CHARACTERIZATION AND BEHAVIOUR OF CLAYEY SLURRIES

CHARACTERIZATION AND BEHAVIOUR OF CLAYEY SLURRIES

A Dissertation

Submitted to the Faculty of Graduate Studies and Research

In Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

in Environmental Systems Engineering

University of Regina

by

Maki Ito

Regina, Saskatchewan

December 18, 2016

© December, 2016: M.Ito

UNIVERSITY OF REGINA

FACULTY OF GRADUATE STUDIES AND RESEARCH

SUPERVISORY AND EXAMINING COMMITTEE

Maki Ito, candidate for the degree of Doctor of Philosophy in Environmental Systems Engineering, has presented a thesis titled, Characterization and Behaviour of Clayey Slurries, in an oral examination held on August 29, 2016. The following committee members have found the thesis acceptable in form and content, and that the candidate demonstrated satisfactory knowledge of the subject material. External Examiner: *Dr. Bruno Bussière, Université du Québec en Abitibi-

Témiscamingue

Supervisor: Dr. Shahid Azam, Environmental Systems Engineering

Committee Member: Dr. Amy Veawab, Environmental Systems Engineering

Committee Member: Dr. Esam Hussein, Faculty of Engineering and Applied Science

Committee Member: **Dr. Guoxiang Chi, Department of Geology

Chair of Defense: Dr. Andrei Volodin, Department of Mathematics and Statistics *Via videoconference **Not present at defense

i

ABSTRACT

The purpose of this research is to develop a fundamental understanding of the

characteristics and behaviour of clayey slurries. A comprehensive research

methodology consisting of laboratory investigations and computational analyses

was adopted. A clayey slurry (uranium leach residue) was selected from the

extraction process to capture the distinct slurry features at the onset of deposition.

The practical impact of this research is that the investigated slurry (new

waste stream) exhibited various components of settling that are important for

developing depositional plans and determining storage capacity of the

containment facility. Likewise, the scientific contribution is the understanding that

solid-liquid composition influences settling of clayey slurries such that the effects

are dominant during sedimentation and the initial phase of consolidation. More

importantly, the conceptual model of flow through settling clayey slurries confirms

that Poiseuille’s law of water flow through porous media is applicable to this class

of materials in the transition zone between sedimentation and consolidation.

The slurry (containing 28% clay size) comprised both non-clay minerals

(46% muscovite and 30% quartz) and clay minerals (8% illite, 5% chlorite and

2% kaolinite) and acidic pore water with large amounts of SO42- (22600 mg/L)

and Mg2+ (1340 mg/L). Settling occurred through sedimentation (25% to 35%

initial solids) and consolidation (40% to 50% initial solids). The average hydraulic

conductivity during sedimentation reduced from 3.0 x 10-6 m/s to 5.3 x 10-8 m/s

along with a void ratio reduction from 7.4 to 2.6. Likewise, volume compressibility

ii

during consolidation showed apparent pre-consolidation at low effective stress

(0.3 kPa to 2 kPa) with a reduction in void ratio from 2.6 to 2.5. The hydraulic

conductivity during consolidation decreased from 2.6 x 10-9 m/s (at e = 2.6) to 2.0

x 10-10 m/s (at e = 2.1).

An image analysis method was developed to identify and quantify slurry

constituents and to determine and validate index properties and hydraulic

conductivity. It was found that the investigated clayey slurry comprised of free

water, hydrated grains, and solids. The proposed solids ratio successfully

separated the hydrated solids into water and solids thereby allowing an accurate

and precise determination of index properties through image analysis (R2 ≥ 0.90).

Likewise, the modified definition of hydraulic radius (average pore throat area

divided by average perimeter of pore) adequately described the water flow

mechanism through clayey slurries because pore area outside of the pore throat

does not contribute to water migration. Furthermore, the proposed RH definition is

independent of spatial distribution of pores and, as such, precludes the use of

tortuosity in determining hydraulic conductivity.

iii

PREFACE

This dissertation is an original intellectual product of the author, M. Ito. Versions

of parts of this dissertation will be submitted for publications as follows:

1. Ito, M. and Azam, S. (2016) Dewatering behaviour of a uranium ore slurry

containing clays. Geotechnical and Geological Engineering.

2. Ito, M. and Azam, S. (2016) Determination of water flow through clayey

slurries using computed micro tomography. Journal of Engineering Geology

and Hydrogeology.

iv

ACKNOWLEDGEMENTS

I express my sincere appreciation to Cameco Corporation, the Natural Science

and Engineering Research Council of Canada, and the Faculty of Graduate

Studies and Research for providing financial support. I would like to acknowledge

the support of University of Regina for providing the laboratories and

computational facility. Part of the research described in this study was performed

at the Canadian Light Source, which is supported by the Canada Foundation for

Innovation, Natural Sciences and Engineering Research Council of Canada, the

University of Saskatchewan, the Government of Saskatchewan, Western

Economic Diversification Canada, the National Research Council Canada, and

the Canadian Institutes of Health Research.

I would like to acknowledge the guidance of my research supervisor Dr.

Shahid Azam, my industry collaborators Dr. Tom Kotzer, Dr. Pat Landine, and Dr.

Jeff Warner. I would also thank my committee members Dr. Guoxiang Chi, Dr.

Esam Hussein, and Dr. Amornvadee Veawab provided the critical technical and

theoretical expertise when this research needed to elaborate. Thanks to the

Radiation Safety Officers Ms. Tianna Gross and Ms. Sarah Posehen, and to Mr.

Faseel Suleman Khan for the friendship and many discussions.

Finally, my family and friends, most importantly, Jason and Yukimi

Grayston are owed special gratitude from me. There wasn’t a single chance to

complete this journey without you. Thanks a lot and I love you most.

v

POST-DIFFENSE ACKNOWLEDGEMENTS

The time and inputs of Dr. Bruno Bussière (external examiner) from the Applied

Sciences Department, Université du Québec en Abitibi-Témiscamingue (UQAT),

Dr. Guoxiang Chi (supervisory committee member) from the Faculty of Science,

University of Regina, Dr. Esam Hussein (supervisory committee member) from

the Faculty of Engineering and Applied Science, University of Regina, Dr.

Amornvadee Veawab (supervisory committee member) from the Faculty of

Engineering and Applied Science, University of Regina, and Dr. Andrei Volodin

(thesis defense chair) from the Faculty of Science, University of Regina, for

serving on my thesis committee.

http://www.uregina.ca/science/mathstat/faculty-staff/faculty/volodin-andrei.html

vi

TABLE OF CONTENTS

ABSTRACT _______________________________________________________ i

PREFACE _______________________________________________________ iii

ACKNOWLEDGEMENTS __________________________________________ iv

POST DIFFENCE ACKNOWLEDGEMENTS ____________________________ v

LIST OF TABLES __________________________________________________ x

LIST OF FIGURES ________________________________________________ xi

LIST OF SYMBOLS ______________________________________________ xiv

Chapter 1 INTRODUCTION __________________________________________ 1

1.1 Problem Statement ___________________________________________ 1

1.2 Research Objectives __________________________________________ 2

1.3 Dissertation Outline __________________________________________ 3

1.4 Expected Contributions _______________________________________ 3

Chapter 2 LITERATURE REVIEW ____________________________________ 4

2.1 General _____________________________________________________ 4

2.2 Assessment of Clay Slurries ___________________________________ 4

2.3 Material Properties ___________________________________________ 6

2.3.1 Solid Composition __________________________________________________ 7

2.3.1.1 Mineralogy ____________________________________________________ 7

2.3.1.2 Cation Exchange Capacity _______________________________________ 10

2.3.2 Liquid Composition ________________________________________________ 11

2.3.2.1 pH and Electrical Conductivity _____________________________________ 11

2.3.2.2 Electrolyte Concentration ________________________________________ 12

vii

2.4 Clay-Water Interaction _______________________________________ 12

2.4.1 Diffuse Double Layer Theory _________________________________________ 12

2.4.2 Derjaguin-Landau-Verwey-Overbeek (DLVO) Theory _______________________ 14

2.5 Settling of Clay Slurries ______________________________________ 16

2.5.1 Sedimentation ____________________________________________________ 16

2.5.1.1 Theoretical Context _____________________________________________ 17

2.5.1.2 Sedimentation Test _____________________________________________ 18

2.5.2 Consolidation _____________________________________________________ 21


2.5.2.2 Consolidation Test _____________________________________________ 22

2.6 Flow Through Clay Slurries ___________________________________ 27

2.6.1 Saturated Hydraulic Conductivity ______________________________________ 27

2.6.1.1Theoritical Context ______________________________________________ 27

2.6.1.2 Measurement Method ___________________________________________ 30

2.6.2 Pore Morphology __________________________________________________ 33


2.6.2.2 Measurement Method ___________________________________________ 40

2.7 Summary___________________________________________________ 44

Chapter 3 RESEARCH METHODOLOGY _____________________________ 46

3.1 General ____________________________________________________ 46

3.2 Rationale of Research Plan ___________________________________ 46

3.3 Material Description _________________________________________ 49

3.3.1 Geology _________________________________________________________ 50

3.3.2 Mining __________________________________________________________ 53

3.4 Solid-liquid Characterization __________________________________ 57

viii

3.4.1 Index Properties ___________________________________________________ 57

3.4.2 Solid Composition _________________________________________________ 59

3.4.2.1 Mineralogy ___________________________________________________ 59

3.4.2.2 Cation Exchange Capacity _______________________________________ 60

3.4.3 Pore Water Composition ____________________________________________ 61

3.4.3.1 pH and Electrical Conductivity _____________________________________ 61

3.4.3.2 Electrolyte Concentration ________________________________________ 62

3.5 Settling Characterization _____________________________________ 62

3.5.1 Sedimentation ____________________________________________________ 62

3.5.2 Consolidation _____________________________________________________ 66

3.6 Flow Through Characterization ________________________________ 69

3.6.1 Pore Morphology __________________________________________________ 69

3.6.2 Saturated Hydraulic Conductivity ______________________________________ 77

3.7 Summary___________________________________________________ 78

Chapter 4 RESULTS AND DISCUSSIONS ____________________________ 79

4.1 General ____________________________________________________ 79

4.2 Solid-liquid Properties _______________________________________ 79

4.2.1 Index Properties ___________________________________________________ 79

4.2.2 Solid Composition _________________________________________________ 82

4.2.3 Pore Water Composition ____________________________________________ 86

4.3 Settling Behaviour ___________________________________________ 88

4.3.1 Sedimentation ____________________________________________________ 88

4.3.2 Consolidation _____________________________________________________ 94

4.4 Flow Through Behaviour ____________________________________ 100

4.4.1 Pore Morphology _________________________________________________ 100

ix

4.4.2 Saturated Hydraulic Conductivity _____________________________________ 115

4.5 Summary__________________________________________________ 124

Chapter 5 CONCLUSIONS AND RECOMMENDATIONS ________________ 125

5.1 Summary__________________________________________________ 125

5.2 Conclusions _______________________________________________ 126

5.3 Recommendations _________________________________________ 128

REFERENCES __________________________________________________ 129

APPENDICES ___________________________________________________ 156

x

LIST OF TABLES

Table 2.1: Properties of common clay (modified after Fang and Daniels, 2006)... 5

Table 2.2: Summary of the techniques for pore morphology investigation of soils

.......................................................................................................... 41

Table 4.1: Summary of geotechnical index properties of uranium slurry ............. 80

Table 4.2: Summary of solids composition of uranium slurry ............................... 85

Table 4.3: Summary of pore liquid composition of uranium slurry ....................... 87

Table 4.4:Summary of sedimentation test initial conditions and calculated

hydraulic conductivity for uranium slurry ......................................... 92

Table 4.5: Summary of settling test results ......................................................... 101

xi

LIST OF FIGURES

Figure 2.1: Schematic diagram of the structure of (a) smectite, (b) illite, and (c)

kaolinite (modified after Holtz and Kovacs 1981) ............................. 9

Figure 2.2: Distribution of ions adjacent to a clay particle (modified after Mitchell

and Soga, 2005) ............................................................................... 13

Figure 2.3: Schematics of attractive and repulsive potentials as a function of

distance between particle surfaces (modified after Mitchell and

Soga, 2005; Rima, 2013) ................................................................. 15

Figure 2.4: Description of dewatering behaviour of clay-rich slurries................... 19

Figure 2.5: Consolidation behaviour of a clayey soil and clay-rich slurry ............ 24

Figure 2.6: Schematics of particle arrangement (modified after Olsen, 1962) .... 34

Figure 2.7: Three types of porosity (modified after Selley, 1985) ........................ 37

Figure 2.8: Concept of effective length in transport through soil (modified after

from Shackelford, 1988) .................................................................. 38

Figure 3.1: Investigation Program ......................................................................... 47

Figure 3.2: Occurrence of uranium deposits and surface geology and mineralogy

of the Athabasca Basin (modified after Earle and Sopuck, 1989;

Jefferson et al., 2007) ...................................................................... 52

Figure 3.3: Simplified process flow chart of the Key Lake milling operation

(modified after Koshinsky et al., 2012) ............................................ 54

Figure 3.4: Sectional view of a thickener (modified after Tavleton and Wakeman,

2006)................................................................................................. 56

Figure 3.5: Sedimentation test setup ..................................................................... 63

Figure 3.6: Consolidation test setup ...................................................................... 68

Figure 3.7: Samples retrieved for CMT test .......................................................... 71

Figure 3.8: Schematics of CMT apparatus (modified after Glesmer, 2007; Bird,

2013)................................................................................................. 72

Figure 3.9: Schematics of 3D image rendering process ....................................... 74

Figure 4.1: Grain size distribution curve of uranium slurry ................................... 81

xii

Figure 4.2: X-ray diffraction analysis of uranium slurry: (a) random bulk sample

and (b) oriented clay sample ........................................................... 83

Figure 4.3: Settling test results in the form of interface height versus elapsed time

for uranium ....................................................................................... 89

Figure 4.4: Settling test results in the form of void ratio versus elapsed time for

uranium slurry................................................................................... 90

Figure 4.5: Hydraulic conductivity versus void ratio relationship for uranium slurry

.......................................................................................................... 93

Figure 4.6: Constitutive relationships for self-weight settling test of uranium

slurry: (a) volume compressibility and (b) hydraulic conductivity ... 95

Figure 4.7: Consolidation test results of uranium slurry in the form of interface

height versus elapsed time .............................................................. 97

Figure 4.8: Constitutive relationships for consolidation test on uranium slurry: (a)

volume compressibility and (b) hydraulic conductivity .................... 98

Figure 4.9: ROIs of selected slurry samples (A, C, and F) ................................. 102

Figure 4.10: Grey-scale histograms corresponding to ROIs of selected slurry

samples: (a) Sample A; (b) Sample B; (c) Sample F .................... 103

Figure 4.11: Application of threshold grey-scale value for sample with three

peaks: (a) entire curve; (b) enlarged view of peak1 and peak 2; (c)

enlarged view of peak 2 and peak3............................................... 105

Figure 4.12: Application of threshold grey-scale value for sample with two peaks:

(a) entire curve; (b) enlarged view of peak1 and peak 2 .............. 107

Figure 4.13: Comparison of index properties measured by geotechnical methods

and estimated through image analysis: (a) solids content; (b) water

content; (c) void ratio; and (d) porosity .......................................... 109

Figure 4.14: Binary images of ROI 1 for sample A, C, and F ............................. 111

Figure 4.15:Relationships between the porosities ((a) total porosity from

geotechnical; (b) total porosity from image analysis; (c) free water

porosity image analysis) and the pore geometrical properties ..... 112

xiii

Figure 4.16: Schematic representations of three dimensional pore and pore

throat configurations ...................................................................... 114

Figure 4.17: Hydraulic radius calculation: (a) Example 1 with pore throat diameter

size is a half of the diameter of entire pore bodies; (b) Example 2

with pore throat diameter size is a quarter of the diameter of entire

pore bodies; .................................................................................... 117

Figure 4.18: Correlations of hydraulic conductivity with index properties .......... 120

Figure 4.19: Comparison of hydraulic conductivity calculation using the proposed

hydraulic radios and the conventional definition ........................... 121

Figure 4.20: Comparison of hydraulic conductivity measured by geotechnical

methods and estimated through image analysis .......................... 122

xiv

LIST OF SYMBOLS

A Total cross-sectional area of sample (cm2) or Activity

a Cross-sectional area of flow channel or cross-sectional area of

stand pipe (cm2)

Ab Cross-sectional area of bundled pores (cm2)

As Specific surface area (m2/kg)

ASTM American Standard Testing Method

BMIT Bio Medical Imaging and Therapy

C Hazen’s empirical coefficient

Cc Compression Index

CCD Counter Current Decantation or Charge-coupled Device

Cs Shape factor

CEC Cation Exchange Capacity (cmol(+)/kg)

CMT Computed Micro Tomography

Cv Coefficient of consolidation

D Dielectric constant (F/m)

DLVO Derjaguin-Landau-Verwey-Overbeek

D10 10 percentile grain size of material (mm)

E Energy of incoming x-ray beam (keV)

EC Electrical Conductivity (Sm-1)

e Void ratio

e0 Initial void ratio

xv

ec Electrical charge (C)

FWHM Full Width at Half Maximum

Gs Specific gravity

GSD Grain Size Distribution

’ Buoyant unit weight (kN/m3)

f Unit weight of fluid (kN/m3)

s Unit weight of solids (kN/m3)

w Unit weight of water (kN/m3)

h Sample thickness (cm)

H0 Initial interface height (cm)

Hf Final interface height (cm)

Ht Interface height at time t (cm)

h1 Initial head (cm)

h2 Final head (cm)

i Hydraulic gradient

I Attenuated x-ray beam (keV)

I0 Incident x-ray beam (keV)

Ip Plasticity index

K Debye length (nm)

kB Boltzmann constant (W m−2 K−4)

k Hydraulic conductivity (m/s)

L Length of flow channel or length of sample (cm)

xvi

Le Effective flow path length (cm)

LVDT Linear Variable Displacement Transducer

Viscosity of fluid (N s/m2)or attenuation coefficient (cm-1)

n Porosity

nCMT Porosity determined by CMT

ns Measured greyscale value

nss Greyscale value at the solid peak

nsw Greyscale value at the water peak

p Perimeter of flow channel (cm)

Pi

R Capillary radius (cm)

R2 Coefficient of linear regression

RH Hydraulic radius (cm)

RHa Hydraulic radius of bundled pores (cm)

RO Reverse Osmosis

ROI Region of Interest

s Solids content (%)

S0 Wetted surface area per unit volume of particles (m²/m³)

sf Final solid content (%)

’ Effective stress (kN/m3)

T Temperature (°C)

Tortuosity

xvii

TCEC Total Cation Exchange Capacity (cmol(+)/kg)

u Pore pressure (kPa) or excess pore pressure (kPa)

V Total volume (m3)

Vs Volume of solids (m3)

Vw Volume of water (m3)

Electrical valence

avg Average flow velocity (cm/min)

s Settling velocity (cm/min)

stoke Stokes velocity (cm/min)

f Fluidization velocity (cm/min)

s-w Relative velocity (cm/min)

w Water content (%)

wl Liquid limit

wp Plastic limit

Ws Weight of all solids from both solid and mix peaks

Ww Weight of all water from both water and mix peaks

x Depth in the Eurelian coordinate system

XRD x-Ray Diffraction

z Depth in the reduced coordinate system

Z Effective atomic number

Chapter 1

1

Chapter 1 INTRODUCTION

1.1 Problem Statement

The management of large volumes of slurries generated as a by-product of ore

beneficiation processes is a key concern for the mining industry. For example,

the oil sand industry in Northern Alberta, Canada, contains tailings in an area of

6400 x 104 m2 (Devenny, 2010). Tailings containment facilities are designed for a

finite storage capacity such that the perimeter dykes provide buffers between

discharged slurries and the surrounding environments. When deposited, the high

water bearing slurries undergo dewatering by gravity as well as overburden

loading. A clear understanding of the characteristics and behaviour of a waste

stream at the onset of disposal is critical over the entire mine life cycle from

extraction, operation, closure, and reclamation.

