Lpile Technical Manual

8/9/2019 Lpile Technical Manual

1/217

Technical Manual for LPile 2013(Using Data Format Version 7)

A Program for the Analysis of Deep Foundations Under Lateral Loading

by

William M. Isenhower, Ph.D., P.E.

Shin-Tower Wang, Ph.D., P.E.

October 2013


2/217

Copyright © 2013 by Ensoft, Inc.

All rights reserved.

This book or any part thereof may not be reproduced in any form without the written permissionof Ensoft, Inc.

Date of Last Revision: October 24, 2013


3/217

iii

Table of Contents

Chapter 1 Introduction .................................................................................................................... 1

1-1 Compatible Designs.............................................................................................................. 1

1-2 Principles of Design.............................................................................................................. 1

1-2-1 Introduction ................................................................................................................... 11-2-2 Nonlinear Response of Soil........................................................................................... 2

1-2-3 Limit States ................................................................................................................... 21-2-4 Step-by-Step Procedure................................................................................................. 21-2-5 Suggestions for the Designing Engineer ....................................................................... 3

1-3 Modeling a Pile Foundation ................................................................................................. 5

1-3-1 Introduction ................................................................................................................... 5

1-3-2 Example Model of Individual Pile Under Three-Dimensional Loadings ..................... 7

1-3-3 Computation of Foundation Stiffness ........................................................................... 81-3-4 Concluding Comments.................................................................................................. 9

1-4 Organization of Technical Manual....................................................................................... 9

Chapter 2 Solution for Pile Response to Lateral Loading ............................................................ 11

2-1 Introduction ........................................................................................................................ 11

2-1-1 Influence of Pile Installation and Loading on Soil Characteristics............................. 11

2-1-1-1 General Review.................................................................................................... 11

2-1-1-2 Static Loading ...................................................................................................... 122-1-1-3 Repeated Cyclic Loading..................................................................................... 13

2-1-1-4 Sustained Loading................................................................................................ 13

2-1-1-5 Dynamic Loading................................................................................................. 142-1-2 Models for Use in Analyses of Single Piles................................................................ 14

2-1-2-1 Elastic Pile and Soil ............................................................................................. 14

2-1-2-2 Elastic Pile and Finite Elements for Soil ............................................................. 162-1-2-3 Rigid Pile and Plastic Soil.................................................................................... 16

2-1-2-4 Rigid Pile and Four-Spring Model for Soil.......................................................... 16

2-1-2-5 Nonlinear Pile and p-y Model for Soil................................................................. 172-1-2-6 Definition of p and y ............................................................................................ 18

2-1-2-7 Comments on the p-y method .............................................................................. 19

2-1-3 Computational Approach for Single Piles................................................................... 19

2-1-3-1 Study of Pile Buckling......................................................................................... 212-1-3-2 Study of Critical Pile Length ............................................................................... 21

2-1-4 Occurrences of Lateral Loads on Piles........................................................................ 22

2-1-4-1 Offshore Platform ................................................................................................ 222-1-4-2 Breasting Dolphin ................................................................................................ 23

2-1-4-3 Single-Pile Support for a Bridge.......................................................................... 24

2-1-4-4 Pile-Supported Overhead Sign............................................................................. 252-1-4-5 Use of Piles to Stabilize Slopes ........................................................................... 27

2-1-4-6 Anchor Pile in a Mooring System........................................................................ 27

2-1-4-7 Other Uses of Laterally Loaded Piles .................................................................. 27


4/217

iv

2-2 Derivation of Differential Equation for the Beam-Column and Methods of Solution....... 28

2-2-1 Derivation of the Differential Equation ...................................................................... 282-2-2 Solution of Reduced Form of Differential Equation................................................... 32

2-2-3 Solution by Finite Difference Equations..................................................................... 37

Chapter 3 Lateral Load-Transfer Curves for Soil and Rock......................................................... 45

3-1 Introduction ........................................................................................................................ 45

3-2 Experimental Measurements of p-y Curves........................................................................ 473-2-1 Direct Measurement of Soil Response ........................................................................ 47

3-2-2 Derivation of Soil Response from Moment Curves Obtained by Experiment............ 47

3-2-3 Nondimensional Methods for Obtaining Soil Response............................................. 493-3 p-y Curves for Cohesive Soils ............................................................................................ 50

3-3-1 Initial Slope of Curves................................................................................................. 50

3-3-2 Analytical Solutions for Ultimate Lateral Resistance................................................. 523-3-3 Influence of Diameter on p-y Curves .......................................................................... 58

3-3-4 Influence of Cyclic Loading........................................................................................ 59

3-3-5 Introduction to Procedures for p-y Curves in Clays.................................................... 61

3-3-5-1 Early Recommendations for p-y Curves in Clay ................................................. 613-3-5-2 Skempton (1951).................................................................................................. 61

3-3-5-3 Terzaghi (1955).................................................................................................... 63

3-3-5-4 McClelland and Focht (1956) .............................................................................. 633-3-6 Procedures for Computing p-y Curves in Clay ........................................................... 64

3-3-7 Response of Soft Clay in the Presence of Free Water................................................. 64

3-3-7-1 Description of Load Test Program....................................................................... 643-3-7-2 Procedure for Computing p-y Curves in Soft Clay for Static Loading................ 65

3-3-7-3 Procedure for Computing p-y Curves in Soft Clay for Cyclic Loading .............. 68

3-3-7-4 Recommended Soil Tests for Soft Clays ............................................................. 68

3-3-7-5 Examples.............................................................................................................. 683-3-8 Response of Stiff Clay in the Presence of Free Water ................................................ 70

3-3-8-1 Procedure for Computing p-y Curves for Static Loading .................................... 70

3-3-8-2 Procedure for Computing p-y Curves for Cyclic Loading................................... 733-3-8-3 Recommended Soil Tests..................................................................................... 74

3-3-8-4 Examples.............................................................................................................. 75

3-3-9 Response of Stiff Clay with No Free Water................................................................ 753-3-9-1 Procedure for Computing p-y Curves for Stiff Clay without Free Water for Static

Loading ............................................................................................................................. 76

3-3-9-2 Procedure for Computing p-y Curves for Stiff Clay without Free Water for CyclicLoading ............................................................................................................................. 78

3-3-9-3 Recommended Soil Tests for Stiff Clays............................................................. 79

3-3-9-4 Examples.............................................................................................................. 793-3-10 Modified p-y Criteria for Stiff Clay with No Free Water ......................................... 803-3-11 Other Recommendations for p-y Curves in Clays..................................................... 80

3-4 p-y Curves for Sands........................................................................................................... 81

3-4-1 Description of p-y Curves in Sands............................................................................. 813-4-1-1 Initial Portion of Curves....................................................................................... 81

3-4-1-2 Analytical Solutions for Ultimate Resistance...................................................... 82

3-4-1-3 Influence of Diameter on p-y Curves................................................................... 83


5/217

v

3-4-1-4 Influence of Cyclic Loading ................................................................................ 84

3-4-1-5 Early Recommendations ...................................................................................... 853-4-1-6 Field Experiments ................................................................................................ 85

3-4-1-7 Response of Sand Above and Below the Water Table ........................................ 85

3-4-2 Response of Sand ........................................................................................................ 85

3-4-2-1 Procedure for Computing p-y Curves in Sand ..................................................... 863-4-2-2 Recommended Soil Tests..................................................................................... 90

3-4-2-3 Example Curves ................................................................................................... 91

