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.
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
2.5.2.1 Theoretical Context _____________________________________________ 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
2.6.2.1 Theoretical Context _____________________________________________ 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
2.5.2.1 Theoretical Context
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
2.6.2.1 Theoretical Context
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).
3.4.2 Solid Composition
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
3.6.1 Pore Morphology
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
3.6.2 Saturated Hydraulic Conductivity
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).
4.2.2 Solid Composition
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
4.4.1 Pore Morphology
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.
4.4.2 Saturated Hydraulic Conductivity
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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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
Figure C2: Greyscale histogram of ROI2from 30% solids content sample
Figure C3: Greyscale histogram of ROI3from 30% solids content sample
APPENDICES
166
Figure C4: Greyscale histogram of ROI4 from 30% solids content sample
Figure C5: Greyscale histogram of ROI1 from 40% solids content sample
APPENDICES
167
Figure C6: Greyscale histogram of ROI2 from 40% solids content sample
Figure C7: Greyscale histogram of ROI3 from 40% solids content sample
APPENDICES
168
Figure C8: Greyscale histogram of ROI4 from 40% solids content sample
Figure C9: Greyscale histogram of ROI1 from 50% solids content sample
APPENDICES
169
Figure C10: Greyscale histogram of ROI2 from 50% solids content sample
Figure C11: Greyscale histogram of ROI3 from 50% solids content sample
APPENDICES
170
Figure C12: Greyscale histogram of ROI4 from 50% solids content sample
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
Figure C16: Determination of threshold greyscale for ROI 4 of s = 30% sample
APPENDICES
175
Figure C17: Determination of threshold greyscale for ROI 1 of s = 40% sample
APPENDICES
176
Figure C18: Determination of threshold greyscale for ROI 2 of s = 40% sample
APPENDICES
177
Figure C19: Determination of threshold greyscale for ROI 3 of s = 40% sample
APPENDICES
178
Figure C20: Determination of threshold greyscale for ROI 4 of s = 40% sample
APPENDICES
179
Figure C21: Determination of threshold greyscale for ROI 1 of s = 50%sample
APPENDICES
180
Figure C22: Determination of threshold greyscale for ROI 2 of s = 50% sample
APPENDICES
181
Figure C23: Determination of threshold greyscale for ROI 3 of s = 50% sample
APPENDICES
182
Figure C24: Determination of threshold greyscale for ROI 4 of s = 50% sample
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).