

kT F ƒ�N� � X exp � exp (12.13)� � � �h RT 2RT

Equation (12.13) applies except for very small stressintensities, where the exponential approximation of thehyperbolic sine is not justified. Equations (12.10) and

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BONDING, EFFECTIVE STRESSES, AND STRENGTH 481

(12.13) or comparable forms have been used to obtaindashpot coefficients for rheological models, to obtainfunctional forms for the influences of different factorson strength and deformation rate, and to study defor-mation rates in soils. For example, Kuhn and Mitchell(1993) used this form as part of the particle contactlaw in discrete element modeling as described in theprevious section. Puzrin and Houlsby (2003) used it asan internal function of a thermomechanical-basedmodel and derived a rate-dependent constitutive modelfor soils.

Soil Deformation as a Rate Process

Although there does not yet appear to be a rigorousproof of the correctness of the detailed statistical me-chanics formulation of rate process theory, even forsimple chemical reactions, the real behavior of manysystems has been substantially in accord with it. Dif-ferent parts of Eq. (12.13) have been tested separately(Mitchell et al., 1968). It was found that the tempera-ture dependence of creep rate and the stress depend-ence of the experimental activation energy [Eq.(12.14)] were in accord with predictions. These resultsdo not prove the correctness of the theory; they do,however, support the concept that soil deformation isa thermally activated process.

Arrhenius Equation

Equation (12.13) may be written

kT E� � X exp � (12.14)� �h RT

where

ƒ�NE � F � (12.15)

2

is termed the experimental activation energy. For allconditions constant except T, and assuming thatX(kT /h) � constant � A,

E� � A exp � (12.16)� �RT

Equation (12.16) is the same as the well-known em-pirical equation proposed by Arrhenius around 1900to describe the temperature dependence of chemicalreaction rates. It has been found suitable also forcharacterization of the temperature dependence ofprocesses such as creep, stress relaxation, secondarycompression, thixotropic strength gain, diffusion, andfluid flow.

12.5 BONDING, EFFECTIVE STRESSES, ANDSTRENGTH

Using rate process theory, the results of time-dependent stress–deformation measurements in soilscan be used to obtain fundamental information aboutsoil structure, interparticle bonding, and the mecha-nisms controlling strength and deformation behavior.

Deformation Parameters from Creep Test Data

If the shear stress on a material is � and it is distributeduniformly among S flow units per unit area, then

�ƒ � (12.17)

S

Displacement of a flow unit requires that interatomicor intermolecular forces be overcome so that it can bemoved. Let it be assumed that the number of flow unitsand the number of interparticle bonds are equal.

If D represents the deviator stress under triaxialstress conditions, the value of ƒ on the plane of max-imum shear stress is

Dƒ � (12.18)

2S

so Eq. (12.13) becomes

kT F D�� X exp � exp (12.19)� � � �h RT 4SkT

This equation describes creep as a steady-stateprocess. Soils do not creep at constant rate, however,because of continued structural changes during de-formation as described in Section 12.3, except forthe special case of large deformations after mobiliza-tion of full strength. Thus, care must be taken in ap-plication of Eq. (12.19) to ensure that comparisons ofcreep rates and evaluations of the influences of differ-ent factors are made under conditions of equal struc-ture. The time dependency of creep rate and thepossible time dependencies of the parameters in Eq.(12.19) are considered in Section 12.8.

Determination of Activation Energy From Eq.(12.14)

� ln(� /T) E� � (12.20)

�(1/T) R

provided strain rates are considered under conditionsof unchanged soil structure. Thus, the value of E canbe determined from the slope of a plot of ver-ln(� /T)sus (1/T). Procedures for evaluation of strain rates for

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Table 12.1 Activation Energies for Creep of Several Materials

MaterialActivation Energy

(kJ/ mol)a Reference

1. Remolded illite, saturated, water contents of30 to 43%

105–165 Mitchell, et al. (1969)

2. Dried illite: samples air-dried fromsaturation, then evacuated

155 Mitchell, et al. (1969)

3. San Francisco Bay mud, undisturbed 105–135 Mitchell, et al. (1969)4. Dry Sacramento River sand �105 Mitchell, et al. (1969)5. Water 16–21 Glasstone, et al. (1941)6. Plastics 30–60 Ree and Eyring (1958)7. Montmorillonite–water paste, dilute 84–109 Ripple and Day (1966)8. Soil asphalt 113 Abdel-Hady and Herrin (1966)9. Lake clay, undisturbed and remolded 96–113 Christensen and Wu (1964)

10. Osaka clay, overconsolidated 120–134 Murayama and Shibata (1961)11. Concrete 226 Polivka and Best (1960)12. Metals 210� Finnie and Heller (1959)13. Frozen soils 393 Andersland and Akili (1967)14. Sault Ste. Marie clay, suspensions,

discontinuous structuresSame as

waterAndersland and Douglas (1970)

15. Sault Ste. Marie clay, Li�, Na�, K� forms,in H2O and CCl4, consolidated

117 Andersland and Douglas (1970)

aThe first four values are experimental activation energies, E. Whether the remainder are values of F or E is notalways clear in the references cited.

soils at different temperatures but at the same structureare given by Mitchell et al. (1968, 1969).

Determination of Number of Bonds For stresseslarge enough to justify approximating the hyperbolicsine function by a simple exponential in the creep rateequation and small enough to avoid tertiary creep, thelogarithm of strain rate varies directly with the deviatorstress. For this case, Eq. (12.19) can be written

� � K(t) exp(�D) (12.21)

where

kT FK(t) � X exp � (12.22)� �h RT

�� (12.23)

4SkT

Parameter � is a constant for a given value of ef-fective consolidation pressure and is given by the slopeof the relationship between log strain rate and stress.It is evaluated using strain rates at the same time afterthe start of creep tests at several stress intensities. With

� known, � /S is calculated as a measure of the numberof interparticle bonds.4

Activation Energies for Soil Creep

Activation energies for the creep of several soils andother materials are given in Table 12.1. The free energyof activation for creep of soils is in the range of about80 to 180 kJ/mol. Four features of the values for soilsin Table 12.1 are significant:

1. The activation energies are relatively large, muchhigher than for viscous flow of water.

2. Variations in water content (including completedrying), adsorbed cation type, consolidation pres-sure, void ratio, and pore fluid have no significanteffect on the required activation energy.

3. The values for sand and clay are about the same.4. Clays in suspension with insufficient solids to

form a continuous structure deform with an ac-tivation energy equal to that of water.

4 A procedure for evaluation of � from the results of a test at asuccession of stress levels on a single sample is given by Mitchellet al. (1969).

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Figure 12.22 Interpretation of � in terms of silicate mineralsurface structure.

Number of Interparticle Bonds

Evaluation of S requires knowledge of �, the separationdistance between successive equilibrium positions inthe interparticle contact structure. A value of 0.28 nm(2.8 A) has been assumed because it is the same as thedistance separating atomic valleys in the surface of asilicate mineral. It is hypothesized that deformation in-volves the displacement of oxygen atoms along con-tacting particle surfaces, as well as periodic rupture ofbonds at interparticle contacts. Figure 12.22 shows thisinterpretation for � schematically. If the above as-sumption for � is incorrect, calculated values of S willstill be in the same correct relative proportion as longas � remains constant during deformation.

Normally Consolidated Clay Results of creep testsat different stress intensities for different consolidationpressures enable computation of S as a function of con-solidation pressure. Values obtained for undisturbedSan Francisco Bay mud are shown in Fig. 12.23. Theopen point is for remolded bay mud. An undisturbedspecimen was consolidated to 400 kPa, rebounded to

50 kPa, and then remolded at constant water content.The effective consolidation pressure dropped to 25 kPaas a result of the remolding. The drop in effectivestress was accompanied by a corresponding decreasein the number of interparticle bonds. Tests on remoldedillite gave comparable results. A continuous inverse re-lationship between the number of bonds and watercontent over a range of water contents from more than40 percent to air-dried and vacuum-desiccated clay isshown in Fig. 12.24. The dried material had a watercontent of 1 percent on the usual oven-dried basis. Thevery large number of bonds developed by drying isresponsible for the high dry strength of clay.

Overconsolidated Clay Samples of undisturbedSan Francisco Bay mud were prepared to overcon-solidation ratios of 1, 2, 4, and 8 following the stresspaths shown in the upper part of Fig. 12.25. The sam-ple represented by the triangular data point was re-molded after consolidation and unloading to point d�,where it had a water content of 52.3 percent. The un-drained compressive strength as a function of consol-idation pressure is shown in the middle section of Fig.12.25, and the number of bonds, deduced from thecreep tests, is shown in the lower part of the figure.The effect of overconsolidation is to increase the num-ber of interparticle bonds over the values for normallyconsolidated clay. Some of the bonds formed duringconsolidation are retained after removal of much of theconsolidation pressure.

Values of compressive strength and numbers ofbonds from Fig. 12.25 are replotted versus each otherin Fig. 12.26. The resulting relationship suggests thatstrength depends only on the number of bonds and isindependent of whether the clay is undisturbed, re-molded, normally consolidated, or overconsolidated.

Dry Sand Creep tests on oven-dried sand yieldedresults of the same type as obtained for clay, as shownin Fig. 12.27, suggesting that the strength-generatingand creep-controlling mechanisms may be similar forboth types of material.

Composite Strength-Bonding Relationship Valuesof S and strength for many soils are combined in Fig.12.28. The same proportionality exists for all the ma-terials, which may seem surprising, but which in realityshould be expected, as discussed further later.

Significance of Activation Energy and Bond NumberValues

The following aspects of activation energies and num-bers of interparticle bonds are important in the under-standing of the deformation and strength behavior ofuncemented soils.

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Figure 12.23 Number of interparticle bonds as a function of consolidation pressure fornormally consolidated San Francisco Bay mud.

Figure 12.24 Number of bonds as a function of water con-tent for illite.

1. The values of activation energy for deformationof soils are high in comparison with other ma-terials and indicate breaking of strong bonds.

2. Similar creep behavior for wet and dry clay andfor wet and dry sand indicates that deformationis not controlled by viscous flow of water.

3. Comparable values of activation energy for wetand dry soil indicate that water is not respon-sible for bonding.

4. Comparable values of activation energy for clayand sand support the concept that interparticlebond strengths are the same for both types ofmaterial. This is supported also by the unique-ness of the strength versus number of bonds re-lationship for all soils.

5. The activation energy and presumably, there-fore, the bonding type are independent of con-solidation pressure, void ratio, and watercontent.

6. The number of bonds is directly proportional toeffective consolidation pressure for normallyconsolidated clays.

7. Overconsolidation leads to more bonds than innormally consolidated clay at the same effectiveconsolidation pressure.

8. Strength depends only on the number of bonds.9. Remolding at constant water content causes a

decrease in the effective consolidation pressure,which means also a decrease in the number ofbonds.

10. There are about 100 times as many bonds in dryclay as in wet clay.

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Figure 12.25 Consolidation pressure, strength, and bond numbers for San Francisco Baymud.

Although it may be possible to explain these resultsin more than one way, the following interpretation ac-counts well for them. The energy F activates a moleof flow units. The movement of each flow unit mayinvolve rupture of single bonds or the simultaneousrupture of several bonds. Shear of dilute montmoril-lonite–water pastes involves breaking single bonds(Ripple and Day, 1966). For viscous flow of water, theactivation energy is approximately that for a single hy-drogen bond rupture per flow unit displacement, eventhough each water molecule may form simultaneously

up to four hydrogen bonds with its neighbors. If thesingle-bond interpretation is also correct for soils, thenconsistency in Eq. (12.10) requires that shear force ƒpertain to the force per bond. On this basis, parameterS indicates the number of single bonds per unit area.In the event activation of a flow unit requires simul-taneous rupture of n bonds, then S represents 1/nth ofthe total bonds in the system.

That the activation energy for deformation of soil iswell into the chemical reaction range (40 to 400 kJ/mol) does not prove that bonding is of the primary

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Figure 12.26 Strength as a function of number of bonds forSan Francisco Bay mud.

Figure 12.28 Composite relationship between shear strengthand number of interparticle bonds (from Matsui and Ito,1977). Reprinted with permission from The Japanese Societyof SMFE.

Figure 12.27 Strength as a function of number of bonds for dry Antioch River sand.

valence type because simultaneous rupture of severalweaker bonds could yield values of the magnitude ob-served. On the other hand, the facts that (1) the acti-vation energy is much greater than for flow of water,(2) it is the same for wet and dry soils, and (3) it isessentially the same for different adsorbed cations and

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pore fluids (Andersland and Douglas, 1970) suggestthat bonding is through solid interparticle contacts.Physical evidence for the existence of solid-to-solidcontact between clay particles has been obtained in theform of photomicrographs of particle surfaces thatwere scratched during shear (Matsui et al., 1977, 1980)and acoustic emissions (Koerner et al., 1977).

Activation energy values of 125 to 190 kJ/mol areof the same order as those for solid-state diffusion ofoxygen in silicate minerals. This supports the conceptthat creep movements of individual particles could re-sult from slow diffusion of oxygen ions in and aroundinterparticle contacts. The important minerals in bothsand and clay are silicates, and their surface layersconsist of oxygen atoms held together by silicon at-oms. Water in some form is adsorbed onto these sur-faces. The water structure consists of oxygens heldtogether by hydrogen. It is not too different from thatof the silicate layer in minerals. Thus, a distinct bound-ary between particle surface and water may not be dis-cernable. Under these conditions, a more or lesscontinuous solid structure containing water moleculesthat propagates through interparticle contacts can bevisualized.

An individual flow unit could be an atom, a groupof atoms or molecules, or a particle. The precedingarguments are based on the interpretation that individ-ual atoms are the flow units. This is consistent withboth the relative and actual values of S that have beendetermined for different soils. Furthermore, by using aformulation of the rate process equation that enabledcalculation of the flow unit volume from creep testdata, Andersland and Douglas (1970) obtained a valueof about 1.7 A3, which is of the same order as that ofindividual atoms. On the other hand, Keedwell (1984)defined flow units between quartz sand particles asconsisting of six O2� ions and six Si4� ions and be-tween two montmorillonite clay particles as consistingof four H2O molecules.

