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Thirty-ninth Canadian Geotechnical Colloquium:

Unsaturated Soil Mechanics: Bridging the Gap Between

Research and Practice

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2016-0709.R1

Manuscript Type: Review

Date Submitted by the Author: 23-Aug-2017

Complete List of Authors: Siemens, Gregory; GeoEngineering Centre at Queens-RMC,

Is the invited manuscript for consideration in a Special

Issue? : N/A

Keyword: unsaturated soils, capillarity, strength, expansive soils, seepage

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

Draft

Siemens (2017) 39th Canadian Geotechnical Colloquium

THIRTY-NINTH CANADIAN GEOTECHNICAL 1

COLLOQUIUM: UNSATURATED SOIL MECHANICS: 2

BRIDGING THE GAP BETWEEN RESEARCH 3

AND PRACTICE 4

Greg A. Siemens 5

Professor and Research Director 6

GeoEngineering Centre at Queen’s-RMC 7

Department of Civil Engineering 8

Royal Military College of Canada 9

Kingston, Ontario, K7K 7B4, CANADA 10

p: +1-613-541-6000 x6396; e: [email protected] 11

ABSTRACT 12

The majority of geoengineering applications occur in the unsaturated zone, which is in the near-surface 13

region forming the connection between meteorological phenomena above and saturated ground below. 14

The key characteristic of the unsaturated zone is that water is in tension or, put another way, pore water 15

pressure is negative. Moisture content, as well as most material properties, vary spatially and temporally 16

in the unsaturated zone and coupled processes are common. In geoengineering applications in the vadose 17

zone, unsaturated soils may be present during part or all of its design life. The question is how or when 18

to consider the unsaturated soils principles in an analysis or design. Although most geoengineering 19

applications have an unsaturated component, use of unsaturated soil mechanics in practice lingers 20

behind the prolific number of publications due uncertain benefit of accounting for unsaturated effects, 21

complexity, and conservativeness among other reasons. The focus of this colloquium is to continue 22

bridging the gap by illustrating unsaturated soils principles using application-driven examples in the 23

areas of capillarity as well as flow, strength, and deformation phenomena. As principles of unsaturated 24

soils become more understood and demand increases for incorporating climate change effects in design, 25

use of unsaturated soils principles in practice will continue to increase. 26

Keywords: 27

unsaturated soils, capillarity, seepage, strength, expansive soils 28

29

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INTRODUCTION 30

The majority of geoengineering applications occur in the unsaturated, or vadose zone, which can 31

be up to hundreds of meters in depth depending on the ground profile and climate. Unsaturated soils 32

applications include foundations, excavations, and buried infrastructure (Figure 1a, Costa et al. 2003, 33

Machmer 2012, Jung et al. 2016), infiltration and landslide triggering (Figure 1b, Iverson 2000; Blatz et 34

al. 2004; Tohari et al. 2007; Cascini et al. 2010; Rahimi et al. 2010; Zhang et al. 2010; Robinson et al. 35

2016), compacted materials (Figure 1c, Siekmeier 2007), cover systems (Figure 1d, Wilson et al. 1994, 36

O’Kane et al. 1998; Aubertin et al. 2009; Dobchuk et al. 2013; Huang et al. 2015; Knidiri et al. 2016), 37

evaporation-aided mine waste consolidation (Bussiere 2007; Qi et al. 2017; Simms 2017), sampling and 38

load tests (Figure 1e, Konrad 1990; Vanapalli and Mohamed 2007; Costa et al. 2003), as well as 39

cryogenic suction processes and contaminant migration (Figure 1f, Konrad and Morgenstern 1980; 40

Lenhard and Parker 1987; Azmatch et al. 2012). The unsaturated component of these examples can be 41

broadly grouped into flow, strength, and deformation phenomena. The key characteristic of the 42

unsaturated zone is that water is in tension or, alternatively, pore water pressure is negative. Soil 43

moisture content, in turn, varies with negative pore pressure or suction. A consequence of variable 44

moisture content is that soil properties, which are relatively constant in the saturated zone, vary spatially 45

and temporally in the unsaturated zone. Unsaturated processes are often coupled, meaning they span 46

across one or more of the flow-strength-deformation groups. For example, infiltration into a slope 47

(Figure 1b) is a flow process, which is coupled with the unsaturated strength of the soil and can lead to 48

landslide triggering. Unsaturated soils, found in the near-surface region, are continually interacting with 49

the surrounding environment as they form the connection between weather systems above and saturated 50

ground below. Thus, in each of the applications in Figure 1, the unsaturated component may be present 51

during part or all of its design life. 52

The question is how or when to consider the unsaturated component in an analysis or design. 53

Unsaturated soils researchers continue to move the state-of-the-art ahead with numerous unsaturated 54

soils conferences every year. Beginning with the first issue (Hamilton 1963) and continuing with several 55

Canadian Geotechnical Colloquiums papers (Fredlund 1979; Barbour, 1998; Bussiere 2007; Simms 56

2017), the Canadian Geotechnical Journal is recognized as one of the key journals for disseminating 57

unsaturated soils research. In practice, use of unsaturated soils principles develops incrementally with 58

local expertise or in applications that have unsaturated effects at their core (e.g. cover systems or deep 59

geological repositories for spent nuclear fuel). Thus, despite numerous geoengineering applications that 60

include an unsaturated component, a gap exists between research and practice. The gap is due to a 61

number of reasons that include the perceived complicated nature of unsaturated soil mechanics. Another 62

perception that, in all cases, ignoring unsaturated effects provides additional safety in the performance of 63

a geo-structure. In some cases, if the unsaturated components are ignored in design, additional safety 64

factor may be available to the designer, which in my opinion is a reasonable approach. For example, 65

ignoring the unsaturated strength component for a foundation above the water table will underestimate 66

the strength and stiffness of the founding soil. However, in other cases, ignoring the unsaturated effects 67

can lead to inefficiencies that affect the expected performance or lead to a false conclusion of a failure 68

mechanism. For example, ignoring unsaturated soils effects in modelling transient triggering of a 69

rainfall-induced landslide. In this paper, unsaturated soils principles are presented to illustrate 70

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opportunities to broaden use of unsaturated soil mechanics. Unsaturated soils principles are illustrated 71

through application-driven examples in the areas of capillarity as well as flow, strength, and deformation 72

phenomena. 73

CAPILLARITY 74

Capillarity is a surface tension phenomenon whereby a pressure change occurs across an air-75

water interface (Lu and Likos 2004, Fredlund et al. 2012). The shape of the air-water interface and the 76

corresponding change in pressure across the interface is described by the classic Young-Laplace 77

Equation (Maxwell and Strutt 1911). Figure 2 includes three examples of capillarity: in zero gravity, in 78

capillary tubes, and on flat surfaces. Canadian astronaut Chris Hadfield is shown in Figure 2a on-board 79

the International Space Station with his hand coated in water. Water preferentially coats his hand as 80

surface tension forces dominate in zero-gravity conditions. Water also forms menisci between his 81

fingers and the direction of the surface tension forces are indicated on the figure. The angle at which 82

surface tension forces act with respect to his fingers is determined by the contact angle shown in Figure 83

2c, which displays a drop of water on horizontal and sloped surfaces. On a horizontal surface, the 84

interaction between air-water and the surface is apparent by the contact angle, α. In this case, the contact 85

angle is less than 90o, which indicates water is the wetting fluid and air is the non-wetting fluid. The 86

solid surface prefers to be in contact with water rather than air. Contact angle is also variable, as 87

illustrated in Figure 2c for the sloped surface. In the sloped case, there is a clear leading contact angle, 88

α1, and trailing contact angle, α2. Contact angle is a property that is unique to each fluid-fluid-solid 89

combination. In some cases, fluids can be wetting while in other cases fluids are wetting. For example, 90

mercury forms beads on a surface indicate air is the wetting fluid for an air-mercury-solid combination. 91

A classic example of capillarity is given in Figure 2b, which is capillary tubes of different sizes 92

placed into a container of water. Capillary forces act to draw water up into the capillary tubes to 93

different heights. The height that water is drawn up the capillary tube is a function of the radius of the 94

tube as well as the surface tension, contact angle, and density of water. Performing vertical force 95

equilibrium by resolving the weight of the water and surface tension forces, and solving for the capillary 96

rise height, h, gives the equation on Figure 2b. The smaller the radius of the tube the greater the height 97

of capillary rise. An important implication of the curved meniscus at the top of each water column is the 98

pressure difference between the air and water in the tube. The pressure difference between the air and 99

water phases also leads to the definition of matric suction (air pressure-water pressure or ua-uw). The 100

force arrows pointing upward and the concave shape of the meniscus indicate that air pressure is greater 101

than the water pressure. This is a physical representation of the Young-Laplace Equation (Maxwell and 102

Strutt 1911), which describes the pressure difference across curved surfaces. 103

In unsaturated ground, water is under the same surface tension forces as in the capillary tubes 104

with surface tension forces pulling soil grains together. For a visual example, Bozkurt et al. (2017) 105

recently measured surface tension forces between two glass spheres connected by a water bridge. Figure 106

3 is a hydrostatic ground profile showing pore pressure and degree of saturation versus elevation. The 107

profile is at hydrostatic equilibrium and no flow is occurring. At the groundwater table, pore pressure is 108

zero and varies hydrostatically above and below. Below the groundwater table, the ground is saturated 109

and degree of saturation is 100%. Moving up from the phreatic surface, three distinct zones are the 110

capillary zone, transition zone, and residual zone. In the capillary zone, degree of saturation remains at, 111