3-4-3 API RP 2A Recommendation for Response of Sand Above and Below the Water Table ..................................................................................................................................... 91

3-4-3-1 Background of API Method for Sand .................................................................. 91

3-4-3-2 Procedure for Computing p-y Curves Using the API Sand Method.................... 923-4-3-3 Example Curves ................................................................................................... 94

3-4-4 Other Recommendations for p-y Curves in Sand........................................................ 96

3-5 p-y Curves in Liquefied Sands............................................................................................ 963-5-1 Response of Piles in Liquefied Sand........................................................................... 96

3-5-2 Procedure for Computing p-y Curves in Liquefied Sand............................................ 983-5-3 Modeling of Lateral Spreading ................................................................................... 99

3-6 p-y Curves in Loess ............................................................................................................ 993-6-1 Background ................................................................................................................. 99

3-6-1-1 Description of Load Test Program....................................................................... 99

3-6-1-2 Soil Profile from Cone Penetration Testing....................................................... 1003-6-2 Procedure for Computing p-y Curves in Loess ......................................................... 101

3-6-2-1 General Description of p-y Curves in Loess...................................................... 101

3-6-2-2 Equations of p-y Model for Loess...................................................................... 1013-6-2-3 Step-by-Step Procedure for Generating p-y Curves........................................... 106

3-6-2-4 Limitations on Conditions for Validity of Model.............................................. 107

3-7 p-y Curves in Soils with Both Cohesion and Internal Friction......................................... 1073-7-1 Background ............................................................................................................... 107

3-7-2 Recommendations for Computing p-y Curves.......................................................... 108

3-7-3 Procedure for Computing p-y Curves in Soils with Both Cohesion and Internal

Friction................................................................................................................................ 1093-7-4 Discussion ................................................................................................................. 112

3-8 Response of Vuggy Limestone Rock ............................................................................... 113

3-8-1 Introduction ............................................................................................................... 1133-8-2 Descriptions of Two Field Experiments.................................................................... 114

3-8-2-1 Islamorada, Florida ............................................................................................ 114

3-8-2-2 San Francisco, California................................................................................... 1153-8-3 Procedure for Computing p-y Curves for Strong Rock (Vuggy Limestone) ............ 119

3-8-4 Procedure for Computing p-y Curves for Weak Rock.............................................. 119

3-8-5 Case Histories for Drilled Shafts in Weak Rock....................................................... 122

3-8-5-1 Islamorada.......................................................................................................... 1223-8-5-2 San Francisco..................................................................................................... 123

3-9 p-y Curves in Massive Rock............................................................................................. 125

3-9-1 Determination of pu Near Ground Surface................................................................ 1273-9-2 Rock Mass Failure at Great Depth ............................................................................ 129


6/217

vi

3-9-3 Initial Tangent to p-y Curve K i.................................................................................. 129

3-9-4 Rock Mass Properties................................................................................................ 1293-9-5 Procedure for Computing p-y Curves in Massive Rock............................................ 131

3-10 p-y Curves in Piedmont Residual Soils .......................................................................... 132

3-11 Response of Layered Soils ............................................................................................. 133

3-11-1 Layering Correction Method of Georgiadis............................................................ 1343-11-2 Example p-y Curves in Layered Soils..................................................................... 134

3-12 Modifications to p-y Curves for Pile Batter and Ground Slope ..................................... 139

3-12-1 Piles in Sloping Ground .......................................................................................... 1393-12-1-1 Equations for Ultimate Resistance in Clay in Sloping Ground ....................... 139

3-12-1-2 Equations for Ultimate Resistance in Sand...................................................... 140

3-12-1-3 Effect of Direction of Loading on Output p-y Curves ..................................... 1413-12-2 Effect of Batter on p-y Curves in Clay and Sand .................................................... 142

3-12-3 Modeling of Piles in Short Slopes........................................................................... 143

3-13 Shearing Force Acting at Pile Tip .................................................................................. 143

Chapter 4 Special Analyses ........................................................................................................ 144

4-1 Introduction ...................................................................................................................... 1444-2 Computation of Top Deflection versus Pile Length......................................................... 144

4-3 Analysis of Piles Loaded by Soil Movements.................................................................. 147

4-4 Analysis of Pile Buckling................................................................................................. 1484-4-1 Procedure for Analysis of Pile Buckling................................................................... 148

4-4-2 Example of Incorrect Analysis.................................................................................. 150

4-4-3 Evaluation of Pile Buckling Capacity ....................................................................... 1514-5 Pushover Analysis of Piles ............................................................................................... 152

4-5-1 Procedure for Pushover Analysis .............................................................................. 153

4-5-2 Example of Pushover Analysis ................................................................................. 153

4-5-3 Evaluation of Pushover Analysis .............................................................................. 155

Chapter 5 Computation of Nonlinear Bending Stiffness and Moment Capacity....................... 157

5-1 Introduction ...................................................................................................................... 157

5-1-1 Application................................................................................................................ 157

5-1-2 Assumptions.............................................................................................................. 1575-1-3 Stress-Strain Curves for Concrete and Steel ............................................................. 158

5-1-4 Cross Sectional Shape Types .................................................................................... 160

5-2 Beam Theory .................................................................................................................... 160

5-2-1 Flexural Behavior...................................................................................................... 1605-2-2 Axial Structural Capacity.......................................................................................... 163

5-3 Validation of Method........................................................................................................ 164

5-3-1 Analysis of Concrete Sections................................................................................... 1645-3-1-1 Computations Using Equations of Section 5-2.................................................. 165

5-3-1-2 Check of Position of the Neutral Axis ............................................................... 165

5-3-1-3 Forces in Reinforcing Steel................................................................................ 1675-3-1-4 Forces in Concrete ............................................................................................. 168

5-3-1-5 Computation of Balance of Axial Thrust Forces ............................................... 170

5-3-1-6 Computation of Bending Moment and EI .......................................................... 1715-3-1-7 Computation of Bending Stiffness Using Approximate Method....................... 172


7/217

vii

5-3-2 Analysis of Steel Pipe Piles....................................................................................... 175

5-3-3 Analysis of Prestressed-Concrete Piles..................................................................... 1775-4 Discussion......................................................................................................................... 180

5-5 Reference Information...................................................................................................... 181

5-5-1 Concrete Reinforcing Steel Sizes.............................................................................. 181

5-5-2 Prestressing Strand Types and Sizes......................................................................... 1825-5-3 Steel H-Piles.............................................................................................................. 183

Chapter 6 Use of Vertical Piles in Stabilizing a Slope ............................................................... 184

6-1 Introduction ...................................................................................................................... 184

6-2 Applications of the Method .............................................................................................. 1846-3 Review of Some Previous Applications ........................................................................... 185

6-4 Analytical Procedure ........................................................................................................ 186

6-5 Alternative Method of Analysis ....................................................................................... 1896-6 Case Studies and Example Computation.......................................................................... 189

6-6-1 Case Studies .............................................................................................................. 189

6-6-2 Example Computation............................................................................................... 190

6-6-3 Conclusions ............................................................................................................... 192

References ...................................................................................................................................194

Name Index .................................................................................................................................202


8/217

viii

List of Figures

Figure 1-1 Example of Modeling a Bridge Foundation................................................................. 6

Figure 1-2 Three-dimensional Soil-Pile Interaction ...................................................................... 7

Figure 1-3 Coefficients of Stiffness Matrix ................................................................................... 8