If particles were the flow units, not only would it bedifficult to visualize their thermal vibrations, but thenS would relate to the number of interparticle contacts.It is then difficult to conceive how simply drying a claycould give a 100-fold increase in the number of inter-particle contacts, as would have to be the case accord-ing to Fig. 12.27. A more plausible interpretation isthat drying, while causing some increase in the numberof interparticle contacts during shrinkage, causesmainly an increase in the number of bonds per contactbecause of increased effective stress.

At any value of effective stress, the value of S isabout the same for both sand and clay. The number ofinterparticle contacts should be vastly different; how-

ever, for equal numbers of contacts per particle, thenumber per unit volume should vary inversely with thecube of particle size. Thus, the number of clay particlesof 1-�m particle size should be some nine orders ofmagnitude greater than for a sand of 1-mm averageparticle size. Each contact between sand particleswould involve many bonds; in clay, the much greaternumber of contacts would mean fewer bonds per par-ticle.

The contact area required to develop bonds in thenumbers indicted in Figs. 12.23 to 12.27 is very small.For example, for a compressive strength of 3 kg/cm2

(� 300 kPa) there are 8 � 1010 bonds/cm2 of shearsurface. Oxygen atoms on the surface of a silicate min-eral have a diameter of 0.28 nm. Allowing an area 0.30nm on a side for each oxygen gives 0.09 nm2, or 9 �10�16 cm2, per bonded oxygen for a total area of 9 �10�16 � 8 � 1010 � 7.2 � 10�5 cm2/cm2 of soil crosssection.

Hypothesis for Bonding, Effective Stress, andStrength

Normal effective stresses and shear stresses can betransmitted only at interparticle contacts in most soils.5

The predominant effects of the long-range physico-chemical forces of interaction are to control the initialsoil fabric and to alter the forces transmitted at contactpoints from what they would be due to applied stressesalone.

Interparticle contacts are effectively solid, and it islikely that both adsorbed water and cations in the con-tact zone participate in the structure. An interparticlecontact may contain many bonds that may be strong,approaching the primary valence type. The number ofbonds at any contact depends on the compressive forcetransmitted at the contact, and the Terzaghi–Bowdenand Tabor adhesion theory of friction presented in Sec-tion 11.4, can account for strength. The macroscopicstrength is directly proportional to the number ofbonds.

For normally consolidated soils the number of bondsis directly proportional to the effective stress. As a re-sult of particle rearrangements and contacts formedduring virgin compression, an overconsolidated soil ata given effective stress has a greater number of bondsand higher strength than a normally consolidated soil.This effect is more pronounced in clays than in sandsbecause the larger and bulky sand grains tend to re-

5 Pure sodium montmorillonite may be an exception since a part ofthe normal stress can be carried by physicochemical forces of inter-action. The true effective stress may be less than the apparent effec-tive stress by R � A as discussed in Chapter 7.

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cover their original shapes when unloaded, thus rup-turing most of the bonds in excess of those needed toresist the lower stress. The strength of the interparticlecontacts can vary over a wide range, depending on thenumber of bonds per contact.

The unique relationship between strength and num-ber of bonds for all soils, as indicted by Fig. 12.28,reflects the fact that the minerals comprising most soilsare silicates, and they all have similar surface struc-tures.

In the absence of chemical cementation, interparticlebonds may form in response to interparticle contactforces generated by either applied stresses, physico-chemical forces of interaction, or both. Any bonds ex-isting in the absence of applied effective stress, that is,when �� 0, are responsible for true cohesion. Thereshould be no difference between friction and cohesionin terms of the shearing process. Complete failure inshear involves simultaneous rupture or slipping of allbonds along the shear plane.

12.6 SHEARING RESISTANCE AS A RATEPROCESS

Deformation at large strain can approach a steady-statecondition where there is little further structural changewith time (such as at critical state). In this case, Eq.(12.19) can be used to describe the shearing resistanceas a function of strain rate and temperature. If the max-imum shear stress � is substituted for the deviator stressD, then

� � �1 3� � (12.24)2

and

kT F �� X exp � exp (12.25)� � � �h RT 2SkT

Taking logarithms of both sides of Eq. (12.25) gives

kT F ��ln � � ln X � � (12.26)� �h RT 2SkT

By assuming X(kT /h) is a constant equal to B(Mitchell, 1964), Eq. (12.26) can be rearranged to give

2S 2SkT �� F � ln (12.27)� ��N � B

From the relationships in Section 12.5, the followingrelationship between bonds per unit area and effectivestress is suggested.

S � a � b�� (12.28)ƒ

where a and b are constants and is the effective��ƒnormal stress on the shear plane. Thus, Eq. (12.27)becomes

2a F 2akT � 2b F 2bkT �� ln � � ln �� ƒ�N � B �N � B

(12.29)

Equation (12.29) is of the same form as the Cou-lomb equation for strength:

� � c � �� tan � (12.30)ƒ

By analogy,

2a F 2akT �c � � ln (12.31)

�N � B

2b F 2bkT �tan � � � ln (12.32)

�N � B

These equations state that both cohesion and frictiondepend on the number of bonds times the bondstrength, as reflected by the activation energy, and thatthe values of c and � should depend on the rate ofdeformation and the temperature.

Strain Rate Effects

All other factors being equal, the shearing resistanceshould increase linearly with the logarithm of the rateof strain. This is shown to be the case in Fig. 12.9,which contains data for 26 clays. Additional data forseveral clays are shown in Fig. 12.29, where shearingresistance as a function of the speed of vane rotationin a vane shear test is plotted. Analysis of the relation-ship between shearing stress and angular rate of vanerotation " shows that � / log " decreases with anincrease in water content. This follows directly fromEq. (12.29) because

d� 2akT 2bkT 2kT� � �� (a � b��)ƒ ƒd ln(� /B) � � �

(12.33)

that is, d� /d ln is proportional to the number of(� /B)bonds, which decreases with increasing water content.

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CREEP AND STRESS RELAXATION 489

Figure 12.29 Effect of rate of shear on shearing resistance of remolded clays as determinedby the laboratory vane apparatus (prepared from the data of Karlsson, 1963).

This interpretation of the data in Figs. 12.9 and 12.29assumes that the effective stress was unaffected bychanges in the strain rate, which may not necessarilybe true in all cases.

Effect of Temperature

Assumptions of reasonable values for parameters showthat the term is less than one (Mitchell, 1964).(� /B)Thus the quantity in Eq. (12.29) is negative,ln(� /B)and an increase in temperature should give a decreasein strength, all other factors being constant. That thisis the case is demonstrated by Fig. 12.30, which showsdeviator stress as a function of temperature for samplesof San Francisco Bay mud compared under conditionsof equal mean effective stress and structure. Other ex-amples of the influence of temperature on strength areshown in Figs. 11.6 and 11.133.

12.7 CREEP AND STRESS RELAXATION

Although the designation of a part of the strain versustime relationship as steady state or secondary creepmay be convenient for some analysis purposes, a truesteady state can exist only for conditions of constantstructure and stress. Such a set of conditions is likelyonly for a fully destructured soil, and a fully destruc-tured state is likely to persist only during deformationat a constant rate, that is, at failure. This state is oftencalled ‘‘steady state,’’ in which the soil is deformingcontinuously at constant volume under constant shearand confining stresses (Castro, 1975; Castro andPoulos, 1977).

Otherwise, bond making and bond breaking occurat different rates as a result of different internal time-and strain-dependent phenomena, which might includethixotropic hardening, viscous flows of water and ad-

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Figure 12.30 Influence of temperature on the shearing re-sistance of San Francisco Bay mud. Comparison is for sam-ples at equal mean effective stress and at the same structure.

Figure 12.31 Variation of creep strain rate with deviatorstress for drained creep of London clay (data from Bishop,1966).

sorbed films, chemical, and biological transformations,and the like. Furthermore, distortions of the soil struc-ture and relative movements between particles causechanges in the ratio of tangential to normal forces atinterparticle contacts that may be responsible for largechanges in creep rate. Because of these time depend-encies some of the parameters in Eq. (12.19) may betime dependent. For example, Feda (1989) accountedfor the time dependency of creep rate by takingchanges in the number of structural bonds into account.Therefore, application of Eq. (12.19) for the determi-nation of the bonding and effective stress relationshipsdiscussed in Section 12.5 required comparison of creeprates under conditions of comparable time and struc-ture.

The influence of creep stress magnitude on the creeprate at a given time after the application of the stressto identical samples of a soil was shown in Fig. 12.3.At low stresses the creep rates are small and of littlepractical importance. The curve shape is compatiblewith the hyperbolic sine function predicted by rateprocess theory, as given by Eq. (12.10). In the mid-range of stresses, a nearly linear relationship is foundbetween logarithm of strain rate and stress, also as pre-dicted by Eq. (12.10) for the case where the argumentof the hyperbolic sine is greater than 1. At stressesapproaching the strength of the material, the strain ratebecomes very large and signals the onset of failure.Other examples of the relationships between logarithmof strain rate and creep stress corresponding to differ-ent times after the application of the creep stress aregiven in Fig. 12.31 for drained tests on London clay

and Fig. 12.32 for undrained tests on undisturbed SanFrancisco Bay mud. Only values for the midrange ofstresses are shown in Figs. 12.31 and 12.32.

Effect of Composition

In general, the higher the clay content and the moreactive the clay, the more important are stress relaxationand creep, as illustrated by Figs. 4.22 and 4.23, wherecreep rates, approximated by steady-state values, arerelated to clay type, clay content, and plasticity. Time-dependent deformations are more important at highwater contents than at low. Deviatoric creep and sec-ondary compression are greater in normally consoli-dated than overconsolidated soils.

Although the magnitude of creep strains and strainrates may be small in sand or dry soil, the form of the

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Figure 12.32 Variation of creep strain rate with deviatorstress for undrained creep of normally consolidated San Fran-cisco Bay mud.

BA

C

D

E2820 min

1450 min

90 min

20 min

2 min0

0.2

0.4

0.6

0.8

1

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Deviator strain (%)

0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4

Strain increment ratio dεv/dεs during creep

(a)

(b)

Drained Triaxial Test

Confining Pressure σ�3 = 414 kPa

Deviator Stress from 344 to 377 kPa

Vol

umet

ric S

trai

n (%

)

Str

ess

ratio

q/

p�

Figure 12.33 Dilatancy relationship obtained from drainedcreep tests on kaolinite: (a) development of volumetric anddeviatoric strains with time and (b) effect of stress ratio onstrain increment ratio d� /d�s (from Walker, 1969).

behavior conforms with the patterns described and il-lustrated above. This is to be expected, as the basiccreep mechanism is the same in all inorganic soils.6

Water may ‘‘lubricate’’ the particles and possibly in-crease the creep rate even though the basic mechanismof creep is the same for dry and wet materials (Losertet al., 2000). Takei et al. (2001) showed that the de-velopment of creep strains due to time-dependentbreakage of talc specimens increased more for satu-rated specimens than dry ones. However, a negligibleeffect of water on creep rate was reported by Ahn-Danet al. (2001) who performed creep tests on unsaturatedand saturated crushed gravel and by Leung et al.(1996) who performed one-dimensional compression

6 Volumetric creep and secondary compression of organic soils, peat,and municipal waste fills can develop also as a result of decompo-sition of organic matter.

creep tests on sands. The conflicting evidence may bedue to the presence or absence of impurities that maylubricate or cement the soil in the presence of water(Human, 1992; Bowman, 2003).

Volume Change and Pore Pressures

Due to the known coupling effects between shearingand volumetric plastic deformations in soils, an in-crease in either mean pressure or deviator stress cangenerate both types of deformations. Creep behavior isno exception. Time-dependent shear deformations areusually referred to as deviatoric creep or shear creep.Time-dependent deformations under constant stress re-ferred to as volumetric creep. Secondary compressionis a special case of volumetric creep.

Deviatoric creep is often accompanied by volumetriccreep. The ratio of volumetric to deviatoric creep fol-

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Figure 12.34 Pore pressure development with time during undrained creep of illite.

lows a plastic dilatancy rule. Walker (1969) inves-tigated the time-dependent change of these two com-ponents from incremental drained triaxial creep testson normally consolidated kaolinite. The increase inshear strains with increase in volumetric strains at dif-ferent times is shown in Fig. 12.33a. At the beginningof the triaxial test, the deviator stress was instantane-ously increased from 344 to 377 kPa and kept constant.After an immediate increase in shear strains at constantvolume (AB in Fig. 12.33a), section BD correspondsto primary consolidation that is controlled by the dis-sipation of pore pressures. After point D, creep oc-curred, and the ratio of volumetric to deviatoric strainswas independent of time. This ratio decreased with in-creasing stress ratio as shown in Fig. 12.33b. This ob-servation led to the time-dependent flow rule, which issimilar to the dilatancy rule described in Section 11.20.

Sand deforms with time in a similar manner. Underprogressive deviatoric creep, the volumetric creep re-sponse is highly dependent on density, the stress level,and the stress path before creep. The rate of both vol-umetric and deviatoric creep increases with confiningpressure, particularly after particle crushing becomesimportant at high stresses (Yamamuro and Lade, 1993).For dense sand under high deviator stress, dilativecreep is observed (Murayama et al., 1984; Mejia et al.,1988). The volumetric response of dense sand andgravel with time is a highly complex function of stress

history, with some samples contracting or dilating(Lade and Liu, 1998; Ahn-Dan et al., 2001). Somedense sand samples contract initially but then dilatewith time (Bowman and Soga, 2003). Further discus-sion of the creep behavior of sands in relation to me-chanical aging phenomena is given in Section 12.11.

The fundamental process of creep strain develop-ment is therefore similar to that of time-independentplastic strains, and the same framework of soil plastic-ity can possibly be used. It can be argued whetherit is necessary to separate the deformation intotime-dependent and independent components. Rate-independent behavior can be considered as the limitingcase of rate-dependent behavior at a very slow rate ofloading.