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or close to, 100%. The soil-air-water representation shows occluded bubbles, which is reflective of a 112

continuous water phase and discontinuous gas phase. From the capillary tube analogy, the height of the 113

capillary zone is reflective of the radius of the largest pores in the soil. Moving upward into the 114

transition zone, degree of saturation decreases with elevation. In this zone, the air phase becomes 115

continuous across the element. Moving upward in the transition zone, degree of saturation continues to 116

decrease until the residual zone is reached. The vertical distance from the groundwater table to the 117

residual zone (indicated on Figure 3) is soil-type dependent and ranges from a few millimeters for 118

gravels to hundreds of meters for clays. From the capillary tube analogy (Figure 2) this vertical distance 119

is related to a continuous set of pores that have a radius less than that associated with the vertical 120

distance above the groundwater table (equation on Figure 2b). Within the residual zone, Sr=0% is 121

approached asymptotically. The air phase is continuous while the water phase has become discontinuous 122

and water only coats the soil grains (since water is the wetting fluid and air is the non-wetting fluid). 123

Storage Function 124

The storage function is the fundamental relationship for unsaturated soils (Brooks and Corey 125

1964, van Genuchten 1980, Fredlund and Xing, 1994, Barbour 1998, Lu and Likos, 2004, Fredlund et al. 126

2012). Also termed the soil water characteristic curve or water retention curve amongst other names, the 127

storage function is the relationship between water content and suction as shown schematically in Figure 128

4a. The storage function provides valuable and important information of the soil. Most often associated 129

with soils, storage functions have also been reported for geosynthetics (Bouazza et al. 2006, Bathurst et 130

al. 2007, 2009; Siemens and Bathurst 2010, Beddoe et al., 2011, Siemens et al. 2012) and are used to 131

develop frozen soil relationships (Azmatch et al. 2012). The storage function is the first, and often only, 132

function that is experimentally measured in unsaturated soils. From the storage function (van Genuchten 133

1980, Fredlund and Xing, 1994) many other unsaturated soil relationships can be estimated including 134

unsaturated hydraulic conductivity (Mualem 1976, Fredlund et al. 1994, Burdine 1953, Leong and 135

Rahardjo 1997), and unsaturated strength (Vanapalli et al. 1996). 136

The storage function in Figure 4a is essentially equivalent to the vertical profile of degree of 137

saturation for the hydrostatic pore pressure profile in Figure 3. Analogous zones and soil-air-water 138

representations appear on Figure 4a to reflect this similarity. Suction, or matric suction (ua-uw) to be 139

more precise, is expressed as the difference between the air pressure (ua) and water pressure (uw). This is 140

consistent with the pressure difference across the air-water interface explained by the Young-Laplace 141

Equation and expressed physically as the curved surface within the capillary tubes in Figure 2c. For the 142

typical case of atmospheric air pressure, suction is equivalent to the absolute value of the negative pore 143

water pressure. Similar to the vertical profile (Figure 3), the magnitude of suction at which the residual 144

water content is reached varies orders of magnitude. Because of this difference, the x-axis is adjusted to 145

ensure the entire storage function can be viewed on a single graph. Coarse-grained soils have suction 146

plotted on an arithmetic axis while fine-grained soils plotted on logarithmic axis. Similar to grain-size 147

curves, logarithmic axes are used for convenience in order to be able to visualize the entire relationship. 148

An important aspect of the storage function is interpretation of material properties including the 149

air entry value and unsaturated hydraulic conductivity function from experimental data. This is 150

especially true for deformable soils, which will experience significant volumetric strains during drying 151

and cause changes to the soil’s pore-size distribution (Romero and Simms 2008). Historically, storage 152

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functions are plotted using a range of moisture content variables including degree of saturation, 153

volumetric water content, or gravimetric water content. These are mostly due to unsaturated soil 154

mechanics taking on aspects of hydrology or agriculture rather than a geo-perspective. AEV is defined 155

as the suction at which air enters the soil. Soils that experience swelling-shrinkage with changes in 156

suction are particularly susceptible to potential errors in AEV interpretation. Using gravimetric or 157

volumetric water content can cause significant errors in determining AEV or unsaturated conductivity 158

curve as changes in moisture content could reflect loss of water rather than air entering the soil. To 159

properly interpret AEV and the unsaturated hydraulic conductivity curve, moisture content must be 160

plotted in terms of degree of saturation (Fredlund et al. 2012). In deformable soils (Fredlund et al. 2011, 161

Wijaya et al. 2015, Saleh-Mbemba et al. 2016), measurement of the shrinkage curve, in addition to the 162

storage function is recommended to ensure proper interpretation of material parameters including AEV 163

and the unsaturated hydraulic conductivity curve. 164

FLOW PHENOMENA 165

Unsaturated flow phenomena commonly occur in the near surface zone with interactions 166

between above-ground weather systems. Examples include infiltration (Figure 1b), cover systems 167

(Figure 1d), water drawn towards a freezing front due to cryogenic suction (Figure 1f), and multi-phase 168

flow applications such as contaminant migration (Figure 1f). In each of these applications, the soil 169

serves as a conveyant for flow while also undergoing changes in storage during transient events. The 170

ability of soil to convey flow applies to movement of water in the near-surface area, water balance 171

calculations, and ground-climate interactions. 172

The fundamental principle that controls flow phenomena in unsaturated ground is that hydraulic 173

conductivity varies with suction as shown in Figure 4b. Saturated hydraulic conductivity alone is one of 174

the most variable material properties fluctuating more than ten orders of magnitude. In unsaturated 175

ground, the hydraulic conductivity of an individual soil also differs orders of magnitude due to changes 176

in moisture content. The shape of the unsaturated conductivity function (Figure 4b) resembles the 177

storage function (Figure 4a) with three distinct zones. In the capillary zone at suctions less than the air 178

entry value, the saturated conductivity is essentially retained. In the transition zone, hydraulic 179

conductivity decreases as pores desaturate and the water phase becomes more disconnected while the air 180

phase becomes continuous. In the residual zone, the water phase becomes discontinuous and hydraulic 181

conductivity decreases to essentially nil. The range of difference from saturated hydraulic conductivity 182

to the minimum is often greater than 4 orders of magnitude and can be greater depending on the soil 183

type. 184

That hydraulic conductivity varies orders of magnitude brings into question the validity of the 185

flow laws for saturated ground. Researchers found that D’arcy’s law (D’Arcy 1856) and Bernoulli’s law 186

apply, however, the process for solving the flow equation becomes more complicated. In saturated 187

ground, the differential equation for flow reduces to the Laplace differential equation, which can be 188

solved graphically. For unsaturated flow, the assumptions of isotropic and homogeneous are invalidated. 189

Therefore, a numerical solution is often used, which may take the form of finite element or finite 190

difference methods. With the advent of numerous groundwater flow software, steady-state unsaturated 191

flow problems can be solved relatively quickly using numerical solutions. 192

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Unsaturated flow phenomena impact all the applications in Figure 1 making its understanding 193

vital for application. Ever more powerful computers and software make solving steady-state unsaturated 194

flow problems possible with relative ease, however, care must be taken to appreciate the underlying 195

assumptions and inputs. Unsaturated flow phenomena will be presented in this section in order to 196

illustrate where appropriate assumptions can be made to obtain a suitable answer and where detailed soil 197

information is necessary. The three applications are steady-state vertical flow, steady-state seepage in a 198

dam, and infiltration in homogeneous and layered ground. The applications will illustrate the 199

consequences of making poor assumptions in an analysis and the implications of those consequences. 200

Steady-State Flow Phenomena 201

Illustrative example #1: Determination of vertical flow direction in unsaturated ground 202

The first example illustrates the driving gradient for flow in unsaturated ground. Figure 5a plots 203

two gravimetric moisture content profiles and the question for both profiles is whether flow is upward or 204

downward. In both profiles (Figure 5a), gravimetric water content increases nonlinearly with depth and a 205

constant value is obtained at 5m depth. An initial temptation is to interpret the direction of flow as 206

following the moisture content gradient or that the both profiles show downward flow due to gravity. 207

However, D’arcy’s law and Bernoulli’s law still hold in unsaturated ground and, therefore, water flows 208

due an energy (i.e. total head) gradient. The equation for total head (Figure 5c) includes both elevation 209

head and pressure head. Thus the determination of direction of flow requires knowledge of the storage 210

function. Figure 5b plots the storage function in terms of gravimetric water content versus both matric 211

suction and matric suction head. 212

In order to properly determine the direction of flow, Bernoulli’s equation (Figure 5c) is 213

employed. A datum is set at 5m depth in order to assess the elevation head of each moisture content 214

measurement. Then the storage function (Figure 5b), is used to calculate the pressure head for each 215

gravimetric water content measurement. The moisture content measurements are plotted on the storage 216

function (ignoring hysteresis) and the matric suction head for each measurement is indicated on Figure 217

5b. Finally, the total head profile can be calculated and plotted in Figure 5c. Despite seemingly 218

comparable moisture content profiles, opposing flow gradients (one up and one down) are indicated by 219

the total head gradients. This example illustrates the principle that unsaturated flow still follows 220

Bernoulli’s equation, with flow from high total head to low total head. 221

Illustrative example #2: Unconfined flow through an earth dam 222

The second example illustrates where assuming a storage function is sufficient to obtain a 223

realistic solution to a flow problem. Terzaghi (1943) used seepage through a dam as an example of 224

where unsaturated principles can be applied. A similar example, given in Figure 6, is an earthen dam 225

with 2H:1V slopes and 2m of freeboard to retain a 10m high water reservoir. A 9m wide toe drain is 226

located on the downstream side of the dam. The solutions provided on Figure 6 include a graphical 227

solution, a finite element method solution which makes an incorrect assumption, and a finite element 228

method solution that employs a sensible unsaturated hydraulic conductivity assumption to obtain an 229

appropriate solution. 230

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The graphical solution is given in Figure 6a and a summary of the flow calculations is given on 231

the figure. In order to draw the flownet, an assumption about the water table is made. The water table is 232

assumed to be a no-flow boundary and the unsaturated component of flow is zero. This is indicated on 233