Figure 2-1 Models of Pile Under Lateral Loading, (a) 3-Dimensional Finite Element

Mesh, and (b) Cross-section of 3-(d) MFAD Model....................................................................................................... 15

Figure 2-2 Model of Pile Under Lateral Loading and p-y Curves............................................... 17

Figure 2-3 Distribution of Stresses Acting on a Pile, (a) Before Lateral Deflection and

(b) After Lateral Deflection y .................................................................................... 18

Figure 2-4 Illustration of General Procedure for Selecting a Pile to Sustain a Given Set of Loads.......................................................................................................................... 20

Figure 2-5 Solution for the Axial Buckling Load........................................................................ 21

Figure 2-6 Solving for Critical Pile Length ................................................................................. 22

Figure 2-7 Simplified Method of Analyzing a Pile for an Offshore Platform............................. 23

Figure 2-8 Analysis of a Breasting Dolphin ................................................................................ 24

Figure 2-9 Loading On a Single Shaft Supporting a Bridge Deck .............................................. 25

Figure 2-10 Foundation Options for an Overhead Sign Structure............................................... 26

Figure 2-11 Use of Piles to Stabilize a Slope Failure .................................................................. 27Figure 2-12 Anchor Pile for a Flexible Bulkhead........................................................................ 28

Figure 2-13 Element of Beam-Column (after Hetenyi, 1946)..................................................... 29

Figure 2-14 Sign Conventions ..................................................................................................... 31

Figure 2-15 Form of Results Obtained for a Complete Solution................................................. 32

Figure 2-16 Boundary Conditions at Top of Pile......................................................................... 33

Figure 2-17 Values of Coefficients A1, B1, C 1, and D1 ................................................................ 35

Figure 2-18 Representation of deflected pile............................................................................... 38

Figure 2-19 Case 1 of Boundary Conditions ............................................................................... 40





Figure 3-1 Conceptual p-y Curves ............................................................................................... 45


9/217

ix

Figure 3-2 p-y Curves from Static Load Test on 24-inch Diameter Pile (Reese, et al.

1975) .......................................................................................................................... 48

Figure 3-3 p-y Curves from Cyclic Load Tests on 24-inch Diameter Pile (Reese, et al.1975) .......................................................................................................................... 49

Figure 3-4 Plot of Ratio of Initial Modulus to Undrained Shear Strength for Unconfined-

compression Tests on Clay ........................................................................................ 51

Figure 3-5 Variation of Initial Modulus with Depth.................................................................... 52

Figure 3-6 Assumed Passive Wedge Failure in Clay Soils, (a) Shape of Wedge, (b)Forces Acting on Wedge ........................................................................................... 53

Figure 3-7 Measured Profiles of Ground Heave Near Piles Due to Static Loading, (a)

Heave at Maximum Load, (b) Residual Heave ......................................................... 54

Figure 3-8 Ultimate Lateral Resistance for Clay Soils ................................................................ 56

Figure 3-9 Assumed Mode of Soil Failure Around Pile in Clay, (a) Section Through

Pile, (b) Mohr-Coulomb Diagram, (c) Forces Acting on Section of Pile................. 57Figure 3-10 Values of Ac and A s................................................................................................... 58

Figure 3-11 Scour Around Pile in Clay During Cyclic Loading, (a) Profile View, (b)

Photograph of Turbulence Causing Erosion During Lateral Load Test.................... 60

Figure 3-12 p-y Curves in Soft Clay,(a) Static Loading, (b) Cyclic Loading.............................. 66

Figure 3-13 Example p-y Curves in Soft Clay Showing Effect of J ............................................ 67

Figure 3-14 Shear Strength Profile Used for Example p-y Curves for Soft Clay........................ 69

Figure 3-15 Example p-y Curves for Soft Clay with the Presence of Free Water....................... 69

Figure 3-16 Characteristic Shape of p-y Curves for Static Loading in Stiff Clay with FreeWater.......................................................................................................................... 71

Figure 3-17 Characteristic Shape of p-y Curves for Cyclic Loading of Stiff Clay with

Free Water ................................................................................................................. 73

Figure 3-18 Example Shear Strength Profile for p-y Curves for Stiff Clay with No Free

Water.......................................................................................................................... 75

Figure 3-19 Example p-y Curves for Stiff Clay in Presence of Free Water for Cyclic

Loading ...................................................................................................................... 76

Figure 3-20 Characteristic Shape of p-y Curve for Static Loading in Stiff Clay without

Free Water ................................................................................................................. 77

Figure 3-21 Characteristic Shape of p-y Curves for Cyclic Loading in Stiff Clay with NoFree Water ................................................................................................................. 78

Figure 3-22 Example p-y Curves for Stiff Clay with No Free Water, Cyclic Loading .............. 79

Figure 3-23 Geometry Assumed for Passive Wedge Failure for Pile in Sand............................. 82

Figure 3-24 Assumed Mode of Soil Failure by Lateral Flow Around Pile in Sand, (a)

Section Though Pile, (b) Mohr-Coulomb Diagram................................................... 84


10/217

x

Figure 3-25 Characteristic Shape of a Set of p-y Curves for Static and Cyclic Loading in

Sand ........................................................................................................................... 86

Figure 3-26 Values of Coefficients and ........................................................................... 88

Figure 3-27 Values of Coefficients Bc and B s .............................................................................. 88

Figure 3-29 Example p-y Curves for Sand Below the Water Table, Static Loading................... 91

Figure 3-30 Coefficients C 1, C 2, and C 3 versus Angle of Internal Friction ................................. 93

Figure 3-31 Value of k , Used for API Sand Criteria.................................................................... 94

Figure 3-32 Example p-y Curves for API Sand Criteria.............................................................. 96

Figure 3-33 Example p-y Curve in Liquefied Sand ..................................................................... 97

Figure 3-34 Idealized Tip Resistance Profile from CPT Testing Used for Analyses. ............... 101

Figure 3-35. Generic p- y curve for Drilled Shafts in Loess Soils.............................................. 102

Figure 3-36 Variation of Modulus Ratio with Normalized Lateral Displacement .................... 104

Figure 3-37 p-y Curves for the 30-inch Diameter Shafts........................................................... 105

Figure 3-38 p-y Curves and Secant Modulus for the 42-inch Diameter Shafts. ........................ 105

Figure 3-39 Cyclic Degradation of p-y Curves for 30-inch Shafts............................................ 106

Figure 3-40 Characteristic Shape of p-y Curves for c- Soil..................................................... 108

Figure 3-41 Representative Values of k for c- Soil.................................................................. 111

Figure 3-42 p-y Curves for c- Soils.......................................................................................... 112

Figure 3-43 Initial Moduli of Rock Measured by Pressuremeter for San Francisco LoadTest .......................................................................................................................... 116

Figure 3-44 Modulus Reduction Ratio versus RQD (Bienawski, 1984) ................................... 117

Figure 3-45 Engineering Properties for Intact Rocks (after Deere, 1968; Peck, 1976; and

Horvath and Kenney, 1979)..................................................................................... 118

Figure 3-46 Characteristic Shape of p-y Curve in Strong Rock ................................................ 119

Figure 3-47 Sketch of p-y Curve for Weak Rock (after Reese, 1997)....................................... 120

Figure 3-48 Comparison of Experimental and Computed Values of Pile-Head Deflection,

Islamorada Test (after Reese, 1997) ........................................................................ 123