Volumetric-deviatoric creep coupling implies thatrapid application of a stress or a strain invariably re-sults in rapid change of pore water pressures in a sat-urated soil under undrained conditions. For a constanttotal minor principal stress, the magnitude of the porepressure change depends on the volume change ten-dencies of the soil when subjected to shear distortions.These tendencies are, in turn, controlled by the voidratio, structure, and effective stress, and can be quan-tified in terms of the pore pressure parameter as dis-Acussed in Chapters 8 and 10. An example showing porepressure increase with time for consolidated undrainedcreep tests on illite at several stress intensities is shownin Fig. 12.34. Figure 12.35 shows a slow decrease in

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Figure 12.35 Normalized pore pressure vs. time relationships during creep of kaolinite.

pore pressure during the sustained loading of kaolinite.Similar behavior was demonstrated in the measuredstress paths of undrained creep test on San FranciscoBay mud (Arulanandan et al., 1971). As shown in Fig.12.36, the effective stress states shifted toward the fail-ure line. At higher stress levels, the specimens even-tually underwent creep rupture. However, soil strengthin terms of effective stresses does not change unlessthere are chemical, biological, or mineralogicalchanges during the creep period. This is illustrated bythe stress paths shown schematically in Fig. 12.37,where the pre- and postcreep strengths fall on the samefailure envelope.

Effects of Temperature

An increase in temperature decreases effective stress,increases pore pressure, and weakens the soil structure.Creep rates ordinarily increase and the relaxationstresses corresponding to specific values of strain de-crease at higher temperature. These effects are illus-trated by the data shown in Figs. 12.38 and 12.39.

Effects of Test Type, Stress System, and Stress Path

Most measurements of time-dependent deformationand stress relaxation in soils have been done on sam-ples consolidated isotropically and tested in triaxialcompression or by measurement of secondary com-pression in oedometer tests. However, most soils innature have been subjected to an anisotropic stress his-tory, and deformation conditions conform more toplane strain than triaxial compression in many cases.Some investigations of these factors have been made.

Although the general form of the stress–strain–timeand stress–strain rate–time relationships are similar tothose shown above for triaxial loading conditions, theactual values may differ considerably.

For example, undisturbed Haney clay, a gray siltyclay from British Columbia, with a sensitivity in therange of 6 to 10, was tested both in triaxial compres-sion and plane strain (Campanella and Vaid, 1974).Samples were normally consolidated both isotropicallyand under K0 conditions to the same vertical effectivestress. Samples consolidated isotropically were testedin triaxial compression. Coefficient K0 consolidationwas used for both K0 triaxial and plane strain tests.The results shown in Fig. 12.40 indicate that the pre-creep stress history had a significant effect on thedeformations. The plane strain and K0 consolidatedtriaxial samples gave about the same creep behaviorunder the same deviatoric stress, which suggests thatpreventing strain in one horizontal direction and/or theintermediate principal stress were not factors of majorimportance for this soil under the test conditions used.

Interaction Between Consolidation and Creep

Experimental evidence suggests that creep occurs dur-ing primary consolidation (Leroueil et al., 1985; Imaiand Tang, 1992). Following the initial large changefollowing load application, the pore pressure may ei-ther dissipate, with accompanying volume change ifdrainage is allowed, or change slowly during creep orstress relaxation, if drainage is prevented. The devel-opment of complete effective stress and void ratioequilibrium may take a long time. One illustration of

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80 160 240 320 400 480 560 64000

80

160

Normal Undrained TriaxialCompression Test: EffectiveStress Path

Total Stress Path ofTriaxial Compression Test

1

3

Possible CriticalState Line

Effective Stress StateAfter 1,000 min Creep

After 20,000 min CreepEffective Stress Pathof Undrained Creep

10 20 30 40 50 60 70 8000

10

20

30

40

50Normal Undrained TriaxialCompression Test: EffectiveStress Path

Total Stress Path ofTriaxial Compression Test

1

3Possible CriticalState Line

Effective Stress StateAfter 1,000 min Creep

After 20,000 min CreepEffective Stress Pathof Undrained Creep

240

320

400

(a)

(b)

Dev

iato

r S

tres

s q

(kP

a)

Dev

iato

r S

tres

s q

(kP

a)



Figure 12.36 Measured stress paths of undrained creep tests of San Francisco Bay mud.Initial confining pressure: (a) 49 kPa and (b) 392 kPa (from Arulanandan et al., 1971).

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Figure 12.37 Effects of undrained creep on the strength of normally consolidated clay.

Figure 12.38 Creep curves for Osaka clay tested at different temperatures—undrained tri-axial compression (Murayama, 1969).

this is given by Fig. 10.5, where it is shown that therelationship between void ratio and effective stress isdependent on the time for compression under anygiven stress. Another is given by Fig. 12.41, whichshows pore pressures during undrained creep of SanFrancisco Bay mud. In each sample, consolidation un-der an effective confining pressure of 100 kPa was al-lowed for 1800 min prior to the cessation of drainageand the start of a creep test. The consolidation periodwas greater than that required for 100 percent primaryconsolidation. The curve marked 0 percent stress levelrefers to a specimen maintained undrained but not sub-ject to a deviator stress. This curve indicates that each

of the other tests was influenced by a pore pressurethat contained a contribution from the prior consoli-dation history.

The magnitude and rate of pore pressure develop-ment if drainage is prevented following primary con-solidation depend on the time allowed for secondarycompression prior to the prevention of further drain-age. This is illustrated by the data in Fig. 12.42, whichshow pore pressure as a function of time for samplesthat have undergone different amounts of secondarycompression.

In summary, creep deformation depends on the ef-fective stress path followed and any changes in stress

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Figure 12.39 Influence of temperature on the initial and final stresses in stress relaxationtests on Osaka clay—undrained triaxial compression (Murayama, 1969).

Figure 12.40 Creep curves for isotropically and K0-consolidated samples of undisturbedHaney clay tested in triaxial and plane strain compression (from Campanella and Vaid, 1974).Reproduced with permission from the National Research Council of Canada.

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RATE EFFECTS ON STRESS–STRAIN RELATIONSHIPS 497

Figure 12.41 Pore pressure development during undrained creep of San Francisco Bay mudafter consolidation at 100 kPa for 1800 min (from Holzer et al., 1973). Reproduced withpermission from the National Research Council of Canada.

Figure 12.42 Pore pressure development under undrained conditions following differentperiods of secondary compression (from Holzer et al., 1973). Reproduced with permissionfrom the National Research Council of Canada.

with time. Furthermore, time-dependent volumetric re-sponse is governed both by the rate of volumetric creepand by the rate of consolidation. The latter is a com-plex function of drainage conditions and material prop-erties, especially the permeability and compressibility.Because the effective stress path is controlled by therate of loading and drainage conditions, the separationof consolidation and creep deformations can be diffi-cult in the early stage of time-dependent deformationas given by section BD in Fig. 12.33a. In some cases,a fully coupled analysis of soil–pore fluid interactionwith an appropriate time-dependent constitutive model

is necessary to reconcile the time-dependent deforma-tions observed in the field and laboratory.

12.8 RATE EFFECTS ON STRESS–STRAINRELATIONSHIPS

An increase in strain rate during soil compression ismanifested by increased stiffness, as was noted in Sec-tion 12.3. In essence, the state of the soil jumps to thestress–strain curve that corresponds to the new strainrate. Commonly, this rate-dependent stress–strain

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5% /h

0.5% /h

0.05% /h

Belfast Clay 4 mσ1c = σ�v0

16%/h

1%/h0.25%/h

Winnipeg Clay 11.5 mσ1c > σ�v0

CAU Triaxial Compression TestsRelaxation Tests (R)

00

0.1

0.2

0.3

0.4

0.5

0.6

4 8 12 16 20

Axial Strain

(σ1 –

σ3)/

2σ1c

R

R

R

SP1 testSP2 test

εv1 = 2.70 & 10–6 s–1.εv2 = 1.05 & 10–7 s–1

εv1

.. εv1

.

εv1.

εv1.

εv1.

εv1.

εv3.εv2

.

εv2.

εv2.

εv2.

εv3 = 1.34 & 10–5 s–1.

30

25

20

15

10

5

00 50 100 150 200 250

Effective Stress σv� (kPa)

Str

ain

ε v (

%)

Figure 12.43 Rate-dependent stress–strain relations ofclays: (a) undrained triaxial compression tests of Belfastand Winnipeg clay (Graham et al., 1983a) and (b) one-dimensional compression tests of Batiscan clay (Leroueil etal., 1985).

curve, noted by Suklje (1957), is the same as if thesoil had been loaded from the beginning at the newstrain rate. This phenomenon is often observed inclays. Examples are given in Fig. 12.43a for undrainedtriaxial compression tests of Belfast and Winnipegclays (Graham et al., 1983a) and Fig. 12.43b for one-dimensional compression tests of Batiscan clay (Ler-oueil et al., 1985).

Yield and Strength Envelopes of Clays

The undrained shear strength and apparent precon-solidation pressure of soils decrease with decreasingstrain rate or increasing duration of testing. Preconsol-idation pressures obtained from one-dimensional con-solidation tests and undrained shear strengths obtainedfrom triaxial tests are just two points on a soil’s yieldenvelope in stress space. For a given metastable soilstructure, the degree of rate dependency of preconsol-idation pressure is similar to that of undrained shearstrength (Soga and Mitchell, 1996). If the apparent pre-consolidation pressure depends on the strain rate atwhich the soil is deforming, then the same analogy canbe expanded to the assumption that the size of the en-tire yield envelope is also strain rate dependent (Tav-enas and Leroueil, 1977). Figure 12.44 shows a familyof strength envelopes corresponding to constant strainrates7 obtained from drained and undrained creep testson stiff plastic Mascouche clay from Quebec (Leroueiland Marques, 1996).

The effective stress failure line of soil is uniquelydefined regardless of the magnitude of the strain rateapplied in undrained compression. Figure 12.45ashows the failure line of Haney clay (Vaid and Cam-panella, 1977). The line represents the stress conditionsat the maximum ratio of The data were obtained�� /��.1 3

by various undrained tests, and a unique failure linecan be observed. Figure 12.45b shows the undrainedstress paths and the critical state line of reconstitutedmixtures of sand and clay with plasticity indices rang-ing from 10 to 30 (Nakase and Kamei, 1986). A uniquecritical state line can be observed although the rates ofshearing are different. The change in undrained shearstrength with strain rate results from a difference ingeneration of excess pore pressures. A decrease instrain rate leads to larger excess pore pressures at fail-ure due to creep deformation.

7 The strain rate is defined as where is the volu-2 2� � � � � , �vs v s vmetric strain rate and is the deviator strain rate (Leroueil and Mar-�s

ques, 1996). Whether the use of this strain rate measure is appropriateor not remains to be investigated.

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Figure 12.44 Influence of strain rate on the yield surface of Masouche clay (from Leroueiland Marques, 1996).

Excess Pore Pressure Generation in NormallyConsolidated Clays

Excess pore pressure development depends primarilyon the collapse of soil structure. Accordingly, strain isthe primary factor controlling pore pressure generation.This is shown in Fig. 12.46 by the undrained stress–strain–pore pressure response of normally consolidatednatural Olga clay (Lefebvre and LeBouef, 1987). Thenatural clay specimens were normally consolidated un-der consolidation pressures larger than the field over-burden pressure and then sheared at different strainrates. Although the deviator stress at any strain in-creases with increasing strain rate, the pore pressureversus strain curves are about the same at all strainrates. At a given deviator stress, the pore pressure gen-eration was larger at slower strain rates as a result ofmore creep under slow loading. This is consistent withthe observation made in connection with undrainedcreep of clays as discussed in Section 12.7. Strain-driven pore pressure generation was also suggested byLarcerda and Houston (1973) who showed that porepressure does not change significantly during triaxial

stress relaxation tests in which the axial strain is keptconstant.

Overconsolidated Clays

Rate dependency of undrained shear strength decreaseswith increasing overconsolidation, since there is nocontraction or collapse tendency observed during creepof heavily overconsolidated clays. Sheahan et al.(1996) prepared reconstituted specimens of Bostonblue clay at different overconsolidation ratios andsheared them at different strain rates in undrained con-ditions. Figure 12.47 shows that the undrained stresspath and the strength were much more strain rate de-pendent for lightly overconsolidated clay (OCR � 1and 2) than for more heavily overconsolidated clay(OCR � 4 and 8). The results also show that thestrength failure envelope is independent of strain rateas discussed earlier.

The strain rate effects on stress–strain–pore pressureresponse of overconsolidated structured Olga clays areshown in Fig. 12.48 (Lefebvre and LeBouef, 1987).The natural samples were reconsolidated to the field

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Const. Stress Creep

Const. Load CreepStep CreepThixotropic Hardened

Const. Rate of Strain ShearConst. Rate of Loading ShearAged Samples

0

0

00.1

0.1

0.2

0.2

0.2

0.3

0.3

0.4

0.4

0.4

0.5 0.6

0.6

0.7 0.8

0.8

(σ1� + σ3�)/2σ�1c

(σ1�

–σ 3

�)/2

σ�1c

(a)

(b)

1.0

0.8

0.6

0.4

0.2

0

–0.2

–0.4

–0.61.0

p�/σ�vc

0 0.2 0.4 0.6 0.8 1.0p�/σ�vc

q�/σ

� vc

1.0

0.8

0.6

0.4

0.2

0

–0.2

–0.4

–0.6

q�/σ

� vc

ε(%/min)M-15

M15 Soil (Plasticity Index = 15) M10 Soil (Plasticity Index = 10)

..

7&10-1: ε1

.7&10-2: ε2

.7&10-3: ε3

ε(%/min).

7&10-1: ε17&10-2: ε2

.

.