The hydro-geotechnical behaviour of slurries is governed by the presence

of clays. Previous experience with such materials has shown a slow rate and a

low amount of dewatering; particularly in the following industries: oil sand (North

America), China clay (U.K.), bauxite (North America and Australia), diamond

(South Africa), and phosphate (U.S.A.) (Alberta Research Council, 1977). This is

attributed to high electrochemical activity of charged particles and ion-rich

process waters. The resulting settling of the slurries occurs over prolonged

periods of time undergoing both sedimentation and consolidation. These distinct

settling regimes are generally identified by the absence or presence of effective

stress (’), respectively (Pane and Schiffman, 1997; Mikasa, 1963; Terzaghi et

Chapter 1

2

al., 1996). Unlike inert sediments, clayey slurries are affected by solid-liquid

interactions in both regimes (Azam, 2011; Imai, 1980; Jeeravipoolvarn et al.,

2009b).

The transition from sedimentation to consolidation is not well understood

because of the following: (i) lack of analytical equations to describe the transition

zone unlike equations formulated for sedimentation (Pane and Schiffman, 1997;

Richardson and Zaki, 1954) and for consolidation (Gibson, et al., 1967; Mikasa,

1963); (ii) limited success of numerical modeling tools for incorporating the

transition zone through the use of the above-mentioned analytical equations

(Azam et al., 2009; Bartholomeeusen et al., 2002); (iii) lack of testing and

analysis methods for clayey slurries exhibiting distinct transition zones as

opposed to most hard rock tailings with negligible transition zones (Demers, et al.,

2015: Qiu and Sego, 2001).

1.2 Research Objectives

The purpose of this research is to develop a fundamental understanding of the

characteristics and behaviour of clayey slurries from the mining industry. A

comprehensive research methodology consisting of laboratory investigations and

computational analyses was adopted. A clayey slurry (uranium leach residue)

was selected from the extraction process to capture the distinct slurry features at

the onset of deposition. The specific objectives are as follows:

1. To evaluate the solid-liquid characteristics including index properties, soil

Chapter 1

3

mineralogy and pore water composition.

2. To determine settling behaviour under hindered sedimentation and large-

strain consolidation.

3. To characterize pore morphology in the transition zone of slurry settling

using computed micro tomography.

4. To develop a conceptual model for determining saturated hydraulic

conductivity during slurry settling.

1.3 Dissertation Outline

Chapter 2 presents a literature review describing solid-liquid composition, the

settling phenomena, and the flow through processes. Chapter 3 describes the

research methodology comprising laboratory investigations and computational

analyses. Chapter 4 presents and discuses the results of laboratory tests and

computation analyses. Chapter 5 summarizes the conclusions and

recommendation drawn from this research. This is followed by a list of references

and appendices.

1.4 Expected Contributions

The potential practical contribution of this research to the mining industry is

detailed geotechnical assessment of a selected stream of uranium clay slurries.

Likewise, the main scientific contribution to the field of geotechnical engineering

is expected to be the development of a new image analysis method for flow

through porous media.

Chapter 2

4

Chapter 2 LITERATURE REVIEW

2.1 General

Given an increasing volume of tailings generated worldwide, an efficient

dewatering of loose sludge is crucial for many mining operations. In addition,

bottom sediments from river and ocean present highly compressible and fluid like

characteristics similar to mine slurries because of organic and clay content. The

classical Kynch’s sedimentation theory and Terzaghi’s consolidation theory has

been modified over the years to account for the highly deformable nature of this

class of materials. However, the prediction of long term dewatering behaviour is

complex task because the process is known to be governed by ore geology

(solids mineralogy) and extraction technology (water chemistry).

2.2 Assessment of Clay Slurries

Table 2.1 provides a summary of basic properties of common clay minerals such

as kaolinite, illite and smectite. The particles of clay mineral are usually less than

0.002 mm in size and clayey soils have an average specific gravity ranging from

2.70 to 2.80. Clayey soils are slightly denser than sand particles composed of

quartz that ranging from 2.60 to 2.65. However, the size and density of the

particle cannot determine the presence of clay minerals. A water retaining

capacity has to be present for a material to contain clay minerals. The

consistency limits are used for preliminary soil assessment. The limits

encompass information about the physical and chemical properties of slurry

constituents (Carrier and Beckman, 1984). The soil liquid limit (wl) is the water

Chapter 2

5

Table 2.1: Properties of common clay (modified after Fang and Daniels, 2006)

Properties Kaolinite Illite Smectite

Specific Gravity, Gs 2.60-2.68 2.60-3.00 2.35-2.70

Liquid Limit, wl 50-62 95-120 150-170

Plastic Limit, wp 33 45-60 55

Plasticity Index, Ip 20-29 32-67 100-650

Activity, A= Ip/C 0.2 0.6 1-6

Specific Surface Area, m2/g 10-20 65-100 50-800

Cation Exchange Capacity, cmol(+)/kg

3-15 10-40 80-150

Chapter 2

6

content above which a soil behaves like a viscous fluid. Likewise, the soil plastic

limit (wp) is the water content at which a soil no longer behaves as a plastic

material. Finally, the plasticity index (Ip) is calculated by subtracting the plastic

limit from the liquid limit indicating the range of water content in which a soil

possesses plastic properties.

The consistency limits of fine grained soils and slurries depend on the

following factors: (i) amount and type of clay minerals, and (ii) type of adsorbed

cation (Fang and Daniels, 2006). The specific surface area (As) and cation

exchange capacity (CEC) mainly govern adsorption capacity of the particles. The

specific surface area is an inherent characteristic of soil mineral and is directly

linked to the extent of the electrical charge that affects solid-liquid interactions.

The total cation exchange capacity is the maximum amount of cations that a soil

can hold while exchanging with the pore fluid at a given pH value (Mitchell and

Soga, 2005). Generally, the consistency limits are the highest for smectite

followed by illite and then by kaolinite, however the consistency limits change

relative to the pore fluid composition in terms of type of ions and concentration.

Factors affecting the consistency limits of clayey slurries are solid

composition that is derived from geological setting during pre- and post- ore

mineralization as well as liquid composition that is derived from the ore

beneficiation process such as acid leaching or caustic leaching.

2.3 Material Properties

Chapter 2

7

The presence of small charged particles, dissolved ions, and water governs

solid-liquid interactions. If the particles having these interactions are adjacent to

each other, their individual force fields overlap and affect the behaviour of the

whole system. This behaviour is especially important for mine slurries because

the constituents are made of disintegrated smaller particles having larger specific

surface area and high content of chemically concentrated liquids.

2.3.1 Solid Composition

2.3.1.1 Mineralogy

Clay minerals are formed through a complicated weathering process from an

assortment of parent materials (Chen, 1988). The weathering of rocks and soils

is a destructive process whereby debris of various sizes, compositions and

shapes are formed. Weathering includes both physical processes and chemical

processes. Physical processes comprise unloading, thermal expansion and

contraction, crystal growth, colloidal plucking, and organic activity. These

processes are generally the forerunner of chemical weathering that includes

hydration, oxidation, and carbonation (Mitchell and Soga, 2005).

Clay minerals are made of two basic structures: the silica tetrahedron and

the alumina octahedral. The silica tetrahedron consists of a silicon atom

surrounded by four oxygen ions. When each oxygen atom is shared by two

tetrahedrons, a plate shaped layer is formed. The alumina octahedral consists of

an aluminum atom surrounded by six oxygen ions. When the aluminum atoms

Chapter 2

8

are shared by two octahedrons, a sheet is formed. The silica sheets and the

alumina sheets combine to form the basic structural units of clay minerals. The

various clay minerals are differentiated from one another because of the basic

stacking configuration (Chen, 1988).

Figure 2.1 shows the stacking configuration of common clay minerals. The

smectite group is known to be a highly active clay mineral. This mineral has a 2:1

silica-alumina structure as shown in Figure 2.1a. Because the bonding by van

der Waal’s forces between the tops of the silica sheets is weak and there is a net

negative charge deficiency in the octahedral sheet, water and exchangeable ions

can easily enter and separate the layers. This weak bonding leads to the

development of small crystals of smectite. Illite also has a 2:1 structure (Figure

2.1b) similar to smectite, but the inter-layers are bonded together with potassium

ions (Holtz and Kovacs, 1981). This inter-layer bonding results in lesser interlayer

expansion of illite. On the contrary, kaolinite minerals are composed of alternate

silica and octahedral sheets as schematically shown in Figure 2.1c. The bonding

existing in between successive layers consists of both van der Waal’s forces and

hydrogen bonds thereby kaolinite minerals show no interlayer expansion in the

presence of water.

Surface charge refers to an excess of positive or negative charge which

exist on the layer as a whole. The origin of this charge is the substitution of

cations in tetrahedral or octahedral (or both) sites which does not possess

charge. Clay particles dispersed in water with breakup into single clay platelets

Chapter 2

9

Figure 2.1: Schematic diagram of the structure of (a) smectite, (b) illite, and (c) kaolinite (modified after Holtz and Kovacs 1981)

Si

Si

Si

Si

Si

Si

Al

Al

Al

Si

Si

Si

Si

Si

Si

Al

Al

Al

K K K K

KKKKnH

2O

lay

ers

and

exch

ang

eab

le c

atio

ns

Fix

ed9.6 Å~10 Å

7.2 Å

Al

Al

Al

Si

Si

Si

(a) (b)

(c)

Chapter 2

10

have a flat sheet-like particle shape and a high aspect ratio. The lattice of an

ideal clay mineral is uncharged, however isomorphous substitution, an atom of

lower valence cation replaces an approximate same-size atom of higher valence

cation can occur (van Olphen, 1964). If a silicon atom is substituted with an

aluminum atom, the net charge of the lattice becomes negative with the possible

exception of kaolinite group. In general, silicon is substituted with aluminum and

aluminum with magnesium in the tetrahedral and the octahedral sheet,

respectively. The excess of negative lattice charges is compensated by

adsorption of cations due to electrical forces acting on the surface much greater

than the gravitational forces. This leads to attraction and retention of cations

which are too large to penetrate into the lattice, on the surface of the unit layer.

2.3.1.2 Cation Exchange Capacity

The actual ion distributions in clay minerals may develop as a result of geological

history and subsequent natural and artificial alternations. The clay minerals

usually exist with varieties of other minerals and ions. Some of the cations which

are compensating the net negative charge on the clay platelets may be

exchanged with other cations in the presence of water, and this ability is called

Cation Exchange Capacity (CEC). The CEC of kaolinite is approximately 1-10

cmol(+)/kg while smectite is approximately 70 cmol(+)/kg (Mitchell and Soga,

2005). The most common exchangeable cations are Ca2+, Mg2+, Na+, K+, and

NH4+ (Chen, 1988). As mentioned in Section 2.3.1.1, an interlayer bonding plays

a critical role in CEC of clay minerals. If hydrogen bonding is developed between

Chapter 2

11

the layers in some minerals such as kaolinite, the effect of presence of water is

negligible, and is shown by a low CEC. In illite, the charge deficiency, as a result

of isomorphous substitution, is partly balanced by potassium ions. Since the

bases of the silica sheet give adequate indents for potassium ions to fit in, a

strong bond is created. Unlike smectite and vermiculite particles that adsorb

water between the unit layers, a tightly held interlayer structure of illite will not

easily separate in the presence of water or polar liquids (Mitchell and Soga,

2005).

2.3.2 Liquid Composition

2.3.2.1 pH and Electrical Conductivity

Chorom and Rengasamy (1996) found that the net charge on a clay particle can

change by changing the pH, electrolyte composition and concentration, thereby

the clay-water interactions can be altered. In aqueous medium, surface hydroxyl

groups of clay particles react with either H+ or OH- at low and high pH

respectively, creating either a positive or a negative surface charge (Moayedi et

al., 2011). An increase in pH results in an increase of the negative charges of the

clay particles due to the deprotonation of surface hydroxyl groups. Similarly, a

decrease in pH results in a decrease of the negative charges of the clay particles

due to H+ adsorption or the protonation of H+ ions. Electrical conductivity (EC) is

the ability of a material to conduct an electrical current and a measurement is

correlated to an amount of salt in a given soil or slurry. A high EC value is usually

observed for a clayey soil because EC is associated with particle size and texture

Chapter 2

12

(Mitchell and Soga, 2005).

2.3.2.2 Electrolyte Concentration

A high electrolyte concentration facilitates flocculation of particles in suspension.

This is because the thickness of water molecules held between particles is

reduced due to a decrease in particle surface potential. Consequently, the

repulsion between the particles is reduced and a clay-water-ion system becomes

flocculated (Mitchell and Soga, 2005).

2.4 Clay-Water Interaction

The electro chemical interactions at the interface of pore water and colloids result

in a double layer of ions around colloids (Mitchell, 1993). Alternating the chemical

composition of pore water affects the properties of the double layer thereby

changing the electro chemical nature of solid-liquid separation of slurries (Sposito,

1984).

2.4.1 Diffuse Double Layer Theory

Figure 2.2 indicates the distribution of ions in the liquid adjacent to a clay particle.

Negatively charged dry clay particles firmly hold adsorbed cations. Firmly

attached counter-ions (oppositely charged ions against the clay) compose the

Stern layer on the clay surface. Charge within the diffuse layer gradually reaches

equilibrium as the concentration of counter-ions steadily reduces and that of co-

ions (ions with charge similar to the clay) steadily increases. These two layers

are together called the diffuse double layer (Chapman, 1913). According to

Chapter 2

13

Figure 2.2: Distribution of ions adjacent to a clay particle (modified after Mitchell

and Soga, 2005)

Chapter 2

14

Mitchell and Soga (2005), the diffuse double layer thickness (1/K) is calculated

by using the following equation:

In the above equation, o is the permittivity of vacuum (8.8542 x 10–12 C2 J-1 m-1),

k is the Boltzmann constant (1.38 x 10–23 J oK-1), D is the dielectric constant of

the medium, T is the Temperature (oK), ec is the electronic charge (1.602 x 10–19

C), no is the ion concentration, and is the ionic valence. According to Eq. (2.1),

it is clear that diffuse double layer thickness mainly depends on the ionic charge

and to a lesser extent on the ion concentration. The presence of monovalent ions

and a low ion concentration in the liquid causes an increase in diffuse double

layer thickness because of the preferential ion adsorption onto clay surfaces. The

monovalent ions create the thickest double layer followed by divalent ions and

then by trivalent ions.

2.4.2 Derjaguin-Landau-Verwey-Overbeek (DLVO) Theory

The DLVO theory uses van der Waals attraction force and the electrostatic

repulsion force to explain behaviour of two adjacent particles to disperse or

flocculate (Mitchell and Soga, 2005). Figure 2.3 schematically shows the net

interaction energy which combines the repulsive and attractive forces as a

function of distance between two particles. The change in repulsive force

depends on the changes in electrolyte concentration, cation valence, dielectric

Chapter 2

15

Figure 2.3: Schematics of attractive and repulsive potentials as a function of distance between particle surfaces (modified after Mitchell and Soga, 2005; Rima, 2013)

Chapter 2

16

constant, and pH. In contrast, the attractive force depends on the dielectric

constant and temperature. The net value indicates repulsive or attractive energy

depending on if it is plotted above or below of zero charge. The net interaction

curve can be affected by the increasing distance between particles thereby it

moves from attraction to repulsion and back to attraction. Neighboring charged

particles in an electrolyte solution start to come together when attractive forces

are dominant and flocculation occurs. On the contrary, when repulsive forces are

strong, the suspension system generates a high repulsive energy barrier

between charged particles thereby resulting in dispersion. Microstructural

configuration derived from material characteristics has a profound effect on the

setting behaviour of slurries (Azam, 2012).

2.5 Settling of Clay Slurries

When a transition from a suspension to soil takes place, it typically goes through

two stages. The first stage is sedimentation which involves the gradual change of

isolated soil particles in a suspension to a loose sediment. As sedimentation

progresses, the solid-liquid interface at top of the slurry drop down due to gravity

and the solid content of the sediment at the bottom increases. During this stage,

effective stress is negligible whereas it starts to develop during consolidation

when the sediment is thick enough so that the grains touch one another.

Although these two stages are sequential as well as simultaneous, it is important

to discuss these distinct phenomena separately.

2.5.1 Sedimentation

Chapter 2

17

2.5.1.1 Theoretical Context

Kynch (1952) developed a framework of gravitational sedimentation based on

kinematics. Therefore, the sedimentation behaviour of solid particles suspended

in a fluid is governed by the solids concentration that can be converted to void

ratio.

Based on the early experimental findings on fluidization (a flow rate Q of a

given fluid is forced upwards through a solid particle beds), settling and fluidizing

velocities are confirmed to be identical at a given void ratio, e. Richardson and

Zaki (1954) achieved the theoretical understanding as:

where is the settling velocity, is the fluidization velocity, and . is the

velocity described by Stokes’s law. The relative velocity between the

two phases of solids and water during settling is given as:

Since the solids particles do not transmit effective stress due to lack of grain-to-

grain contacts, total stress is equal to the total pore pressure (combination of

hydrostatic pressure, u0 plus excess pore pressure, u) and the vertical

equilibrium of solids and water mixture respect to the Eulerian coordinate x can

be expressed in terms of the buoyant unit weight, ’ of the mixture as follows:

Chapter 2

18

where s is the unit weight of solids and w is the unit weight of water.

2.5.1.2 Sedimentation Test

Figure 2.4 describes the sedimentation test results for Speswhite kaolin,

comprising about 75% clay (Pane and Schiffman, 1997) and Osaka bay mud,

comprising about 60% clay (Imai, 1980). The slurry (at a known initial water

content) was poured in a graduated sedimentation column and was allowed to

settle under gravity while recording the deformation at regular time intervals

(Pane and Schiffman, 1997; Richardson and Zaki, 1954). The data are presented

in the form of solid-liquid interface height versus elapsed time using a regular

scale (Figure 2.4a and Figure 2.4b) and in the form of void ratio (e) versus

elapsed time on a semi-logarithmic scale (Figure 2.4c and Figure 2.4d).