Figure 3-49 Computed Curves of Lateral Deflection and Bending Moment versus Depth,

Islamorada Test, Lateral Load of 334 kN (after Reese, 1997) ................................ 124Figure 3-50 Comparison of Experimental and Computed Values of Pile-Head Deflection

for Different Values of EI , San Francisco Test ....................................................... 125

Figure 3-51 Values of EI for three methods, San Francisco test ............................................... 126

Figure 3-52 Comparison of Experimental and Computed Values of Maximum Bending

Moments for Different Values of EI , San Francisco Test ....................................... 126


11/217

xi

Figure 3-53 p-y Curve in Massive Rock .................................................................................... 127

Figure 3-54 Model of Passive Wedge for Drilled Shafts in Rock ............................................. 128

Figure 3-55 Equation for Estimating Modulus Reduction Ratio from Geological Strength

Index ........................................................................................................................ 131

Figure 3-56 Degradation Plot for E s .......................................................................................... 133

Figure 3-57 p-y Curve for Piedmont Residual Soil.................................................................... 133

Figure 3-58 Illustration of Equivalent Depths in a Multi-layer Soil Profile.............................. 135

Figure 3-59 Soil Profile for Example of Layered Soils ............................................................. 135

Figure 3-60 Example p-y Curves for Layered Soil.................................................................... 136

Figure 3-61 Equivalent Depths of Soil Layers Used for Computing p-y Curves ...................... 136

Figure 3-62 Pile in Sloping Ground and Battered Pile .............................................................. 139

Figure 3-63 Soil Resistance Ratios for p-y Curves for Battered Piles from Experiment

from Kubo (1964) and Awoshika and Reese (1971) ............................................... 142

Figure 4-1 Pile and Soil Profile for Example Problem .............................................................. 145

Figure 4-2 Variation of Top Deflection versus Depth for Example Problem............................ 145

Figure 4-3 Pile-head Load versus Deflection for Example........................................................ 146

Figure 4-4 Top Deflection versus Pile Length for Example...................................................... 146

Figure 4-5 p-y Curve Displaced by Soil Movement .................................................................. 148

Figure 4-6 Examples of Pile Buckling Curves for Different Shear Force Values..................... 149

Figure 4-7 Examples of Correct and Incorrect Pile Buckling Analyses.................................... 150

Figure 4-8 Typical Results from Pile Buckling Analysis .......................................................... 151

Figure 4-9 Pile Buckling Results Showing a and b ................................................................... 152

Figure 4-10 Dialog for Controls for Pushover Analysis............................................................ 153

Figure 4-11 Pile-head Shear Force versus Displacement from Pushover Analysis................... 154

Figure 4-12 Maximum Moment Developed in Pile versus Displacement from Pushover

Analysis ................................................................................................................... 154

Figure 5-1 Stress-Strain Relationship for Concrete Used by LPile ........................................... 158

Figure 5-2 Stress-Strain Relationship for Reinforcing Steel Used by LPile.............................. 159

Figure 5-3 Element of Beam Subjected to Pure Bending .......................................................... 161

Figure 5-4 Validation Problem for Mechanistic Analysis of Rectangular Section.................... 165

Figure 5-5 Free Body Diagram Used for Computing Nominal Moment Capacity of Reinforced Concrete Section................................................................................... 172

Figure 5-6 Bending Moment versus Curvature.......................................................................... 173

Figure 5-7 Bending Moment versus Bending Stiffness............................................................. 174


12/217

xii

Figure 5-8 Interaction Diagram for Nominal Moment Capacity ............................................... 174

Figure 5-9 Example Pipe Section for Computation of Plastic Moment Capacity ..................... 175

Figure 5-10 Moment versus Curvature of Example Pipe Section ............................................. 175

Figure 5-11 Elasto-plastic Stress Distribution Computed by LPile........................................... 177

Figure 5-12 Stress-Strain Curves of Prestressing Strands Recommended by PCI DesignHandbook, 5

thEdition.............................................................................................. 178

Figure 5-13 Sections for Prestressed Concrete Piles Modeled in LPile .................................... 180

Figure 6-1 Scheme for Installing Pile in a Slope Subject to Sliding.......................................... 185

Figure 6-2 Forces from Soil Acting Against a Pile in a Sliding Slope, (a) Pile, Slope, and

Slip Surface Geometry, (b) Distribution of Mobilized Forces, (c) Free-bodyDiagram of Pile Below the Slip Surface.................................................................. 186

Figure 6-3 Influence of Stabilizing Pile on Factor of Safety Against Sliding ........................... 187

Figure 6-4 Matching of Computed and Assumed Values of h p

................................................. 189

Figure 6-5 Soil Conditions for Analysis of Slope for Low Water............................................. 190

Figure 6-6 Preliminary Design of Stabilizing Piles ................................................................... 191

Figure 6-7 Load Distribution from Stabilizing Piles for Slope Stability Analysis .................... 192


13/217

xiii

List of Tables

Table 3-1.

Stiff Clay (no longer recommended) ......................................................................... 63

Table 3-2. Representative Values of 50....................................................................................... 65

Table 3-3. Representative Values of k for Stiff Clays.................................................................. 71

Table 3-4. Representative Values of 50 for Stiff Clays............................................................... 72

Table 3-5 ues of k for Laterally Loaded Piles in

Sand ........................................................................................................................... 81

Table 3-6. Representative Values of k for Submerged Sand for Static and Cyclic Loading ....... 89

Table 3-7. Representative Values of k for Sand Above Water Table for Static and Cyclic

Loading ...................................................................................................................... 89

Table 3-8. Results of Grout Plug Tests by Schmertmann (1977) .............................................. 115

Table 3-9. Values of Compressive Strength at San Francisco................................................... 117

Table 5-1. LPile Output for Rectangular Concrete Section ....................................................... 166

Table 5-2. Comparison of Results from Hand Computation versus Computer Solution........... 173


14/217


15/217

1

Chapter 1Introduction

1-1 Compatible Designs

The program LPile provides the capability to analyze piles for a variety of applications inwhich lateral loading is applied to a deep foundation. The analysis is based on solution of a

differential equation describing the behavior of a beam-column with nonlinear support. The

solution obtained ensures that the computed deformations and stresses in the foundation andsupporting soil agree. Analyses of this type have been in use in the practice of civil engineering

for some time and the analytical procedures that are used are widely accepted.

The one goal of foundation engineering is to predict how a foundation will deform and

deflect in response to loading. In advanced analyses, the analysis of the foundation performance

can be combined with that those for the superstructure to provide a global solution in which bothequilibrium of forces and moment and compatibility of displacements and rotations is achieved.

Analyses of this type are possible because of the power of computer software for analysis

and computer graphics. Calibration and verification of the analyses is possible because of theavailability of sophisticated instruments for observing the behavior of structural systems.

Some problems can be solved only by using the concepts of soil-structure interaction.

Presented herein are analyses for isolated piles that achieve the pile response while satisfying

simultaneously the appropriate nonlinear response of the soil. The pile is treated as a beam-column and the soil is replaced with nonlinear Winkler-type mechanisms. These mechanisms can

accurately predict the response of the soil and provide a means of obtaining solutions to a

number of practical problems.

1-2 Principles of Design

1-2-1 Introduction

The design of a pile foundation to sustain a combination of lateral and axial loading

requires the designing engineer to consider factors involving both performance of the foundation

to support loading and the costs and methods of construction for different types of foundations.