.7&10-3: ε3

M-10K 0

-Line

K 0-L

ine

Crit

ical

-Sta

te L

ine

Crit

ical

-Sta

te L

ine

Critical-State Line

Critical-State Line

Figure 12.45 Strain rate independent failure line: (a) Haney clay (from Vaid and Campa-nella, 1977) and (b) reconstituted mixtures of sand and clay (from Nakase and Kamei, 1986).

overburden pressure. The deformation is brittle, withstrain softening indicating development of localizedshear failure planes. Up to the peak stress, the responsefollows what has been described previously, that is thestress–strain response is rate dependent and the porepressure generation is strain dependent but indepen-dent of rate. However, after the peak, the pore pressure

generation becomes rate dependent. This is due to localdrainage within the specimens as the deformation be-comes localized. As the time to failure increased, thereis more opportunity for local drainage toward the di-lating shear band and the measured pore pressure maynot represent the overall behavior of the specimens.The difference in softening due to swelling at the fail-

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0.1 %/hr0.5 %/hr2.6 %/hr12.3 %/hr

Axial Strain Rate

Axial Strain (%)1 2 3 4 5 6 7 8

Axial Strain (%)1 2 3 4 5 6 7 8

0

20

40

60

80

100

120

0

20

40

60

80

120

140

100

0.1 %/hr0.5 %/hr2.6 %/hr12.3 %/hr

Axial Strain Rate

Normally Consolidated Olga ClayUndrained Triaxial Compression TestsInitial Isotropic Confining Pressure =137 kPa

Dev

iato

r S

tres

s q

(kP

a)E

xces

s P

ore

Pre

ssur

e Δu

(kP

a)

Figure 12.46 Stress–strain and pore pressure–strain curvesfor normally consolidated Olga clay (from Lefebvre andLeBouef, 1987).

0.1 %/hr0.5 %/hr2.6 %/hr12.3 %/hr

Axial Strain Rate

Axial Strain (%)1 2 3 4 5 6 7 8

Axial Strain (%)

1 2 3 4 5 6 7 8

0

10

20

40

50

0

10

0.1 %/hr0.5 %/hr2.5 %/hr12.3 %/hr

Axial Strain Rate

Overconsolidated Olga ClayUndrained Triaxial Compression TestsInitial Isotropic Confining Pressure = 17.6 kPa

30

60

70

20

Devia

tor

Str

ess q

(kP

a)

Excess P

ore

Pre

ssure

Δu

(kP

a)

Figure 12.48 Stress–strain and pore pressure–strain curvesfor overconsolidated Olga clay (from Lefebvre and LeBouef,1987).

OCR=1

OCR=2

OCR=4

OCR=8

OCR=2OCR=4

Effective Stress Path for AxialStrain Rate = 0.50 %/hr

0.80.60.40.20.0

0.1

0.2

0.3

0.4

-0.1

Effective Stress State at Peak forAxial Strain Rate = 0.051 %/hrAxial Strain Rate = 0.50 %/hrAxial Strain Rate = 5.0 %/hrAxial Strain Rate = 49 %/hr

Initial K0 Consolidation State

(σ�a + σ�r)/2σ�vm

(σ� a

–σ�

r)/2

σ�vm

OCR=1LargeRateEffectOCR=8

NegligibleRate Effect

Figure 12.47 Rate dependency stress path and strength ofoverconsolidated Boston blue clay (from Sheahan et al.,1996).

ure plane results in apparent rate dependency at largestrains. Similar observations were made by Atkinsonand Richardson (1987) who examined local drainageeffects by measuring the angles of intersection of shearbands with very different times of failure.

Rate Effects on Sands

Similar rate-dependent stress–strain behavior is ob-served in sands (Lade et al., 1997), but the effects arequite small in many cases (Tatsuoka et al., 1997; DiBenedetto et al., 2002). An example of time depend-ency observed for drained plane strain compressiontests of Hostun sand is shown in Fig. 12.49 (Matsushitaet al., 1999). The stress–strain curves for three differ-ent strain rates (1.25 � 10�1, 1.25 � 10�2, and 1.25 �10�3 %/min) are very similar, indicating very smallrate effects when the specimens are sheared at a con-stant strain rate. On the other hand, the change fromone rate to another temporarily increases or decreasesthe resistance to shear. The influence of accelerationrather than the rate is reflected by the significant creepdeformation and stress relaxation of this rate-insensitive material as shown the figure. This is differ-

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0 1 2 3 4 5 6 7 83.0

3.5

4.0

4.5

5.0

5.5

6.0

Variation of Stress-strain curve by ConstantStrain Rate Tests at Axial Strain Rates = 0.125,0.0125 and 0.00125 %/min. A Very Small RateEffect Is Observed for Continuous Loading.

CRS at 0.125%/min

Creep

CRS at 0.125%/min

Creep

CRS at 0.00125%/min

Creep

CRS at0.125%/min

CRS at0.125%/min

Stress Relaxation

Creep

CRS at 0.00125%/min

Accidental Pressure Drop Followedby Relaxation Stage

Str

ess

Rat

io σ

� a/σ

� r

Shear Strain γ = εa – εr (%)

Figure 12.49 Creep and stress relaxation of Hostun sand(from Matsushita et al., 1999).

NSF-ClayIsotropicallyConsolidatedp�0 = 300 kPaEmax = 239 MPa

Esec = Δq/εa, Eeq = (Δq)SA / (εa)SA

0

200

100

300

You

ng's

Mod

ulus

,Ese

cor

Eeq

(MP

a)

10-3 10-2 10-1 100

Axial Strain, εa orSingle Amplitude of Cyclic Axial Strain, (εa)SA (%)

Figure 12.50 Clay stiffness degradation curves at threestrain rates (from Shibuya et al., 1996).

Co

effi

cien

t o

f S

trai

n R

ate,

�(γ

)

Shear Strain, γ (%)

Figure 12.51 Strain rate parameter �G and strain level forseveral clays (from Lo Presti et al., 1996).

ent from the observations made for clays as shown inFig. 12.43 in which a unique stress–strain–strain raterelationship was observed. Hence, the modeling ofstress–strain–rate behavior of sands appears to bemore complicated than that of clays, and further in-vestigation is needed, as time-dependent behavior ofsands can be of significance in geotechnical construc-tion as discussed further in Section 12.10.

Stiffness at Small and Intermediate Strains

Although the magnitude is small, the strain rate de-pendency of the stress–strain relationship is observedeven at small strain levels for clays. The stiffness in-creases less than 6 percent per 10-fold increase instrain rate (Leroueil and Marques, 1996). The rate de-pendency on stiffness degradation curves measured bymonotonic loading of a reconstituted clay is shown inFig. 12.50 (Shibuya et al., 1996). At different strainlevels, the increase in the secant shear modulus withshear strain rate is often expressed by the followingequation (Akai et al., 1975; Isenhower and Stokoe,1981; Lo Presti et al., 1996; Tatsuoka et al., 1997):

G� () � (12.34)G log � G(, )ref

where G is the increase in secant shear modulus withincrease in log strain rate log and is the, G(, )ref

secant shear modulus at strain and reference strainrate The magnitude is large in clays, considerably .ref

less in silty and clayey sands, and small in clean sands(Lo Presti et al., 1996; Stokoe et al., 1999). The vari-ation of �G with strain is shown in Fig. 12.51 for dif-

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MODELING OF STRESS–STRAIN–TIME BEHAVIOR 503

250

200

150

100

50

010-2 10-1 100 101 102

Frequency (Hz)

Sandy Silty Clay

Sandy Elastic Silt

Kaolin

Vallencca Clay

Kaolin

Sandy Lean Clay

Kaolin SubgradeFat Clay

She

ar M

odul

us G

(M

Pa)

Figure 12.52 Rate dependency of cyclic small strain stiffness of a sandy elastic silt (fromMeng and Rix, 2004).

ferent plasticity clays (Lo Presti et al., 1996). Themagnitude of rate dependency increases with strainlevel, especially for strain levels larger than 0.01 per-cent, which is within the preplastic region zone 3 de-scribed in Section 11.17.

Rate Effects During Cyclic Loading

The frequencies of cyclic loading to which a soil issubjected can vary widely. For example, the frequencyof sea and ocean waves is in the range of 10�2 to 10�1

Hz, earthquakes are in the range of 0.1 to a few hertz,and machine foundations are in the range of 10 to 100Hz. Similarly to monotonic loading, the effect of load-ing frequency on shear modulus degradation is smallin clean, coarse-grained soils (Bolton and Wilson,1989; Stokoe et al., 1995), but the effect becomes moresignificant in fine-grained soils (Stokoe et al., 1995;d’Onofrio et al., 1999; Matesic and Vucetic, 2003;Meng and Rix, 2004). An example of frequency effectson a shear modulus degradation curve for a clay ob-tained from cyclic loading is shown in Fig. 12.50 alongwith the monotonic data. Figure 12.52 shows the effectof frequency on shear modulus of several soils at verysmall shear strains (less than 10�3 percent) measuredby torsional shear and resonant column apparatuses(Meng and Rix, 2004). The effect is 10 percent in-crease per log cycle at most.

At a given frequency of cyclic loading, the strainrate applied to a soil increases with applied shear strainas shown by the equation below:

� 4ƒ (12.35)c

where ƒ is the frequency and c is the cyclic shearstrain amplitude. Using Eq. (12.35), Matesic and Vu-cetic (2003) report values of �G of 2 to 11 percent forclays and 0.2 to 6 percent for sands as the strain rateincreases 10-fold. The values of �G in general de-creased when the applied cyclic shear strain increasedfrom 5 � 10�4 percent to 1 � 10�2 percent. It shouldbe noted that the strain range examined is within thenon-linear elastic range (zone 1 to zone 2 in Section11.17). The monotonic loading data presented in Fig.12.51 show that the rate effect becomes more pro-nounced at larger strain, that is, as plastic deformationsbecome more significant. Hence, it is possible that thefundamental mechanisms of rate dependency are dif-ferent at small elastic strain levels than at larger plasticstrains.

Small strain damping shows more complex fre-quency dependency, as shown in Fig. 12.53 (Shibuyaet al., 1995; Meng and Rix, 2004). At a frequency ofmore than 10 Hz, the damping ratio increases withincreased frequency, possibly due to pore fluid viscos-ity effects. As the applied frequency decreases, thedamping ratio decreases. However, at a frequency lessthan 0.1 Hz, the damping ratio starts to increase withdecreasing frequency. This may result from creep ofthe soil (Shibuya et al., 1995).

12.9 MODELING OF STRESS–STRAIN–TIMEBEHAVIOR

Constitutive models are needed for the solution of geo-technical problems requiring the determination of de-

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10210110010-110-2

Frequency (Hz)

1

2

3

4

5

6

Sandy Silty Clay

Sandy Elastic Silt

Kaolin

Vallencca Clay Fat Clay

Sandy Lean Clay

Clayey Subgrades

Pisa Clay

Augusta ClayD

ampi

ng (

%)

Figure 12.53 Effect of strain rate of damping ratio of soils (from Shibuya et al., 1995 andMeng and Rix, 2004).

formations, displacements, and strength and stabilitychanges that occur over time periods of differentlengths. Various approaches have been used, includingempirical curve fitting, extensions of rate processtheory, rheological models, and advanced theoriesof viscoelasticity and viscoplasticity. Owing to thecomplexity of stress states, the many factors that influ-ence the creep and stress relaxation properties of a soil,and the difficulty of accounting for concurrent volu-metric and deviatoric deformations in systems that aremany times undergoing consolidation as well as sec-ondary compression or creep, it is not surprising thatdevelopment of general models that can be readily im-plemented in engineering practice is a challenging un-dertaking.

Nonetheless, some progress has been made in estab-lishing functional forms and relationships that can beapplied for simple analyses and comparisons, and oneof these is developed in this section. A complete re-view and development of all recent theories and pro-posed relationships for creep and stress relaxation isbeyond the scope of this book. Comprehensive reviewsof many models for representation of the time-dependent plastic response of soils are given in Adachiet al. (1996).

General Stress–Strain–Time Function

Strain Rate Relationships between axial strain rateand time t of the type shown in Figs. 12.4 and 12.5�

can be expressed by

� tln � �m ln (12.36)� �

�(t ,D) t1 1

or

tln � � ln �(t ,D) � m ln (12.37)� �1 t1

where is the axial strain rate at unit time and�(t ,D)1

is a function of stress intensity D, m is the absolutevalue of the slope of the straight line on the log strainrate versus log time plot, and t1 is a reference time, forexample, 1 min. Values of m generally fall in the rangeof 0.7 to 1.3 for triaxial creep tests; lower values arereported for undrained conditions than for drained con-ditions. For the development shown here, the stressintensity D is taken as the deviator stress (�1 � �3). Ashear stress or stress level could also be used.

The same data plotted in the form of Figs. 12.3,12.31, and 12.32 can be expressed by

�ln � �D (12.38) �

�(t,D )0

or

ln � � ln �(t,D ) � �D (12.39)0

in which is a fictitious value of strain rate at�(t,D )0

D � 0, a function of time after start of creep, and �is the slope of the linear part of the log strain rateversus stress plot. From Eqs. (12.37) and (12.39)

tln �(t ,D) � m ln � ln �(t,D ) � �D (12.40)� �1 0t1

For D � 0,

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Figure 12.54 Influence of creep stress magnitude on thecreep rate at a given time after stress application.

tln �(t,D ) � ln �(t ,D ) � m ln (12.41)� �0 1 0 t1

in which is the value of strain rate obtained by�(t ,D )1 0

projecting the straight-line portion of the relationshipbetween log strain rate and deviator stress at unit timeto a value of D � 0. Designation of this value by Aand substitution of Eq. (12.41) into Eq. (12.39) gives

tln � � ln A � �D � m ln (12.42)� �t1

which may be written

mt1�D� � Ae (12.43)� �tThis simple three-parameter equation has been

found suitable for the description of the creep rate be-havior of a wide variety of soils. The parameter A isshown in Fig. 12.54. Since it reflects an order of mag-nitude for the creep rate under a given set of condi-tions, it is in a sense a soil property. A minimum oftwo creep tests are needed to establish the values of A,�, and m for a soil. If identical specimens are testedusing different creep stress intensities, a plot of logstrain rate versus log time yields the value of m, anda plot of log strain rate versus stress for different valuesof time can be used to find � and A from the slopeand the intercept at unit time, respectively.