Figure 6a as K=0 in the unsaturated zone and K=Ksat in the saturated zone. Flow of 144 L/d/m of dam 234

was calculated using the flownet solution and a Ksat=10-6 m/s. 235

A second solution is shown in Figure 6b, which illustrates an incorrect, or ‘black box’, approach 236

to finite element modelling. With some effort, flow calculations can be performed using software, 237

however, proper care is required even for straightforward problems. In the case displayed in Figure 6b 238

the saturated hydraulic conductivity has been applied to the entire domain, which is indicated on the 239

figure as K=Ksat above and below the water table. This assumption could be made to be ‘conservative’ 240

or by mistake. Comparing the flow calculations for Figure 6a and 6b indicate they are significantly 241

different. Assuming that the entire domain has saturated conductivity increases the total flow to 227 242

L/d/m with 86 L/d/m being the unsaturated component. The flow below the water table (141 L/d/m) is 243

comparable to the flow net (144 L/d/m). Therefore, the issue is with the unsaturated component, which 244

is too high. 245

A third solution, which sensibly accounts for the unsaturated component of flow, is shown in 246

Figure 6c. In this case, the unsaturated hydraulic conductivity curve was assumed using ‘stock’ storage 247

function from within the software. The only input required is a saturated hydraulic conductivity and the 248

soil type. The solution, shown in Figure 6c, shows the total head contours are similar to Figure 6b. 249

However, the flow calculations are significantly different. Flow below the water table is principally 250

equivalent (141 versus 142 L/d/m) while the unsaturated component is just 13 L/d/m compared with 86 251

L/d/m in the ‘black box’ solution. 252

The most representative solution for estimating unconfined flow within a homogeneous earthen 253

dam can be made using a finite element model solution with an assumed unsaturated conductivity 254

function (Figure 6c). The flownet solution ignored the unsaturated component of flow and 255

underestimated flow by 10%. The ‘black box’ solution which applied saturated hydraulic conductivity to 256

the entire domain overestimated flow by 40% and the unsaturated component of flow by 500%. For 257

cases in which the saturated conductivity is known, assuming the unsaturated conductivity function is 258

normally acceptable for steady-state problems. In these applications, the impact of the unsaturated 259

conductivity function serves to decrease in conductivity above the water table. With some practice, 260

steady-state problems can be solved relatively quickly. Sensitivity analyses can also be performed to get 261

a sense of the impact of uncertainties in the geometry, material properties, and boundary conditions. 262

Transient Flow Phenomena 263

Transient unsaturated flow phenomena are inherently more complicated compared with steady-264

state and require a higher level of material property measurements. For example, in cover systems 265

(Figure 1d, Wilson et al. 1994, O’Kane et al. 1998; Aubertin et al. 2009; Dobchuk et al. 2013; Huang et 266

al. 2015; Knidiri et al. 2016) transient analysis allows for consideration of soil-weather interactions, 267

which are coupled problems that include heat transfer, vapour flow, and liquid flow, to calculate 268

evaporation from the soil surface (Bitelli et al. 2008; Lehman et al. 2008; Or et al. 2013). In this section, 269

transient flow phenomena are illustrated using unsaturated transparent soil. An unsaturated transparent 270

soil experiment is shown in Figure 7a, which is a series of digital photos of infiltration in a layered 271

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profile. Transparent soil is formed by matching the refractive indices of a soil and pore fluid and several 272

combinations of transparent soil are found in the literature (Iskander et al. 2015). Saturated transparent 273

soil allows for direct observation from within the soil mass of deformations, strains and soil-structure 274

interaction rather then at the boundary of an experiment. Unsaturated transparent soil takes this concept 275

in another direction (Peters et al. 2011). Observations in unsaturated experiments are often limited by the 276

number of measurement devices that can be located within an experimental apparatus. A nominal 277

number of discrete measurement points are normally included to measure pore pressure, suction, and/or 278

moisture content. Unsaturated transparent soil, combined with digital image analysis, allows for 279

measurement of degree of saturation to the millimeter resolution, which is orders of magnitude more 280

data than can be obtained from discrete measurements. 281

To illustrate transient moisture migration in a heterogeneous profile, a transparent infiltration 282

experiment is shown in Figure 7a with a fine layer between two coarse layers. A 10cm high pond was 283

placed at the surface and the wetting front descends through the profile. Digital images were collected 284

every 5s in this experiment and a select number are shown in the figure. The wetting front is clearly 285

visible and is indicated by the black arrow. As the wetting front reaches the fine layer, ponding occurs, 286

the soil above the fine layer changes to a darker colour associated with an increase in saturation. In the 287

final photo, ponding is complete and the wetting front continues to descend through the fine layer. These 288

images visually illustrate how moisture migration is affected by a relatively thin finer layer. The finer 289

layer serves as a bottleneck to the system and causes saturation above as well as development of positive 290

pore pressure. 291

Transparent soil allows for clear identification of the wetting front and measurement of the 292

degree of saturation within the profile at high spatial and temporal resolution. Each digital image is 293

processed by normalizing the image intensity between an image of a dry profile (white) and a saturated 294

profile (black) to calculate the normalized intensity, IN at the pixel scale. The calibration curve plotted in 295

Figure 7b is used to convert normalized intensity to degree of saturation. On the plot are calibration 296

points as well as a predicted curve. At IN=0, the soil is dry and IN=1, degree of saturation is 100%. At 297

90%, discrete air bubbles are visible while at lower saturations the soil visually lightens continually until 298

its dry. Details on the digital image process can be found in Peters et al. (2011) and Sills et al. (2016). 299

Transparent soil used at RMC is formed from fused quartz and comes in two types, termed the coarse 300

and fine gradations (Figure 7c). Both gradations are uniform sands with D10 equal to 0.75mm and 301

0.13mm respectively. The saturated conductivity of the two gradations differ by less than one order of 302

magnitude. 303

Impact of heterogeneities on infiltration 304

To quantitatively illustrate the impact of minor heterogeneities on unsaturated processes, detailed 305

results from two infiltration experiments are plotted in Figure 8 including degree of saturation profiles 306

during the two experiments, wetting front location versus time, and pore pressure profiles from the 307

beginning and end of the experiments. The only difference between the two experiments is the 120mm 308

fine layer placed at 510mm depth below the surface. The D10 of the finer layer is just 0.62mm less than 309

the coarse layers. The water table is located a 180mm elevation and a 10cm pond is placed on the 310

surface at the beginning of the experiment. The uniform profile experiment shows the dry degree of 311

saturation profile to start and the wetting front starting to descend at time=0s. As the wetting front 312

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descends the soil increases Sr behind the wetting front and the experiment is completed at 380s. The 313

wetting front versus time (Figure 8c) shows the wetting front descending linearly from the surface down 314

to the water table. The initial and final pore pressure results show the initial vertical suction profile 315

which then becomes a linear decrease in pore pressure from the 10cm pond at the surface to 0kPa at the 316

water table. 317

Infiltration in a layered profile shows the impact of a fine layer with D10 differing just 0.62mm 318

between the two gradations. Prior to the wetting front reaching the fine layer, the experimental results 319

are identical in terms of the change in saturation and the wetting front descent rate. As the wetting front 320

reaches the fine layer, the wetting front slows down significantly (Figure 8c). The wetting front 321

continues to descend at a slower constant rate below the top of the fine layer until the water table is 322

reached at the end of the test. The wetting front encountering the fine layer causes a ponding above the 323

top of the fine layer and a hydrostatic pore pressure profile occurs (Figure 8d). The pore pressure 324

dissipates across the fine layer and is essentially 0 kPa in the lower coarse layer. 325

Small heterogeneities affect the mobility of the wetting front, infiltration rate, and pore pressure 326

response during infiltration. In the field, small differences in grain-size leading to a layered profile often 327

occur naturally or during construction. Comparing the degree of saturation profiles at the end of 328

infiltration (last profiles on Figure 8a and 8b) shows they are identical above the fine layer in the 329

uniform and layered experiments. The wetting front also descends at the same rate until the sharp change 330

when the fine layer is reached. Below the fine layer, the wetting front moves 4-times slower compared 331

with the uniform profile. From a flow perspective, the fine layer serves as a bottleneck which reduces 332

the transmissive capacity of the system. The pore pressure response at the end of the test is also 333

significantly different. Pore pressure in the uniform coarse profile decreases from the 10cm pond at the 334

surface to 0kPa at the water table (Figure 8d). In the layered experiment, a hydrostatic profile occurs 335

above the fine layer with the initial suction dissipated below the fine layer. These experiments illustrate 336

the impact of a thin and minor heterogeneity on infiltration. The fine gradation layer is just, 120mm 337

thick and the D10 is only 0.62mm different. However, the fine layer caused important differences to the 338

pore pressure response and water balance calculations. 339

In the steady-state examples given above, estimations of the unsaturated functions were adequate 340

to model the results. However, in transient applications, the unsaturated functions have a more 341

significant role in the results. The two experiments plotted in Figure 8 were modelled using the finite 342

element method (Siemens et al. 2014) and the results are plotted on Figure 8c and 8d. The storage 343

functions and unsaturated conductivity functions were measured for coarse and fine gradations. The 344

results match the model values throughout the experiments, however, the both the experiments and 345

numerical simulations require experience to obtain reliable results. If infiltration rate is the most 346

important consideration, another option is to use Green-Ampt model (Green and Ampt 1911), which 347

gives the infiltration rate and wetting front location (Siemens et al. 2013). With proper calibration of the 348