Presentation of complete designs as examples and a discussion many practical details related toconstruction of piles is outside the scope for this manual.

The discussion of the analytical methods presented herein address two aspects of design

that are helpful to the user. These aspects of design are computation of the loading at which a particular pile will fail as a structural member and identification of the level of loading that willcause an unacceptable lateral deflection. The analysis made using LPile includes computation of

deflection, bending moment, and shear force along the length of a pile under loading. Additional

considerations that are useful are selection of the minimum required length of a pile foundationand evaluation of the buckling capacity of a pile that extends above the ground line.


16/217

Chapter 1 Introduction

2

1-2-2 Nonlinear Response of Soil

In one sense, the design of a pile under lateral loading is no different that the design of any foundation. One needs to determine first the loading of the foundation that will cause failure

and then to apply a global factor of safety or load and resistance factors to set the allowable

loading for the foundation. What is different for analysis of lateral loading is that the failure

cannot be found by solving the equations of static equilibrium. Instead, the lateral capacity of thefoundation can only be found by solving a differential equation governing its behavior and then

evaluating the results of the solution. Furthermore, as noted below, a closed-form solution of the

differential equation, as with the use a constant modulus of subgrade reaction is inappropriate inthe vast majority of cases.

To illustrate the nonlinear response of soil to lateral loading of a pile, curves of response

of soil obtained from the results of a full-scale lateral load test of a steel-pipe pile are presented

in Chapter 2. This test pile was instrumented for measurement of bending moment and wasinstalled into overconsolidated clay with free water present above the ground surface. The results

for static load testing definitely show that the soil resistance is nonlinear with pile deflection and

increases with depth. With cyclic loading, frequently encountered in practice, the nonlinearity inload-deflection response is greatly increased. Thus, if a linear analysis shows a tolerable level of

stress in a pile and of deflection, an increase in loading could cause a failure by collapse or by

excessive deflection. Therefore, a basic principle of compatible design is that nonlinear responseof the soil to lateral loading must be considered.

1-2-3 Limit States

In most instances, failure of a pile is initiated by a bending moment that would cause the

development of a plastic hinge. However, in some instances the failure could be due to excessive

deflection, or, in a small fraction of cases, by shear failure of the pile. Therefore, pile design is based on a decision of what constitutes a limit state for structural failure or excessive deflection.

Then, computations are made to determine if the loading considered exceeds the limit states.

A global factor of safety is normally employed to find the allowable loading, the service

load level, or the working load level.

An approach using partial load and resistance factors may be employed. However,analyses employed in applying load and resistance factors is implemented herein by using upper-

bound and lower-bound values of the important parameters.

1-2-4 Step-by-Step Procedure

1. Assemble all relevant data, including soil properties, magnitude and nature of the loading,and performance requirements for the structure.

2. Select a pile type and size for analysis.

3. Compute curves of nominal bending moment capacity as a function of axial thrust load and

curvature; compute the corresponding values of nonlinear bending stiffness.

4. Select p-y curve types for the analysis, along with average, upper bound, and lower bound

values of input variables.

5. Make a series of solutions, starting with a small load and increasing the load in increments,

with consideration of the manner the pile is fastened to the superstructure.


17/217


3

6. Obtain curves showing maximum moment in the pile and lateral pile-head deflection versus

lateral shear loading and curves of lateral deflection, bending moment and shear force versusdepth along the pile.

7. Change the pile dimensions or pile type, if necessary and repeat the analyses until a range of

suitable pile types and sizes have been identified.

8. Identify the pile type and size for which the global factor of safety is adequate and the most

efficient cost of the pile and construction is estimate.

9. Compute behavior of pile under working loads.

Virtually none of the examples in this manual follow all steps indicated above. However,

in most cases, the examples do show the curves that are indicated in Step 6.

1-2-5 Suggestions for the Designing Engineer

As will be explained in some detail, there are five sets of boundary conditions that can be

employed; examples will be shown for the use of these different boundary conditions. However,the manner in which the top of the pile is fastened to the pile cap or to the superstructure has a

significant influence on deflections and bending moments that are computed. The engineer may be required to perform an analysis of the superstructure, or request that one be made, in order toensure that the boundary conditions at the top of the pile are satisfied as well as possible.

With regard to boundary conditions at the pile head, it is important to note the versatility

of LPile. For example, piles that are driven with an accidental batter or an accidental eccentricity

can be easily analyzed. It is merely necessary to define the appropriate conditions for theanalysis.

As noted earlier, selection of upper and lower bound values of soil properties is a

practical procedure. Parametric solutions are easily done and relatively inexpensive and such

solutions are recommended. With the range of maximum values of bending moment that result

from the parametric studies, for example, the insight and judgment of the engineer can beimproved and a design can probably be selected that is both safe and economical. Alternatively,

one may perform a first-order, second moment reliability analysis to evaluate variance in

performance for selected random variables. For further guidance on this topic, the reader isreferred to the textbook by Baecher and Christian (2003).

If the axial load is small or negligible, it is recommended to make solutions with piles of

various lengths. In the case of short piles, the mobilization shear force at the bottom of the pile

can be defined along with the soil properties. In most cases, the installation of a few extra feet of pile length will add little cost to the project and, if there is doubt, a pile with a few feet of

additional length could possibly prevent a failure due to excessive deflection. If the base of the

pile is founded in rock, available evidence shows that often only a short socket will be necessaryto anchor the bottom of the pile. In all cases, the designer must assure that the pile has adequate

bending stiffness over its full length.

A useful activity for a designer is to use LPile to analyze piles for which experimental

results are available. It is, of course, necessary to know the appropriate details from the loadtests; pile geometry and bending stiffness, stratigraphy and soil properties, magnitude and point

of application of loading, and the type of loading (either static or cyclic). Many such experiments

have been run in the past. Comparison of the results from analysis and from experiment can yield


18/217


4

valuable information and insight to the designer. Some comparisons are provided in thisdocument, but those made by the user could be more site-specific and more valuable.

In some instances, the parametric studies may reveal that a field test is indicated. Such a

case occurs when a large project is planned and when the expected savings from an improved

design exceeds the cost of the testing. Savings in construction costs may be derived either by

proving a more economical foundation design is feasible, by permitting use of a lower factor of safety or, in the case of a load and resistance factor design, use of an increased strength reduction

factor for the soil resistance.

There are two types of field tests. In one instance, the pile may be fully instrumented sothat experimental p-y curves are obtained. The second type of test requires no internal instru-

mentation in the pile but only the pile-head settlement, deflection, and rotation will be found as a

function of applied load. LPile can be used to analyze the experiment and the soil properties can

be adjusted until agreement is reached between the results from the computer and those from theexperiment. The adjusted soil properties can be used in the design of the production piles.

In performing the experiment, no attempt should be made to maintain the conditions at

the pile head identical to those in the design. Such a procedure could be virtually impossible.Rather, the pile and the experiment should be designed so that the maximum amount of deflection is achieved. Thus, the greatest amount of information can be obtained on soil

response.

The nature of the loading during testing; whether static, cyclic, or otherwise; should be

consistent for both the experimental pile and the production piles.

The two types of problems concerning the performance of pile groups of piles are

computation of the distribution of loading from the pile cap to a widely spaced group of piles and

the computation of the behavior of spaced-closely piles.

The first of these problems involves the solutions of the equations of structural mechanics

that govern the distribution of moments and forces to the piles in the pile group (Hrennikoff,1950; Awoshika and Reese, 1971; Akinmusuru, 1980). For all but the most simple group

geometries, solution of this problem requires the use of a computer program developed for its

solution.