Three straight-line segments (solid lines in Figure 2.4a and Figure 2.4b)

formed the settling curves. The solid-liquid interface height change was governed

by flocculation with an initial low decrease followed by hindered sedimentation of

the flocs with a rapid decrease and then by self-weight consolidation with a slow

decrease. An increase in the flocculation time with decreasing initial water

content was observed in the data. The mutual distance of ions around charged

particles having interacting double layers is governed by the type and

concentration of solids and the type and concentration of electrolytes in the fluid

(Mitchell and Soga, 2005). Generally, a high initial water content results in a high

dewatering rate (steeper slope) and high dewatering amount (greater length of

the line). Decreasing water content results in both of these features gradually

Chapter 2

19

Figure 2.4: Description of dewatering behaviour of clay-rich slurries

Chapter 2

20

reduced because of an increased friction between interacting flocculated

aggregates (Imai, 1980). The limited data in the settling tests show the

consolidation segment of the curve appears to be parallel but is expected to

converge over long duration.

Moreover, at lower initial water contents (less than 1000%), the

investigated materials are considered to be flocculated slurries that undergo

consolidation due to self-weight almost immediately (dashed lines in Figure 2.4b)

without showing hindered sedimentation regime.

A gradually decreasing rate of change in the settling velocity can be used

as an indicator of the transition from self-weight settling to consolidation. The

maximum slurry void ratio (em) pertains to the initial development of a distinct

slurry microstructure. This void ratio occurs at the point of inflection from the

hindered sedimentation line (determined from interface height versus time plot)

such that the thickness of the sediment (growing from the bottom) is at a

maximum. The investigated data indicate that the transition from sedimentation

to consolidation is more abrupt at high water contents and the curves become

more gradual with decreasing water content.

Figure 2.4c indicates that em values merge around 30 for Speswhite kaolin

under the investigated range of initial water contents. Pane and Schiffman (1997)

concluded that the maximum slurry void ratio is an intrinsic material property for a

given clay-water mixture. This is confirmed by the results for Osaka Bay mud

(Figure 2.4d) that shows a constant em value of 25 for initial void ratios from 68 to

Chapter 2

21

34. The em is not discernible for samples with no distinct sedimentation zones

(initial void ratios from 27 to 14). This means that the microstructure at low initial

void ratios has already developed. Although the settling test is relatively quick

and easy investigation method, the liquid-solid interface is not visible to carry out

the test when initial void ratio is low, because then the slurry undergoes self-

weight consolidation.

2.5.2 Consolidation


The large-strain consolidation theory for tailings is formulated based on the

following governing equation for infinitesimal consolidation of clays (Terzaghi,

1943):

where t is time, x is the depth with respect to datum, u is the excess pore water

pressure, and Cv is the coefficient of consolidation which depends on the

saturated hydraulic conductivity (Cv = k / w (av / (1+e)): where av is coefficient of

compressibility. This equation is derived from the 1D diffusion equation and

describes the spatial-temporal variation of excess pore pressure. The

development of effective stress σ’ in the clay is governed by the rate of excess

pore pressure dissipation. This is related to a re-adjustment of clay

microstructure induced by the total vertical stress. Eq. (2.5) can be re-written in

terms of void ratio (e), which is easier for geotechnical understanding. Some

Chapter 2

22

assumptions are employed in Terzaghi’s theory of consolidation such as a linear

stress-strain relationship, a constant saturated hydraulic conductivity, and

infinitesimal strain. Since natural clayey soils show a lower compressibility due to

field moisture content influenced by the environment, the Eulerian coordinate

system is sufficient for solving this consolidation equation. However, this is not

applicable to slurries because of the large volume change behaviour due to the

self weight of materials (Ito and Azam, 2013b). The compressibility (dσ’ / de) and

the saturated hydraulic conductivity (k / (1 + e)) relationships associated with this

large settlement become nonlinear functions. Gibson et al. (1967) employed the

material coordinate system, z to overcome this nonlinearity issue. Denoting the

unit weight of soil solids by s, the unit weight of water by w, the elapsed time by t,

the governing equation for the large-strain consolidation was formulated as:

The nonlinear relationships of compressibility and saturated hydraulic

conductivity are determined through laboratory testing to solve the above

governing equation. The first term in Eq. (2.6) represents the self-weight

consolidation process. When neglecting the effect of self-weight and nonlinearity

of the constitutive relationships, Eq. (2.6) becomes identical to Terzaghi’s

equation (Eq. 2.5). Been (1980) showed that when effective stress is set to zero,

the governing equation reduces to Kynch’s (1952) theory of sedimentation.

2.5.2.2 Consolidation Test

Chapter 2

23

Figure 2.5 presents the consolidation behaviour of clay slurries using test results

on oil sand tailings comprising about 55% clay (Suthaker, 1995). The test was

conducted by incrementally loading the slurry sediment and measuring the

saturated hydraulic conductivity after each load (Pollock, 1988; Suthaker and

Scott, 1996). The data are presented in the form of void ratio versus effective

stress (Figure 2.5a) and saturated hydraulic conductivity versus void ratio (Figure

2.5b) using semi-logarithmic scales. The volume compressibility plots (σ’- e) are

obtained from several plots similar to Figure 2.4 in Section 2.5.1.2 for each load

increment whereas the saturated hydraulic conductivity plots (k - e) are derived

from flow measurement versus time after each load increment.

The σ’- e plot (Figure 2.5a) shows that the curves for the various initial

void ratios consist of three straight-line segments: an initial low decrease due to

apparent pre-consolidation followed by a rapid decrease due to primary

consolidation and then by a slow decrease under secondary consolidation. The

initial condition governs the volume compressibility (not a unique curve) in terms

of void ratio at a given effective stress and the slope of each straight line

segment of the curve.

For the selected data, the slurry sample resisted compression at low

effective stress (0.01 kPa to around 0.1 kPa) with an associated average

reduction in void ratio of 1.1. Khan and Azam (2016) summarized the reasons for

apparent pre-consolidation as follows: “(i) initial slurry conditions such as void

Chapter 2

24

Figure 2.5: Consolidation behaviour of a clayey soil and clay-rich slurry

Chapter 2

25

ratio and water content (Scully et al., 1984); (ii) electrochemical interactions in

the colloid liquid mixture (Pane, 1985); (iii) tortuous flow paths and inaccessible

pores in the clay fabric (Mitchell and Soga, 2005); and (iv) thixotropic strength

which is highest at liquid limit (Seng and Tanaka, 2012)”.

Figure 2.5a indicates that an increase in effective stress from 0.1 kPa to

20 kPa overcame the resistance to volume change during primary consolidation

and resulted in an average void ratio reduction of 4.35. Such a large change in

void ratio under primary consolidation is attributed to micro-structural collapse

similar to quick clays (Alshwmar, 2014; Tavenas, 1983) and dissipation of excess

pore water pressure in clays (Kaufman and Sheman, 1964). The average

compression index (Cc) was found to be 2.62, which exceeds the value for most

clays under field conditions (Soil Solidification Research, 1951): 0.2 to 0.3 for

kaolinite, 0.5 to 1.1 for illite, and 1.0 to 2.6 for smectite. This is due to the

relatively loose fabric of slurries as opposed to the dense and aggregated

morphology of natural clays. Further increase in effective stress from 20 kPa to

300 kPa reduced the void ratio by 0.4 during secondary consolidation. The

selected slurry underwent a higher compression compared to natural clays

because of flow channels formed by the escape of re-dispersed particles

(detached from the flocs). Mitchell and Soga (2005) concluded that reconstituted

soils experience higher compression than undisturbed soils owing to micro-fabric

breakage. In contrast, the relatively low settlement in natural clays is due to

plastic adjustment of micro fabric after complete dissipation of excess pore water

Chapter 2

26

pressure (Das, 2009).

Figure 2.5b gives the k – e plot of oil sand tailings at different initial void

ratios pertaining to the samples in Figure 2.5a (Suthaker, 1995) as well as zones

of typical k ranges for fine grained soils (Das, 2009). The figure shows that the

saturated hydraulic conductivity scattered at high void ratio and the relationship

with void ratio converged to be more unique at void ratio less than 2.0. The

saturated hydraulic conductivity of the selected slurry decreased by about six

orders of magnitude (10-4 m/s to 10-10 m/s) over a void ratio change of about 8.0.

The k values of 10-4 m/s to 10-8 m/s (at void ratios between 8.0 and 2.0) are

similar to fine sands and silty clays albeit the latter two soils exit at field void

ratios of 1 ± 0.1. Thereafter, the saturated hydraulic conductivity of the selected

slurry is similar to intact clays, that is, in the range of 10-8 m/s to 10-10 m/s at

comparable void ratios.

The observed k values for slurry (similar to fine sands and silty clays) at

higher void ratios is attributed to the morphology of oil sand tailings (Doan et al.,

2012). A high void ratio of the tailings is due to voluminous flocs containing the

following three types of water (Zlotchevskaia and Korolev, 1997): bound water

(tightly held onto the particle surfaces in the Stern layer); osmotic water (mainly

held between interacting diffuse layers); and entrapped water (mainly held within

the micropores and existing beyond the diffuse layer). Furthermore, free water

occupies most of the inter-floc pores, which are larger than the micropores. Bulk

of the water flow occurs during apparent pre-consolidation through the inter-floc

Chapter 2

27

pores because these relatively bigger void spaces provide paths of least

resistance to the movement of free water. However, larger preferential flow

channels that are normally seen in natural soils are absent in slurry

microstructures hence pore tortuosity (meandering flow paths) and pore

connectivity (dead ends and occluded pores) result in low hydraulic conductivity

at high void ratios.

The k value significantly decreases during primary consolidation because

of a gradual rearrangement of the microstructure (Azam, 2011; Delage and

Lefebvre, 1984). The entrapped floc water becomes available to escape through

the newly-formed pores during primary consolidation. The saturated hydraulic

conductivity steadily reduces due to a reduction in the pore size (reducing void

ratio) along with increased tortuosity and decreased connectivity. Additional

compression of these pores during secondary consolidation and escape of re-

dispersed particles result in additional water release at lower rates. Whereas it is

difficult to separate the three zones of consolidation in the k – e plot, k values

eventually become similar to clays at identical void ratios (as shown for oil sand

tailings in Figure 2.5b). It is important to note that bound water and osmotic water

are not released during consolidation (Donahue, 2004).

2.6 Flow Through Clay Slurries

2.6.1 Saturated Hydraulic Conductivity

2.6.1.1Theoritical Context

Chapter 2

28

Darcy’s law states that there is a direct proportionality between flow rate (q) and

hydraulic gradient, i:

where A is the total cross-sectional area of the soil normal to the flow direction.

Poiseuille’s law for flow through a round capillary tube is used to

determine the average flow velocity, avg through porous media according to:

where μ is viscosity of fluid, R is capillary radius, f is unit weight of fluid, and i is

hydraulic gradient. To encompass various sizes of flow channels in a soil, the

hydraulic radius, RHa is defined as the cross-sectional area, a of a flow channel

divided by its wetted perimeter (p):

Kozeny (1927) and Carman (1937) realized that water does not move in straight

paths but through irregularly shaped pores around solid particles and, as such,

introduced a shape factor, Cs. Using vavg (Eq. 2.8) and RHa (Eq. 2.9), the flow rate

through a soil can be determined according to the equation:

where Cs ranges from 0.2 to 0.5 (depends on particle shape, surface roughness,

pore connectivity, and void tortuosity; Chapuis and Aubertin, 2003). Appendix D

Chapter 2

29

shows the validation of Cs range. Furthermore, Eq. (2.10) can be written for a

bundle of pores of constant but irregular aggregate cross-sectional area (Ab= a).

The term Ab is related to the total cross-sectional area of the soil (A) through

porosity (n) according to the following expression:

Eq. (2.10) becomes:

Using Eq. (2.11) and Eq. (2.12), Darcy’s law (Eq. 2.7) can be written as follows:

Alternatively, RHb (the cross-sectional area of a bundle of flow channel

divided by their wetted perimeters) is the volume of water available for flow

divided by wetted area:

where (P= p) is the total wetted perimeter, L is the length of flow channel, Vw is

the volume of water, Vs is the volume of solids, and S0 is the wetted surface area

per unit volume of particles. Using void ratio, e, the volume of water can be

related to the volume of solids as (Vw = eVs) and Eq. (2.12) becomes:

Chapter 2

30

Using Eq. (2.15) and Darcy’s law (Eq. 2.7), Eq. (2.15) can be written as follows:

Eq. 2.16 is commonly known as the Kozeny-Carman equation and reasonably

estimates the saturated hydraulic conductivity of uniformly graded non-cohesive

sands and silts. The above equation requires measurement of the specific

surface area. To estimate the specific surface area, Chapuis and Légaré (1992)

developed a piecewise method using grain size distribution of granular soils and

Muhunthan (1991) suggested an empirical expression using liquid limit of clayey

soils. However, limited success has been reported for estimation of k of clayey

slurries (Chapuis and Aubertin, 2003). These authors further highlighted the

difficulty in laboratory determination of the shape factor due to the above-

mentioned factors.

2.6.1.2 Measurement Method

The saturated hydraulic conductivity, k is a property of the material assuming the

soil volume does not change. Darcy’s law is widely used in the laboratory

determination of the saturated hydraulic conductivity, such as falling head

method and constant head method (Das, 2009). Furthermore, this equation is

applicable for the laboratory determination of k for slurries for which the void ratio

is kept constant after every load increment in a consolidation test (Suthaker and

Scott, 1996). Prior to consolidation, flocculated solids (connected

particles/aggregates forming a three-dimensional network) settle under gravity

Chapter 2

31

and the volume changes with respect to time. This phenomenon is termed as

sedimentation and is characterized by settling of solids under gravity and upward

movement of water through the pore spaces. Pane and Schiffman (1997) used

the slope of the initial straight-line portion of the settling curve to obtain the

settling velocity (Vs) of the solids and calculated the k of slurries according to the

equation:

where w is the unit weight of water, s is the unit weight of solids, and e is void

ratio. When this equation is employed, effective stress (’) is assume to be

absent. In addition, Tan et al. (1990) assumed the presence of effective stress

during the sedimentation regime and formulated a version of Eq. (2.17). This will

be discussed in Chapter 3.

As described earlier, large volumetric reduction is incorporated in the

large-strain consolidation equation (Eq. 2.6) by having compressibility and

saturated hydraulic conductivity functions. These functions are obtained through

consolidation test. Similar to the sedimentation test, the compressibility is

determined by measuring the deformation of sediment under normal loads. For

the saturated hydraulic conductivity, the two general laboratory methods are the

constant-head and the falling-head hydraulic conductivity tests. The constant

head test method is commonly used for permeable soils (k>10-6 m/s) and the

falling head test is mainly used for less permeable soils (k<10-6 m/s) (Das, 2009).

Chapter 2

32

Both tests can be used as long as the applied hydraulic gradient is lower than the

calculated critical gradient to minimize seepage induced consolidation. The

hydraulic conductivity is directly measured by maintaining small pore pressure

while water is migrating through a sample in the constant head test (Suthaker,

1995). From knowledge of the cross-sectional area of sample A, the cross-

sectional area of stand pipe a, the test duration t, the length of sample L, and

hydraulic gradient gradients h1 and h2 (The initial head h1 is recorded at time t = 0,

and the final head h2 is recorded at time t = t2.), the saturated hydraulic

conductivity is determined by the expression (Das, 2009):

Blight (2009) suggests that the falling head method is preferable because of the

magnification attained by increasing the ratio of sample area to stand pipe area

as well as time required for waiting to achieve steady-state flow.

The use of solids concentration and the cross-sectional area of entire

sample for the calculation of saturated hydraulic conductivity is applicable for the

sedimentation regime and the consolidation regime, respectively. Because the

former has rapid change in the interface height and the latter has minute change

in the interface height thereby these regimes are investigated separately.

However, the intermediate part between two settling regimes has not been fully

understood because seepage induced consolidation during the falling head test

at low effective stress (less than 0.5 kPa) is difficult to manage. A fundamental

Chapter 2

33

understanding of the flow through mechanism of intermediate part is yet to be

established.

2.6.2 Pore Morphology


The arrangement of particle, particle groups and pore spaces in a soil is refer to

as soil fabric (Mitchell and Soga, 2005). Soil fabric is one of primal building

blocks of soil structure which coincide with the combined effect of soil

composition, pore water chemistry, past and present state of stress history, and

environment. Generally, irreversibility of fabric as a result of chemical

environment applies to fine particles like clays due to their highly

physicochemical nature (Bennett and Hurlbut, 1986). This states that a

chemically influenced fabric will remain unchanged unless the application of force

is overcoming electrochemical force acting between aggregates. Beyond initial

flocculation, the chemistry is a less governing factor in influencing fabric changes

as mechanical energy rather than chemical energy dominates.

Figure 2.6 schematically presents pore arrangement of a typical soil. The

three levels of soil fabric typically exist such as microfabric, minifabric, and

macrofabric. The micro-level arrangement is influenced by electrochemical

interactions between clay minerals and pore water. Clay particle aggregates and

very tiny intra-aggregate pores (size up to 1 m) form. The mini-level includes

assemblage of microfabrics forming inter-aggregate pores with size up to several

Chapter 2

34

Figure 2.6: Schematics of particle arrangement (modified after Olsen, 1962)

Chapter 2

35

tens of micrometers. The macro-level incorporates micro and mini levels of fabric

as well as larger macro-level pores such as cracks, fissures, and biological holes

(Mitchell and Soga, 2005). Ito and Azam (2013a) reported that these larger pores

with size up to 2 mm can allow preferential flow thereby natural clayey soils show

much higher hydraulic conductivity (from 10-5 to 10-9 m/s) at lower void ratio (from

1.5 to 0.3) compared to clayey slurries shown in Figure 2.5b (k is ranging from

10-5 to 10-9 m/s while e is ranging from 6.0 to 0.3). Due to the adsorption of water

on clay particles, the macro-level pores (size up to 2 mm) are absent in slurries

and the flow of water through intra-aggregate pores is almost negligible under

self-weight condition because water present in these micropores is essentially

immobile. According to Zlotchevskaia and Korolev (1997), free water occupies

most of the inter-aggregate pores, which are larger than the micropores.

Therefore, it is postulated that the bulk of the water flow occurs through these

relatively bigger (size up to several tens of micrometers) void spaces providing

paths of least resistance to the movement of free water.