Green-Ampt parameters and knowledge of the conductivity of the transmissive zone these models are 349

options depending on the requirements of the application. 350

Flow Phenomena Summary 351

Flow phenomena impact most geotechnical applications that include an unsaturated component. 352

Applications in unsaturated ground (Figure 1) are inherently connected to the weather systems above 353

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ground and therefore will interact hydraulically. Flow mechanisms in unsaturated ground are impacted 354

by the hydraulic conductivity function which varies with suction. This section illustrated that the driving 355

energy for flow follows Bernoulli’s law, showed how reasonable assumptions can be made for steady-356

state applications, and demonstrated the influence that small heterogeneities have on transient 357

unsaturated flow. 358

STRENGTH PHENOMENA 359

Geotechnical applications that include an unsaturated strength component include foundations 360

(Figure 1a), buried infrastructure (Figure 1a), landslides (Figure 1b), compacted construction materials 361

(Figure 1c), and pile and plate load tests (Figure 1e). For these type of applications located in the vadose 362

zone, a component of their performance is dependent on unsaturated soil principles. Within the 363

unsaturated zone, strength is a function of suction. Commonly found evidence of unsaturated strength 364

principles are sand castles constructed from a coarse-grained (also termed cohesionless) soils as depicted 365

on Figure 9. If a coarse-grained soil is dry (Sr=0) or saturated (Sr=1), the maximum slope the soil is 366

stable at is the angle of repose or angle of internal friction. However, if the soil is unsaturated it is stable 367

at steeper slopes, which allows for creation of impressive structures such as the one shown in Figure 9. 368

In an unsaturated state, surface tension forces act at the granular level to increase the normal stress 369

between particles. In this framework, the friction angle of the soil remains constant while the apparent 370

cohesion intercept is affected by suction. Figure 9 shows a Mohr-Coulomb strength envelope for 371

saturated and unsaturated soils. For saturated and dry soils (Sr=1 and Sr=0), apparent cohesion is nil and 372

the strength envelope is dependent only on the friction angle of the soil. For unsaturated soils, an 373

apparent cohesion term elevates the strength envelope vertically. The amount of apparent cohesion is 374

related to the storage function. The apparent cohesion intercept increases through the capillary zone and 375

transition zone and decreases in the residual zone (Vanapalli et al. 1996, Lu and Likos 2004, Fredlund et 376

al. 2012). 377

All soils in the vadose zone have an unsaturated component of strength associated with apparent 378

cohesion. In practice, the unsaturated component is infrequently counted on in design due to its inherent 379

transient nature. In this section, the focus is placed on examples in which ignoring unsaturated strength 380

would have led to the wrong answer/development of an application. An interesting historical example of 381

unsaturated soil strength as well as the effect of suction on plate load experiments are examined. 382

Historical Example 383

An historical application of unsaturated soil mechanics is illustrated in Figure 10a, which is a 384

wall painting from a tomb in southeastern Egypt (Newberry 1895). The wall painting shows a statue on 385

a sled being dragged over the sandy desert. The application of unsaturated soil mechanics is shown by 386

the person adding water to the ground directly in front of the sled. Once thought to be a ceremonial act, 387

he is actually using unsaturated principles to minimize interface friction between the sand and the 388

bottom of the sled. 389

In order to test this hypothesis, Fall et al. (2014) performed a set of experiments to examine the 390

influence of moisture content on interface friction. The experiment (plotted in Figure 10b as Load versus 391

Displacement) consisted of placing a mass on top of a 11x7.5cm sled and pulling it across a sandy 392

material prepared at specified water contents. The results (Figure 10b) show that an initial stiff response 393

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transitions to one where load remains constant with displacement. The volumetric moisture content of 394

each experiment is noted on Figure 10b. The authors observed that when the sand was dry or at high 395

moisture content the sled sank into the ground and plowed sand out of the way. Between these two 396

extreme moisture contents, the sled sank less into the soil and less plowing occurred. Figure 10b 397

indicates that when the soil is dry or saturated the effort to pull the sled across the sand is high compared 398

with a minimal load for VWC=5%. At VWC=5%, for this particular sandy material, the strength of the 399

material is maximized and the load to pull the sled is minimized. 400

The unsaturated soil principle illustrated in Figure 9 is displayed with this historical application. 401

Figure 9 shows that apparent cohesion is a function of saturation. At Sr=100% or Sr=0%, strength 402

reduces to the saturated value, which from an interface-friction perspective, led to plowing of the sled 403

through the sand and an increase in pulling load. At VWC=5%, the soil strength was maximized, the 404

sled slid on top of the sand and the pulling load was minimized. The Egyptians wanted to maximize 405

speed and mobility for transport of statues and construction materials. Therefore, minimizing the 406

interface friction between the sled and the ground allowed for more efficient transport. In a dry desert 407

environment, the near-surface sand would be at a moisture content less than this optimal value. Thus the 408

person on the front of the sled wetting up the surficial sand would temporarily increase the sand strength 409

and minimize pulling effort. From Figure 10b a 30% reduction in pulling load was found for the 410

optimized moisture content compared with both dry and wetter sand. Thus an 30% efficiency was 411

gained by taking advantage of unsaturated principles. 412

Plate Load Tests 413

The effect of suction on unsaturated soil strength can be important in back analysis of failures as 414

well as interpretation of insitu tests. Understanding the impact of suction on the unsaturated strength 415

envelope can significantly impact interpretation of the failure mechanism. To understand the 416

significance of suction on surface loads, Vanapalli and Mohamed (2007) performed a series of 417

laboratory experiments where they applied a vertical pressure to the surface of a soil formed at specified 418

moisture contents. The experiments were performed in a 90x90x75cm (width x length x height) 419

reinforced box and the loading surface was 10x10cm. The soil is characterized as a sandy-gravel with 420

the storage function plotted in Figure 11a. The soil has an AEV of 3 kPa (~30 cm) and its residual 421

saturation is obtained at a suction of just 8 kPa (~80 cm). The friction angle of the soil is φ’=39o. 422

The question is, what impact could 6kPa suction have on the failure load. The four plate load 423

experiments were performed at suctions of 0, 2, 4, and 6kPa with the results plotted in Figure 11b. The 424

results show that the applied stress-settlement curves differ due to the suction. In each test a peak stress 425

is obtained followed by some decrease for the lower suction tests. A stiffer response to the load is 426

notable for the unsaturated experiments. A less stiff response and a lower peak stress is apparent for the 427

test performed at 0 kPa suction (i.e. saturated). The peak value increases with increasing suction over the 428

range of tests performed. At just 6kPa suction, the peak load capacity increases 7-fold compared with 429

the saturated test. 430

Practical implications can be drawn from these tests. The only difference in the plate load 431

experiments was the moisture content of the soil. Reducing the moisture content increases suction and, 432

in turn, increases the apparent cohesion intercept of the failure envelope (Figure 9). The implication for 433

interpreting plate load tests in the field is the need to measure moisture content in the zone of influence. 434

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Any variation in moisture content will have a corresponding effect on the strength of the soil. In the 435

experiments presented in Figure 11, the degree of saturation varied from 58-100% and had a 7-fold 436

effect on the peak capacity of the load test. 437

Strength Phenomena Summary 438

Unsaturated soils experience an increase in apparent cohesion associated with capillary forces 439

acting at the granular scale. However, owing to the inherent transient nature moisture migration within 440

the unsaturated zone, apparent cohesion is also a transient. In analysis of failures, and insitu tests 441

knowledge of unsaturated strength principles is recommended in order to correctly identify the 442

governing mechanisms. 443

DEFORMATION PHENOMENA 444

Deformation phenomena associated with unsaturated soils often coincide with a change in the 445

environmental conditions that alter the moisture regime. The key characteristic with respect to 446

deformation phenomena is that unsaturated soils can experience volumetric strains due to fluctuations in 447

both stress and moisture content (i.e. suction). Volumetric deformations associated with stress are 448

perhaps more intuitive compared with deformations associated with moisture fluctuations. Classic 449

examples of volumetric deformations associated with moisture changes are expansive soils and 450

collapsible soils. Expansive soils respond to wetting and drying cycles with significant volumetric 451

swelling and shrinkage as displayed on Figure 12 due to their clay mineralogy. Collapsible soils are 452

recently deposited or altered soils, which have a high void ratio, high sensitivity, and low inter-particle 453

bonding. In contrast to expansive soils, collapsible soils respond to wetting by subsiding or 454

hydroconsolidating with significant settlement (Clemence and Finbarr, 1981; Basma and Erdil 1992; 455

Rogers et al. 1994; Houston et al. 2001). Problems associated with collapsible soils include identifying 456

and characterizing them during a site investigation, predicting the magnitude of wetting, quantitative 457

predictions of collapse strains, and selecting design or mitigation alternatives (Houston et al. 2001). In 458

this section, the main principles of unsaturated soil deformation phenomena associated with wetting-459

drying of expansive clay soils are illustrated and a conceptual framework for swelling potential is 460

presented. 461

The most well-known soils that encounter deformations associated with moisture fluctuations are 462

expansive soils. The most susceptible structures to expansive soil effects are lightly loaded infrastructure 463

such as shallow foundations (Figure 12a, Domaschuk 1986). The American Society of Civil Engineers 464

report that expansive soils cause owners more financial loss than the combined effect of hurricanes, 465

earthquakes, and tornadoes. For reference Hurricane Sandy caused approximately $65.6 billion of 466

damage (Wikipedia). In the basement schematic (Figure 12a), a combination of events induces both 467

swelling and shrinkage, which leads to damaging differential displacements. Prior to construction often a 468

vegetative layer is removed. The vegetative layer provides an elevated suction environment through the 469

root systems, which uptake moisture from the ground. Once the vegetative layer is removed and the area 470

covered, the soil beneath the house experiences a suction decrease as the house cuts off direct access to 471

the ground surface. The soil swells and the house heaves in response to the decrease in suction. Adjacent 472

to the house, a shrinkage scenario ensues as a large tree is planted and the root systems descend deep 473

below the ground in the area next to the foundation. A growing tree continually requires more moisture 474