The second of the two problems is more difficult because less data from full-scale

experiments is available (and is often difficult to obtain). Some full-scale experiments have been

performed in recent years and have been reported (Brown, et al., 1987; Brown et al., 1988).

These and additional references are of assistance to the designer (Bogard and Matlock, 1983;Focht and Koch, 1973; , et al., 1977).

The technical literature includes significant findings from time to time on piles under

lateral loading. Ensoft will take advantage of the new information as it becomes available andverified by loading testing and will issue new versions of LPile when appropriate. However, thematerial that follows in the remaining sections of this document shows that there is an

opportunity for rewarding research on the topic of this document, and the user is urged to stay

current with the literature as much as possible.


19/217


5

1-3 Modeling a Pile Foundation

1-3-1 Introduction

As a problem in foundation engineering, the analysis of a pile under combined axial andlateral loading is complicated by the fact that the mobilized soil reaction is in proportion to the

pile movement, and the pile movement, on the other hand, is dependent on the soil response.This is the basic problem of soil-structure interaction. The question about how to simulate the behavior of the pile in the analysis arises when the foundation engineer attempts to use boundary

conditions for the connection between the structure and the foundation. Ideally, a program can be

developed by combining the structure, piles, and soils into a single model. However, special purpose programs that permit development of a global model are currently unavailable. Instead,

the approach described below is commonly used for solving for the nonlinear response of the

pile foundation so that equilibrium and compatibility can be achieved with the superstructure.

The use of models for the analysis of the behavior of a bridge is shown in Figure 1-1(a).A simple, two-span bridge is shown with spans in the order of 30 m and with piles supporting the

abutments and the central span. The girders and columns are modeled by lumped masses and the

foundations are modeled by nonlinear springs, as shown in Figure 1-1(b). If the loading is three-dimensional, the pile head at the central span will undergo three translations and three rotations.A simple matrix-formulation for the pile foundation is shown in Figure 1-1(c), assuming two-

dimensional loading, along with a set of mechanisms for the modeling of the foundation. Three

springs are shown as symbols of the response of the pile head to loading; one for axial load, onefor lateral load, and one for moment.

The assumption is made in analysis that the nonlinear curve for axial loading is not

greatly influenced by lateral loading (shear) and moment. This assumption is not strictly true

because lateral loading can cause gapping in overconsolidated clay at the top of the pile with aconsequent loss of load transfer in skin friction along the upper portion of the pile. However, in

such a case, the soil near the ground surface could be ignored above the first point of zero lateral

deflection. The practical result of such a practice in most cases is that the curve of axial loadversus settlement and the stiffness coefficient K 11 are negligibly affected.

The curves representing the response to shear and moment at the top of the pile are

certainly multidimensional and unavoidably so. Figure 1-1(c) shows a curve and identifies one of

the stiffness terms K 32. A single-valued curve is shown only because a given ratio of moment M 1and shear V 1 was selected in computing the curve. Therefore, because such a ratio would be

unknown in the general case, iteration is required between the solutions for the superstructure

and the foundation.

The conventional procedure is to select values for shear and moment at the pile head andto compute the initial stiffness terms so that the solution of the superstructure can proceed for the

most critical cases of loading. With revised values of shear and moment at the pile head, themodel for the pile can be resolved and revised terms for the stiffnesses can be used in a new

solution of the model for the superstructure. The procedure could be performed automatically if acomputer program capable of analyzing the global model were available but the use of

independent models allows the designer to exercise engineering judgment in achieving

compatibility and equilibrium for the entire system for a given case of loading.


20/217


21/217


7

1-3-2 Example Model of Individual Pile Under Three-Dimensional Loadings

An interesting presentation of the forces that resist the displacement of an individual pile

is shown in Figure 1-2 (Bryant, 1977). Figure 1-2(a) shows a single pile beneath a cap along withthe three-dimensional displacements and rotations. The assumption is made that the top of the

pile is fixed or partially fixed into the cap and that bending moments and a torsion will develop

as a result of the three-dimensional rotations of the cap. The various reactions of the soil alongthe pile are shown in Figure 1-2(b), and the load-transfer curves are shown in Figure 1-2(c). The

argument given earlier about the curve for axial displacement being single-value pertains as well

to the curve for axial torque. However, the curve for lateral deflection is certainly a function of the shear forces and moments that cause such deflection. When computing lateral deflection, a

complication may arise because the loading and deflection may not be in a two-dimensional

plane. The recommendations that have been made for correlating the lateral resistance with pile

geometry and soil properties all depend on the results of loading in a two-dimensional plane.

Figure 1-2 Three-dimensional Soil-Pile Interaction

Torsional Pile

Displacement,

Lateral Pile

Displacement, y

(a) Three-dimensional

pile displacements

Axial Soil

Reaction, q

Torsional Soil

Reaction, t

Lateral Soil

Reaction, p

y

x

z Axial Pile

Displacement, u

(b) Pile reactions (c) Nonlinear load-transfer

curves

P x

P y

P z

M y

M x

M z

q

u

p

y

t

Axial

Lateral

Torsional

Torsional Pile

Displacement,

Lateral Pile

Displacement, y

(a) Three-dimensional

pile displacements

Axial Soil

Reaction, q

Torsional Soil

Reaction, t

Lateral Soil

Reaction, p

y

x

z Axial Pile

Displacement, u

(b) Pile reactions (c) Nonlinear load-transfer

curves

P x

P y

P z

M y

M x

M z

q

u

p

y

t

Axial

Lateral

Torsional


22/217


8

1-3-3 Computation of Foundation Stiffness

Stiffness matrices are often used to model foundations in structural analyses and LPile provides an option for evaluating the lateral stiffness of a deep foundation. This feature in LPile

allows the user to solve for coefficients, as illustrated by the sketches shown in Figure 1-3, of

pile-head movements and rotations as functions of incremental loadings. The program divides

the loads specified at the pile head into increments and then computes the pile head response for each individual loading. The deflection of the pile head is computed for each lateral-load

increment with the rotation at the pile head being restrained to zero. Next, the rotation of the pile

head is computed for each bending-moment increment with the lateral deflection at the pile head being restrained to zero. The user can thus define the stiffness matrix directly based on the

relationship between computed deformation and applied load. For instance, the stiffness

coefficient K 33, shown in Figure 1-1(c), can be obtained by dividing the applied moment M bythe computed rotation at the pile top.

Figure 1-3 Coefficients of Stiffness Matrix

Stiffnesses K 22 and K 23 are computed using the

shear-rotation pile-head condition, for which the

user enters the lateral load V at the pile head.

LPile computes pile-head deflection andreaction moment M at the pile head using zero

slope at the pile head (pile head rotation = 0).

K 22 = V / and K 32 = M / .

M

P

V

Stiffnesses K 32 and K 33 are computed using the

displacement-moment pile-head condition, for

which the user enters the moment M at the pile

head. LPile computes the lateral reaction force, H , and pile-head rotation using zero deflection

at the pile head ( = 0).

K 23 = V / and K 33 = M / .

M

P

V


23/217


9

Most analytical methods in structural mechanics can employ either the stiffness matrix or

the flexibility matrix to define the support condition at the pile head. If the user prefers to use thestiffness matrix in the structural model, Figure 1-3 illustrates basic procedures used to compute a

stiffness matrix. The initial coefficients for the stiffness matrix may be defined based on the

magnitude of the service load. The user may need to make several iterations before achieving

acceptable agreement.1-3-4 Concluding Comments

The correct modeling of the problem of the single pile to respond to axial and lateral

loading is challenging and complex, and the modeling of a group of piles is even more complex.