The parameter � has units of reciprocal stress. Ifstress is expressed as the ratio of creep stress tostrength at the beginning of creep, D /Dmax, then thedimensionless quantity �Dmax should be used. For agiven soil and test type, values of �Dmax do not varygreatly for different water contents, as the change in �with water content is compensated by a change inDmax. Thus the strain rate versus time behavior for anystress at any water content can be predicted from theresults of creep tests at any other water content, pro-

vided the variation of strength with water content isknown. Since normal strength tests are considerablysimpler and less time consuming than creep tests, theuniqueness of the quantity �Dmax can be useful becausethe results of a limited number of tests can be used topredict behavior over a range of conditions. A furthergeneralization of Eq. (12.43) then is

mt1� � A exp(�D) (12.44)� �twhere

D� � �D D � (12.45)max Dmax

Strain A general relationship between strain � andtime is obtained by integration of Eq. (12.43). Twosolutions are obtained, depending on the value of m.If � � �1 at t � t1 � 1, then

A 1�m� � � � exp (�D)(t � 1) when m 11 1 � m

(12.46)

and

� � � � A exp (�D)ln t when m � 1 (12.47)1

Creep curve shapes corresponding to these relation-ships are shown in Fig. 12.55. These curves encompassthe variety of shapes shown in Fig. 12.2. A similarequation to Eq. (12.46) was developed by Mesri et al.(1981) from Eq. (12.43). The initial time-independentstrain was neglected, and the resulting equation is

1�mAt t1� � exp(�D) (12.48)� �1 � m t1

It may be seen in Fig. 12.56 that this equation de-scribes the uniaxial creep behavior of three clays verywell. Data for both drained and undrained creep areshown.

Stress Relaxation Stress decay during stress relax-ation is approximately linear with logarithm of timeuntil it levels off at some residual stress after a longtime. There is equivalency between creep and stressrelaxation in that a general phenomenological modelthat predicts one can be used to predict the other, asshown by Akai et al. (1975), Lacerda (1976), Borja(1992), and others. For example, Eq. (12.44) takes thefollowing form when stress relaxation is started afterdeformation at constant rate of strain (Lacerda andHouston, 1973):

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Figure 12.55 Creep curve shapes predicted by the general stress–strain–time function ofEqs. (12.46) and (12.47).

D D t� � 1 � s log (t � t ) (12.49)0D tD0 00

where s is the slope of the stress relaxation curve, andthe zero subscript refers to conditions at the start ofstress relaxation. Also

#s � (12.50)

D

where

2.3(1 � m)# � (12.51)

�

The validity of this equation has been establishedfor m � 1.0. Pore pressures decrease slightly duringundrained stress relaxation.

Stresses may not begin to relax immediately afterthe strain rate is reduced to zero. The time t0 betweenthe time that the strain rate is reduced to zero and thebeginning of relaxation is a variable that depends onthe soil type and the prior strain rate. This is shownschematically in Fig. 12.57. The greater the initial rateof strain to a given deformation, the more quickly re-laxation begins. This is a direct reflection of the rela-tive differences in equilibrium soil structures duringand after deformation. Values of t0 as a function ofprior strain rate are shown in Fig. 12.58 for severalsoils. These curves can be described empirically by

h0t � (12.52)0 �

where h0 is the strain rate to give a delay time of t0 �1 min before stresses begin to relax. The data presentedby Lacerda and Houston (1973) indicate that the valuesof # and h0 increase with increasing plasticity of thesoil.

Constitutive Models

Different rheological models have been proposed forthe mathematical description of the stress–strain–timebehavior of soils that are made up of combinations oflinear springs, viscous dashpots, and sliders. In theMurayama and Shibata (1958), Christensen and Wu(1964), and Abdel-Hady and Herrin (1966) models, thedashpots are nonlinear, with stress–flow rate responsegoverned by rate process theory. Rheological modelsare useful conceptually to aid in recognition of elasticand plastic components of deformation. They are help-ful for visualization by analogy of viscous flow thataccompanies time-dependent change of structure to amore stable state. Mathematical relationships can bedeveloped in a straightforward manner for the descrip-tion of creep, stress relaxation, steady-state deforma-tion, and the like in terms of the model constants. Inmost cases, these relationships are complex and neces-sitate the evaluation of several parameters that may notbe valid for different stress intensities or soil states.Only one-dimensional stresses and deformations are

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Figure 12.56 Correspondence between creep strain predicted by Eq. (12.48) and measuredvalues. Diagrams are from Mesri et al. (1981), which were based on analyses by Semple(1973).

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Figure 12.57 Influence of prior strain rate on stress relaxa-tion.

Figure 12.58 Influence of prior strain rate on the time tostart of stress relaxation (adapted from Lacerda and Houston,1973).

considered. None appears to exist that has the gener-ality and simplicity of the three-parameter creep Eqs.(12.43), (12.46), and (12.47).

Both plasticity and creep are controlled by the mo-tion of dislocations or breakage among soil particles,so it may be physically more correct to predict bothplastic and creep deformations with one equation. Twoparticularly promising approaches are based on an ex-tension of the Cam-clay model to take into accounttime-dependent volumetric and deviatoric deforma-tions (Kavazanjian and Mitchell, 1980; Borja and Ka-vazanjian, 1985; Kaliakin and Dafalias, 1990; Borja,1992; Al-Shamrani and Sture, 1998; Hashiguchi andOkayasu, 2000) and on an elasto-viscoplastic equationdeveloped using flow surface theory (Sekiguchi, 1977,1984; Matsui and Abe, 1985, 1986, 1988; Matsui etal., 1989; Yin and Graham, 1999) and overstress theory(Adachi and Oka, 1982; Katona, 1984: Kutter andSathialingham, 1992; Rocchi et al., 2003).

12.10 CREEP RUPTURE

As discussed in Section 12.2 and shown in Fig. 12.6,the strength of a soil and the stress–strain curve maybe changed as a result of creep. In some cases, suchas the drained creep of a compressive soil, the strengthmay be increased. Changes in strength may be as muchas 50 percent or more of the strength measured in nor-mal undrained tests prior to creep.

Causes of Strength Loss During Creep

Loss of strength during creep is particularly importantin soft clays deformed under undrained conditions andheavily overconsolidated clays in drained shear. Bothof these conditions are pertinent to certain types ofengineering problems: the former in connection withstability of soft clays immediately after construction,and the latter in connection with problems of long-termstability.

The loss of strength as a result of creep may beexplained in terms of the following principles of be-havior:

1. If a significant portion of the strength of a soil isdue to cementation, and creep deformationscause failure of cemented bonds, then strengthwill be lost.

2. In the absence of chemical or mineralogicalchanges the strength depends on effectivestresses. If creep causes changes in effectivestress, then strength changes will also occur.

3. In almost all soils, shear causes changes in porepressure during undrained deformation andchanges in water content during drained defor-mation.

4. Water content changes cause strength changes.

These processes are illustrated by the stress pathsand effective stress envelope shown schematically inFig. 12.37.

Strength loss in saturated, heavily overconsolidatedclays tested under undrained conditions has also beenreported, for example, Casagrande and Wilson (1951),Goldstein and Ter-Stepanian (1957), and Vialov andSkibitsky (1957). This may be explained as follows.Shear deformations cause dilation and the developmentof negative pore pressures, which do not develop uni-formly throughout the sample but concentrate alongplanes where the greatest shearing stresses and strainsdevelop. With time during sustained loading, water mi-grates into zones of high negative pore pressures lead-ing to softening and strength decrease relative to thestrength in ‘‘normal’’ undrained strength tests. Thisleads to shear band formation.

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CREEP RUPTURE 509

Figure 12.59 Stress paths for normal undrained shear and drained creep of heavily over-consolidated clay.

This process is shown in Fig. 12.59 with referenceto an effective stress failure envelope for a heavily ov-erconsolidated clay. The effective stress path is repre-sented by AB, and AC represents the total stress pathin a conventional consolidated-undrained (CU) test.The negative pore pressure at failure is CB. If a creepstress DE is applied to the same clay, a negative porepressure EF is induced. This negative pore pressuredissipates during creep, and the clay in the shear zoneswells. At the end of the creep period, the effectivestress will be as represented by point E. Further shearstarting from these conditions leads to strength G,which is less than the original value at B. It is evidentalso that if the negative pore water pressure is largeenough, and the sustained load is applied long enough,then point E could reach the failure envelope. Thisappears to have been the conditions that developed inseveral cuts in heavily overconsolidated brown Londonclay, which failed some 40 to 70 years after excava-tions were made (Skempton, 1977).

Time to Failure

The time to failure of soils susceptible to strength lossunder sustained stresses depends on the rates at whichpore pressures develop and at which water can migrateinto or out of the critical shear zone. These rates are,

in turn, a function of deformation rates, the hydraulicconductivity, and the surrounding water pressure anddrainage conditions. The time to failure of heavily ov-erconsolidated clays in which negative pore water pres-sures develop as a result of unloading is best estimatedon the basis of drained strengths, effective stresses, andconsideration of the rate of swelling that is possiblefor the particular clay and ambient stress and ground-water conditions. An exception would be whenstrength loss results from the time-dependent ruptureof cementing bonds. In this case, sustained load creeptests in the laboratory may allow establishment of astress level versus time-to-failure relationship.

For soils subject to failure during undrained creep,the time to failure is usually a negative exponentialfunction of the stress, for stresses greater than somelimiting value below which no failure develops evenafter very long times.8 The relationship between devi-ator stress, normalized to the pretest major principaleffective stress, and time to failure for Haney clay isshown in Fig. 12.60. These and similar data define cer-

8 This critical stress below which creep rupture does not occur hasbeen termed the upper yield, the lower yield being the stress belowwhich deformations are elastic (Murayama and Shibata 1958, 1964).

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Figure 12.60 Time to rupture as a function of creep stressfor Haney clay (Campanella and Vaid, 1972).

Figure 12.61 Creep rate behavior of K0-consolidated, undisturbed Haney clay under axi-symmetric loading (Campanella and Vaid, 1972).

tain principles relating to the probability of creep rup-ture and the time to failure:

1. Values of the parameter m less than 1.0 in Eqs.(12.43) through (12.46) are indicative of a highpotential strength loss during creep and eventualfailure (Singh and Mitchell, 1969).

2. The minimum strain rate prior to the onset�min

of creep rupture decreases, and the time to failureincreases, as the stress intensity decreases, asshown in Fig. 12.61 for Haney clay. The rela-tionship is unique, as may be seen in Fig. 12.62,which shows that

Ct � (12.53)ƒ �min

Values of the constant C accurate to about �0.2log cycles are given in Table 12.2.

3. The strain at failure is a constant independent ofstress level, as shown in Fig. 12.63. The failure

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SAND AGING EFFECTS AND THEIR SIGNIFICANCE 511

Figure 12.62 Relationship between time to failure and min-imum creep rate (from Campanella and Vaid, 1974). Repro-duced with permission from the National Research Councilof Canada.

strain is taken as the strain corresponding to theminimum strain rate. For the case of undrainedcreep rupture, this is consistent with the conceptthat pore pressure development is uniquely re-lated to strain and independent of the rate atwhich it accumulates (Lo, 1969a, 1969b).

The relationship expressed by Eq. (12.53) results di-rectly from the fact that the strain at the point of min-imum strain rate is a constant independent of stress orstrain rate. The general stress–strain rate–time function[see Eq. (12.43)] describes the strain rate–time behav-ior until is reached. For t1 � 1 and � � 0 at t ��min

0, the corresponding strain–time equation is

A 1�m� � exp(�D)t (12.54)1 � m

By setting � � 0 at t � 0, the assumption is madethat there is no instantaneous deformation. Substitutionfor A exp(�D) in Eq. (12.54) gives

1 m 1�m� � �t t (12.55)1 � m

which at the point of minimum strain rate becomes

1 C� � constant � � t � (12.56)ƒ min ƒ1 � m 1 � m

Thus, the constant in Eq. (12.53) is defined by

C � (1 � m)� (12.57)ƒ

Values of �ƒ for Haney clay tested in three ways areshown in Fig. 12.63, and values of C and m are inTable 12.3. The agreement between predicted and mea-sured values of C is reasonable.

Predictions of the time to failure under a given stressmay be made in the following way. Strain at failurecan be determined by either a creep rupture test or bya normal shear or compression test. If a normalstrength test is used, then the rate of strain must beslow enough to allow pore pressure equalization ordrainage, depending on the conditions of interest, andthe stress history and stress system should simulatethose in the field. Parameter m can be established froma creep test, and then C can be computed from Eq.(12.57). Values of A and � are established from creeptests at two stress intensities. Then, for t1 � 1,

1�mC � � t � A exp(�D)t (12.58)min ƒ ƒ

and corresponding values of D and tƒ can be calculatedusing Eq. (12.58) rewritten as

1 Cln t � ln � �D (12.59) � � �ƒ 1 � m A

Other constitutive models are available to model thecomplex time-dependent behavior under various load-ing conditions. For example, Sekiguchi (1977) de-veloped a viscoplastic model that gives excellentrepresentations of strain rate effects on undrainedstress–strain behavior, stress relaxation, and creep rup-ture of normally consolidated clays. Other modelslisted in Section 12.9 are able to simulate time-dependent behavior in a similar manner.

12.11 SAND AGING EFFECTS AND THEIRSIGNIFICANCE

Over geological time, lithification and chemical reac-tions can change sand into sandstone or clay into mud-stone or shale. However, even over engineering time,behavior of soils can alter as stresses redistribute afterconstruction (Fookes et al., 1988). As discussed in theprevious sections, it is well established that fine-grained soils and clays have properties and behaviorthat change over time as a result of consolidation,

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Table 12.2 Creep Rupture Parameters for Several Clays

SoilTest

Typea

CreepRate

Parameter,m

C � (� t )min ƒ

(�0.2 logcycles)

Undisturbed Haneyclay, N.C.b

ICU 0.7 1.2


ACU 0.4� 0.2


ACU-PS 0.5 0.3

Undisturbed Seattleclay, O.C.c

ICU 0.5 0.6

UndisturbedTonegawa loamc

U 0.8 1.6

UndisturbedRedwood Cityclay, N.C.c

ICU 0.75 2.8

Undisturbed Bangkokmudc

ICU 0.70 1.4

Undisturbed Osakaclayc

1.0 0.07

aICU, isotropic consolidated, undrained triaxial; ACU, K0 consoli-dated, undrained triaxial; ACU-PS, K0 consolidated, plane strain; andU, compression test.

bData from Campanella and Vaid (1974).cData from Singh and Mitchell (1969).

Figure 12.63 Axial strain at minimum strain rate as a function of creep stress for undis-turbed Haney clay (from Campanella and Vaid, 1974). Reproduced with permission fromthe National Research Council of Canada.

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Table 12.3 Predicted and Measured Values of C forHaney Clay

TestCondition

Creep RateParameterm (from

Table12.2)

�ƒ

(fromFig.