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from the ground, which comes from its roots and leads to an increase in suction around the perimeter 475

foundation. Owing to the increasing suction, the soil shrinks in response. The overall effect of the 476

swelling under the center of the house and the shrinkage on the periphery is differential settlements and 477

cracking of the basement. The damaging cost to owners is worsened as they often occur to personal 478

dwellings and few options may be apparent, which leads to extreme actions. The photograph in Figure 479

12b shows an example of extreme actions with basement walls being removed from a house, which were 480

then replaced along with the foundation (Siemens 2007). 481

To illustrate the magnitude of volumetric strains that can occur in expansive soils, digital images 482

from a shrinkage experiment and a swelling experiment are given in Figure 12d and 12e. In the 483

shrinkage experiment (Figure 12d), the test begins with an initially saturated sample. The specimen is 484

initially located within a test ring to provide confinement, which is later removed once separation 485

between the ring and the specimen occurs. The specimen dries in the low humidity laboratory 486

environment and shrinks. After 8 days, the specimen shrinks 75% of its initial volume. The suction-487

volumetric strain path for the shrinkage experiment is illustrated in Figure 12c, which is a constitutive 488

model for volumetric strains in unsaturated soil for both matric suction and net normal stress. Initially 489

saturated, the specimen is at 0 kPa matric suction. As evaporation of the pore water occurs, matric 490

suction increases and the soil shrinks in response. In the swelling experiment (Figure 12e), an 491

unsaturated expansive soil is given access to water through filter paper strips in contact with a water 492

reservoir (Lim and Siemens 2013). The initially unsaturated sample takes on water and swells in 493

response. After 10 days, the soil swells to -59.4% volumetric strain. Figure 12c plots the volumetric 494

strain-matric suction path, which is followed during the swelling experiment. The specimen is initially 495

unsaturated and at elevated suction. As the specimen is given access to water, matric suction decreases 496

and the sample swells in response. 497

Unifying Concept of Swelling Potential 498

Owing to the cost of damage to infrastructure constructed in expansive soils as well as their 499

importance for use as environmental barriers (i.e. landfill liners), much research has sought to 500

characterize the swelling potential of expansive soils. Swelling potential is measured in the laboratory 501

(ASTM D4546) and also estimated from index properties (Komine and Ogata 2003; Prakash and 502

Sridharan 2004; Cui et al. 2012; Ito and Azam 2013). Concepts for analysis and prediction of 503

infrastructure constructed in expansive soil are based on moisture content changes, suction, or 504

empirically based (Fredlund 1983; Briaud et al. 2003; Houston et al. 2011; Vanapalli and Lu 2012; 505

Puppala et al. 2014). Owing to the number of continuing resources and publications associated with 506

expansive soils, the research and practice communities are still in need of a practical methodology to 507

assess the effect of swelling potential to infrastructure. 508

Swell Equilibrium Limit Concept 509

A unifying concept for swelling potential is illustrated in Figure 13a using the application of a 510

retaining wall. The retaining wall is constructed on swelling ground and expansive soil is also used as 511

backfill material. An extended infiltration event occurs to induce wetting conditions to the system. 512

During wetting, swelling potential can be satisfied by a combination of volumetric expansion and 513

swelling-induced stresses, which depend on the boundary conditions during wetting. Three cases are 514

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illustrated in Figure 13a and their stress-volume paths plotted in Figure 13b in terms of specific volume 515

(V=e+1) versus mean stress (p=(σ1+σ2+σ3)/3). The three cases are unconfined swelling, swelling under 516

the foundation and swelling adjacent to the retaining wall. For the first case, in front of the retaining wall 517

swelling occurs under unconfined conditions like the laboratory experiment in Figure 12e. In Figure 518

13b, the stress-volume path begins at zero stress and moves vertically upward until the swelling 519

potential is satisfied. The second case for swelling is under the foundation. In this case the expansive soil 520

is subjected to an elevated stress level prior to the infiltration event, which serves to attenuate the 521

magnitude of swelling compared with the unconfined case. In Figure 13b, the stress-volume path begins 522

at an elevated stress level and moves vertically upward until the swelling potential is satisfied. The third 523

case for swelling is adjacent to the retaining wall. In this case, volumetric confinement is provided by 524

the retaining wall, which restricts expansion. Thus swelling potential is satisfied by swelling-induced 525

stresses during wetting. From a stress-volume perspective, the soil state begins at a location associated 526

with the stress level equal to the overburden stress and a volume equivalent to the end of construction. 527

During wetting, the stress-volume path is sloped upward to the right as expansion is limited by the 528

existence of the stiff retaining wall. At equilibrium, all three soil elements’ swelling potential have been 529

satisfied and their end-points are on the Swelling Equilibrium Limit (SEL, Siemens and Blatz 2009). 530

Measurement of Swelling Equilibrium Limit 531

The SEL is unique for each soil and is measured experimentally with a series of swelling 532

experiments such as those presented in Figure 13b. The experimental methodology (Siemens and Blatz 533

2007, Lim and Siemens 2013) consists of bringing identically prepared unsaturated specimens to defined 534

initial conditions and then wetting under idealized boundary conditions (Figure 13b). Results from three 535

triaxial swelling experiments to define a SEL are plotted on Figure 13b. In each test, the specimen is 536

brought to an initial stress condition and then given access to water. During the swelling phase, 537

controlled boundary conditions define the stress-volume path followed during the test. In Figure 13b 538

each test was brought to an initial stress state of 250 kPa and then the swelling phase was initiated. The 539

three boundary conditions applied during the tests were constant mean stress (CMS, vertical path), 540

constant stiffness (CS, upward sloping path), and constant volume (CV, horizontal path). The constant 541

mean stress-volume path is equivalent to the soil swelling under the foundation in Figure 13a as the 542

initial total stress is maintained during the swelling phase. When subjected to a constant mean stress, 543

swelling potential is satisfied by volumetric expansion. The constant stiffness stress-volume path is an 544

idealized representation of swelling adjacent to the retaining wall (Figure 13b). In the experiment, the 545

soil swells against a linear-elastic spring boundary condition. The third swelling test is constant volume, 546

in which swelling potential is satisfied entirely with swelling-induced stresses. The initial volume is 547

maintained constant during swelling and a horizontal path is followed during swelling. At the end of 548

each test, swelling potential is satisfied and the soil state lies on the SEL. 549

The unifying concept of swelling potential is illustrated for three soils in Figure 13c-e, which 550

include their SELs and unsaturated isotropic compression lines. The SEL is defined by fitting a 551

logarithmic curve to the end of swelling test points as shown in Figure 13c-e for bentonite-sand buffer, 552

Bearpaw clay, and Lake Agassiz clay. The triaxial swelling experiments shown in Figure 13b have their 553

end of swelling test states plotted in Figure 13c for reference. Also on SEL plots are shown the isotropic 554

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compression line on which each of the swelling tests was initiated. The area between the SEL and the 555

isotropic compression line is the swelling potential for each soil. The swelling potential is at a maximum 556

at zero stress and decreases with increasing stress. The isotropic compression curve and SEL converge at 557

higher stresses where the confining stress overcomes the swelling potential of the expansive soil. 558

Use of Swell Equilibrium Limit 559

Practical use of SEL concept relies on knowing the initial stress and volume states of a soil and 560

the boundary conditions during swelling. For a house foundation or a retaining wall these are defined for 561

constant mean stress areas and strategies are being developed for more complex cases (Lim 2014). Finite 562

element modelling of foundations (Siemens and Blatz 2008) have shown the potential for analysis tools. 563

The question arises whether SELs can only be defined in the laboratory or whether they can be estimated 564

from readily measured material properties as has been used in other analyses (Komine and Ogata 2003; 565

Prakash and Sridharan 2004; Cui et al. 2012; Ito and Azam 2013). Lim and Siemens (2016) showed that 566

SELs can be estimated from liquid limit, free swell potential, plasticity index, and initial specific 567

volume. The process involved fitting SEL equation parameters (VSEL=A+Bln(p)) to the material 568

properties for the soils as plotted in Figure 14a-b for liquid limit. In the plots SEL parameter ‘A’ 569

increases with increasing liquid limit while SEL parameter ‘B’ decreases. Parameter ‘A’ is the y-570

intercept of the SEL equation at zero mean stress while ‘B’ is related to the curvature. In both plots 571

Figure 14a and Figure 14b linear fits are provide although, in the future, non-linear fits may be justified 572

when the database size is increased. Using the predicted values from Figure 14a-b the SEL for Regina 573

clay was estimated based on its liquid limit of 76% (Fredlund 1975). The resulting SEL is plotted 574

alongside experimental data in Figure 14c and the results are comparable. 575

Deformation Phenomena Summary 576

Expansive soils display most distinctly that volumetric deformations in unsaturated soils are 577

induced by changes in suction. Due to this susceptibility, expansive soils annually cause similar 578

financial loss as the combined effect of hurricanes, earthquakes, and tornadoes (ASCE). The SEL 579

provides a conceptual framework to analyze and predict swelling behaviour and the ability to predict 580