The amount of water present in a slurry fabric can be expressed in terms

of porosity or void ratio. The total pore spaces or void ratio are calculated to be

equal to the sum of intra-and inter-aggregate pores. Although this is quite

intuitive representation, a conventional laboratory procedure to measure void

ratio or porosity is only capable of determining the bulk value derived from the

amount of free water and adsorbed water (Olsen, 1962; Selly, 1985). Because

the laboratory procedure requires oven drying of a sample at 105 °C and this

Chapter 2

36

process cannot regulate which water to remove from the sample. Although the

sedimentation test and the consolidation test (described earlier in Section

2.6.1.2) use void ratio to determine the saturated hydraulic conductivity, a

technical constrain during the determination of void ratio has never been

addressed upon calculation of saturated hydraulic conductivity. In other word,

water flow through mechanism has not been fully understood in terms of effective

water passages.

The amount and structure of void (pore) spaces immensely influences

fluid flow through porous media (Vallabh et al., 2010). As already mentioned,

quantitative measurements of void spaces are generally determined by void ratio

and/or porosity, but the characterization of void space structure is complex and

challenging. Void ratio and porosity is related and the total porosity is composed

of ineffective and effective porosities. Figure 2.7 shows schematics of three

different types of porosity. Ineffective porosity does not have a passage for fluids

to go through. Effective porosity consists of Catenary pore and Cul-de-sac pore

(dead end pore). Catenary pore has two passages and the latter has a single

drainage (Selley, 1985). Since these pores are structured to create three

dimensional channels in slurry fabric, the complexity of an entire pore network

system is significant. As a result, the pathways for fluid migration become more

tortuous.

The measured hydraulic conductivity of slurries can be influenced by the

arrangement of solids and pores, the pore and solid space geometry, thus

Chapter 2

37

Figure 2.7: Three types of porosity (modified after Selley, 1985)

Chapter 2

38

Figure 2.8: Concept of effective length in transport through soil (modified after

from Shackelford, 1988)

Soil ParticlesEffective Length, Le

L

Le > L

Chapter 2

39

tortuosity (Ouellet et al., 2008; Vervoort and Cattle, 2003). Figure 2.8 illustrates

the effective path length concept and the tortuosity is defined to be the ratio of

actual average flow path length, Le to the length (thickness), L of the porous

medium in the direction of flow (Vallabh et al., 2010).

Tortuosity in porous materials such as sedimentary rocks, soils, and

sphere packing can be correlated to diffusion measurements (Vallabh et al.,

2010). The diffusion cell apparatus is commonly used to determine diffusion

property of a porous material sandwiched between a tracer reservoir and a

collection reservoir (Boving and Grathwohl, 2001). Fellah (2003) employed an

acoustic method that involving ultrasonic reflectivity for measuring porosity and

tortuosity of porous materials. However these methods are only suitable for

porous materials with rigid structures. Electrical resistance measurements to

determine tortuosity of porous materials have been attempted for porcelain,

packed activated alumina, packed glass beads, and sandstones, Pyrex glass by

Garrouch et al. (2001) and carbonate rocks by Glemser (2007) and Bird (2013).

Suman and Ruth (1993) argued the validity of electrical resistance

measurements in a porous media because fluid flow is largely influenced by

factors like the shape of channels unlike electrical flow which only depends upon

the total cross-sectional area of channels.

Vogel (1997) quantified the pore connectivity as a function of the minimum

Chapter 2

40

pore diameter using serial images captured by eroding soil sample surface.

However, the link between structural and functional properties of soil remained a

challenge and methods of tortuosity measurements for soft materials have not

been developed.

2.6.2.2 Measurement Method

Table 2.2 summarizes techniques for investigating pore morphology of

soils. All of the methods (except magnetic resonance imaging and computed

micro tomography) require some type of sample preparation that can potentially

cause changes in pore morphology. Preparation techniques include air-drying,

oven-drying, and freeze-drying. Together with optical microscopy and scanning

electron microscopy, environmental scanning electron microscopy does not

produce a three-dimensional network of pores because of the two-dimensional

and qualitative nature of these methods. Although mercury intrusion porosimetry

generates quantitative three-dimensional representative pore size data, liquid

and air must be removed from the pore space before mercury can enter (Giesche,

2006). In addition, un-connected pores cannot be reported by this technique.

Similar data can be obtained using magnetic resonance imaging but its use is

hindered by the presence of ferro-magnetic constituents (resulting in image

distortion (Lens, 2005)), as is the case of mining slurries. Therefore, computed

micro tomography appears to be the most suitable investigation method.

Computed micro tomography is widely accepted for visual characterization

and image analysis of pore spaces in rocks (Dong et al., 2007; Al-Kharusi and

Chapter 2

41

Table 2.2: Summary of the techniques for pore morphology investigation of soils

Method / Reference Basis / sample preparation / scale / output / limitations

Optical microscope

Cuisinier and Masrouri (2005); Mitchell and Soga (2005); van Oort et al. (1994)

Direct observation using visible light

Thin soil section with water

1 mm

2 D image

Pore re-arrangement due to sample preparation

Scanning electron microscope

Al-Rawas and McGown (1999); Azam (2012); Cui et al. (2002); Katti and Shanmugasundaram (2001); Lilly and Sargent (1990)

Direct observation using electron beam

Thin soil section with water removed/frozen

0.01 μm

2 D image

Pore re-arrangement due to sample preparation

Environmental scanning electron microscope

Bogner et al. (2006); Jenkins and Donald (2000); Komine and Ogata (2004); Ouellet et al. (2008); Romero and Simms (2008); Wei and Wang (2003)

Direct observation using electron beam

Thin section with water present

0.01 μm

2 D image

Mercury intrusion porosimetry

Aung et al. (2001); Casini et al. (2012); Cuisinier and Laloui (2004); Delage and Cui (2007); Giesche (2006); Kong et al. (2005); Romero and Simms (2008)

Forced intrusion of non-wetting fluid

1 cm3 soil cube with water removed

0.01 μm to 10 μm

3 D representation

Pore re-arrangement during testing and inability to capture un-connected pores

Magnetic resonance imaging Cislerova et al. (1999); Guilfoyle et al. (1992); Lens (2005); Lens and van As (2003); Nestle et al. (2002); Rosin-Poumier et al. (2014); Votrubova et al. (2003)

Measurement of proton excitation in water through magnetic resonance

0.1 mm through 1.0 m sample size with water present

0.1 μm to 50 μm

3D images

Ferro-magnetic materials cause images distortions

Computed micro tomography Anderson et al. (2010); Kikuchi et al. (2003); Hussein et al. (2015); Kikkawa et al. (2013); Takahashi, et al. (2010); Beckingham et al. (2013)

Measurement of density by X-ray attenuation

0.1 mm through 1.0 m sample size with water present

0.1 μm to 50 μm

3D image

Chapter 2

42

Blunt, 2007) and soils (Mokwa and Nielsen, 2006; Cortina-Januchs, et al., 2011).

Furthermore, the derived data can be correlated with geoenvironmental

parameters such as material density (Kikkawa et al., 2013), diffusive transport

(Agbogun et al., 2013), and permeability (Glemser et al., 2007). The application

of this method requires the use of adequate image processing to eliminate

effects related to material composition (pore water, hydrated grain, and inert

grain) and equipment type (generating monochromatic or multichromatic x-ray

beam). Commonly used image processing include the following: (i) thresholding

method using the grayscale value and associated probability density function

derived from the image histogram (Taud et al., 2005); (ii) calibration method

using two scans with different fluids saturating the porous medium to establish

the quantified attributes values (Akin and Kovscek, 2003); and (iii) calibration free

method comparing images resulting from samples saturated with a contrast

solution as well as a transport solution (Hussein et al., 2015). The slurry not only

possesses a fragile pore morphology but also varies in material composition.

Computed micro tomography (CMT) was developed in the medical field

and the technology has been increasingly applied for pore morphology

investigations of rocks and soils. The basic component of CMT technique is an

X-ray source, an object, and a detector. The source generates an X-ray beam

and the beam is progressively attenuated while it is going through the rotating

object. Subsequently, the detector measures and records the transmitted X-ray

intensity (Simons et al., 1997).

Chapter 2

43

A rate of attenuation depends primarily on the bulk density of the material

and partly on the effective atomic number (Ruiz de Argandona et al., 2003).

Beer’s law expressed the attenuation of an X-ray radiation as:

where is the linear attenuation coefficient of the x-ray in the material, I0 and I

are the incident and attenuated X-ray, respectively and h is the thickness of the

scanned object. Further, the linear attenuation coefficient depends on the density

of the material, the effective atomic number, Z and energy, E of the incoming X-

ray beam (Denison et al., 1997):

where a and b are energy-dependent coefficients.

Recorded X-ray intensities are stored as series of two dimensional

radiographs that consists of the same number of stepwise rotations. A set of

radiographs is reconstructed by using algorithms to yield two dimensional

attenuation coefficient image slices that are merged together to produce specially

resolved three dimensional images in voxel elements (Agbogun, et al., 2013).

Hidajat et al. (2002) used CMT to generate images to develop a three

dimensional pore system image inside of sandstone. Coles et al. (1996) used

CMT for visualizing and determining the porosity and pore distribution. The data

showed better quality and the data was used to calculate the saturated hydraulic

Chapter 2

44

conductivity. Takahashi et al. (2010) conducted diffusion measurement to assess

tortuosity in a sedimentary rock. Increasing applications of the CMT technology

to visualize and to quantify the internal structure of porous materials is apparent

and expanding the technology for the investigation of slurry morphology is

feasible based upon the reported successes.

2.7 Summary

The inherent properties of solid and liquid phases of a clayey slurry govern the

settling behavior of these materials. Electrochemical interactions at phase

boundaries result in either dispersive or flocculated microstructure. This means

that material characterization is essential to correlate microstructural

configuration with setting behaviour. Previous research focused on empirically

correlating solid-liquid composition with slurry dewatering: laterite slurries (Azam

et al., 2005); oil sand tailings (Miller et al., 2010); and phosphate slimes

(Zindarcic, et al., 1994). Furthermore, water migrates upward during the

processes of sedimentation and consolidation. The flow rate of water is

correlated with saturated hydraulic conductivity, k, but the determination of this

property for slurries can be complicated because of significant volume reduction

during settling. Pane and Schiffman (1997) partly resolved this issue within the

sedimentation regime by formulating a saturated hydraulic conductivity equation

based on changing solids concentration. Likewise, Suthaker and Scott (1996)

implemented incremental k measurements with controlled critical head during the

consolidation regime. However, the determination of k in the transition zone has

Chapter 2

45

not been well investigated. Three dimensional pore morphology can provide

qualitative and quantitative information to clearly understand water flow in the

transition zone.

Based on this literature review, the following research needs have been

identified: (i) a better understanding of the settling behaviour of clay slurries

under hindered sedimentation and large-strain consolidation by correlating with

solid-liquid characteristics at the onset of deposition; (ii) the development of a

comprehensive testing and analysis method using computed micro tomography

technology to investigate the flow through behaviour of clay slurries.

Chapter 3

46

Chapter 3 RESEARCH METHODOLOGY

3.1 General

A comprehensive research methodology was enacted to fulfill the objectives of

this research, as summarized in Figure 3.1. The program was divided into the

following categories: (i) determination of index properties as well as detailed

characterization of the solid and liquid phases of the slurry; (ii) investigation of

settling behaviour by conducting sedimentation test and consolidation test; (iii)

investigation of flow through mechanism by capturing pore morphology through

computed micro tomography; and (iv) determination of saturated hydraulic

conductivity using pore morphology and settling test results.

3.2 Rationale of Research Plan

First, the composition of clay mineral and pore water dictate the settling and flow

through processes. This is based on the reported water release in oil sand

tailings that is related to thixotropic gel formation (Mercier et al., 2012).

Thixotropy is the reversible property that a viscous material reduces its gel

strength upon agitation but gains back the strength at rest (Barnes, 1997; Miller

et al., 2010). Primary contributors for this behaviour are identified as the

presence of critical amount of clays around 10-15% (Tu et al., 2005) and

sufficient concentration of divalent cations such as Ca2+ and Mg2+ (Mercier et al.,

2012). Similar behaviour was observed for the phosphate slime by Wissa et al.

Chapter 3

47

Figure 3.1: Investigation Program

Chapter 3

48

(1986). The dewatering behaviour of slurries becomes more electrochemical in

nature as clay and water content increase. Therefore, detailed material

characterization was conducted on a selected clayey slurry.

Second, the interactions between clay mineral and pore water are

predominant during the sedimentation and initial stages of consolidation. This is

based on experience with china clay slurries, phosphate slimes, bauxite tailings,

and oil sand tailings (Znidarcic et al., 1986; Cooling,1985; Miller et al., 2010)

Such settling processes are important for understanding slurry behaviour in the

counter current decantation (CCD) circuits, thickening vessels, and fresh tailings

deposits. Therefore, sedimentation tests and large-strain consolidation tests (at

low effective stress) were conducted on the selected clayey slurry.

Third, the morphology developed due to the interaction of clay mineral and

pore water governs the flow of water through clayey slurries. This is based on the

scanning electron microscopy results reported for oil sand tailings

(Jeeravipoolvarn, 2010) and laterite slurries (Azam et al., 2005). The main issues

related to microstructural capture of slurries are related to freezing artifacts, two

dimensional images, and volume decrease during settling. Therefore, computed

micro tomography was used to develop three-dimensional pore morphology of

the selected clayey slurry.

Fourth, the hydraulic conductivity for clayey slurries is determined using

methods based on solids concentration during sedimentation (Pane and

Chapter 3

49

Schiffman, 1997) and cross-sectional area during consolidation (Suthaker and

Scott, 1996). Theoretical equation for saturated hydraulic conductivity is related

to physical properties of soils (hydraulic radius determined from pore

morphology) and permeating fluid (viscosity and unit volume) based on

Poiseuille’s law (Mitchell and Soga, 2005). However, this approach has not been

investigated for slurries especially in the transition zone between sedimentation

and consolidation. Therefore, a conceptual model was developed for determining

saturated hydraulic conductivity in the transition zone of slurry settling.

3.3 Material Description

A clayey slurry (uranium leach residual) retrieved from the extraction process

was selected as a material to capture the distinct slurry characteristics and

behaviour at the onset of deposition. The ore was obtained from the Cameco

Millennium exploration site, SK, Canada. The slurry was generated in the

metallurgical laboratory at Port Hope, ON, Canada. The 1L Nalgene sample

bottles were encased in a lead radioactive shielding box to ensure thorough

gamma radiation protection during transportation. The samples were shipped

from the Port Hope in a van to the Radioactive Tailings Research Laboratory at

the University of Regina where they were stored at a constant temperature

(23°C). A detailed laboratory characterization program was conducted for the

uranium slurry. Sub-samples for each test were obtained by homogenizing the

slurry using a metal stirrer. All of the laboratory tests were performed in a fume

Chapter 3

50

hood in accordance with the occupational health and safety requirements as per

the ASTM Standard Guide for Radiological Protection Training for Nuclear

Facility Workers (E1168-95-2013). After the completion of laboratory testing, the

used samples were shipped back to the mine site for disposal in the tailings

containment facility.

3.3.1 Geology

The Millennium ore is a basement-hosted unconformity-related uranium deposit

located in the Paleoproterozoic Athabasca Basin at 35 km north of the Key Lake

mine and 35 km south-west of the McArthur River mine in Saskatchewan,

Canada. The deposit is located at a depth of 650 m at an average ore grade of

16000 ppm (ranging from 3000 ppm to 73000 ppm) U3O8 concentration. At the

Millennium site, only the Manitou Falls Formation of the Athabasca Group which

was deposited in braided river systems is preserved (Ramaekers et al., 2007).

This Formation consists of four members namely; the Bird, Warnes, Collins, and

Dunlop, in which the proportion of conglomerate and clay differ in the order of no

clay to more than 0.6% of clay content (Power et al., 2012). According to Roy et

al. (2005), there are variable mineral alteration zones and muscovite is the

predominant non-clay mineral present in the deposit (Power et al., 2012). When

compared with other basement-hosted ores commonly found in the Athabasca

Basin, the clay mineralogy of Millennium ore is predominantly consist of illite

rather than illite-chlorite mix (Cloutier et al. 2009).

Chapter 3

51

The geological process that formed the uranium ore largely influenced the

composition of the solid phase of the slurry. Figure 3.2a gives the occurrence

and simplified geology of uranium deposits in the Athabasca Basin

(Saskatchewan, Canada). About one-third of the known worldwide reserves are

found in the region as large deposits of high-grade uranium ores (>20000 ppm)

(Kyser and Cuney, 2008). The basin covers an area of about 100,000 km2 in

Saskatchewan (Ruzicka, 1996) and geologically consists of the 2950 to 1800 x

106 years BP Archean to Paleoproterozoic metamorphic basement rocks (Lewry

and Sibbald, 1980; Tran et al., 2003; Annesley et al., 2005) along with 1800 to

1600 x 106 years BP Paleoproterozoic to Mesoproterozoic sedimentary

sandstones (Kyser et al., 2000; Rainbird et al., 2003; Creaser and Statiuk, 2007).

Most of the uranium deposits are located at the transition between a crystalline

basement of the western Wollaston Domain and the eastern Mudjatik Domain

(Cloutier et al., 2009; Cumming and Krstic, 1992). The ores were formed where

reducing fluids carrying silica from the basement rocks encountered oxidizing

fluids from the Athabasca Group in the faults. Generally, uranium mineralization

occurred in basement rocks immediately below (basement-hosted or ingress-

style) and in sandstones immediately above (sandstone-hosted or egress-style)

the unconformity (Jefferson et al., 2007; Chi et al., 2013).

Figure 3.2b gives the regional occurrence of various clay minerals (illite,

chlorite, and dravite) in surficial materials and outcrops of the Athabasca Group.

Chapter 3

52

Figure 3.2: Occurrence of uranium deposits and surface geology and mineralogy

of the Athabasca Basin (modified after Earle and Sopuck, 1989; Jefferson et al., 2007)

Chapter 3

53

Predominantly detrital kaolinite with minor amount of smectite, chlorite, and illite

comprised the original clay minerals of the Athabasca Basin (Nickel and Nichols,

1991). Generally, weathering by meteoric waters is the primal reason for the

early precipitation of kaolinite (Lanson et al., 2002). The reaction with diagenetic

fluids and the original clay minerals transformed kaolinite to dickite (Wasyliuk,

2002). K-feldspar and mica-rich rocks provided lithologically and hydrothermally

available potassium in the surrounding brine causing the ubiquitous illite

formation in the south-eastern part of the basin (Hoeve and Quirt, 1984).

Illitization in the Athabasca Basin was directly associated with diagenesis,

mineralization, and host-rock alteration events thereby illite can be used as the

pathfinder mineral for uranium ore (Quirt, 2010).

3.3.2 Mining

The composition of the liquid phase of the slurry is governed by the extraction

method. Although in situ leaching is being increasingly utilized to reduce surface

disturbance and tailings generation, this method is not readily applicable to ore

bodies that restrict the solution permeation pregnant liquor recovery (World

Nuclear Association, 2014). A conventional blasthole stoping mining method that

is similar to what is employed at the Rabbit Lake operation is expected to be

employed for the Millennium deposit. Blasthole stoping involves establishing drill

access at both above and below the mineralization. The area between the upper

and lower access levels (the stope) is then drilled off and blasted.