12.63)

CPredicted

by Eq.(12.57)

CMeasured

ICUa 0.7 2.8 0.84 1.2ACUb 0.4 0.3 0.18 0.20ACU-PSc 0.5 0.5 0.25 0.30

aIsotropic consolidated, undrained triaxial.bAnisotropic, consolidated, undrained triaxial.cAnisotropic consolidated, undrained, plane strain.Data from Campanella and Vaid (1974).

0 20 40 60 80 1000.00

0.05

0.10

0.15

0.20

0.25

0.30

ΔG/G1000 = 0.03PI 0.5

ΔG : Modulus Increase in Every 10-fold Time IncreaseG1000 : Modulus at 1,000 min

Marcuson et al. (1972)Afifi et al. (1973)Trudeau et al. (1973)Anderson et al. (1973)Zen et al. (1978)Kokusho et al. (1982)Umehara et al. (1985)

Jamiolkowski (1996)

a, b

cd

e

f

a = Ticino Sand (Silica)b = Hokksund Sand (Silica)c = Messina Sand and Gravel (Silica)d = Glauconite Sand(Quartz/Glauconite)e = Quiou Sand (Carbonate)f = Kenya Sand (Carbonate)

Sand

Clay

Mod

ulus

Incr

ease

Rat

io Δ

G/

G10

00

Plasticity Index PI

Figure 12.64 Modulus increase ratio for clays (from Ko-kusho, 1987), supplemented by the data for sands (fromJamiolkowski, 1996).

shear, swelling, chemical and biological changes, andthe like. Until recently it has not been appreciated thatcohesionless soils exhibit this behavior as well. Muchrecent field evidence of the changing properties ofgranular soils over time is now available and these datasuggest that recently disturbed or deposited granularsoils gain stiffness and strength over time at constanteffective stress—a phenomenon called aging. The ev-idence includes the time-dependent increase in stiff-ness and strength of densified sands as measured bycone penetration resistance (Mitchell and Solymer,1984; Thomann and Hryciw, 1992; Ng et al., 1998)and the setup of displacement piles in granular mate-rials (Astedt et al., 1992; York et al., 1994; Chow etal., 1998; Jardine and Standing, 1999; Axelsson,2000). Hypotheses to explain this phenomenon includeboth creep processes and chemical and biological ce-mentation processes. The discussion in this section isfocused primarily on granular soils as the relevant as-pects for clays are treated in detail throughout othersections of the book.

Increase in Shear Modulus with Time

As discussed in Section 12.3, the shear modulus atsmall strain is known to increase with time under aconfining stress, and this is considered to be the con-sequence of aging. This behavior can be quantified bya coefficient of shear modulus increase with time usingthe following formula (Anderson and Stokoe, 1978):

I � G / log(t / t ) (12.60)G 2 1

N � I /G (12.61)G G 1000

where IG is the coefficient of shear modulus increasewith time, t1 is a reference time after primary consol-

idation, t2 is some time of interest thereafter, G is thechange in small strain shear modulus from t1 to t2,G1000 is the shear modulus measured after 1000 min ofconstant confining pressure, which must be after com-pletion of primary consolidation, and NG is the nor-malized shear modulus increase with time. Largeincrease in stiffness due to aging is represented bylarge values of IG or NG. In general, the measured NG

value for clays ranges between 0.05 and 0.25. The ag-ing effect also increases with an increasing plasticityindex as shown in Fig. 12.64 (Kokusho, 1987). Thedata in the figure have been supplemented by valuesof G /G for several sands compiled by Jamiolkowski(1996). Mesri et al. (1990) report that NG for sandsvaries between 0.01 and 0.03 and increases as the soilbecomes finer. Jamiolkowski and Manassero (1995)give values of 0.01 to 0.03 for silica sands, 0.039 forsand with 50 percent mica, and 0.05 to 0.12 for car-bonate sand. Experimental results show that the rate ofincrease in stiffness with time for very loose carbonatesand increases as the stress level increases (Howie etal., 2002). Isotropic stress state resulted in a slowerrate of increase in stiffness.

There is only limited field data that shows evidenceof aging effects on stiffness. Troncoso and Garces(2000) measured shear wave velocities using downhole

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Figure 12.65 Normalized shear modulus as function of ag-ing of tailings (from Troncoso and Garces, 2000).

Figure 12.66 Effect of time on the cone penetration resis-tance of sand following blast densification at the Jebba Damsite.

wave propagation tests in low-plasticity silts with finescontents from 50 to 99 percent at four abandoned tail-ing dams in Chile. The shear modulus normalized bythe vertical effective stress is plotted against the ageof the deposit in Fig. 12.65. The age of the deposits isexpressed as the time since deposition. Although thesoil properties vary to some degree at the four sites,9

very significant increase in stiffness at small strains canbe observed after 10 to 40 years of aging. The degreeto which secondary compression could have contrib-uted to this increase is not known.

Time-Dependent Behavior after GroundImprovement

Stiffness and strength of sand increase with time afterdisturbance and densification by mechanical processessuch as blasting and vibrocompaction. Up to 50 per-cent or more increase in strength has been observedover 6 months (Mitchell and Solymer, 1984; Thomannand Hryciw, 1992; Charlie et al., 1992; Ng et al., 1998;Ashford, et al., 2004) as measured by cone penetrationtesting.

The Jebba Dam project on the Niger River, Nigeria,was an early well-documented field case where agingeffects in sands were both significant and widespread(Mitchell and Solymer, 1984). The project involved thetreatment of foundation soils beneath a 42-m-high dam

9 The four sites identified by Troncoso and Garces (2000) are calledBarahona, Cauquenes, La Cocinera, and Veta del Agua and the agingtimes between abandonment and testing were 28, 19, 5, and 2 years,respectively. The tailing deposits at Barahona had a liquid limit of41 percent and a plastic limit of 14 percent, whereas those at theother three sites had liquid limits of 23 to 29 percent and plasticlimits of 2 to 6 percent.

and seepage blanket. Due to large depths of the loosesand deposit requiring densification, a two-stage den-sification program was performed. The upper 25 m ofsand (and a 5- to 10-m-thick sand pad placed by hy-draulic filling of the river) was densified using vibro-compaction. Deposits between depths of 25 to 40 mwere densified by deep blasting.

During the blasting operations, it was observed thatthe sand exhibited both sensitivity—that is, strengthloss on disturbance—and aging effects. A typical ex-ample of the initial decrease in penetration resistanceafter blasting densification and subsequent increasewith time is shown in Fig. 12.66. Initially after im-provement, there was in some cases a decrease in pen-etration resistance, despite the fact that surfacesettlements ranging from 0.3 to 1.1 m were measured.With time (measured up to 124 days after improve-ment), however, the cone penetration resistance was

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Figure 12.68 Effect of time on the cone penetration resis-tance of hydraulic fill sand after placement at the Jebba Damsite.

-10 0 10 20 30 400.02

0.1

1.0

Temperature (°C)

Jefferies et al. (1988)

Charlie et al. (1992)

Mitchell andSolymer (1984)

Schmertmann (1987) andFordham et al. (1991)

Em

piric

al C

onst

ant K

Figure 12.69 Rate of increase of normalized CPT tip resis-tance against temperature for different cases of reported ag-ing effects after blasting (by Charlie et al., 1992).

Figure 12.67 Effect of time on the cone penetration resis-tance of sand following vibrocompaction densification at theJebba Dam site.

found to increase by approximately 50 to 100 percentof the original values. Similar behavior was found fol-lowing blast densification of hydraulic fill sand thathad been placed for construction of Treasure Island inSan Francisco Bay more than 60 years previously(Ashford et al., 2004).

Aging effects were also observed after placement ofhydraulic fill working platforms in the river at theJebba Dam site and after densification by vibrocom-paction as shown in Figs. 12.67 and 12.68. In the caseof vibrocompaction, however, there was considerablevariability in the magnitude of aging effects throughoutthe site. Because of the greater density increase causedby vibrocompaction than by blast densification, no in-itial decrease in the penetration resistance was ob-served at the end of the compaction process.

Charlie et al. (1992) found a greater rate of agingafter densification by blasting for sands in hotter cli-mates than in cooler climates and suggested a corre-lation between the rate of aging and mean annual airtemperature for available field data as shown in Fig.12.69. In the figure, the increase in the CPT tip resis-tance (qc) with time is expressed by the followingequation:

q (N weeks)c � 1 � K log N (12.62)q (1 week)c

where N is the number of weeks since disturbance andK expresses the rate of increase in tip resistance inlogarithmic time.

Schmertmann (1991) postulated that a ‘‘complicatedsoil structure’’ is present in freshly deposited soil. Thestructure then becomes more stable by ‘‘drained dis-persive movements’’ of soil particles. He suggests thatstresses would arch from softer, weaker areas to stifferzones with time, leading to an increase in K0 with time.Mitchell and Solymar (1984) suggested that the ce-mentation of particles may be the mechanism of aging

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Figure 12.70 Increase in total and shaft capacity with timefor displacement piles in sand (from Chow et al., 1998 andBowman, 2003).

of sands, similar to diagenesis in locked sands andyoung rocks (Dusseault and Morgenstern, 1979; Bar-ton, 1993) in which grain overgrowth has been ob-served. However, others have questioned whethersignificant chemical reactions can occur over the shorttime of observations. In addition, there is some evi-dence of aging in dry sands wherein chemical proc-esses would be anticipated to be very slow.

Setup of Displacement Piles

Much field data indicates that the load-carrying capac-ity of a pile driven into sand may increase dramaticallyover several months, long after pore pressures havedissipated (e.g., Chow et al., 1998; Jardine and Stand-ing, 1999). The amount of increase is highly variable,ranging from 20 to 170 percent per log cycle of timeas shown in Fig. 12.70 (Chow et al., 1998; Bowman,2002). Most of the increase in capacity occurs alongthe shaft of the pile as the radial stress at rest increases

with time (Axelsson, 2000). Evidence suggests thatpiles in silts and find sands set up more than those incoarse sands and gravels (York et al., 1994). Bothdriven and jacked piles exhibit setup, whereas boredpiles do not. Hence, the stress–strain state achievedduring the construction processes of pile driving havean influence on this time-dependent behavior and var-ious mechanisms have been suggested to explain this(Astedt et al., 1992; Chow et al., 1998; Bowman,2002). Unfortunately, at present, there is no conclusiveevidence to confirm any of the proposed hypotheses.

Despite the many field examples and laboratorystudies on aging effects, there is still uncertainty aboutthe mechanism(s) responsible for the phenomenon.Understanding the mechanism(s) that cause aging is ofdirect practical importance in the design and evaluationof ground improvement, driven pile capacity, and sta-bility problems where strength and deformation prop-erties and their potential changes with time areimportant. Mechanical, chemical, and biological fac-tors have been hypothesized for the cause of aging.Biological processes have so far been little studied;however, mechanical and chemical phenomena havebeen investigated in more detail, and some current un-derstanding is summarized below.

12.12 MECHANICAL PROCESSES OF AGING

Creep is hypothesized as the dominant mechanism ofaging of granular systems on an engineering timescaleby Mesri et al. (1990) and Schmertmann (1991). In-creased strength and stiffness does not occur solelyfrom the change in density that occurs during second-ary compression. Rather, it is due to a continued re-arrangement of particles resulting in the increasedmacrointerlocking of particles and the increased mi-crointerlocking of surface roughness. This is supportedby the existence of locked sands (Barton, 1993; Rich-ards and Barton, 1999), which exhibit a tensile strengtheven without the presence of binding cement. Somemicromechanical explanations of the process are givenin Section 12.3.

Although no increase in stiffness was detected whenglass balls were loaded isotropically (Losert et al.,2000), sand has been found to increase in strength andstiffness under isotropic stress conditions (Daramola,1980; Human, 1992). These increases develop even un-der isotropic confinement because the angular particlescan lock together in an anisotropic fabric. It has beenshown that more angular particles produce materialsmore susceptible to creep deformations (Mejia et al.,1988, Human, 1992, Leung et al., 1996). Isotropic

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CHEMICAL PROCESSES OF AGING 517

Time (s)

100 101 102 103 104 105

101 102 103 104 105

0.00

-0.05

0.05

-0.10

-0.15

-0.20

-0.25

-0.30

0.00

0.05

0.10

0.15

0.20

0.25

Glass Ball

Leighton BuzzardUniform Silica Sand

Glass Ball

Dilation

MontpellierNatural Sand

Leighton BuzzardUniform Silica Sand

Montpellier Natural Sand

Stress State at Creep: p� = 600 kPa and q = 800 kPaAll Samples Were Prepared With Relative Density ofApproximately 70%.

Vol

umet

ric S

trai

n (%

)D

evia

toric

Str

ain

(%)

Figure 12.71 Dilative creep observed in triaxial creep testsof dense fine sand (by Bowman and Soga, 2003).

compression tests by Kuwano (1999) showed that ra-dial creep strains were greater than axial strains in soilswith angular particles than in soils with rounded par-ticles due to a more anisotropic initial fabric. Angularparticles can result in longer duration of creep and agreater aging effect since they have a larger range ofstable contacts and the particles can interlock. Asspherical particles rearrange more easily than elon-gated ones (Oda, 1972a), rounder particles initiallycreep at a higher rate before settling into a stable state.Hence, any aging effect on rounded particles tends todisappear quickly when the soil is subjected to newstress state.

When a constant shear stress is applied to loosesand, large creep accompanied by volumetric contrac-tion is observed (Bopp and Lade, 1997). Higher con-tact forces due to loose assemblies contribute toincreased particle crushing, contributing to contractionbehavior. Hence, decrease in volume by soil crushingleads to increase in stiffness and strength.

Field data suggest that displacement piles inmedium-dense to dense sands set up more than thosein loose sand (York et al., 1994). Dense granular ma-terials may dilate with time depending on the appliedstress level during creep as shown in Fig. 12.71 (Bow-man and Soga, 2003). Initially, the soil contracts withtime, but then at some point the creep vector rotatesand the dilation follows. Similar observations weremade by Murayama et al. (1984) and Lade and Lui(1998). This implies that sands at a high relative den-sity will set up more as more interlock between par-ticles may occur (Bowman, 2002). The laboratoryobservation of initial contraction followed by dilationconveniently explains the field data of dynamic com-paction where the greater initial losses and eventualgains in stiffness and strength of sands are found closeto the point of application where larger shear stressesare applied to give dilation (Dowding and Hryciw,1986; Thomann and Hryciw, 1992; Charlie et al.,1992).