SELs from index properties gives more encouragement to its use. Future research is directed at 581

development of a practical analysis tool. 582

SUMMARY 583

Unsaturated soils are found throughout nature in the vadose zone and form the connection 584

between above ground meteorological systems and saturated ground below. Geoengineering applications 585

in the vadose zone include an unsaturated component during some or all of their design lives (Figure 1). 586

Use of unsaturated principles is increasing in practice owing to knowledge accessibility, appreciation of 587

unsaturated effects on soil behavior, and increase in computing capabilities to incorporate unsaturated 588

relationships. This paper serves to make unsaturated soil mechanics more accessible and broaden their 589

use in practice. More and more designs are asked to incorporate climate change effects to predict 590

performance decades into the future. Incorporating climate change effects into design, will only serve to 591

increase the use of unsaturated soil mechanics in practice. 592

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ACKNOWLEDGEMENTS 593

The author is very grateful to the Canadian Foundation for Geotechnique and the Colloquium 594

Selection Committee for the honour of giving the Colloquium Lecture and opportunity to prepare this 595

manuscript. Contributions from current and past collaborators and graduate students have made this 596

work possible. Collaborators that have contributed to research on unsaturated soils from within the 597

GeoEngineering Centre at Queen’s-RMC including Richard Bathurst, Ryley Beddoe, Richard 598

Brachman, Kerry Rowe, and Andy Take and as well as graduate students: Pedram Abootalebi, John 599

Kingswood, Stephen Laporte, Bee Fong Lim, Jesse McCaw, Chris Oldroyd, Stephen Peters, Suzanne 600

Powell, Lee-Ann Sills, and Bardia Tabiatnejad. Funding from Natural Sciences and Engineering 601

Research Council, Nuclear Waste Management Organization, Royal Military College of Canada, and 602

Canada’s Department of National Defence is gratefully acknowledged. 603

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NOTATION 604 o degrees 605

A, B SEL equation parameters 606

AEV air entry value 607

CMS constant mean stress 608

CS constant stiffness 609

CV constant volume 610

c’’ apparent cohesion 611

d day 612

D10 10% passing 613

e void ratio 614

FEM finite element model 615

h height 616

h capillary rise 617

he elevation head 618

hp pressure head 619

ht total head 620

IN normalized pixel intensity 621

K hydraulic conductivity 622

Ksat saturated hydraulic conductivity 623

L liter 624

l length 625

m meter 626

627

P horizontal load 628

p mean stress 629

q applied stress 630

r capillary tube radius 631

S settlement 632

SEL Swelling Equilibrium Limit 633

Sr degree of saturation 634

Ts surface tension 635

ua air pressure 636

ua-uw matric suction 637

uw water pressure 638

V specific volume, e+1 639

w width 640

w gravimetric water content 641

α contact angle 642

γw unit weight of water 643

εv volumetric strain 644

∆ displacement 645

ρw density of water 646

φ’ friction angle 647

σ1, σ2, σ3 principal stresses 648

τ shear strength649

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REFERENCES 650

ASTM. 2003. Standard test methods for one-dimensional swell or settlement potential of cohesive soils. 651

ASTM standard D4546. American Society for Testing and Materials (ASTM), West 652

Conshoshocken, Pa. 653

Aubertin, M., Cifuentes, E., Apithy, S.A., Bussiere, B. Molson, J. and Chapuis, R.P. 2009. Analyses of 654

water diversion along inclined covers with capillary barrier effects. Canadian Geotechnical 655

Journal, 46(10): 1146-1164. 656

Azmatch, T.F., Sego, D.C., Arenson, L.U. and Biggar, K.W. 2012. Using soil freezing characteristic 657

curve to estimate the hydraulic conductivity function of partially frozen soils. Cold Regions 658

Science and Technology. 83-84: 103-109. 659

Barbour, S.L. 1998. Nineteenth Canadian Geotechnical Colloquium: The soil-water characteristic curve: 660

a historical perspective. Canadian Geotechnical Journal, 35:5 873-894. 661

Basma, A.A. and Erdil, R.T. 1992. Evaluation and control of collapsible soils. Journal of Geotechnical 662

Engineering. 118(10): 1491-1504. 663

Bathurst, R.J., Ho, A.F., and Siemens, G.A. 2007. A column apparatus for investigation of 1-D 664

unsaturated-saturated response of sand-geotextile systems. ASTM Geotechnical Testing Journal. 665

30(6): 433-441[doi: 10.1520/GTJ100954]. 666

Bathurst, R.J., Siemens, G.A. and Ho, A.F. 2009. Experimental investigation of infiltration ponding in 667

one-dimensional sand-geotextile columns. Geosynthetics International, 16(3): 158-172 [doi: 668

10.1680/gein.2009.16.3.158]. 669

Beddoe, R.A., Take, W.A. and Rowe, R.K. 2011. Water-retention behavior of geosynthetic clay liners. 670

ASCE Journal of Geotechnical & Geoenvironmental Engineering, 137(11): 1028-1038. 671

Bittelli, M., Ventura, F., Campbell, G.S., Snyder, R., Gallegati, F., and Pisa, P. 2008. Coupling of heat, 672

water vapor, and liquid water fluxes to compute evaporation in bare soils. J. Hydrol., 362: 191–673

205. 674

Blatz, J.A., Ferreira, N.J., and Graham, J. 2004. Effects of near-surface environmental conditions on 675

instability of an unsaturated soil slope. Canadian Geotechnical Journal, 41: 1111–1126. 676

Bouazza, A., Zornberg, J.G., McCartney, J.S. and Nahlawi, H. 2006. Significance of unsaturated 677

behaviour of geotextiles in earthen structures, Australian Geomechanics, 41(3): 133-142. 678

Bozkurt, M.B., Fratta, D., and Likos, W.J. 2017. Capillary forces between equally sized moving glass 679

beads: an experimental study. Canadian Geotechnical Journal. 10pp. Available at: 680

http:dx.doi.org/10.1139/cgj-2016-0213. Accessed 15 August 2017. 681

Briaud, J.L., Zhang, X., and Moon, S. 2003. Shrink test–water content method for shrink and swell 682

predictions. Journal of Geotechnical & Geoenvironmental Engineering, 129(7): 590-600. 683

Brooks, R.H., and Corey, A.T., 1964, Hydraulic properties of porous media: Hydrology Papers,. 684

Colorado State University, 24 p. 685

Page 18 of 37



Draft


Burdine, N.T. 1953, Relative permeability calculations from pore-size distribution data, Petr. 686

Trans., Inst. Mining Metall. Eng. 198: 71-77. 687

Bussiere, B., 2007. Colloquium 2004: Hydrogeotechnical properties of hard rock tailings from metal 688

mines and emerging geoenvironmental disposal approaches. Canadian Geotechnical Journal, 44: 689

1019–1052. 690

Cascini, L., Cuomo, S., Pastor, M. and Sorbino, G. 2010. Modeling of Rainfall-Induced Shallow 691

Landslides of the Flow-Type. J. Geotech. Geoenviron. Eng., 136(1): 85-98 692

Clemence, S. P., and Finbarr, A. O., 1981. Design considerations for collapsible soils. Journal of Soil 693

Mechanics and Foundation Engineering, GT3, 107: 305–317. 694

Costa, Y.D., Cintra, J.C., and Zornberg, J.G. 2003. Influence of matric suction on the results of plate 695

load tests performed on a lateritic soil deposit. ASTM Geotechnical Testing Journal. 26(2): 1-9. 696

Cui, S., Zhang, H. and Zhang, M. 2012. Swelling characteristics of compacted GMZ bentonite–sand 697

mixtures as a buffer/backfill material in China. Engineering Geology, 141-142: 65-73. 698

D’Arcy, H, 1856, Les fontaines publiques de la Ville de Dijon, Dalmont, Paris, Victor Dalmont. 699

Dobchuk, B., Nichol, C., Wilson, G.W., and Aubertin., M. 2013. Evaluation of a single-layer 700

desulphurized tailings cover. Canadian Geotechnical Journal, 50(7): 777-792. 701

Domaschuk, L. 1986. Is your house suffering? University of Manitoba, Department of Civil 702

Engineering, ISBN 0921267002, 18pp. 703

Fall, A., Weber, B., Pakpour, M., Lenoir, N., Shahidzadeh, J., Fiscina, C., Wagner, C., and Bonn, D. 704

2014. Sliding friction on wet and dry sand. Physical Review Letters, 112:17, 175502, 4 pp. 705

Fredlund, D.G. 1975. Engineering properties of expansive clays. In Proceedings of the Seminar on 706

Shallow Foundations on Expansive Clays, Regina, Saskatchewan, 27-28 October 1975, pp. 1-58. 707

Fredlund, D.G. 1979. Second Canadian Geotechnical Colloquium: Appropriate concepts and technology 708

for unsaturated soils. Canadian Geotechnical Journal, 16: 121-139. 709

Fredlund, D.G. 1983. Prediction of ground movements in swelling clays. In Proceedings of the 31st 710

Annual Soil Mechanics and Foundation Engineering Conference, Earle Brown Centre, 711

University of Minnesota, Minneapolis, Minnesota, 1 February 1983, pp. 1-48. 712

Fredlund, D.G., Rahardjo, H., and Fredlund, M.D. 2012. Unsaturated soil mechanics in engineering 713

practice. John Wiley & Sons, Hoboken New Jersey, 926 pp. 714

Fredlund, D.G., Stone, J., Stianson, J., and Sedgwick, A. 2011. Determination of water storage and 715

permeability functions for oil sands tailings. Proceedings Tailings and Mine Waste 2011, 716