However, in spite of the fact that research is continuing, the following chapters will demonstratethat usable solutions are at hand.

New developments in computer technology allow a complete solution to be readily

developed, including automatic generation of the nonlinear responses of the soil around a pile

and iteration to achieve force equilibrium and compatibility.

1-4 Organization of Technical ManualChapters 2 to 4 provide the user with the background information on soil-pile interaction

for lateral loading and present the equations that are solved when obtaining a solution for the

beam-column problem when including the effects of the nonlinear response of the soil. Also,

information on the verification of the validity of a particular set of output is given. The user isurged to read carefully these latter two sections. Output from the computer should be viewed

with caution unless verified, and the selection of the appropriate soil response ( p-y curves)

is the most critical aspect of most computations.

Not all engineers will have a computer program available that can be used to predict thelevel of bending moment in a reinforced-concrete section at which a plastic hinge will develop,

while taking into account the influence of axial thrust loading. Chapter 4 of this manual describesa program feature that can be provided for this purpose. The program can compute the flexuralrigidity of the section as a function of the bending moment.

If one is performing an elastic analysis, it is suggested that reduced values of flexural

rigidity be used in the region of maximum bending moment for each value of lateral load

because the flexural rigidity varies as a function of the bending moment. However, experiencehas often found that the lateral response of a pile is not critically dependent on the value of

flexural rigidity for smaller lateral loads. Recommendations are provided for the selection of

flexural rigidity that will yield results that are considered to be acceptable. However, the user could use the results from Chapter 4 as input to the coding for Chapter 2 to investigate the

importance of entering accurate values of flexural rigidity.

Finally, Chapter 5 includes the development of a solution that is designed to give the user

some guidance in the use of piles to stabilize a slope. While no special coding is necessary for the purpose indicated, the number of steps in the solution is such that a separate section is

desirable rather than including this example with those in the LPile


24/217


10

(This page was deliberately left blank)


25/217

11

Chapter 2Solution for Pile Response to Lateral Loading

2-1 Introduction

Many pile-supported structures will be subjected to horizontal loads during their functional lifetime. If the loads are relatively small, a design can be made by building code

provisions that list allowable loads for vertical piles as a function of pile diameter and properties

of the soil. However, if the load per pile is large, the piles are frequently installed at a batter. Theanalyst may assume that the horizontal load on the structure is resisted by components of the

axial loads on the battered piles. The implicit assumption in the procedure is that the piles do not

deflect laterally which, of course, is not true. Rational methods for the analysis of single pilesunder lateral load, where the piles are vertical or battered, will be discussed herein, and methods

are given for investigating a wide variety of parameters. The problem of the analysis of a groupof piles is discussed in another publication.

As a foundation problem, the analysis of a pile under lateral loading is complicated because the soil reaction (resistance) at any point along a pile is a function of pile deflection. The

pile deflection, on the other hand, is dependent on the soil resistance; therefore, solving for the

response of a pile under lateral loading is one of a class of soil-structure-interaction problems.

The conditions of compatibility and equilibrium must be satisfied between the pile and soil and between the pile and the superstructure. Thus, the deformation and movement of the

superstructure, ranging from a concrete mat to an offshore platform, and the manner in which the

pile is attached to the superstructure, must be known or computed in order to obtain a correctsolution to most problems.

2-1-1 Influence of Pile Installation and Loading on Soil Characteristics

2-1-1-1 General Review

The most critical factor in solving for the response of a pile under lateral loading is the

prediction of the soil resistance at any point along a pile as a function of the pile deflection. Anyserious attempt to develop predictions of soil resistance must address the stress-deformation

characteristics of the soil. The properties to be considered, however, are those that exist after the

pile has been installed. Furthermore, the influence of lateral loading on soil behavior must be

taken into account.

The deformations of the soil from the driving of a pile into clay cause important and

significant changes in soil characteristics. Different but important effects are caused by drivingof piles into granular soils. Changes in soil properties are also associated with the installation of

bored piles. While definitive research is yet to be done, evidence clearly shows that the soilimmediately adjacent to a pile wall is most affected. Investigators (Malek, et al., 1989) have

suggested that the direct-simple-shear test can be used to predict the behavior of an axially

loaded pile, which suggests that the soil just next to the pile wall will control axial behavior.However, the lateral deflection of a pile will cause strains and stresses to develop from the pile


26/217

Chapter 2 Solution for Pile Response to Lateral Loading

12

wall to several diameters away. Therefore, the changes in soil characteristics due to pileinstallation are less important for laterally loaded piles than for axially loaded piles.

The influence of the loading of the pile on soil response is another matter. Four classes of

lateral loading can be identified: short-term, repeated, sustained, and dynamic. The first three

classes are discussed herein, but the response of piles to dynamic loading is beyond the scope of

this document. The use of a pseudo-horizontal load as an approximation in making earthquake-resistant designs should be noted, however.

The influence of sustained or cyclic loading on the response of the soil will be discussed

in some detail in Chapter 3; however, some discussion is appropriate here to provide a basis for evaluating the models that are presented in this chapter. If a pile is in granular soil or

overconsolidated clay, sustained loading, as from earth pressure, will likely cause only a

negligible amount of long-term lateral deflection. A pile in normally consolidated clay, on the

other hand, will experience long-term deflection, but, at present, the magnitude of suchdeflection can only be approximated. A rigorous solution requires solution of the three-

dimensional consolidation equation stepwise with time. At some time, the pile-head will

experience an additional deflection that will cause a change in the horizontal stresses in thecontinuum.

Methods have been developed, as reviewed later, for getting answers to the problem of

short-term loading by use of correlations between soil response and the in situ undrained strength

of clay and the in-important because they can be used for sustained loading in some cases and because an initial

condition is provided for taking the influence of repeated loading into account. Experience has

shown that the loss of lateral resistance due to repeated loading is significant, especially if the piles are installed in clay below free water. The clay can be pushed away from the pile wall and

the soil response can be significantly decreased. Predictions for the effect of cyclic loading are

given in Chapter 3.

Four general types of loading are recognized above and each of these types is further discussed in the following sections. The importance of consideration and evaluation of loading

when analyzing a pile subjected to lateral loading cannot be overemphasized.

Many of the load tests described later in this chapter were performed by applying a lateral

load in increments, holding that load for a few minutes, and reading all the instruments that gavethe response of the pile. The data that were taken allowed p-y curves to be computed; analytical

expressions are developed from the experimental results and these expressions yield p-y curves

following section.

2-1-1-2 Static Loading

The static p-y curves can be thought of as backbone curves that can be correlated to some

extent with soil properties. Thus, the curves are useful for providing some theoretical basis to the

p-y method.

From the standpoint of design, the static p-y curves have application in the followingcases: where loadings are short-term and not repeated (probably not encountered); and for

sustained loadings, as in earth-pressure loadings, where the soil around the pile is not susceptible

to consolidation and creep (overconsolidated clays, clean sands, and rock).


27/217

Chapter 2 - Solution for Pile Response to Lateral Loading

13

As will be noted later in this chapter, the use of the p-y curves for repeated loading, a typeof loading that is frequently encountered in practice, will often yield significant increases in pile

deflection and bending moment. The engineer may wish to make computations with both the

static curves and with the repeated (cyclic) curves so that the influence of the loading on pile

response can be seen clearly.