Increased strength and stiffness due to mechanicalaging occurs predominantly in the direction of previ-ously applied stress during creep (Howie et al., 2002).No increase was observed when the sand was loadedin a direction orthogonal to that of the applied shearstress during creep (Losert et al., 2000).

12.13 CHEMICAL PROCESSES OF AGING

Chemical processes are a possible cause of aging. His-torically, the most widespread theory used to explainaging effects in sand has involved interparticle bond-

ing. Terzaghi originally referred to a ‘‘bond strength’’in connection with the presence of a quasi-preconsolidation pressure in the field (Schmertmann,1991). Generally, this mechanism has been thought ofas type of cementation, which would increase the co-hesion of a soil without affecting its friction angle.

Denisov and Reltov (1961) showed that quartz sandgrains adhered to a glass plate over time. They placedindividual sand grains on a vibrating quartz or glassplate and measured the force necessary to move thegrains as shown in Fig. 12.72. The dry grains wereallowed to sit on the plate for varying times and thenthe plate was submerged, also for varying times, beforevibrating began. It was found that the force requiredto move the sand grains continued to increase up toabout 15 days of immersion in water. The cementatingagent was thought to be silica-acid gel, which has anamorphous structure and would form a precipitate at

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�

�

�

��

�

�

& &

&

&�

ff0––– 3.0

2.0

1.0

0

4

3

21

10 min 2h 20hTime

(1) Without Soaking(2) 42-hour Soaking(3) 6-day Soaking(4) 14-day Soaking

(1) Glass or Quartz Plate(2) To the Oscillation Generator

1

2

Figure 12.72 Results of vibrating plate experiment fromDenisov and Reltov (1961). Term ƒ/ƒ0 is a measure of thebonding force between sand and glass or quartz plate.

Figure 12.73 Effect of aging on the penetration resistance of River sand (from Joshi et al.,1995).

particle contacts (Mitchell and Solymer, 1984). The in-creased strength is derived from crystal overgrowthscaused by pressure solution and compaction.

Strong evidence of a chemical mechanism being re-sponsible for some aging was obtained by Joshi et al.(1995). A laboratory study was made of the effect oftime on penetration resistance of specimens preparedwith different sands (river sand and sea sand) and porefluid compositions (air, distilled water, and seawater).After loading under a vertical stress of 100 kPa, thevalues of penetration resistance were obtained afterdifferent times up to 2 years. Strength and stiffnessincreases were observed in all cases, and a typical plotof load–displacement curves at various times is shownin Fig. 12.73. The effects of aging were greater for thesubmerged sand than for the dry specimens. Scanningelectron micrographs of the aged specimens in distilledwater and seawater showed precipitates on and in be-tween sand grains. For the river sand in distilled water,the precipitates were composed of calcium (the solublefraction of the sand) and possibly silica. For the riversand in seawater, the precipitates were composed ofsodium chloride.

However, there are several reported cases in whichcementation was an unlikely mechanism of aging, atleast in the short term. For example, dry granular soilscan show an increase in stiffness and strength withtime (Human, 1992; Joshi et al., 1995; Losert et al.,2000). Cementation in dry sand is unlikely, as moistureis required to drive solution and precipitation reactionsinvolving silica or other cementation agents.

Mesri et al. (1990) used the triaxial test data fromDaramola (1980) to argue against a chemical mecha-

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CHEMICAL PROCESSES OF AGING 519

Figure 12.74 Effect of aging on stress–strain relationship of Ham River sand (from Dara-mola, 1980).

nism responsible for aging effects in sands. Figure12.74 shows the effects of aging on both the stiffnessand shear strength of Ham River sand. Four consoli-dated drained triaxial tests were performed on sampleswith the same relative density and confining pressure(400 kPa) but consolidated for different periods of time(0, 10, 30, and 152 days) prior to the start of the tri-axial tests. The results showed that the stiffness in-creased and the strain to failure decreased withincreasing time of consolidation. Although increasedvalues of modulus were observed, the strain at failureis approximately 3 percent. Mesri et al. (1990) arguethat this large strain would destroy any cementation,and therefore another less brittle mechanism must beresponsible for the increase in stiffness.

In summary, experimental evidence indicates thatmechanical aging behavior is enhanced by shear stress

application in denser materials. It is also associatedwith the microinterlocking occurring during the gen-eration of creep strain. The increase in stiffness andstrength is observed in the direction of the appliedstresses, but the aging effect disappears rather quicklywhen loads are applied in other directions. Chemicalaging can also occur within days depending on suchfactors as chemical environment and temperature.

Some conditions in natural deposits are not repli-cated in small-scale laboratory testing. Most laboratorytests are done using clean granular materials, whereasin the field there will be impurities, biological activity,and heterogeneity of void ratio and fabric. Further-more, the introduction of air and other gases duringground improvement may have consequences that haveso far not been fully evaluated. Arching associatedwith dissipation of blast gases and the redistribution of

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stresses through the soil skeleton may also play a role(Baxter and Mitchell, 2004). The boundary conditionsassociated with penetration testing in rigid-wall cylin-ders in the laboratory may prevent detection of time-dependent increases in penetration resistance that aremeasured under the free-field conditions in the field.


With exception of settlement rate predictions, most soilmechanics analyses used in geotechnical engineeringassume limit equilibrium and are based on the as-sumption of time-independent properties and defor-mations. In reality, time-dependent deformations andstress changes that result from the time-dependent orviscous rearrangement of the soil structure may be re-sponsible for a significant part of the total ground re-sponse.

Rate process theory has proven a particularly fruitfulapproach for the study of time-dependent phenomenain soils at consistencies of most interest in engineeringproblems, that is, at water contents from about theplastic limit to the liquid limit. From an analysis of theinfluences of stress and temperature on deformationrates and other evidence, it has been possible to deducethat interparticle contacts are essentially solid and thatclay strength derives from interatomic bonding in thesecontacts. The strength depends on the number of bondsper unit area, and the constant of proportionality be-tween number of bonds and strength is essentially thesame for all silicate minerals, probably because of theirsimilar surface structures.

Recognition of the fact that any macroscopic stressapplied to a soil mass induces both tangential and nor-mal forces at the interparticle contacts is essential tothe understanding of rheological behavior. The resultsof discrete particle simulations show that changes increep rate with time can be explained by changes inthe tangential and normal force ratio at interparticlecontacts that result from particle rearrangement duringdeformation. The change in microfabric in relation tostrong particle networks and weak clusters leads topossible explanation of the mechanical aging process.

Time-dependent deformations and stress relaxationfollow predictable patterns that are essentially the samefor all soil types. Simple constitutive equations can rea-sonably describe time-dependent behavior under lim-ited conditions. Much remains to be learned, however,about the influences of combined stress states, stresshistory and transient drainage conditions on creep,stress relaxation, and creep rupture before reliable

analyses and predictions can be made for large andcomplex geotechnical structures.


1. Find an article about a problem, project, or issuethat involves some aspect of the long-term behaviorof a soil as an important component. The articlemay be from a technical journal or magazine orelsewhere. The only requirement is that it involvesconsideration of time-dependent ground behavior insome way.a. Prepare a one-page informative abstract of the

article.b. Summarize the important geotechnical issues in

the article and write down what you believe youwould need to know to understand them wellenough to solve the problem, resolve the issue,advise a client, and so forth. Do not exceed twopages.

c. Identify topics, figures, equations, and other ma-terial in Chapter 12, if any, that might be usefulin addressing the problems.

2. The figure below shows relationships between (1)number of interparticle bonds and effective consol-idation pressure and (2) compressive strength andnumber of interparticle bonds for three soils as de-termined using rate process theory. Determine ��theangle of internal friction in terms of effectivestresses (as determined from CU tests with porepressure measurements), for each soil. Assume Aƒ

� 0, 0.3, and 0.3 for the sand, illite, and Bay mud,respectively, in the range 0 � (�1 � �3)ƒ � 500kPa, where is the ratio of pore pressure at failureAƒ

to the deviator stress at failure (�1 � �3)ƒ.

00

10

20

30

40

100 200 300 400 500

Num

ber

of B

onds

- 1

010cm

- 2

σ�c = Effective Consolidation Pressure (kPa)

Sand

Bay Mud

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0 5 10 15 20 25

Number of Bonds - 1010cm-2

0

200

400

600

800

1000

Sand, Illite, Bay Mud

(σ1

–σ 3

) max

(kP

a)

3. Equation (12.43) is a simple three-parameter equa-tion for strain rate during constant stress creep ofsoils.a. Show the meaning of �, D, and m on a clearly

labeled sketch.b. Modify Eq. (12.43) and indicate the information

needed to permit prediction of creep rates for agiven soil at any value of water content andstress intensity from a knowledge of creep ratesat a single water content corresponding to dif-ferent stress intensities.

c. Develop a relationship between stress intensityand time to failure for a soil subject to strengthloss under the application of a sustained stress.

4. The results of triaxial compression creep tests onsamples of overconsolidated Bay mud at three stress

D = 100 kPa

D = 85 kPa

D = 68 kPa

RuptureX

10 100 1000 10,00010

20

30

40

50

Axi

al S

trai

n (%

) Water Content = 60%Dmax = 125 kPa

Time (min)

90

80

70

60

50

40

30

Wat

er C

onte

nt (

%)

Compressive Strength (kPa)20 40 80 100 200 400

intensities are shown below, as is the variation ofcompressive strength with water content. A tem-porary excavation is planned that will create a slopewith an average factor of safety of 1.5. The averagewater content of the clay in the vicinity of the cutis 50 percent. The excavation is planned to remainopen for a period of 4 months. Prepare a plot ofstrain rate versus time for an element of clay andassess the probability of a creep rupture failure oc-curring during this period.

5. Given thata. The creep rate of a soil, for times up to the onset

of failure, can be expressed by Eq. (12.43), inwhich D is the deviator stress, and

b. The time to failure by creep rupture, tƒ, can betaken as the time corresponding to minimumstrain rate, prior to acceleration of defor-� ,min

mation and failure, and tests have shown that

� t � constantmin ƒ

If a test embankment designed at a factor ofsafety of 1.05 based on shear strength deter-mined in a short-term test fails in creep ruptureafter 3 months, how long should it be beforefailure of a prototype embankment having a fac-tor of safety of 1.3? From a plot of deformationrate versus time for the test embankment, it hasbeen found that m � 0.75. The results of short-term creep tests have shown also that �Dmax �6.0. The factor of safety is defined as thestrength available divided by the strength thatmust be mobilized for stability.

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6. Would you expect that creep and stress relaxationwill be significant contributors to the stress–deformation and long-term strength of soils on theMoon? Why?

7. List possible causes of sand aging wherein the stiff-ness and strength (usually as determined by pene-

tration tests) can increase significantly over time pe-riods as short as weeks or months following depo-sition and/or densification. Outline a test programthat might be done to test the validity of one ofthese causes.

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523

List of Symbols

a areaa coefficient for harmonicsa cross-sectional area of a tubea crystallographic axis direction or distancea effective cluster contact areaa volumetric air contenta thermal diffusivityac effective area of interparticle contactam coefficient of compressibility with respect

to changes in water contentat coefficient of compressibility with respect

to changes in (� � ua)av coefficient of compressibility in one di-

mensional compressionA activityA areaA creep rate parameterA cross section area normal to the direction

of flowA Hamaker constantA long-range interparticle attractionsA Skempton’s pore pressure parameterA thermal diffusivityA van der Waal’s constantA� short-range attractive stressA pore pressure parameter � u /

(�1 � �3)A0 concentration of charges on pore wallA0 surface charge density per unit pore vol-

umeAc solid contact areaAƒ area of flow passagesAƒ pore pressure parameter at failureAh Hamaker constantAi state parameter in disturbed stateAi total surface area of the ith grain

0Ai state parameter at equilibrium

As specific surface area per unit weight ofsolids

A Angstrom unit � 1 � 10�10 mb coefficient of harmonicsb crystallographic axis direction or distanceb intermediate stress parameterB parameter in rate process equation �

X(kT /h)B Bishop’s pore water pressure coefficientBq grain breakage parameterBr Hardin’s relative breakage parameterc cohesionc cohesion intercept in total stressc concentrationc molar concentrationc crystallographic axis direction or distancec undrained shear strengthc velocity of lightc� cohesion intercept in effective stressc0 equilibrium solution concentration, bulk

solution concentrationc0

� cation equilibrium solution concentrationc0

� anion equilibrium solution concentrationca mid-plane anion concentrationce, c�e Hvorslev’s cohesion parametercec cation exchange capacitycic, cc mid-plane cation concentrationci 0 equilibrium solution concentrationcm mid-plane concentrationc�m mid-plane anion concentrationcu undrained shear strengthcv coefficient of consolidationcw concentration of waterC capacitanceC chemical concentrationC clay content by weightC composition

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524 LIST OF SYMBOLS

C electrical capacitanceC short-range repulsive force between con-

tacting particlesC soil compressibilityC speed of light in vacuum or in air, 3 �

108 m/secC volumetric heatC volumetric heat capacityCc compression indexC*c intrinsic compression indexCl compressibility of pore fluidCn coordination numberCR compression ratioCRR cyclic resistance ratioCs compressibility of a solidCs shape coefficientCs swelling indexCu coefficient of uniformityCu compressibility of soil skeleton by pore

pressure changeCW compressibility of waterC�, C�e coefficient of secondary compressiond diameterd distanced10 sieve size that 10% of the particles by

weight pass throughd60 sieve size that 60% of the particles by

weight pass throughdx incremental horizontal displacement at

peakdy incremental vertical displacement at peakD diameter of particleD dielectric constant, relative permittivityD diffusion coefficientD deviator stressD stress level � D /Dmax

D0 molecular diffusivity of water vapor in airD0 self-diffusion coefficientD50 sieve size that 50% of the particles by

weight pass throughDeƒƒ effective diameterDeV isothermal vapor diffusivityDmax strength at the beginning of creepDR, Dr relative densityDs characteristic grain sizeDTV thermal vapor diffusivityD* effective diffusion coefficiente electronic charge � 4.8029 � 10�10 esu