Vancouver B.C., 6-9 November 2011, 15 pp. 717

Fredlund, D.G., Xing, A., 1994. Equations for the soil-water characteristics curve. Canadian 718

Geotechnical Journal 31(4): 521–532. 719

Page 19 of 37



Draft


Fredlund, D.G., Xing, A. and Huang, S. 1994. Predicting the permeability function for unsaturated soils 720

using the soil-water characteristic curve. Canadian Geotechnical Journal. 31(4): 533-546. 721

Green, W. H., and G. A, Ampt, 1911, Studies on Soil Physics, J. Agric. Sci. 4(1): 1-24. 722

Hamilton, J.J. 1963. Volume changes in undisturbed clay profiles in Western Canada. Canadian 723

Geotechnical Journal. 1(1): 27-42. 724

Houston, S., Dye, H., Zapata, C., Walsh, K., and Houston, W. 2011. Study of expansive soils and 725

residential foundations on expansive soils in Arizona. Journal of Performance of Constructed 726

Facilities, 25(1): 31-44. 727

Houston, S.L., Houston, W.N., Zapata, C.E., and Lawrence, C. 2001. Geotechnical engineering practice 728

for collapsible soils. Geotechnical and Geological Engineering. 19: 333-355. 729

Huang, M., Barbour, S.L., and Carey, S.K. 2015. The impact of reclamation cover depth on the 730

performance of reclaimed shale overburden at an oil sands mine in Northern Alberta, Canada. 731

Hydrological Processes, 29: 2840–2854. 732

Iskander, M., R. Bathurst, and M. Omidvar. 2015. Past, present, and future of transparent soils. Geotech. 733

Test. J. 38(5): 557-573. doi:10.1520/GTJ20150079. 734

Ito, M. and Azam, S. 2013. Engineering properties of a vertisolic expansive soil deposit. Engineering 735

Geology, 152(1): 10-16. 736

Iverson, R.M. 2000. Landslide triggering by rain infiltration. Water Resources Research. 36(7): 1897-737

1910. 738

Jung, J.K., O’Rourke, T.D., and Argyrou, C. 2016. Multi-directional force-displacement response of 739

underground pipe in sand. Canadian Geotechnical Journal. 53: 1763-1781. 740

Knidiri, J., Bussiere, B., Hakkou, R., Bosse, B., Maqsoud, A., and Benzaazoua, M. 2016. 741

Hydrogeological behaviour of an inclined store-and-release cover experimental cell made with 742

phosphate mine waste. Canadian Geotechnical Journal, In press and available online, [doi: 743

10.1139/cgh-2015-0530]. 744

Komine, H. and Ogata, N. 1994. Experimental study on swelling characteristics of compacted bentonite. 745

Canadian Geotechnical Journal, 31(4): 478-490. 746

Konrad, J. 1990. Sampling of Saturated and Unsaturated Sands by Freezing. Geotechnical Testing 747

Journal, 13(2): 88-96. 748

Konrad, J.-M. and Morgenstern, N.R. 1980. A mechanistic theory of ice lens formation in fine-grained 749

soils. Canadian Geotechnical Journal. 17: 473-486. 750

Lehman, P., Assouline, S., and Or, D. 2008. Characteristic lengths affecting evaporative drying of 751

porous media. Physical Review. 77: 056309, 16 pp. 752

Lenhard, R.J., and J.C. Parker. 1987. Measurement and prediction of saturation-pressure relationships in 753

three-phase porous media systems. J. Contam. Hydrol. 1: 407-424. 754

Page 20 of 37



Draft


Leong, E.C. and Rahardjo, H. 1997. Permeability functions for unsaturated soils. Journal of 755

Geotechnical and Geoenvironmental Engineering, 123(12): 1118-1126. 756

Lim, B.F. 2014. Advanced testing and a numerical tool for swell equilibrium limit of expansive soils. 757

Ph.D. thesis, Department of Civil Engineering, Royal Military College of Canada, Kingston, ON. 758

Lim, B.F. and Siemens, G.A. 2013. An unconfined swelling test for clayey soils that incorporates 759

digital image correlation. ASTM Geotechnical Testing Journal. 36(6): 823-833 760

[doi: 10.1520/GTJ20120220]. 761

Lim, B.F. and Siemens, G.A. 2016. A unifying framework for modeling swelling soil behaviour. 762

Canadian Geotechnical Journal 53(9): 1495-1509 [doi: 10.1139/cgj-2015-0049]. 763

Lu, N. and Likos, W.J. 2004. Unsaturated soil mechanics. Wiley, 584 pages 764

Machmer, B. 2012. Understanding the behavior of a pile foundation in unsaturated soils subjected to 765

lateral loading. Masters of Science Thesis, Civil Engineering, Clemson University, 184 pp. 766

Maxwell, J.C., Strutt, J.W. 1911. Capillary Action. Encyclopædia Britannica. 5 (11th ed.) 256–275 767

(https://en.wikipedia.org/wiki/Young–Laplace_equation. Accessed 15 August 2017). 768

Mualem, Y. (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media, 769

Water Resources Research, 12(3): 513–522. 770

Newberry, P.E. 1895. El Bersheh: The Tomb of Tehuti-Hetep. Egypt Exploration Fund, London, Vol. 1. 771

O’Kane, M., Wilson, G.W., and Barbour, S.L. 1998. Instrumentation and monitoring of an engineered 772

soil cover system for mine waste rock. Canadian Geotechnical Journal, 35: 828-846. 773

Or, D., Lehmann, P., Shahraeeni, E., and Shokrim, N. 2013. Advances in Soil Evaporation Physics—A 774

Review. Vadose Zone Journal. 12(4): 16 pp. 775

Peters, S.B., Siemens, G., Take, W.A. 2011. Characterization of transparent soil for unsaturated 776

applications. ASTM Geotechnical Testing Journal Special Issue on Innovations in Characterizing 777

the Mechanical and Hydrological Properties of Unsaturated Soil, 34(5): 445-456. 778

[doi: 10.1520/GTJ103580]. 779

Powell, J.S., Siemens, G.A., Take, W.A. and Remenda, V.H. 2013. Characterizing the swell potential 780

of Bearpaw Shale. Engineering Geology. 158: 89-97 [doi: 10.1016/j.enggeo.2013.03.006]. 781

Prakash, K. and Sridharan, A. 2004. Free swell ratio and clay mineralogy of fine-grained soils. 782

Geotechnical Testing Journal, 27(2): 1-6. 783

Puppala, A.J., Manosuthikij, T. and Chittoori, B.C.S. 2014. Swell and shrinkage strain prediction models 784

for expansive clays. Engineering Geology, 168: 1-8. 785

Qi, S., Simms, P., Vanapalli, S. and Soleimani, S. 2017. Piecewise-Linear Formulation of Coupled 786

Large-Strain Consolidation and Unsaturated Flow. II: Testing and Performance. J. Geotech. 787

Geoenviron. Eng., 143(7): 04017019. 788

Page 21 of 37



Draft


Rahimi, A., Rahardjo, H., and Leong, E.-C. 2010. Effect of hydraulic properties of soil on rainfall-789

induced slope failure. Engineering Geology 114: 135–143. 790

Robinson, J.D., Vahedifard, F., and AghaKouchak, A. 2016. Rainfall-triggered slope instabilities under 791

a changing climate: comparative study using historical and projected precipitation extremes. Can. 792

Geotech. J. in press, doi: 10.1139/cgj-2015-0602. 793

Rogers, C.D.F., Dijkstra, T.A., Smalley, I.J. 1994. Hydroconsolidation and subsidence of loess: Studies 794

from China, Russia, North America and Europe: In memory of Jan Sajgalik. Engineering 795

Geology. 37(2): 83-113 796

Romero, E. and Simms, P. 2008. Microstructure Investigation in Unsaturated Soils: A Review with 797

Special Attention to Contribution of Mercury Intrusion Porosimetry and Environmental Scanning 798

Electron Microscopy. Geotechnical and Geological Engineering. 26(6): 705-727. 799

Saleh-Mbemba, F. Aubertin, M., and Mbonimpa, M. and Li, L. 2016. Experimental characterization of 800

the shrinkage and water retention behaviour of tailings from hard rock mines. Geotechnical and 801

Geological Engineering, 34(1): 251-266. doi: 10.1007/s10706-015-9942-0 802

Siekmeier, J. 2007. Implementation of unsaturated soil mechanics during pavement construction QA. 803

Geo-Strata —Geo Institute of ASCE, 2011, 15(1): pg. 36,38,40,43. 804

Siemens, G.A. 2007. Replacement of a 30-year-old shallow foundation on swelling soil: a case study. 805

2nd Canadian Young Geotechnical Engineers and Geoscientists Conference (cYGEGC), 806

Ganonoque, Ontario, 25-27 October 2007, CD Proceedings. 807

Siemens, G.A. and Bathurst, R.J. 2010. Numerical parametric investigation of infiltration in one-808

dimensional sand-geotextile columns. Geotextiles and Geomembranes. 28: 460-476 809

[doi:10.1016/j.geotexmem.20 09.12.0 09]. 810

Siemens, G.A. and Blatz, J.A. 2007. A triaxial apparatus for applying liquid infiltration with controlled 811

boundary conditions and internal suction measurement. Journal of Geotechnical and 812

Geoenvironmental Engineering. 133(6): 748-752 [doi: 10.1061/(ASCE)1090-0241]. 813

Siemens, G.A. and Blatz, J.A. 2008. Numerical modelling of shallow foundations on swelling clay soil 814

using the swelling equilibrium limit. 1st European Conference on Unsaturated Soils (E-815