Chapter 3

54

Figure 3.3: Simplified process flow chart of the Key Lake milling operation (modified after Koshinsky et al., 2012)

Chapter 3

55

The broken rock is collected and crushed in an underground mill, pumped to the

surface in slurry form, and transported to the extraction process (Cameco 2009).

Figure 3.3 presents a simplified flow chart of the milling operation. Sulfuric

acid (H2SO4) is used to solubilize uranium from the ore slurries. The liquid and

the solid phases in the slurries are separated in the counter current decantation

(CCD) wash circuit at slightly elevated temperature (Kim and Mines, 1977). The

decanted uranium bearing liquid from the CCD circuit is fed to the organic solvent

extraction circuit to collect uranium (Flöter, 1985) and the acidic raffinate (a liquid

from which impurities have been removed by solvent extraction process) is

incrementally neutralized using lime (Shaw et al., 2011). The reverse osmosis

(RO) plant further cleans the liquids to be recycled in the grinding and blending

process. The separated solids that are collected from underflow of the CCD

circuit as leach residues are recombined with underflow materials from the

neutralization circuit and non-recyclable treated liquids from the RO process to

form tailings in the tailings thickener.

Solids-liquids separation is a fundamental aspect of efficient mineral

processing and the CCD circuit is used for the following advantages (Tarleton

and Wakeman, 2006): (i) a minimum number of moving parts is existed; (ii) a

small number of large units is required; (iii) the possibility of recycling raffinate. A

vessel used in the CCD circuit is primarily a sedimentation device that is similar

to the one used in the tailings thickening process.

Chapter 3

56

Figure 3.4: Sectional view of a thickener (modified after Tavleton and Wakeman, 2006)

Chapter 3

57

Figure 3.4 schematically illustrates a sectional view of sedimentation

vessel called thickener. As a feed stream enters the thickener, the solids settle to

the bottom. Clarified liquids overflow to the top and settled solids underflow is

removed from the bottom. The clear zone, which is the clear overflow liquids, is

essentially free of solids. The hindered settling zone consists of fairly uniform

solids consistency, which is near the same solids content as the feed stream.

The self-weight consolidation zone shows the settled sediments undergoing

further dewatering due to compression of the solids forcing the liquids out of

pores (Mula et al., 2002). This industrial dewatering process can be scaled down

to laboratory experiments that will be discussed later. Ore mineralogy and mining

process reflect in the composition of solids phase and liquids phase of mine

slurries (Jeeravipoolvarn et al., 2009a). An assessment of characteristics of clay-

rich uranium slurries and a fundamental understanding of dewatering process are

necessary to develop a sustainable mineral production for the nuclear industry.

3.4 Solid-liquid Characterization

3.4.1 Index Properties

Index properties were determined for slurry characterization and preliminary

assessment of the interaction of clay with pore fluid as well as for subsequent

use in laboratory investigation of the settling behavior.

Water content (w) is the amount of water present in a soil and is

expressed as a percentage quantity. The water content was determined at as

Chapter 3

58

received condition according to the ASTM Standard Test Methods for Laboratory

Determination of Water (Moisture) Content of Soil and Rock by Mass (D 2216-

05). A reduced temperature of 60 C was used to preclude the removal of

structural water associated with gypsum that is formed due to lime addition in the

extraction process (Azam et al., 2014). This temperature was used in the entire

subsequent laboratory test involving the determination of water content.

Water content was translated to solids content (s), which is the mass of

soil solids divided by the total mass of the tailings. Based on the phase

relationship, such conversion was made as follows:

Specific gravity (Gs) is the ratio of the mass of soil solid to the mass of an

equal volume of distilled water at 4 ºC. The specific gravity was determined by

the ASTM Standard Test Method for Specific Gravity of Soil Solids by Water

Pycnometer (D 854-06). Specific gravity of the tailings was used to calculate the

void ratio, which is the ratio of the volume of voids to the volume of solids.

Assuming the complete saturation and using unity for the specific gravity of water,

void ratio (e) was estimated according to:

The grain size distribution (GSD) was determined in accordance with the

ASTM Standard Test Method for Particle-Size Analysis of Soils (D 422-63). A

Chapter 3

59

hydrometer was used to determine the GSD for material finer than 0.075 mm.

Slurry was classified in accordance with the ASTM Standard Test Method for

Classification of Soils for Engineering Purposes (Unified Soil Classification

System) (D2487-11).

Liquid limit (wl) is defined as water content above which soils flow like a

liquid, whereas plastic limit (wp) is the water content above which soils exhibit a

plastic behaviour. The liquid limit and the plastic limit were determined by using

the ASTM Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity

Index of Soils (D 4318-05) to evaluate the water holding capacity of the slurry.

The soil was classified in accordance with the ASTM Standard Practice for

Classification of Soils for Engineering Purposes (Unified Soil Classification

System, D2487-11). The data are presented in Appendix (Table A4).


Solid composition was determined to confirm the amount and type of clay

minerals and non-clay materials in the ore that have developed through

geological processes. Elemental analysis was not warranted as such data are

difficult to correlate with mixed mineralogy. Instead, the electrical charges on the

various minerals were investigated by determining cation exchange capacity

(CEC).

3.4.2.1 Mineralogy

The mineral composition was investigated through X-ray diffraction (XRD)

Chapter 3

60

analysis using a Bruker diffractometer, Model D4 Endeavor that had a Cu broad

focus tube at 40 kV and 40 mA alongside a monochromatic incident ray. Bulk

mineral composition was determined by oven-drying the slurry, manually

pulverizing the whole sample and obtaining the grain size distribution. Randomly

oriented specimens were prepared in rectangular metal holders by pressing the

former against a rough glass to increase packing randomness. Clay mineral

composition was determined using preferentially oriented samples of clay size

fraction. This was achieved by preparing a suspension of clay size material and

distilled water, filtering the suspension onto a membrane, and transferring the

deposited clay film onto a glass slide (Drever, 1973). Samples were scanned

from 5° through 70° angle (2) for bulk XRD and from 5° through 20° angle (2)

for clay XRD at a speed of 1° 2/min. The diffraction patterns were matched with

the standard patterns prepared by the Joint Committee of Powder Diffraction

Data Service (JCPDS). Semi-quantitative estimates of the constituent minerals

were made by the Reference Intensity Ratio method (Moore and Reynolds,

1997).

3.4.2.2 Cation Exchange Capacity

To correlate mineralogy with ion exchange, the cation exchange capacity (CEC)

and individual cations (Na+, K+, Ca2+ and Mg2+) were measured by NH4O method

for which the sample was buffered at pH = 7.0 (Hendershot et al., 2006).

NH4OAc (1 mol/L concentration) solution was prepared in a 50 mL centrifuge

tube and approximately 100 mg of sample was poured into it. Subsequently, the

Chapter 3

61

tube was agitated for 15 min at 115 rpm. The solution was left overnight and

transferred to the Buchner funnel having a Whatman No. 42 filter paper. The

NH4+ saturated leachate was added with KCl (1 mol/L concentration) to replace

NH4+ by K+ and the filtrate was analyzed in a volumetric flask. The amount of

displaced K+ was used to determine individual cations present in the sample. The

ion types were quantified using suitable dilution factors and blanks’

concentrations. The sum of ions was reported as total cation exchange capacity.

3.4.3 Pore Water Composition

Pore water composition was determined to confirm the presence of ions in the

slurry water that originated from the extraction process. The resulting data were

used along with solid composition to assess slurry morphology.

3.4.3.1 pH and Electrical Conductivity

The pH is a measure of the activity of the hydrogen (H+) ion that measures the H+

ion concentration in solution. This measurement confirms the sample collection

stage in the extraction process. Electrical conductivity (EC) is defined as the

ability of a solution to carry an electrical current. This property can be correlated

with the type of ion and total ion concentration of pore water. The pH and EC

were measured for the uranium slurry samples at as received condition. The pH

and EC were measured using a pH/EC meter (D-54) as per ASTM Standard Test

Method for pH of Soils [D4972-01(2007)] and ASTM Standard Test Methods for

Electrical Conductivity and Resistivity of Water [D1125-95(2009)], respectively.

Chapter 3

62

The instrument was calibrated with standard solutions for both pH and EC prior

to each analysis. The determination of reduction–oxidation reaction potential (to

predict mineral precipitation using thermodynamic equilibrium model) was

beyond the scope of this research.

3.4.3.2 Electrolyte Concentration

The qualitative and quantitative pore water chemistry can be used to assess the

double layer thickness. Concentrations of Na+, K+, Mg2+, Ca2+, Mn2+, Co2+, Ni2+,

Cu2+, Sr2+, Al3+, V3+, Cr3+, Fe3+, and SO42- (based on the assumption that all S is

associated with the sulfate ion) were determined by the inductively coupled

plasma method in a Thermal Jarrell Ash IRIS Advantage, whereas the automated

ferricyanide method using colorimetric centripetal analyzer (COBAS FARA II)

determined Cl.

3.5 Settling Characterization

3.5.1 Sedimentation

The sedimentation test was intended to determine the settling behaviour of

slurries in impoundments by varying the initial solids content from 25% to 50% to

mimic the operational conditions of slurry disposal. This facilitated the

determination of the anticipated shift in settling behaviour from sedimentation to

the transition regime.

Figure 3.5 presents a laboratory setup utilized for sedimentation tests. The

principle of the test is similar to that of used in the reported sedimentation test in

Chapter 3

63

Figure 3.5: Sedimentation test setup

Chapter 3

64

Section 2.5.1.2. However, the currently introduced sedimentation test is

customized to measure a high initial solids content range to obtain sub-samples

undergoing the transition regime. The tests were conducted using a 90 mm

diameter graduated transparent glass cylinder. The initial height of the sample

was kept close to 90 mm to maintain 1:1 vertical-to-horizontal ratio thereby

minimizing wall effects (Khaled and Azam 2014). The settling velocity is affected

by friction between the column wall and the particles and the effect is minimal at

D/H = 1 and is maximum D/H = 0.2 (Rao et al., 2010). Samples with selected

nominal initial solid contents of 25%, 30%, 35%, 40%, 45% and 50% were tested

to investigate the various setting modes (Imai, 1980). Each sample was prepared

by manually mixing the ‘as received slurry’ with a known amount of distilled

water: addition of supernatant fluid would potential result in mineral precipitation.

The ingredients were gently rotated for 2 minutes using a steel rod to ensure

sample homogeneity and minimize microstructural disturbance. The pH was

measured during the dilution process to ensure that it is within the range (1.0 to

3.5) for initial neutralization process mimicked in this research (Shaw et al., 2011).

The diluted slurry was poured in the graduated test cylinder and allowed to settle

under self-weight. The change of solid-liquid interface height was recorded at

equal time intervals using a digital camera with macro lenses for image

magnification of up to 6 times. When two consecutive readings over a 24 hour

period were found to be less than 0.5 mm (minimum discernible resolution), the

test was terminated. The digital image files were analyzed and the data were

Chapter 3

65

plotted as interface height versus time. Errors associated with the manual

observation were significantly reduced by digital enlargement of the captured

solid-liquid interfaces. The interface height data were converted to void ratio

using the initial void ratio (e0), the initial interface height (H0), and the interface

height at time t (Ht) in accordance with the equation:

Saturated hydraulic conductivity was determined under two opposing

assumptions at the start of the test, namely: (i) absence of effective stress using

Eq. (3.4) for the slope of the initial straight-line segment of the settling curve

(Pane and Schifman 1997) and (ii) presence of effective stress using Eq. (3.5) for

a best-fit representing the entire settling curve (Tan et al., 1990). Denoting the

settling velocity by Vs, void ratio by e, the unit weight of solids by s, and the unit

weight of water by w., the two equations are written as:

In the latter case, the effective stress was calculated from knowledge of the final

sample height (Hf) according to the equation:

The above data were used to plot the two constitutive relationships of void ratio

Chapter 3

66

versus effective stress and the void ratio versus saturated hydraulic conductivity.

3.5.2 Consolidation

The consolidation test was focused to mimic the settling behaviour of deposited

slurries in the containment facility. Based on the sedimentation test results

(described in Chapter 4), an initial solids content of 50% was selected to capture

the consolidation regime of settling. A range of the applied vertical loads (from

0.3 kPa to 30 kPa) was used to imitate the anticipated effective stress of fresh

deposits. This facilitated the anticipated apparent pre-consolidation behavior

associated with clayey slurries.

Figure 3.6 presents a laboratory setup utilized for consolidation test. A

consolidometer cell with the capability of independently measuring the saturated

hydraulic conductivity was designed and fabricated, as presented in Appendix B

(Figure B1). This modified cell was intended to test lower effective stress range

that capable of characterizing between the transition zone and the consolidation

regime. A similar setup to those reported by Qiu and Sego (2001), Pedroni and

Aubertin (2013), and Bhuiyan and Azam (2014) was used. The cell (110 mm

internal diameter, 200 mm height, and a wall 6.5 mm thickness) was cut from a

plexiglass tube to ensure transparency and avoid buckling during load application.

A porous plate wrapped with a geotextile was used above and below the sample

to minimize fines escape and eccentric loading. The slurry at an initial solids

content of 50% was poured in the cell up to a 110 mm height (maintaining 1:1

ratio, as above) and allowing the capture of expected large strains in excess of

Chapter 3

67

10% (Besson et al. 2010). Once self-weight settling ceased, the sample was

subjected to an effective stress (0.3 kPa to 31 kPa) that captured the anticipated

transition from sedimentation to consolidation in a freshly deposited clay slurry.

Applied incrementally, each previous load was doubled after the completion of

primary consolidation. A Linear Variable Displacement Transducer (LVDT) was

used to monitor volumetric deformations and the data were collected using a

data acquisition system. The solid-liquid interface height was recorded and the

captured image files were processed and cross-referenced with the strain data.

The data were plotted in the form of interface height versus time. The final

interface height was converted to void ratio for a given applied pressure to

develop the σ’- e relationship.

The vertical saturated hydraulic conductivity was determined at the end of

each load increment using the falling head method by allowing water in a

graduated standpipe to migrate from the cell bottom. Sample boiling during

measurement were prevented by maintaining the vertical hydraulic gradient

under the calculated critical gradient (that varied between 0.27 and 0.65). A

constant water level was maintained in the cell by continuously collecting the

decant water in an outflow beaker. A predetermined initial head condition (h1) in

the stand pipe was recorded and water was allowed to flow through the sample

under the hydraulic gradient until the water in the standpipe reached a lower limit

(h2). The time required for the water in the standpipe to drop from the upper to

the lower level was recorded. Denoting sample height by L, sample cross-

Chapter 3

68

Figure 3.6: Consolidation test setup

Chapter 3

69

sectional area by A, standpipe cross-sectional area by a, and time for water to

flow between h1 and h2 by Δt, the saturated hydraulic conductivity was calculated

according to the equation:

As before, the entire data were used to plot the k – e relationship.

3.6 Flow Through Characterization


Pore morphology was observed to identify various component of the three

dimensional microstructural configuration in the transition zone. A sample

preparation procedure was developed to preserve the microstructure during

settling. Likewise, a new image analysis approach was developed to identify and

separate the solids, free water, and hydrated grains as well as to convert these

phases into quantities. This was followed by converting the slurry constituents

into index properties for comparison with data from geotechnical tests.

The computed micro tomography (CMT) was carried out at the Bio

Medical Imaging and Therapy (BMIT) beamline in the Canadian Light Source

(Saskatoon, Canada) and using selected samples with predetermined index

properties (w, s, e and n). To capture the variation in pore configuration during

slurry dewatering, samples at known initial conditions were allowed to undergo

sedimentation in a graduated beaker. The test was terminated when no further

settling was observed over 24 hours.

Chapter 3

70

Figure 3.7 presents the samples retrieved for the CMT test. Sub-samples

for CMT were collected from the settled samples by slowly inserting a

polypropylene drinking straw (0.1 mm thickness and 4.5 mm diameter) up to the

mid-height of graduated beakers. When the straw was filled up to a 20 mm height,

it was taken out from the beaker and the top and bottom were sealed using

plastic plugs. Sample preservation, transportation, and disposal followed the

same procedure as described in Section 3.3.

Figure 3.8 shows a schematic of the CMT apparatus. The synchrotron

based CMT used an x-ray bending magnet, monochromatic beam with the

average energy 20 keV and beam size 240 mm H x 7 mm V at 23 m distance.

The slurry sample was placed in a cylindrical sample holder (4.5 mm in diameter

and 20 mm in length) and rotated around an axis normal to the incoming

synchrotron beam at projection angles between 0 and 180.2°. The angle viewing

step size was set at 0.1° degree intervals resulting in a total of 1,801 parallel

projections. After penetration of the sample, the X-rays were attenuated by

scattering and absorption due to the density and chemical composition of

materials in the sample. A 0.01 mm thick gadolinium oxysulfide scintillator emits

visible light that depends on the intensity of attenuated X-rays, this is recorded by

a detector to produce radiographs for every step rotation. Projection images were

digitized by a high-resolution (2,048×2,048 pixels) ultra-fast read-out charge-

coupled device camera (Hamamatsu C9300) with an exposure time of 1

sec/frame and two-frame averaging was employed for each of the 1801

Chapter 3

71

Sedimentation tests

Sample holders

20 m

m0.1 mm thickness 5 mm diameter

polypropylene tubes

Initial: s = 49% s = 38% s = 25%

Final: s = 50% s = 40% s = 30%

a)

b)

Figure 3.7: Samples retrieved for CMT test

Chapter 3

72

Figure 3.8: Schematics of CMT apparatus (modified after Glesmer, 2007; Bird,

2013)

Syncrotron

X-rays

Sample

Rotation Stage

Scintillation

Plate

Visible Light

Objectuve

Lens

CCD Camera

Chapter 3

73

projections thereby resulting in a scan time of approximately 80 min. This set-up

resulted in a field-of-view of 8 mm H × 3 mm V and an original resolution of 4.3

μm. After raw data collection, the ImageJ software (Schneider et al., 2012) was

used to render the result and evaluate the image quality.

The first stage of image analysis was completed by converting a total of

687 2D grey-scale images from 16 bit to 8 bit. These 2D images are called slices

and the 3D reconstruction was done by vertically stacking 687 slices to represent

the 3 mm high sample using the ImageJ software (Figure 3.9).