� 1.60206 � 10�10

coulombe void ratioe0 initial void ratioe*100 intrinsic void ratio under effective vertical

stress of 100 kPaec intracluster void ratio

ecs void ratio at critical stateeƒƒ void ratio at failureeg, eG void ratio of the granular phase, granular

void ratioeini initial void ratioeL void ratio at liquid limitemax maximum void ratioemin minimum void ratioep intercluster void ratioeT total void ratioE experimental activation energyE potential energyE Young’s modulusE voltage, electrical potentialE50 secant modulus at 50 percent of peak

strengthEmax small strain Young’s modulusEr rebound modulusESP exchangeable sodium percentageE(�) distribution function for interparticle con-

tact plane normalsƒ force acting on a flow unitƒ frequencyƒi fraction of particles between two sizesƒn normal forceƒt tangential forceF force of electrostatic attractionF formation factorF free energyF freezing indexF pressure-temperature parameterF tensile strengthF, F0 Faraday constant � 96,500 coulombsF partial molar free energy on adsorptionFd free energy of the double layer per unit

area at a plate spacing of 2d F free energy of activationFE electrical force per unit lengthFH hydraulic seepage force per unit length

causing flowFI fabric indexF� free energy of a single non-interacting

double layerg acceleration due to gravityG shear modulusG source-sinkG1000 shear modulus measured after 1000

minutes of constant confining pressureGg shear modulus of grainsGmax small strain shear modulusGs secant shear modulusGs specific gravity of soil solidsGSC specific gravity of clay particlesGSG specific gravity of the granular particles

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LIST OF SYMBOLS 525

h head or head lossh relative humidity of air in poresh Planck’s constant � 6.624 � 10�27 erg sechm matrix or capillary headhs osmotic or solute headH maximum distance to drainage boundaryH stress historyH thicknessH total headH water transport by ion hydrationH partial molar heat contenti gradienti unit vectoric chemical gradientie electrical gradientih hydraulic gradientit thermal gradientI electrical currentI intensityI1, I2, I3 stress invariantsIG coefficient of shear modulus increase with

timeIR dilatancy indexIv void indexJc chemical flow rateJD chemical flow rateJi flux of constituent iJi value of property i in clay-water systemJs flow rate of salt relative to fixed soil layerJv volume flow rate of solutionJw flow rate of water

0Ji value of property i in pure waterk Boltzmann’s constant � 1.38045 �

10�23 J/ �Kk hydraulic conductivity, hydraulic perme-

abilityk mean coordination number of a graink selectivity coefficientk thermal conductivityk true cohesion in a solidk0 pore shape factorkc osmotic conductivityke electro-osmotic conductivitykh hydraulic conductivityki constant characteristic of a propertykr relative permeabilityks saturated conductivityk(S) saturation dependent hydraulic conductiv-

itykt thermal conductivityk� unsaturated hydraulic conductivityK absolute permeability or intrinsic perme-

abilityK bulk modulus

K double-layer parameter �(8�n0e

2v2 /DRT)1 / 2

K pore shape factorK rate of increase in tip resistance in loga-

rithmic timeK0 coefficient of lateral earth pressure at restKa coefficient of active earth pressureKc principal stress ratioKc principal stress ratio during consolidationKd distribution coefficientKp coefficient of passive earth pressureKso stress-optical material constantK� wavelengths of monochromatic radiationl lengthl material thicknessl total number of pore classesL latent heat of fusionL lengthLij coupling coefficient or conductivity coef-

ficientLI liquidity indexLIeq equivalent liquidity indexLL liquid limitLs latent heat of fusion of waterm slope of relationship between log creep

strain rate and log timem total mass per unit total volumem total number of pore classesmc mass of clayms compressibility of mineral solids under

hydrostatic pressurem�s compressibility of mineral solids under

concentrated loadingsmv compressibilitymw compressibility of watermw mass of waterM constrained modulus or coefficient of vol-

ume changeM metal cationsM monovalent cation concentrationn concentration, ions per unit volumen harmonic numbern integern number of grains in an ideal breakage

planen porosityn total number of pore classesn unspecified atomic ration0 concentration in external solutionn1 number of bonds per unit of normal forcene effective porosityni Refractive index in i directionN Avogadro’s number � 6.0232 � 1023

mole�1

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526 LIST OF SYMBOLS

N coordination numberN monovalent cation concentrationN normal load or forceN number of moles of hydration water per

mole of ionN number of particles per cluster in a cluster

structureN number of weeks since disturbanceN total number of harmonicsN1 number of load cycles to cause liquefac-

tionNe number of load cyclesNG normalized shear modulus increase with

timeNs moles of water per unit volume of sedi-

mentNw moles of salt per unit volume of sedimentOCR overconsolidation ratiop constant that accounts for the interaction

of pores of various sizesp hydrostatic pressurep matrix or osmotic pressurep pressurep partial pressure of water vapor in pore

spacep vertical consolidation pressurep� mean effective pressurepo present overburden pressurepa atmospheric pressurepc preconsolidation pressurep�cs mean effective pressure at critical stateps osmotic or solute pressurepz gravitational pressureP areaP bond strength per contact zoneP concentration of divalent cationsP power consumptionP total gas pressure in pore spaceP total pressureP wetted perimeterPc capillary pressurePc capillary pressure at air entryPƒ injection pressure that causes clay to frac-

turePI plasticity indexPinj injection pressurePL plastic limitPN probability distribution of normal contact

forcePR peak ratioPs swelling pressurePT probability distribution of tangential con-

tact force

q degree of connectivity between water-conducting pores

q deviator stressq flow rateq hydraulic flow rateqc CPT tip resistanceqcs deviator stress at critical stateqƒ deviator stress at failureqh hydraulic flow rateqhc osmotic flow rateqhe electro-osmotic flow rateqi concentration of solidsqt heat flow rateqvap vapor flux densityqw water flow rateQ electrical chargeQ quantity of heatr pore radiusr radiusrk ratio of horizontal to vertical hydraulic

conductivitiesrp pore sizerp tube radiusR coefficient of roundnessR electrical resistanceR gas constant � 1.98726 cal/ �K-mole

8.31470 joules/�K-mole82.0597 cm3 atm/ �K-mole

R long-range repulsion pressureR ratio of cations and anionsR source or sink mass transfer termR sphere radiusR tube radiusRd retardation factorRH hydraulic radiusRp average particle radiusR(�) radius at angle �s slope of stress relaxation curvesu undrained shear strengthS entropyS fraction of molecules striking a surface

that stick to itS number of flow units per unit areaS partial molar entropyS saturationS specific surface area per unit volume of

solidsS structureS swellS partial molar entropyS0 specific surface per unit volume of soil

particlesSAR sodium adsorption ratio

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LIST OF SYMBOLS 527

St sensitivitySu undrained shear strengthSw water saturation ratioSx, Sy, Sz projected areas of interparticle contact

surfacest average thicknesst tetrahedral coordinationst timet transport numbert1 reference timetƒ time to failuretm time for adsorption of a monolayerT intercluster tortuosityT shear forceT temperatureT time factorT0 initial temperatureTc intracluster tortuosityTc temperature at consolidationTFP freezing temperatureTs surface temperatureTs temperature of shear for consolidated un-

drained direct shear testsTV time factoru excess pore pressureu ionic mobilityu midplane potential functionu pore water pressureu pore water pressure in the interparticle

zoneu pressureu thermal energyu* effective ionic mobilityu0 initial pore pressureu0 pore water pressure remote from the in-

terparticle zoneUƒ pore pressure at failureU average degree of consolidationv flow velocityv frequency of activationv ionic valancev settling velocityv specific volume � 1 � evave average flow velocityvc

0 specific volume of the pure clayvcs specific volume at critical statevh apparent water flow velocityV areaV difference in self-potentialsV electrical potentialV speedV valenceV voltage

V volumeV0 initial volumeVA attractive energyVDR volume of water drainedVGS volume of granular solidsVm total volume of soil massVp compression wave velocityVR repulsive energyVs shear wave velocityVs volume of solidsVw partial molar volume of waterVw volume of waterw water contentwL, wl liquid limitwP, wp plastic limitW water contentW widthW fluid volumeW water transportW weightx distance from the clay surfaceX distanceX friction coefficientXi driving forcey potential function � ve� /kTz direction of gravityz distance from drainage surfacez electrolytez ionic valenceZ elevation or elevation headZ number of molecules per second striking

a surfaceZ potential function � 'e�0 /kT� angle between b and c crystallographic

axes� directional parameter� disturbance factor� geometrical packing parameter� inclination of failure plane to horizontal

plane� slope of the relationship between loga-

rithm of creep rate and creep stress� thermal ratio� tortuosity factor�G normalized strain rate parameter�s thermal expansion coefficient of soil sol-

ids�ST thermal expansion coefficient of soil

structure�w thermal expansion coefficient of water� angle between a and c crystallographic

axes� birefringence ratio

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528 LIST OF SYMBOLS

� disturbance factor� geometrical packing parameter� rotation angle of yield envelope�0, �i constant characteristic of the property and

the clay� Bishop’s unsaturated effective stress pa-

rameter� clay plate thickness measured between

centers of surface layer atoms� deformation parameter in Hertz theory� displacement, distance� solid fraction of a contact area� relative retardation�p particle eccentricity distance� dielectric constant, permittivity� porosity� strain� strain rate�0 permittivity of vacuum, 8.85 �

10�12 C2/(Nm2)�1 axial strain�a vertical strain rate in one dimensional

consolidation�ƒ strain at failure�min minimum strain rate�rd volumetric strain that would occur if

drainage were permitted�s deviator strain�s deviator strain rate�v volumetric strain�v volumetric strain rate E energy dissipated per cycle per unit vol-

ume� friction angle� local electrical potential�� friction angle in effective stress�b angle defining the rate of increase in shear

strength with respect to soil suction�c characteristic friction angle��crit friction angle at critical state�e, ��e Hvorslev friction parameter��ƒ friction angle corrected for the work of

dilation��m peak mobilized friction angle��r residual friction angle�repose angle of repose�v apparent specific volume of the water in

a clay/water system of volume V��, �� intergrain sliding friction angle# dissipation function activity coefficient angle between a and b crystallographic

axes unit weight

shear strain ratec applied shear strain or cyclic shear strain

amplituded dry unit weight% double layer charge% specific volume intercept at unit pressure� dynamic viscosity� fraction of pore pressure that gives effec-

tive stress�0 initial anisotropy! swelling index!� real relative permittivity!� polarization loss, imaginary relative per-

mittivity� compression index� correction coefficient for frost depth pre-

diction equation� damping ratio� decay constant� pore size distribution index� separation distance between successive

positions in a structure� wave length of X ray� wave length of light�cs critical state compression index� chemical potential� coefficient of friction� dipole moment� fusion parameter� Poisson’s ratio� viscosity( critical state stress ratio� Poisson’s ratio�b Poisson’s ratio of soil skeleton� osmotic or swelling pressure� angle of bedding plane relative to the

maximum principal stress direction� contact angle� geometrical packing parameter� liquid-to-solid contact angle� orientation angle� volumetric water content�m volumetric water content at full saturation�r residual water content�s volumetric water content at full saturation� bulk dry density� charge density� mass density�d bulk dry density�T resistivity of saturated soil�w density of water�W resistivity of soil water� area occupied per absorbed molecule on

a surface

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LIST OF SYMBOLS 529

� double-layer charge� electrical conductivity� entropy production� normal stress� surface tension of water� surface charge density� total stress�� effective stress��0 initial effective confining pressure�1 major principal total stress�1 tensile strength of the interface bond��1 major principal effective stress�1c major principal stress during consolida-

tion�1ƒ major principal stress at failure��1ƒƒ major principal effective stress at failure��2 intermediate principal effective stress�3 minor principal total stress��3 minor principal effective stress�3c minor principal stress during consolida-

tion��3ƒƒ minor principal effective stress at failure��a axial effective stress��ac axial consolidation stress�as interfacial tension between air and solid�aw interfacial tension between air and water�c crushing strength of particles�c tensile strength of cement�e electrical conductivity��e equivalent consolidation pressure�eƒƒ effective AC conductivity�ƒ partial stress increment for fluid phase��ƒ effective normal stress on shear plane�ƒƒ normal total stress on failure plane��ƒƒ normal effective stress on failure plane�h electrical conductivity due to hydraulic

flow��h0 initial horizontal effective stress��i effective stress in the i-direction��i intergranular stress��i isotropic consolidation�iso isotropic total stress�max maximum principal stress�min minimum principal stress��n effective normal stress��p preconsolidation pressure�r radial total stress��r radial effective stress��rc radial consolidation stress�s conductivity of soil surface�s partial stress increment for solid phase�s tensile strength of the sphere�T electrical conductivity of saturated soil�T , ��t tensile strength of cemented soil

�v vertical stress��v vertical effective stress�v0 overburden vertical effective stress��v0 overburden effective stress��vm maximum past overburden effective stress��vp vertical preconsolidation stress�W electrical conductivity of pore water�ws interfacial tension between water and

solid�y yield strength�� circumferential stress� shear strength� shear stress� surface tension� swelling pressure or matric suction� undrained shear strength�a apparent tortuosity factor�c applied shear stress�c contaminant film strength�cy undrained cyclic shear stress�d drained shear strength�ƒƒ shear stress at failure on failure plane�i shear strength�i shear strength of contact�m shear strength of solid material in yielded

zone�peak applied shear stress at peak�� initial static shear stress' mass flow factor' cation valence� distance function � Kx, double-layer the-

ory� ratio of average temperature gradient in

air filled pores to overall temperature gra-dient

� dilation angle� electrical potential� intrinsic friction angle� matric suction�0 surface potential of double layer�d displacement pressure� electrical potential� state parameter� total potential of soil water�0 electrical potential at the surface�s gravitational potential�m matrix or capillary potential�p gas pressure potential�s osmotic or solute potential" angular velocity" frequency" osmotic efficiency true electroosmotic flow� zeta potential

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Documents

38.Fundamentals of Soil Behaviour 3nd Edition (James K.mitchell&Kenichi Soga