2-1-1-3 Repeated Cyclic Loading

The full-scale field tests that were performed included repeated or cyclic loading as well as the

static loading described above. An increment of load was applied, the instruments were read, and

the load was repeated a number of times. In some instances, the load was forward and backward,and in other cases only forward. The instruments were read after a given number of cycles and

the cycling was continued until there was no obvious increase in ground line deflection or in

bending moments. Another increment was applied and the procedure was repeated. The final

load that was applied brought the maximum bending moment close to the moment that wouldcause the steel to yield plastically.

Four specific sets of recommendations for p-y curves for cyclic loading are described in

Chapter 3. For three of the sets, the recommendations that are given -case. That is, the data that were used to develop the p-y curves were from cases where theground-line deflection had substantially ceased with repetitions in loading. In the other case, for

stiff clay where there was no free water at the ground surface, the recommendations for p-y

curves are based on the number of cycles of load application, as well as other factors.

The presence of free water at the ground surface for clay soils can be significant in regardto the loss of soil resistance due to cyclic loading (Long, 1984). After a deflection is exceeded

when the load is released. Free water moves into this space and on the next load application thewater is ejected bringing soil particles with it. This erosion causes a loss of soil resistance in

addition to the losses due to remolding of the soil as a result of the cyclic strains. At this point

the use of judgment in the design of the piles under lateral load should be emphasized. For example, if the clay is below a layer of sand, or if provision could be made to supply sand around

the pile, the sand will settle around the pile, and probably restore the soil resistance that was lost

due to the cyclic loading.

Pile-supported structures are subjected to cyclic loading in many instances. Somecommon cases are wind load against overhead signs and high-rise buildings, traffic loads on

bridge structures, wave loads against offshore structures, impact loads against docks and dolphin

structures, and ice loads against locks and dams. The nature of the loading must be consideredcarefully. Factors to be considered are frequency, magnitude, duration, and direction. The

engineer will be required to use a considerable amount of judgment in the selection of the soil

parameters and response curves.2-1-1-4 Sustained Loading

If the soil resisting the lateral deflection of a pile is overconsolidated clay, the influenceof sustained loading would probably be small. The maximum lateral stress from the pile against

the clay would probably be less than the previous lateral stress; thus, the additional deflection

due to consolidation and creep in the clay should be small or negligible.


28/217


14

If the soil that is effective in resisting lateral deflection of a pile is a granular material thatis freely-draining, the creep would be expected to be small in most cases. However, if the pile is

subjected to vibrations, there could be densification of the sand and a considerable amount of

additional deflection. Thus, the judgment of the engineer in making the design should be brought

into play.

If the soil resisting lateral deflection of a pile is soft, saturated clay, the stress applied bythe pile to the soil could cause a considerable amount of additional deflection due to

consolidation (if positive pore water pressures were generated) and creep. An initial solution

could be made, the properties of the clay could be employed, and an estimate could be made of the additional deflection. The p-y curves could be modified to reflect the additional deflection

and a second solution obtained with the computer. In this manner, convergence could be

achieved. The writers know of no rational way to solve the three-dimensional, time-dependent problem of the additional deflection that would occur so, again, the judgment and integrity of the

engineer will play an important role in obtaining an acceptable solution.

2-1-1-5 Dynamic Loading

Two types of problems involving dynamic loading are frequently encountered in design:machine foundations and earthquakes. The deflection from the vibratory loading from machinefoundations is usually quite small and the problem would be solved using the dynamic properties

of the soil. Equations yielding the response of the structure under dynamic loading would be

employed and the p-y method described herein would not be employed.

With regard to earthquakes, a rational solution should proceed from the definition of thefree-field motion of the near-surface soil due to the earthquake. Thus, the p-y method described

herein could not be used directly. In some cases, an approximate solution to the earthquake

problem has been made by applying a horizontal load to the superstructure that is assumed toreflect the effect of the earthquake. In such a case, the p-y method can be used but such solutions

would plainly be approximate.

2-1-2 Models for Use in Analyses of Single Piles

A number of models have been proposed for the pile and soil system. The following are

brief descriptions for a few of them.

2-1-2-1 Elastic Pile and Soil

The model shown in Figure 2-1(a) depicts a pile in an elastic soil. A model of this sort

has been widely used in analysis. Terzaghi (1955) gave values of subgrade modulus that can be

used to solve for deflection and bending moment, but he went on to qualify hisrecommendations. The standard equation for a beam was employed in a manner that had been

suggested earlier by such writers as Hetenyi (1946). Terzaghi stated that the tabulated values of

subgrade modulus could not be used for cases where the computed soil resistance was more thanone-half of the bearing capacity of the soil. However, recommendations were not included for the computation of the bearing capacity under lateral load, nor were any comparisons given

between the results of computations and experiments.

The values of subgrade moduli published by Terzaghi have proved to be useful and

provide evidence that Terzaghi had excellent insight into the problem. However, in a privateconversation with the senior writer, Terzaghi said that he had not been enthusiastic about writing


29/217

Chapter 2 - Solution for Pile Response to Lateral Loading

15

the paper and only did so in response to numerous requests. The method illustrated by Figure 2-1(a) serves well in obtaining the response of a pile under small loads, in illustrating the various

interrelationships in the response, and in giving an overall insight into the nature of the problem.

The method cannot be employed without modification in solving for the loading at which a

plastic hinge will develop in the pile.

(a) (b)

(c) (d)

Figure 2-1 Models of Pile Under Lateral Loading, (a) 3-Dimensional Finite Element Mesh, and(b) Cross-section of 3-D Finite Element Mesh,

M t

P t

M t

P t

M t

P t

M t

P t


30/217


16

2-1-2-2 Elastic Pile and Finite Elements for Soil

The case shown in Figure 2-1(b) is the same as the previous case except that the soil has been modeled by finite elements. No attempt is made in the sketch to indicate an appropriate size

of the map, boundary constraints, special interface elements, most favorable shape and size of

elements, or other details. The finite elements may be axially symmetric with non-symmetric

loading or full three-dimensional models. The elements may be selected as linear or nonlinear.

In view of the computational power that is now available, the model shown in Figure 2-

1(b) appears to be practical to solve the pile problem. The elements can be three-dimensional and

nonlinear. However, the selection of an appropriate constitutive model for the soil involves notonly the parameters that define the model but methods of dealing with tensile stresses, modeling

layered soils, separation between pile and soil during repeated loading, and the changes in soil

characteristics that are associated with the various types of loading.

Yegian and Wright (1973) and Thompson (1977) used a plane-stress model and obtainedsoil-response curves that agree well with results at or near the ground surface from full-scale

experiments. The writers are aware of research that is underway with three-dimensional,

nonlinear, finite and boundary elements, and are of the opinion that in time such a model willlead to results that can be used in practice. More discussion on the use of the finite-elementmethod is presented in a later chapter where p-y curves are described.

2-1-2-3 Rigid Pile and Plastic Soil

Broms (1964a, 1964b, 1965) employed the model shown in Figure 2-1(c) to derive

equations for the loading that causes a failure, either because of excessive stresses in the soil or because of a plastic hinge, or hinges, in the pile. The rigid pile is assumed and a solution is found

using the equations of statics for the distribution of ultimate resistance of the soil that pu

Documents

Lpile Technical Manual