The circular sample was divided into four equal squares (373 × 373 pixels)

of regions of interest (ROI). This maximized the use of available computational

capacity, eliminated areas redundant to the analysis, and precluded wall effects

of the sample holder. A greyscale histogram was obtained for every 100 th slice

and compared with the average of 687 slices. The images were filtered to

eliminate noises and subsequently segmented by applying threshold greyscale

values to identify voxels representing water, solids, and mixture of water and

solids. The statistical approach of Bazi et al. (2007) was used to ensure

reproducibility of results. An optimal greyscale value, corresponding to the

intersection between two normal distribution curves, was selected. This selection

was based on the central limit theorem, which states that the occurrence of

arithmetic mean of a sufficiently large number of random variables resulting

under the same conditions becomes highest. Therefore, the probability

distribution corresponding to the occurrence of all values of the random variables

Chapter 3

74

Figure 3.9: Schematics of 3D image rendering process

Chapter 3

75

shows a bell-shaped curve with a peak located at the mean value (Watt and van

den Berg, 2002).A single threshold was considered adequate because the

monochromatic synchrotron radiation ensures that the absorption coefficient for

each voxel remains the same independent of the projection angle (Rennert et al.,

2011).

The second stage of image analysis was completed by counting voxels

under the water peak as well as the solids peak gave the total volume for each of

these constituent. Under the mixed peak (hydrated grains), the solids were

identified by comparing the measured greyscale value (ns) with those for the

water peak (nsw) and the solids peak (nss) according to:

The volume of solids in the mixed peak was the voxel count identified as solid

and the sum of the remaining voxels was water volume. The weight of each of

the constituent was calculated by multiplying the voxel count (material volume)

with the corresponding grey-scale value (material density). The solids content (s)

was calculated according to:

where Ws is weight of all solids obtained from the solids peak and the mixed

peak and Ww is weight of all solids obtained from the solids peak and the mixed

peak. Furthermore, the solids content was converted to other geotechnical

Chapter 3

76

parameters according to:

where Vv is the volume of void, Vs is the volume of solids, V is the total volume,

w is the unit weight of water, and Gs is the specific gravity of the slurry and

complete saturation is also assumed. Examples of constituent delineation are

presented and all of the above image analysis based parameters were compared

with independently measured values in Section 4.4. The calculated geotechnical

indices were evaluated in terms of data accuracy and precision. Dunnicliff (1993)

stated accuracy and precision as follows; “Accuracy is the closeness of approach

of a measurement to the true value of the quantity measured.”; “Precision is the

closeness of approach of each of a number of similar measurements to the

arithmetic mean.” Specifically, the true values defined in this study lie on a 45

degree angle line (theoretical line) made between measurement data from

geotechnical methods and image analysis. Since this theoretical line is

expressed as y = ax + b (a = 1 and b = 0), a data set expressed with the

coefficients a as close as 1 considered to have better accuracy. The difference

from the arithmetic mean is expressed as the coefficients of linear regression

(R2). These evaluations are together presented in Section 4.4.

Chapter 3

77


Saturated hydraulic conductivity in the transition zone was determined to

understand the parameters governing the flow through behaviour in slurries.

Based on image processing, porosity and a newly defined hydraulic radius

RHc,were used in the Poiseuille’s law of water flow through porous media.

Image processing was completed by converting a total of 687 2D

greyscale images from 16 bit to 8 bit followed by conversion to binary images

(using a threshold value) and then by reconstructing a 3D stack of the 3 mm high

sample using the ImageJ software. The binary images consisted of white pixels

representing water (filling the pore spaces) and black pixels representing solids

(including hydrated grains). The examples are given in Section 4.4. The pore

area in the converted images was measured in terms of square area (4.3 μm x

4.3 μm) of the white pixels for each 2D binary image and the volume summation

of all 687 images gave the total pore volume. To calculate hydraulic radius, RHc,

the pore throat cross-sectional area (less than the pore cross-sectional area used

in Eq. (2.9) that governs fluid flow (Beckingham et al., 2013)) was divided by the

pore perimeter obtained from the summation of white pixel length (4.3 μm) in

each 2D binary image. An average hydraulic radius was determined for the 687

images representing the sample height. The circular pore throat cross-sectional

area was calculated by measuring the diameter of water filled pores in the 3D

reconstructed stack using an ImageJ plug-in, BoneJ (Doube et al., 2010),

according to the method developed by Hildebrand and Ruegsegger (1997).

Chapter 3

78

Using the above definition of hydraulic radius, k was calculated according

to the following version of the Poiseuille’s equation (Lebron et al., 1999):

Where f = 9.81 kN/m3, μ = 1.002 x 10-3 N.s / m2 at 20 °C, G = 8 for circular pore

geometry, τ = 1 for linear flow channels, and porosity (nCMT) as determined from

the CMT image analysis as a volumetric ratio of free water versus total sample.

The validation of CMT results using known material such as glass beads was not

conducted due to the unavailability beam time.

3.7 Summary

A detailed research methodology comprising laboratory investigations and

computational analyses was devised of fundamental understanding of the

characteristics and behaviour of clayey slurries. Laboratory test methods were

modified to capture the unique features of the investigated uranium leach residue,

primarily ore geology and extraction process as well as sedimentation, transition,

and consolidation zones of settling. Likewise, an image analysis approach was

developed especially for the qualitative and quantitative analysis of the hydrated

grains. This approach captured slurry constituents that were converted to

verifiable quantities. Finally, a newly defined hydraulic radius RHc,was used in the

Poiseuille’s law of water flow through porous media.

Chapter 4

79

Chapter 4 RESULTS AND DISCUSSIONS

4.1 General

This chapter first presents the geotechnical index properties. This is followed by

the solids and pore water composition results to give an understanding of

electrochemical properties of the uranium slurry. Next, the sedimentation test

results are discussed in terms of different initial solids content. Then the result

from the consolidation test is discussed in light of the material characteristics.

Finally, pore morphology measured using the CMT technology, the saturated

hydraulic conductivity calculation, and a water flow conceptual model based on

the analysis of the pore morphology is presented.

4.2 Solid-liquid Properties

4.2.1 Index Properties

Table 4.1 provides a summary of the geotechnical index properties of the

investigated slurry. The water content and the solid content of the ‘as received’

sample measured 104% and 49%, respectively. The test data are presented in

Appendix A (Table A1). The void ratio at this water content was calculated to be

2.89. The specific gravity was determined to be 2.78 (test data are presented in

Appendix A (Table A2), which is in the range for sedimentary clays (2.6 - 2.9)

and similar to the McArthur river mill feed (2.73), as reported by Khaled and

Azam (2014). The presence of clays may have influenced the specific gravity of

the Millennium ore slurry measured to be slightly higher. The grain size

Chapter 4

80

Table 4.1: Summary of geotechnical index properties of uranium slurry

Property ASTM Standard Value

As Received Condition

Water Content, w (%) D2216-10 104.1 Solids Content, s* (%) - 49.0 Void Ratio, e† - 2.89

Soil Classification

Specific Gravity, Gs D854-10 2.78 < 0.075 mm (%) D422-63 55.0 < 0.002 mm (%) D422-63 28.0 Liquid Limit, wl (%) D4318-10 59.0 Plastic Limit, wp (%) D4318-10 36.4 Plasticity Index, Ip (%) D4318-10 22.6 Activity, A = Ip/C - 0.80 USCS Symbol D2487-11 MH

*s = 1 / (1+w) †e = w * Gs

Chapter 4

81

Figure 4.1: Grain size distribution curve of uranium slurry

Chapter 4

82

distribution curve (Figure 4.1) shows that 55% of the material is finer than 0.075

mm and 28% finer than 0.002 mm (test data are given in Appendix A (Table A3)).

A liquid limit was measured to be 59% and a plastic limit was measured to be

36% (test data is presented in Appendix A (Table A4) and (Figrue A1)). This is

indicative of a moderate affinity for water adsorption (Mitchell and Soga, 2005).

The activity (A) of the soil was found to be 0.8 using the plasticity index (Ip =

23%). This is similar to illite clay mineral (A = 0.9) and the value pertains to

moderate plasticity. Overall, the slurry was classified as MH (silt with high

plasticity).


Figure 4.2 presents the XRD patterns for the investigated slurry. The bulk

diffractogram (Figure 4.2a) shows non-clay minerals associated with the distinct

quartz peaks (2 = 20.9°, 26.7°, 42.5°, 50.2°, 55.0°, and 60.2°) that originated

from the basement feldspar-rich granitoid rocks (Annesley et al., 2005). The

primary minerals present in the rock were 40% quartz, 25% plagioclase, and

20% biotite, (Cloutier, et al., 2009). The accuracy of the analysis for other

minerals in the investigated slurry was supported by the clear quartz peaks

(Mitchell and Soga, 2005). According to Cloutier et al. (2009) and Roy et al.

(2005), clinochlore peaks (2 = 6.4°, 12.4°, and 18.8°) and muscovite peaks (2

= 8.9°, 17.7°, 20.4°, 29.8°, 35.1°, and 37.9° ) are associated with alteration of the

primary minerals in the basement rock. Moreover, secondary detrital materials in

Chapter 4

83

Figure 4.2: X-ray diffraction analysis of uranium slurry: (a) random bulk sample and (b) oriented clay sample

Chapter 4

84

the basement rocks can be related to the anatase peaks (2 = 25.4°, 45.9°,

55.0°). According to Khaled and Azam, (2014) partial lime neutralization during

the extraction process could be a reason of the presence of gypsum peaks (2 =

11.7°, 20.9° 55.0°, and 62.0°) Furthermore, illite (2 = 8.9° and 17.8°),

chlorite/kaolinite (2 = 12.6° and 18.9°), and smectite (2 = 6.4°) clay mineral

formation is associate with various stages of mineral transformations.

Table 4.2 gives a summary of the solids mineralogy of the investigated

slurry. The non-clay minerals were dominated by ore geology (46% muscovite,

30% quartz, 4% clinochlore, and 2% anatase) and the extraction processes (5%

gypsum). Total clay mineral content was determined to be 15% including 8% illite,

5% chlorite, 2% kaolinite, and 0.4% smectite. A part of clay size materials (finer

than 0.002 mm) measured to be 28% in the grain size distribution analysis were

identified as clay minerals. The XRD analysis is better suited for the identification

of homogeneous, single mineral phase, and well crystallized materials.

Amorphous minerals (measured to be 13% in the sample) may have adversary

contributed to create peak overlay in the diffractogram thereby the identification

and quantification of minerals were also affected (Mitchell and Soga, 2005).

The TCEC measured 41 cmol(+)/kg that mainly comprised of Ca2+ ion (23

cmol(+)/kg ) Mg2+ ion (16 cmol(+)/kg ). The abundance of Ca2+ and Mg2+ cations

on negatively charged clay mineral surfaces can be linked to the non-marine

geological origin of the ore. The CEC data corroborate well with the clay mineral

Chapter 4

85

Table 4.2: Summary of solids composition of uranium slurry

Property Value

Minerals *(%)

Non--Clay

Muscovite (46); Quartz (30); Gypsum (5); Clinochlore (4); Anatase (2); Amorphous (13)

Clay Illite (8); Chlorite (5); Kaolinite (2); Smectite (0.4)

Exchangeable

Cations (cmol(+)/kg)

Na+ (0.4); K+ (1.9); Ca2+ (23.0); Mg2+ (15.6)

Total CEC (cmol(+)/kg) 41.0

* Accuracy ±1%

Chapter 4

86

composition of the sample that showed illite (10-40 cmol(+)/kg), chlorite (10-

40cmol(+)/kg), kaolinite (3-15 cmol(+)/kg), and smectite (80-150 cmol(+)/kg): the

ranges of CEC for the minerals are compiled from Mitchell and Soga (2005).

4.2.3 Pore Water Composition

Table 4.3 shows the pore water chemistry of the investigated slurry. The

measured pH fell in the acidic range at 3.1. According to Gomez et al. (2013),

this is a typical pH value of process water at the start of neutralization. The

presence of gypsum (5%), as reported in XRD analysis (Table 4.2) results from

the over saturation of sulfuric acid (H2SO4) rich raffinate and calcium during the

initial stages of neutralization. The EC was measured to be 17600 μS/cm. The

dominant cations were found to be Al3+ (3012 mg/L) and Mg2+ (1340 mg/L)

whereas the major anion was determined to be SO42-(22600 mg/L). The cations

are related to acid leaching of the uranium ore whereas the presence of SO42- is

attributed to H2SO4 addition during the extraction process (Gomez et al., 2013).

The low concentrations of Na+ (93 mg/L) and Cl- (43 mg/L) ions are associated

with the presence of low amounts of salts in the slurry that, in turn, is associated

with the non-marine geology of uranium ore (Ramaekers et al., 2007).

Furthermore, the presence of Na+, K+, Mg2+, Ca2+, Al3+, and Fe3+ is indicative of

clay minerals in the investigated ore. Overall, the validity of measurements were

assessed by the electrical neutrality calculated to be less than 4% (smaller is

better). The ionic strength was used to calculate the thickness of the interacting

Chapter 4

87

Table 4.3: Summary of pore liquid composition of uranium slurry

Property Value

pH 3.1

Electrical Conductivity, EC (μS/cm)

17600

Dissolved Ions (mg/L) Na+ (93); K+ (360); Mg2+ (1340); Ca2+ (390);

Al3+(3012); Fe3+(118) ; Cl-(43); SO42-(22600)

Ionic Strength (mol/L)* 1.15

Debye Length (Å) † 2.89

*

where Ci is molar concentration of ion and Zi is valence of ion

†

Chapter 4

88

diffuse double layer between adjacent colloidal particles.

For the investigated sample, this thickness was found to be 2.9 Å at the

molar concentration of 1.15 mol/L. Mitchell and Soga (2005) concluded that the

debye length (half the distance between two particles) decreases from 100 Å to

10 Å with an increase in solution concentration from 0.001 mol/L to 0.1 mol/L.

Therefore, the above-mentioned calculated value suggests a densely flocculated

microstructure with relatively small floc/aggregate sizes (Likos et al, 2000).

4.3 Settling Behaviour

4.3.1 Sedimentation

Figure 4.3 shows the settling curves plotted on an arithmetical time scale. An

increase in the initial solids content (from 25% to 50%) was associated with a

decrease in pH (from 3.43 to 3.11). This small change in pH indicates that

dilution by distilled water to change the initial condition had a negligible effect on

the pore water composition of the samples. Distinct hindered sedimentation

zones were clearly observed for the settling curves of low initial solids content

samples (s = 25%, 30%, and 35%). These settling curves gradually approached

self-weight consolidation. In contrast, the hindered sedimentation zones were

absent for the high initial solids content samples (s = 40%, 45%, and 50%) and

the settling curves showed prolonged self-weight consolidation zones. Overall,

distinct flocculation zones reported in the literature were difficult to observe due

to the high initial solids content for all of the samples.

Chapter 4

89

Figure 4.3: Settling test results in the form of interface height versus elapsed time for uranium

6.5

7.0

7.5

8.0

8.5

9.0In

terf

ace H

eig

ht

(cm

)

6.5

7.0

7.5

8.0

8.5

9.0

Inte

rface H

eig

ht

(cm

)

0 2000 4000 6000 8000 10000Time (min)

6.5

7.0

7.5

8.0

8.5

9.0

Inte

rface H

eig

ht

(cm

)

6.5

7.0

7.5

8.0

8.5

9.0

Inte

rface H

eig

ht

(cm

)

6.5

7.0

7.5

8.0

8.5

9.0

Inte

rface H

eig

ht

(cm

)

0 2000 4000 6000 8000 10000Time (min)

6.5

7.0

7.5

8.0

8.5

9.0

Inte

rface H

eig

ht

(cm

)

Y = -6.48E-04*X + 8.897

Y = -4.42E-04*X + 8.913

Y = -2.14E-04*X + 8.896

s0 = 25%

w0 = 300%

e0 = 8.34

pH = 3.34 s0 = 40%

w0 = 150%

e0 = 4.17

pH = 3.21

s0 = 45%

w0 = 122%

e0 = 3.40

pH = 3.15

s0 = 50%

w0 = 100%

e0 = 2.67

pH = 3.11

s0 = 30%

w0 = 233%

e0 = 6.49

pH = 3.29

s0 = 35%

w0 = 186%

e0 = 5.16

pH = 3.24

Chapter 4

90

Figure 4.4: Settling test results in the form of void ratio versus elapsed time for uranium slurry

Chapter 4

91

Figure 4.4 gives the settling test results in the form of void ratio versus

elapsed time on a semi-logarithmic scale. Significant change in void ratio from

the initial value was shown for the low initial solids content samples (s = 25%,

30%, and 35%) to be 1.99, 1.09, and 0.60, respectively. On contrary, small

change in void ratio was shown for the high initial solids content samples (s =

40%, 45%, and 50%) to be 0.35, 0.21, and 0.09, respectively. Overall, the data

implies that the larger particle distances in the lower initial solids content samples

resulted in a reduced friction between particles thereby causing more volume

reduction (Imai 1980). A unique em was not determined in the current

investigation because of the high initial solids contents: the lowest s = 25% in this

study as compared to the highest s = 13% in the literature (Imai, 1980).

Table 4.4 summarizes the sedimentation test initial conditions and the

calculated saturated hydraulic conductivities. The parameter Vs which is the

slope of the sedimentation curve was directly related to the saturated hydraulic

conductivity. Steeper the slope, the larger the hydraulic conductivity became. For

the low initial solids content samples (s = 25%, 30%, and 35%), the initial

saturated hydraulic conductivity (calculated using Eq. (3.4)), was found to be 3.0

x 10-6 m/s, 9.5 x 10-7 m/s and 2.5 x 10-7 m/s, respectively. These values are

validated and discussed in Section 4.4.2. Overall, the investigate slurry sample

showed the hydraulic conductivity similar to typical hard rock tailings (Bussiere,

2007) at this initial condition. For entire range of investigated initial solids content,

the saturated hydraulic conductivity was extrapolated from the best fit curve

Chapter 4

92

Table 4.4: Summary of sedimentation test initial conditions and calculated hydraulic conductivity for uranium slurry

Property Nominal Solids Content (%)

49 45 40 35 30 25

Initial condition

H0 (cm) 9.0 9.0 9.0 9.0 9.0 9.0

s0 (%) 49.0 43.5 38.6 35.0 29.5 25.0

e0 2.89 4.42 4.17 5.16 6.49 8.34

Hydraulic conductivity during the sedimentation test

Vs x 10-4(cm/min) --- --- --- 4.2 13.6 33.8

k x10-7 (m/s) --- ---- --- 2.5 9.5 29.5

Chapter 4

93

Figure 4.5: Saturated hydraulic conductivity versus void ratio relationship for uranium slurry

Chapter 4

94

obtained for the saturated hydraulic conductivity versus void ratio relationship as

shown in Figure 4.5. Figure 4.6 plots the constitutive relationships for the settling

test. The volume compressibility relationships (Figure 4.6a) show that the various

samples gained effective stress of 0.08 kPa (initial s = 25%) to 0.21 kPa (initial s

= 50%) along with a void ratio reduction from 8.3 to 2.7. These data are similar to

other comparable slurries such as sandy uranium tailings from Key lake that

generated a σ’ of up to 0.27 kPa when the void ratio changed from 8 to 4

(Bhuiyan et al., 2015) and fine oil sand tailings that generated a σ’ of up to 4.8

kPa while the void ratio reduced from 5 to 2 (Jeeravipoorvarn et al., 2009b).

Figure 4.6b presents the hydraulic conductivity relationships for the

method assuming σ’ presence using Eq. (3.5) and the method assuming σ’

absence using Eq. (3.6). The k based on the former method decreased by about

two orders of magnitude for the various samples. Although the initial k (using Eq.

3.4) plotted on the high side of the k range as expected, the arithmetic average of

the entire k (using Eq. 3.4) was found to correlate well with the initial k values of

low initial solids content samples (s = 25%, 30%, and 35%). The average k

reduced from 4.0 x 10-7 m/s (initial s = 25%) to 5.3 x 10-8 m/s (initial s = 50%)

along with a void ratio reduction from 7.5 to 2.6. The saturated hydraulic

conductivity of slurries containing clays is governed by the microstructure (Tan et

al., 1990) and, as such, the k – e relationship during self-weight settling is

different from that under loading (Imai, 1980), as given later.

4.3.2 Consolidation

Chapter 4

95

Figure 4.6: Constitutive relationships for self-weight settling test of uranium slurry: (a) volume compressibility and (b) hydraulic conductivity

Chapter 4

96

Figure 4.7 plots the consolidation test results in terms of interface height

versus elapsed time on a semi logarithmic scale. The interface height changed

from 110 mm (e = 2.67 and s = 51%) to 86 mm (e = 2.13 and s = 57%) while the

change in effective stress from 0.3 kPa to 31 kPa, respectively. The raw data are

presented in Appendix B Figure 2 and Figure 3. The total strain (height change

divided by initial height) was calculated to be 22%. This strain rate is relatively

low compared to 58% for acid mine drainage treatment sludge (Pedroni and

Aubertin, 2013), 63% for oil sand tailings (Moore et al. 2013), 42% for sandy

uranium tailings (Bhuiyan et al., 2015). Material properties as well as the initial

conditions and applied loading during testing can be primarily reasons.

Figure 4.8 plots the constitutive relationships for the consolidation test.

The volume compressibility relationship (Figure 4.8a) showed two straight-line

segments. First, the low void ratio reduction of 0.1 at low effective stress range

(from 0.25 kPa to around 2 kPa) due to apparent pre-consolidation and a rapid

void ratio decrease of 0.36 due to primary consolidation from 2 kPa to 31 kPa.

The initial part is attributed to the microstructural resistance against compression

and it sustained the effective stress up to about 2 kPa. The average compression

index under primary consolidation was found to be 0.31 (similar to kaolinite). This

apparent pre-consolidation could be correlated to the thixotropic nature of the

investigated material comprised of clay minerals and ion-rich pore water similar

to oil sand tailings (Suthaker and Scott, 1996). The test data are presented in

Appendix B (Figure B1 and B2).

Chapter 4

97

Figure 4.7: Consolidation test results of uranium slurry in the form of interface height versus elapsed time

Chapter 4

98

Figure 4.8: Constitutive relationships for consolidation test on uranium slurry: (a) volume compressibility and (b) hydraulic conductivity

Chapter 4

99

Thixotropy is the reversible property of a viscous material pertaining to the

loss in strength upon agitation and regaining the same at rest (Miller et al., 2010).

Tu et al. (2005) and Mercier et al. (2012) identified the primary reason for this

behaviour as flocculation of slurry due to the presence of about 10% clay

minerals and the sufficient concentration of divalent cations such as Ca2+ and

Mg2+ in porewater. These conditions are relevant to the investigated slurry (Table

4.2 and Table 4.3) and, as such, the slurry resisted compression at low effective

stress of up to 2 kPa. The corresponding structural void ratio (es) was found to be

2.46. A bi-power law function (e = 2.5σ-0.02: e = 2.6σ-0.1) was found to best fit

volume compressibility of the investigated slurry. The primary consolidation part

of the function, as represented by the compression index (Cc) was found to be

0.54. This value is similar to other uranium tailings such as Eliot Lake (Cc = 0.48

(Matyas et al., 1984)) and Key Lake (Cc = 0.67 (Bhuiyan et al., 2015)). The

previously published data are not presented in the figure because of variations in

the initial conditions.

The measured saturated hydraulic conductivity (Figure 4.8b) decreased by

one order of magnitude from 2.6 x 10-9 m/s (at e = 2.57) to 2.0 x 10-10 m/s (at e =

2.1) and the k – e relationship was found to follow a bi-power law function (e =

0.03k4.47: e = 0.12k32.97), similar to laterite slurries (Azam, 2011) and oil sand fine

tailings (Jeeravipoolvarn et al., 2009a). The test data are presented in Appendix

B (Figure B3). The reduction in saturated hydraulic conductivity is attributed to

compressible pore spaces (small pore throats) and high tortuosity (longer flow

Chapter 4

100

channel) of the slurry. Likewise, the scatter at high void ratios is due to the low

hydraulic gradient maintained to prevent sample boiling (Suthaker and Scott,

1996). The reduced accuracy of manually recorded readings (only possible

method), as opposed to digitally recorded volume compressibility results, partly

contributed to data scatter in this plot.

4.4 Flow Through Behaviour


Table 4.5 gives the initial and final conditions of the selected test samples. Figure

4.9 gives the CMT images of selected slurry samples: A, C, and F. The sample

holder is clearly distinguishable beyond which the images represent air of the

surrounding area. Sample A consists of a large very dark rounded object (1.5

mm size in ROI 2), several tiny dark grey and light grey objects (~0.1 mm size),

and a few small bright objects (0.5 mm size). The greyscale value reflecting the

attenuation coefficient (ease of X-ray penetration in a material based on bulk

density and atomic number) generally increases as per the following order: air <

water < solids (Ruiz de Argandona et al. 2003). Air (very dark) in the sample was

identified by comparing with that outside the sample holder whereas the solids

were identified as the brightest color in the images. Likewise, the two shades of

grey were assigned to water (dark grey) and hydrated grains (light grey). The

figure shows that grey-scale values from one sample did not apply to other

samples because of variations in source x-ray energy due to possible energy

degradation over a 17 hr test period. Samples C and F showed a comparable

Chapter 4

101

Table 4.5: Summary of settling test results

Property Sample Identification

A B C D E F

Initial test condition

Solids Content, s

(%)

25.0 29.5 35.0 38.6 43.5 49.0

Water content, w

(%)

300 239 186 159 130 104

Void ratio, e 8.34 6.49 5.16 4.17 3.40 2.89

Porosity, n 0.89 0.87 0.84 0.81 0.77 0.74

Final test condition

Solids Content, s

(%)

30.5 34.0 37.9 40.6 46.6 50.4

Water content, w

(%)

228 195 164 147 115 98

Void ratio, e 6.35 5.41 4.56 4.07 3.19 2.73

Porosity, n 0.86 0.84 0.82 0.80 0.76 0.73

Chapter 4

102

Figure 4.9: ROIs of selected slurry samples (A, C, and F)

Chapter 4

103

Figure 4.10: Grey-scale histograms corresponding to ROIs of selected slurry samples: (a) Sample A; (b) Sample B; (c) Sample F

Chapter 4

104

arrangement of objects (commensurate with their respective solids contents, that

is, denser structures for increased solids content) but different greyscale values.

As such, the above-mentioned descriptors were used in a relative sense within

each sample.

Figure 4.10 gives average grey-scale histograms for various ROIs in the

selected slurry samples. The large object (0.5 mm) in ROI 2 of sample A was

identified as air (first peak in Figure 2a-ROI 2) because the grey-scale was the

same as that external to the sample holder. The remainder of the histograms for

this sample showed three peaks representing water, hydrated grains, and solids

at average grey-scale values 98.5 ± 0.5, 126.5 ± 0.5, and 166.5 ± 0.5,

respectively. Likewise, sample C showed trimodal histograms for all ROIs with air

at 66.5 ± 0.5, hydrated grains at 81 ± 0, and water at 101.5 ± 1.5. In contrast,

sample F showed one peak for water at 94 ± 0 and one peak for solids at 116.5 ±

1.5. The test data are presented in Appendix C (from Figure C1 and Figure C12).

Figure 4.11 describes the determination of optimum threshold greyscale

values using ROI 1 from Sample A, as an example. The three peaks (Figure

4.11a) were enlarged in Figure 4.11b to differentiate between the water peak and

the hydrated grain peak and in Figure 4.11c to differentiate between the hydrated

grain peak and the solids peak. Based on normal probability distributions for

each peak, the Full Width at Half Maximum (FWHM) was determined and divided

by 2.355 to obtain the standard deviation. A normal distribution function was

Chapter 4

105

Figure 4.11: Application of threshold grey-scale value for sample with three peaks: (a) entire curve; (b) enlarged view of peak1 and peak 2; (c) enlarged view of peak 2 and peak3

Chapter 4

106

obtained for each peak from the peak voxel count (a), the peak greyscale value

(b), and the standard deviation (c) according to the following equation (Bazi, et al.,

2007):

An intersection point grey-scale value of 110 was found to be the

threshold between water (98) and hydrated grains (126) whereas a greyscale

value of 150 was to be the threshold between hydrated grains (126) and solids

(167). This procedure was applied to all of the ROIs in samples A and C. It was

found that the mixed peak (hydrated grains) consisted of 60% water and 40%

solids for both samples A and C based on the solids ratio. When this ratio

(expressed in Eq. 3.8) is converted to the water content, the value is 150%.

According to Martin (1962), the adsorbed water content shows maximum value at

the liquid limit for a given clay mineral. The adsorbed water content for illite clay

mineral at its liquid limit was found to be 125% (Fang and Daniels, 2006). A

slightly higher value is obtained because all the samples used in this

investigation have the water content exceeding the liquid limit and some marginal

free water may have been included. However, the determined ratio found to fall

in a reasonable range. The test data are presented in Appendix C (from Figure

C13 and Figure C20).

Figure 4.12 gives the determination of the optimum threshold grey-scale

Chapter 4

107

Figure 4.12: Application of threshold grey-scale value for sample with two peaks: (a) entire curve; (b) enlarged view of peak1 and peak 2

Chapter 4

108

values for the bimodal histogram of Sample F using ROI 1, as an example. The

normal distribution curve did not fit the first peak suggesting the existence of an

embedded water peak on the left and a hydrated grains peak on the right. The

above solids ratio was applied to the latter peak to determine threshold 1 (84)

between water and hydrated grains whereas threshold 2 (150) between hydrated

grains and solids was determined as before. The data obtained from the

threshold image processing (described as ambiguous and arbitrary (Hussein et al,

2015)) were validated using independently measured geotechnical properties.

Therefore, the method was also adopted for Sample F where the minimum height

approach was not applicable because of the absence of three distinct peaks. The

same reason applies to the use of average gray-scale of histogram peaks and

valleys (Ouellet et al., 2008). The test data are presented in Appendix C (from

Figure C21 and Figure C24).

Figure 4.13 compares index properties measured by geotechnical

methods and estimated through image analysis of solids content (s, weight

based parameter with the maximum value of 100%), water content (w, weight

based parameter with infinity as the maximum value), void ratio (e, volume based

parameter with infinity as the maximum value); and porosity (n, volume based

parameter with a maximum value of 100%). The data points pertain to the

various ROIs in each of the three samples. Best-fit lines were determined for

each of the index properties by minimizing the sum of squares of the offsets of

Chapter 4

109

Figure 4.13: Comparison of index properties measured by geotechnical methods and estimated through image analysis: (a) solids content; (b) water content; (c)

void ratio; and (d) porosity

Chapter 4

110

the data points from the lines. Because of the above definitions and ranges, data

trend and scatter of s corresponded inversely with those of n whereas data trend

and scatter of w was comparable to those of e. This is further corroborated by the

coefficients of linear regression (R2), which were found to be 0.95, 0.92, 0.95,

and 0.92 for s, w, e, and n, respectively. Higher R2 values are associated with

higher precision implying good repeatability of analysis.

Furthermore, the data obtained plotted closer to the line of equality with an

average value for the coefficient of the best fit lines was 0.82. This is indicating a

higher accuracy and excellent correlations between measured and estimated

properties for the proposed method within the investigated ranges of index

properties. The deviation from the line of equality is partly attributed to the fact

that pore sizes smaller than 4.3 μm were not discernible in the CMT images.

These results support the adequacy of the current statistics based thresholding

method to be applied for not only the samples depicting clear peaks for each

constituent (water, hydrated grains, and solids) such as sample A and C but also

the samples missing an independent water peak such as sample F.

Figure 4.14 presents the binary images of ROI1 from sample A, C and F

with the index properties determined by the geotechnical method denoted as a

superscript g and by the image analysis denoted as a superscript i. A grayscale

threshold value which distinguishes free water from the rest of the constituents in

the sample was selected. The pixels present in the image were assigned to

Chapter 4

111

Figure 4.14: Binary images of ROI 1 for sample A, C, and F

Chapter 4

112

Figure 4.15: Relationships between the porosities ((a) total porosity from geotechnical; (b) total porosity from image analysis; (c) free water porosity image analysis) and the pore geometrical properties

Chapter 4

113

grayscale, white (free water filled pores) or black (hydrated grains and solids)

depending on each pixel’s grayscale value. The areas occupied by white in the

images progressively decreased as the solids content determined by the

geotechnical method, sg of samples increased (sg = 30.5%, 37.9%, and 50.4%

for sample A, C, and F, respectively). These white pixels representing free water

filled pores were summed together to obtain the free water porosity, nif. This

porosity was smaller (nif = 0.52, 0.47, and 0.19 for sample A, C, and F,

respectively) than the values determined by the conventional geotechnical

method (ng = 0.84, 0.82, and 0.74 for sample A, C, and F, respectively) because

the latter method included both free water and adsorbed water. Furthermore,

identified pore areas were isolated to individual pores based on the software

algorithm to calculate average pore area and the average pore perimeter. The

volume obtained through voxel calculation was used to obtain the average pore

throat diameter. The area was then calculated.

Figure 4.15 compares pore area, pore throat area, and pore area

perimeter calculated by image analysis and various porosities such as (i) total

porosity that is combining free water and adsorbed water determined by the

geotechnical method; (ii) total porosity estimated through image analysis; (iii) free

water porosity estimated by image analysis. Best-fit lines were determined for

each set of comparisons and the corresponding coefficients of linear regression

(R2) were averaged to be 0.95. Furthermore, the pore throat area showed better

correlations (R2 = 0.99) with the total porosities determined by both geotechnical

Chapter 4

114

Figure 4.16: Schematic representations of three dimensional pore and pore throat configurations

Chapter 4

115

and image analysis methods. The pore area perimeter indicated a slightly better

correlation with the free water porosity (R2 = 0.96). Overall, all the pore

parameters proportionally related to the porosity determined either from total or

free water portions.


Figure 4.16 schematically presents a three dimensional pore configuration and

flow through conceptual model based on the images captured by CMT. Pore

area in each image slice corresponds to a two-dimensional cross section of the

three dimensional pore structures. Meandering and twisted arrangements of

pores often reduce the connectivity and increase the tortuosity (Vogel,

1997).Therefore, the only viable passages facilitating the water flow present

where a part of the detected pore area in each slice overlapped in a vertical

direction. Pore throats that are narrowing parts within pore structures determine

the maximum conduit size for any given pore. Therefore, the area of pore throat

can be a limiting factor for water flow.

Having a limiting factor for the estimation of saturated hydraulic

conductivity is similar to the empirical equation formulated by Hazen (1930).

Using D10 (mm) that is the 10th percentile grain size of material and Hazen’s

empirical coefficient C that varies from 1.0 to 1.5. The equation is given as:

One critical shortcoming of Hazen’s equation is that D10 is determined as an

Chapter 4

116

intrinsic value for a given material thereby a change in porosity or void ratio

during settling can’t be accounted for. As introduced earlier in Chapter 2, Eq.

(2.13) can partially overcome this issue because the equation uses hydraulic

radius and porosity as limiting factors. This equation is also not suitable for

estimating the saturated hydraulic conductivity of clayey materials despite

successful application to non-cohesive sands and silts. Two main reasons that

can be addressed for the ineffectiveness of this equation for such materials are

the inaccurately defined porosity and the hydraulic radius for clayey materials.

Unlike non-cohesive materials, the laboratory determined porosity for the clayey

materials dose not equate to the amount of water readily mobile in the material

due to adsorbed water. Hence the free water has to be distinguished through

image analysis and the corresponding porosity for this portion of water has to be

determined as shown in Figure 4.15. This porosity is associated with the

maximum water flow through potential for a given porous material and an

accurate tortuosity measurement is required if only this porosity is incorporated in

Eq. (3.13). The tortuosity measurement is extremely difficult because the flow

passage is connected not only vertically but also horizontally. A use of a small

sample which has finite x and y directions for the CMT test virtually precludes to

reasonably quantify tortuosity. To overcome this experimental constraint, the

tortuosity was kept at unity and partially incorporated by eliminating the pore area

that is not contributing to the water flow.

Figure 4.17 explains the calculation to obtain the hydraulic radius used in

Chapter 4

117

Figure 4.17: Hydraulic radius calculation: (a) Example 1 with pore throat diameter size is a half of the diameter of entire pore bodies; (b) Example 2 with pore throat diameter size is a quarter of the diameter of entire pore bodies;

Chapter 4

118

the proposed model. There are several classes of pores present in porous

mediums according to literature. The size definition suggested by Luxmoore

(1981) was followed in this investigation. Micropore, Mesopore, and Macropore

refer to the equivalent pore diameter of < 10 μm, 10 μm to 1000 μm, and > 1000

μm, respectively. Based on these size criteria, pores filled with free water present

in porous media can be separated into two structures as shown in Fig 4.17: (i)

pore throats that are classified in the Micropore size transport pore fluids and

directly control the hydraulic conductivity; (iii) pore spaces that are classified in

the Mesopore size and occupied by fluids but not entirely contributing to pore

fluid migration. Example 1 and 2 in Fig 4.17 shows hydraulic radius calculations

for different pore throat diameter sizes that are a half and a quarter of the

diameter of entire pore bodies, respectively. It is found that the conventional

hydraulic radius (pore body area divided by pore body perimeter) (RH1) is directly

proportional to the pore throat diameter. Contrarily, the hydraulic radius of pore

spaces that are not part of fluids transportation (RH3) is inversely proportional to

the pore throat diameter. The hydraulic radius defined for the proposed model

uses a ratio of the pore throat area (A2) to the perimeter of the entire pore body

(P1). This ratio value exactly matches with the difference in conventional

hydraulic radius and the one defined for the area not contributing to flow (RH1 –

RH3) as follows:

Chapter 4

119

The newly defined hydraulic radius expressed in Eq. (4.3) and (4.5) are further

decreasing the ratio of area and perimeter by excluding the ineffective pore

spaces for water flow. Thus the definition potentially encompasses the tortuosity

generated by the three-dimensional configuration consisting of meandering and

dead-end pore spaces. Moreover, because the suggested hydraulic radius is

taken as a ratio, spatial information of pores such as locations of pore throats

and associated tortuosity usually considered in pore-network modeling is no

longer required. Therefore, the shape factor Cs in Eq. (2.13) is reduced to a

constant value.

Figure 4.18 correlates hydraulic conductivity with index properties for use

in engineering practice. Exponential functions were found to best fit the

correlations between k and the various index properties such that R2 were 0.91

for s and n and 0.97 for w and e.

Figure 4.19 compares the estimated and the laboratory measured

hydraulic conductivities. First, the free water porosity and the conventional

hydraulic radius determined for the pores under consideration were used in Eq.

(3.11) with the tortuosity set to unity. The saturated hydraulic conductivity was

Chapter 4

120

Figure 4.18: Correlations of hydraulic conductivity with index properties

Chapter 4

121

Figure 4.19: Comparison of saturated hydraulic conductivity calculation using the proposed hydraulic radios and the conventional definition

Chapter 4

122

Figure 4.20: Comparison of saturated hydraulic conductivity measured by geotechnical methods and estimated through image analysis

Chapter 4

123

reduced from 4.7 x 10-6 m/s to 1.7 x 10-7 m/s and the plot did not agree with the

laboratory determined data. Second, the free water porosity and the newly

suggested hydraulic radius using pore throat size measurement were used again

in Eq. (3.11) with the tortuosity set to unity. Tortuosity could have been estimated

using the approach presented in Ouellet et al. (2008). However, this was not

done because of a lack of appropriate method to independently validate the

results. The saturated hydraulic conductivity was reduced from 2.9 x 10 -7 m/s to

1.8 x 10-8 m/s and the plot corresponded well with the laboratory measured data

as discussed in the earlier section. These two estimations resulted in

approximately one order of magnitude difference. This clearly contrasts the first

estimation method in which the tortuosity measurement of free water pores is

prerequisite and the second estimation method in which the tortuosity is

inessential because it is already partially incorporated in the defined hydraulic

radius.

Likewise, Figure 4.20 shows that the measured k (obtained from settling

tests using Eq. (2.17) closely matched the estimated k (pertaining to the various

ROIs in each of the three samples). The corresponding precision indicated as R2

was found to be 0.94 and accuracy indicated as the slope of best-fit line found to

be 0.7 for the investigated range of k (10-6 m/s to 10-8 m/s). Furthermore, the k

variation was found to be within a range of 1/3 order of magnitude. This means

that the definition of hydraulic radius used in the current study adequately

described the water flow mechanism through slurries because pore area outside

Chapter 4

124

of the pore throat does not contribute to water migration. Furthermore, the use of

τ = 1 in Eq. 3.13 is justified because RH is independent of the spatial distribution

of pores.

4.5 Summary

Results comprising laboratory investigations and computational analyses were

presented to develop a fundamental understanding of the characteristics and

behaviour of clayey slurries. As expected, inherent slurry characteristics (derived

from ore geology and extraction process) of the investigated clay slurry resulted

in a distinct transition zone between sedimentation and consolidation. Likewise,

the new image analysis approach identified and separated slurry constituents.

Finally, the newly defined hydraulic radius confirmed that saturated hydraulic

conductivity in the transition zone follows the Poiseuille’s law of water flow

through porous media .

Chapter 5

125

Chapter 5 CONCLUSIONS AND RECOMMENDATIONS

5.1 Summary

Knowledge of the characteristics and behavior of waste slurries is pivotal for

developing efficient extraction processes and sustainable mine waste

management strategies during operation, closure, and reclamation. This is

particularly true for clayey slurries because of their low settling and slow flow

through behaviour derived from complex solid-liquid interactions. A clayey slurry

(uranium leach residue from Saskatchewan, Canada) was selected from the

extraction process to capture the distinct slurry features at the onset of deposition.

A comprehensive laboratory investigation and computational modeling program

was enacted to investigate the characteristics and behavior of a selected

uranium ore slurry and develop fundamental understanding of flow through a

settling clayey slurry.

The main contribution of this research to industrial practice is the

geotechnical assessment of the investigated clay slurry. The slurry was found to

be flocculated under ambient conditions derived from ore geology (solid

composition) and from extraction process (water composition). More importantly,

the slurry exhibited various components of settling that are important for

developing depositional plans and determining storage capacity of the

containment facility. These data are critical for the operation, closure, and

reclamation of the new waste stream.

Chapter 5

126

The main contribution of this research to the field of geotechnical

engineering is the understanding that solid-liquid composition influences settling

of clayey slurries such that the effects are dominant during sedimentation and the

initial phase of consolidation. More importantly, the material characterization

using computed micro tomography images was found to be comparable to

conventional geotechnical tests. The conceptual model of flow through settling

clayey slurries confirms that Poiseuille’s law of water flow through porous media

is applicable to this class of materials in the transition zone between

sedimentation and consolidation.

5.2 Conclusions

The main conclusions of this research are summarized as follows:

1. The slurry 55% passing 0.075 and 28% passing 0.002 mm exhibited

moderate water adsorption capacity (wl = 59% and wp = 36%). The non-

clay minerals were primarily muscovite (46%) and quartz (30%) whereas

the clay minerals were identified as illite (8%), chlorite (5%) and kaolinite

(2%). The CEC measured 41 (cmol(+)/kg) with Ca2+ and Mg2+ as the

dominant cations. Likewise, the high EC (17600 μS/cm) and ionic strength

(0.61 mol/L) indicated a flocculated microstructure for the slurry. SO42-

(22600 mg/L) and Mg2+ (1340 mg/L) were found to be the dominant ions in

the slurry water.

2. Settling at low initial solids contents (25% to 35%) was governed by

sedimentation whereas transition was observed at high initial solids

Chapter 5

127

contents (40% to 50%). Distinct flocculation zones and a unique em were

not discernible for the investigated slurry. The average k changed from 3.0

x 10-6 m/s (initial s = 25%) to 5.3 x 10-8 m/s (initial s = 50%) along with a

void ratio reduction from 7.5 to 2.6.

3. Volume compressibility during consolidation showed apparent pre-

consolidation at low effective stress (0.3 kPa to 2 kPa) with a reduction in

void ratio from 2.6 to 2.5. This is attributed to thixotropic strength that, in

turn, is derived from slurry compositions and initial conditions. The

structural void ratio was found to be 2.46 at σ’ = 2 kPa and was followed

by a steeper slope with the void ratio reducing to 2.1 at σ’ = 31 kPa.

Likewise, the saturated hydraulic conductivity during consolidation

decreased by one order of magnitude from 2.6 x 10-9 m/s (e = 2.6) to 2.0 x

10-10 m/s (e = 2.1).

4. An image analysis method using normal distribution functions and newly

defined “solids ratio” identified and quantified three slurry constituents that

are free water, hydrated grains, and solids. This method indicated

satisfactory accuracy and precision in the calculation of geotechnical index

properties shown in the best fit regression equations with an average

value for the coefficient a was 0.81 and R2 was more than 0.90.

5. The modified definition of hydraulic radius (average pore throat area

divided by average perimeter of pore) reasonably calculated the saturated

hydraulic conductivity shown in the best fit regression equations with an

Chapter 5

128

average value for the coefficient a was 0.70 and R2 was more than 0.90.

This hydraulic radius describes water flow through clayey slurries more

realistically because pore area beyond pore throat does not contribute to

water migration. This definition is confirmed to be independent of spatial

distribution of pores and, as such, precludes the use of tortuosity in

determining hydraulic conductivity.

5.3 Recommendations

Recommendations for future research are summarized as follows:

1. Application of higher loading of up to 1000 kPa during settling is

recommended to understand the behavior of deposits at larger depths in

containment facilities. Likewise, direct measurement of solid density by x-

ray or gamma ray should be carried out to investigate the evolution of

effective stress during the settling process.

2. Pore morphology should be investigated for higher solids content samples

to capture the variation of flow paths during consolidation. For

consolidated materials, the microstructure should also be confirmed using

other techniques such as mercury intrusion porosimetry.

3. The proposed conceptual model using the newly defined hydraulic radius

should be expanded to a wide range of pore sizes existing in earthen

materials (clays, sands, rocks). Likewise, the proposed method should be

evaluated by using Kozeny-Carman equation along with measured

specific surface and the shape factor.

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129

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APPENDICES

156

APPENDICES

Appendix A

Determination of water content

Determination of void ratio

Determination of specific gravity

Hydrometer analysis

Consistency limits test

Appendix B

Consolidation test cell design

Consolidation test

Appendix C

Threshold method for Image analysis

Appendix D

Validation of the shape factor

Conversion of the viscosity

APPENDICES

157

Appendix A

In situ water content

Table A1: Results from water content determination

MLM Sample

Mass of can, g 44.9

Mass of can and slurry, g 93.15

Mass of can and dry slurry, g 68.54

Mass of dry slurry, g 23.64

Mass of water, g 24.61

Water content, % 104.1

Water content of the sample was calculated by following equation:

w(%) Mcms Mcds Mcds Mc

100

where:

w = water content (%)

Mcms = mass of moisture can and slurry

Mcds = mass of moisture can and dry slurry

Mc = mass of moisture can

APPENDICES

158

Void ratio

In situ void ratio was determined as follows:

where:

Gs = Specific gravity of the slurry

w = Water content

2.78 * 104.1= 2.89

Specific gravity

Table A2: Results from specific gravity determination

Test temperature, 20Cº Trial No.

Sample ID: MLM 1 2 3

Pychnometer and water, g, W1 706.55 679.53 697.27

Pychnometer and slurry, g, W2 755.17 726.08 746.43

Mass of dry slurry, g, Ws 76.03 72.71 76.85

Mass of equalvolume of water as the

slurry solids, g; Ww =(W1 +Ws)-W2 76.03 72.71 76.85

Specific gravity at test temperature, Gt

= Ws /Ww 2.77380518 2.779434 2.77537

Temperature correction Non Non Non

Specific gravity was obtained by average of three trials as follows:

Gs = (2.77+2.78+2.78)/3 = 2.78

APPENDICES

159

Grain size distribution

Table A3: Results from hydrometer analysis

Liquid limit

The following data is from the liquid limit tests conducted on three different

samples. The following equation was used to compute the liquid limits for three

samples:

LL wN (%)N

25

0.121

where:

LL = liquid limit,

WN(%) = moisture content, in percent, for 12.7 mm groove closure in the liquid

limit device at N (between 20 and 30) number of bows.

Hydrometer & Sieve Analysis Mass of Soil (dry) : 54.03

Sieve Mass % Passing

Date Tested: 13/06/2013 Sample Number: Millenium Leach Residual 4.0 0.00 100.00

By: Maki Sample Description: Radio active slurry 10.0 0.00 100.00

18.0 0.23 99.80

Hydrometer Type : 152 H Zero Correction : 4 Meniscus Correction : 1 40.0 0.00 95.68

Dispersing Agent : Calgon Amount used : 0.5298 70.0 0.00 68.60

100.0 0.00 62.57

Specific Gravity Gs : 2.78 CF a = .97 140.0 3.19 57.61

% Finer than #200 Sieve : 54.0 200.0 0.00 54.74

pan 54.03

0.5298

Elapsed Hydrometer Temp Corr. Hyd. Hyd. Corr. only Eff. Depth Adjusted Diameter Percentage

Date Hour:min Time (min) Reading (C) Ct Reading for meniscus L (cm) L/t K % Finer % Finer (mm) of Fine

06/13/13 9:40 0

06/13/13 9:40 0.5 50.0 20 0.00 46.0 51.0 7.9 15.8618 0.0129 81.99 44.15 0.0514 100.00

06/13/13 9:41 1 47.0 20 0.00 43.0 48.0 8.4 8.4232 0.0129 76.64 41.27 0.0374 93.48

06/13/13 9:42 2 46.0 20 0.00 42.0 47.0 8.6 4.2937 0.0129 74.86 40.31 0.0267 91.30

06/13/13 9:44 4 44.0 20 0.00 40.0 45.0 8.9 2.2289 0.0129 71.29 38.39 0.0193 86.96

06/13/13 9:48 8 42.0 20 0.00 38.0 43.0 9.2 1.1555 0.0129 67.73 36.47 0.0139 82.61

06/13/13 9:55 15 41.0 20 0.00 37.0 42.0 9.4 0.6272 0.0129 65.95 35.51 0.0102 80.43

06/13/13 10:10 30 38.0 20 0.00 34.0 39.0 9.9 0.3300 0.0129 60.60 32.63 0.0074 73.91

06/13/13 10:40 60 36.0 20 0.00 32.0 37.0 10.2 0.1705 0.0129 57.03 30.71 0.0053 69.57

06/13/13 11:40 120 33.0 20 0.00 29.0 34.0 10.7 0.0893 0.0129 51.69 27.83 0.0039 63.04

06/13/13 13:40 240 30.0 20 0.00 26.0 31.0 11.2 0.0467 0.0129 46.34 24.96 0.0028 56.52

06/13/13 16:40 420 29.0 20 0.00 25.0 30.0 11.4 0.0271 0.0129 44.56 24.00 0.0021 54.35

06/14/13 16:40 1380 24.0 20 0.00 20.0 25.0 12.2 0.0088 0.0129 35.65 19.20 0.0012 43.48

06/15/13 16:40 2820 21 20 0.00 17.0 22.0 12.7 0.0045 0.0129 30.30 16.32 0.0009 36.96

APPENDICES

160

Table A4: Results from liquid limit determination

Sample ID: MLM

Trial No. 1 2 3

Mass of Can, g 44.95 44.92 45.49

Mass of Can + Slurry, g 65.52 70.68 75.05

Mass of Can + Dry slurry, g 57.49 61.21 64.7

Mass of Water, g 12.54 16.29 19.21

Mass of Dry slurry, g 8.03 9.47 10.35

Water Content, (%) 64.0350877 58.1338244 53.8781884

Number of Blows 14 20 44

wl = -0.2925*25 + 66.287 = 58.97

Figure A1: Determination of liquid limit

Appendix B

y = -0.2925x + 66.287 R² = 0.8287

52

54

56

58

60

62

64

66

0 10 20 30 40 50

Wat

er C

on

ten

t, %

Number of Blows

APPENDICES

161

Consolidation

APPENDICES

162

Figure B1: Consolidation cell

Figure B2: Square root of time versus sample height for loading 0.26 kPa, 0.48

kPa, 0.97 kPa, and 1.94 kPa

APPENDICES

163

Figure B3: Square root of time versus sample height for loading 3.87 kPa, 7.44

kPa, 15.5 kPa, and 31.2 kPa

APPENDICES

164

Figure B4: Time versus Hydraulic conductivity for loading 0.26 kPa, 0.48 kPa,

0.97 kPa, 1.94 kPa, 3.87 kPa, 7.44 kPa, 15.5 kPa, and 31.2 kPa

Appendix C

Image Analysis

Figure C1: Greyscale histogram of ROI1from 30% solids content sample

APPENDICES

165



APPENDICES

166

Figure C4: Greyscale histogram of ROI4 from 30% solids content sample


APPENDICES

167



APPENDICES

168



APPENDICES

169



APPENDICES

170


APPENDICES

171

Figure C13: Determination of threshold greyscale for ROI 1 of s =30% sample

APPENDICES

172

Figure C14: Determination of threshold greyscale for ROI 2 of s =% sample

APPENDICES

173

Figure C15: Determination of threshold greyscale for ROI 3 of s = 30% sample

APPENDICES

174


APPENDICES

175


APPENDICES

176


APPENDICES

177


APPENDICES

178


APPENDICES

179

Figure C21: Determination of threshold greyscale for ROI 1 of s = 50%sample

APPENDICES

180


APPENDICES

181


APPENDICES

182


APPENDICES

183

Appendix D

Calculation of Cs: Shape factor

Assumptions:

1. Kozeny-Carman equation was formulated for sandy materials;

2. Hydraulic conductivities selected was within a range of the sandy

materials;

3. The average radius of sandy materials were chosen to be 50 μm (0.005

cm), 35 μm (0.0035 cm), and 20μm (0.002 cm);

4. A 10 cm diameter sample was used;

5. The dynamic viscosity at 20 degree Celsius was used.

Table D1: Calculation of flow rate

Parameter Example 1 Example 2 Example 3

k hydraulic conductivity, cm/s 1.00E-08 5.00E-09 7.00E-10

i hydraulic gradient 1.0 1.0 1.0

A

total cross-sectional area of

10 cm diameter sample, cm2 78.575 78.575 78.575

q flow rate, cm3/s 7.86E-07 3.93E-07 5.50E-08

APPENDICES

184

Table D2: Calculation of shape factor

Parameter Example 1 Example 2 Example 3

f unit weight of fluid, kN/cm2 0.000981 0.000981 0.000981

RH hydraulic radius (a/p), cm 0.0025 0.00175 0.001

r

radius of a flow channel,

cm 0.005 0.0035 0.002

a

cross-sectional area of a

flow channel, cm2 0.0000785 3.847E-05 1.256E-05

p

wetted perimeter of a flow

channel, cm 0.0314 0.02198 0.01256

μ

dinamic viscosity at 20

degree celsius, N-s/cm2 1.00E-07 1.00E-07 1.00E-07

Cs shape factor 0.16 0.34 0.45

Therefore, the shape factor can be between 0.15 and 0.45. In the manuscript,

these values have been rounded off to 0.2 to 0.5, respectively.

Conversion from dynamic viscosity to kinematic viscosity

The hydraulic conductivity equation suggested by Blair et al. (1996) is expressed

as follows:

where Cs is shape factor, f is unit weight of water (9.81 kN/m3), RH is hydraulic

radius (cm), e is void ratio, and μ is dynamic viscosity (1.002 x 10-3 Ns/m2 at

20 °C). The unit weight of water is expressed as f = ρfg (where ρf is density of

APPENDICES

185

water (1000 kg/m3) g is acceleration of gravity (9.81 m/s2)). Equation [1] can be

re-written to be:

Since the dynamic viscosity can be expressed using the kinematic viscosity,

((1.002 x 10-6 m2/s at 20 °C) as μ = ρf, equation [2] can be re-written as follows;

Equation [3] can be re-written by using porosity = e/(1+e)as follows;

where C is from Poiseuille’s equation. The Poiseuille’s equation is expressed as

follows:

where, is G is pore geometry (8 for parallel circular pore), τ is tortuosity (1 for

parallel circular pore).

Unit conversion

9.81 m/s2 = 981 cm/s2

1.002 x 10-6 m2/s = 10020 x 10-6 m2/s

The constant part (g/ ) of the Poiseuille’s equation [5] is calculated to be;

981 cm/s2 / 10020 x 10-6 m2/s = 97904.19162 cm*s -1 =8.46 x 10-9 cm*day-1

This value corresponds to the value presented in Lebron et al. (1999).

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CHARACTERIZATION AND BEHAVIOUR OF CLAYEY SLURRIES