UNSAT), Durham, United Kingdom, 2-5 July 2008, 855-860. 816

Siemens, G.A. and Blatz, J.A. 2009. Evaluation of the influence of boundary confinement on the 817

behaviour of unsaturated swelling clay soils. Canadian Geotechnical Journal. 46(3): 339-356 818

[doi: 10.1139/T08-125]. 819

Siemens, G.A., Peters, S.B. and Take, W.A. 2013. Comparison of confined and unconfined infiltration 820

in transparent porous media. Water Resources Research. 49: 851-863 [doi: 821

10.1002/wrcr.20101]. 822

Siemens, G.A., Take, W.A. and Peters, S.B. 2014. Physical and numerical modeling of infiltration 823

including consideration of the pore air phase. Canadian Geotechnical Journal – Thematic Issue 824

on Unsaturated Soils. 51: 1475–1487 [doi: 10.1139/cgj-2013-0447]. 825

Page 22 of 37



Draft


Siemens, G., Take, W.A., Rowe, R.K.R. and Brachman, R.W.I. 2012. Numerical investigation of 826

transient hydration of unsaturated geosynthetic clay liners. Geosynthetics International, 19(3): 827

232-251 [doi: 10.1680/gein.12.00011]. 828

Sills, L-A.S., Mumford, K.G., and Siemens, G.A. 2016. Quantification of fluid saturations in transparent 829

porous media. In press, Vadose Zone Journal, (October 2016, #VZJ-2016-06-0052-ORA). 830

Simms, P. 2017. 2013 Colloquium of the Canadian Geotechnical Society: Geotechnical and 831

geoenvironmental behaviour of high-density tailings. Canadian Geotechnical Journal, 54: 455–832

468. 833

Terzaghi, K. 1943. Theoretical soil mechanics. John Wiley & Sons. 528 pp. 834

Tohari, A., Nishigaki, M., and Komatsu, M. 2007. Laboratory Rainfall-Induced Slope Failure with 835

Moisture Content Measurement. J. Geotech. Geoenviron. Eng., 133(5): 575-587 836

van Genuchten, M.Th., 1980, A Closed-Form Equation for Predicting the Hydraulic Conductivity of 837

Unsaturated Soils, Soil Science Society of America Journal, 44: 892-898 838

Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. and Clifton, A.W. 1996. Model for the prediction of shear 839

strength with respect to soil suction. Canadian Geotechnical Journal, 33: 379-392. 840

Vanapalli, S.K. and Lu, L. 2012. A state-of-the art review of 1-D heave prediction methods for 841

expansive soils. International Journal of Geotechnical Engineering, 6: 15-41. 842

Vanapalli, S.K. and Mohamed, F.M.O. 2007. Bearing capacity of model footings in unsaturated soils. 843

Experimental Unsaturated Soil Mechanics, Ed. T. Schanz. 112: 483-493. 844

Wijaya, M., Leong, E.C. and Rahardjo, H. 2015. Effect of shrinkage on air-entry value of soils. Soils 845

and Foundations. 55(1): 166-180. 846

Wilson, G.W., Fredlund, D.G. and Barbour, S.L. 1994. Coupled soil-atmosphere modelling for soil 847

evaporation. Canadian Geotechnical Journal 31: 151-161. 848

Zhang, L.L., Zhang, J., Zhang, L.M., and Tang, W.H. 2011. Stability analysis of rainfall-induced slope 849

failure: a review. Proceedings of the Institution of Civil Engineers Geotechnical Engineering 164 850

Issue GE5, 299–316. 851

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Draft

Precipitation

Potential slip surface

Infiltration

Water content (%)

Dry

den

sity

(M

g/m

3)

Sr=100%

Protectedarea

Precipitation

Evaporation

Deflected infiltration

a) Foundations, tunnels, and excavations b) Infiltration and landslide triggering

c) Compacted materials for construction d) Cover systems

e) Sampling, pile and plate load tests

Descending freezing front

Water drawn upto freezing front

f) Cryogenic suction and contaminant migration

Figure 1. Geotechnical applications that include an unsaturated component: a) Foundations, tunnels and excavations, b) Infiltration and landslide triggering, c) Construction materials for construction, d) Cover systems, e) Sampling, pile and plate load tests, and f) Cryogenic suction and contaminant migration.

Road

Reinforced wall

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DraftTs

Ts

a)

b)

c)

Figure 2. Capillarity: a) Capillarity in zero gravity (image captured from Canada Space Agency video https://www.youtube.com/watch?v=o8TssbmY-GM accessed 29 November 2016), b) Capillary rise in tubes, and b) Contact angle on flat and sloped surfaces.

Page 25 of 37



Draft

Pore pressureNegative (-) (+) Positive Degree of saturation, Sr

Residual zone

Transition zone

Capillary zone

Saturated ground

Soiltype

GravelSand SiltClay

Capillary rise~mm~cm ~m

100m+

Figure 3. Hydrostatic ground profile highlighting soil type effect on capillary rise.

1m

Hydrostaticpore pressure

profile

Page 26 of 37



DraftSuction

Deg

ree

of s

atura

tion

, Sr

(%)

Ksat

Residualwater

content

Suction

Hyd

raulic

con

duct

ivity

>104

100%

Air entryvalue, AEV

a)

b)

Figure 4. Typical a) Storage function and b) unsaturated hydraulic conductivity function.

Capillaryzone

Transitionzone

Residualzone

Soil-typedependent

Page 27 of 37



Draft0 10 20 30 40

0

1

2

3

4

5

6

Dep

th (

m)

Gravimetric water content, w (%)

0.1 1 10 1000

10

20

30

40

Gra

vim

etric

wat

er c

onte

nt, w

(%

)

Matric suction, ua-uw (kPa)

a)

b)

Pressure head, hp (m)-0.01 -0.1 -1 -10

Flow directionup or down?

-10-8 -6 -4 -2 0 2 4Total head, ht (m)

c)

5

4

3

2

1

0

-1

Ele

vatio

n he

ad, h

e (m

)

Datum

Upw

ard flow

Dow

nw

ard flo

w

Figure 5. Vertical flow illustrative example: a) Two gravimetric water content profiles, b) Storage functionwith gravimetric water content values added to interpret suction, and c) Total head profiles with flow direction indicated.

ht = he + hphp =-(ua-uw)

22

22

Page 28 of 37



DraftK=Ksat

K=Ksat

K=Ksat

K=f(Sr)

K=0

10 86 4

2

108 6

42

K=Ksat

SaturatedUnsaturatedTotal

HydcondKsat

f(Sr)

FlowL/d/m14213155


HydcondKsat

Ksat

FlowL/d/m14186227


HydcondKsat

0

FlowL/d/m1440144

a)

b)

c)

Figure 6. Steady-state flow comparison for: a) traditional flownet, b) FEMassuming saturated conductivity in unsaturated zone, and c) FEM with assumed unsaturated conductivity function.

%1000

%6238

%928

No flow

Page 29 of 37



Draft

a)

b)

Sr=1.0

Sr=0.9

Sr=0.7

Sr=0.6

Sr=00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sat

ura

tion,

Sr

(−)

Normalized intensity, IN (−)

Predicted

Peterset al.2011

Sillset al.2016

CoarseFine

Coarse and Fine

c)

Figure 7. Transparent soil for unsaturated applications showing: a) Series of photos from an infiltration test in a layered system (Siemens et al. 2014), b) Calibration curve for image analysis (after Sills et al. 2016, and c) Grain-size distributions for coarse and fine transparent soils (after Siemens et al. 2014).

Coarse FineD10 (mm) 0.75 0.13

Page 30 of 37



Draft

Wettingfront

Degree of saturation, Sr

Initialprofile

Coarse

a)

b)

c) d)

Figure 8. Impact of heterogeneities on infiltration; a) Saturation profiles from open infiltration in coarse transparent soil, b) Saturation profiles from open infiltration in layered soil profile, c) Elevation of wetting front versus time, and d) Equilibrium pore pressure profile (after Siemens et al. 2014).

Additional pore pressure

Page 31 of 37



Draft

Figure 9. Unsaturated strength phenomena illustrating variation in

apparent cohesion with degree of saturation.

Page 32 of 37



Draft

0 5 10 15 200

2

4

6

Load

, P (

N)

Displacement, Δ (mm)

VWC

7.4%Dry

1.5%

5%

Sand with variablemoisture content

P

Δ

Mass

Real-time moisture control

30% reduction

in load

P

a)

b)

Figure 10. a) Wall painting from tomb of Djehutihotep in southeastern Egypt (after Newberry 1895), and b) Interface friction experiments plotted as load versus displacement.

Page 33 of 37



Draft0 2 4 6 8 10

0

20

40

60

80

100

Sat

ura

tion,

Sr

(%)

Suction, ua−uw (kPa)

0 5 10 15 20 25 300

200

400

600

800

1000

App

lied

stre

ss, q

(kP

a)

Settlement, S (mm)

q

Sand =39o

ua-uw=6 kPa

ua-uw=4 kPa

ua-uw=2 kPa

ua-uw=0 kPa

a)

b)

Figure 11. Effect of suction on plate load experiments in sand (afterVanapalli and Mohamed 2007) showing a) Storage function and b) Applied stress versus settlement.

7-foldincreasefor 6 kPasuction

suction range from 0-6kPa

saturationrange from ~60-100%

Page 34 of 37



Draft

Shrinkage due to

increase inmatric suction

Swelling due to decrease in matric suction

Figure 12. Unsaturated deformation phenomena including a) Combined effects of heave and shrinkage on a residential structure (after Domaschuk 1986), b) Removal of basement walls from a residential structure affected byexpansive soils, c) Constitutive model for volumetric strains due to changes in suction and net normal stress, d) Shrinkage experiment, and e) Free swell experiment (after Lim and Siemens 2013).

a)

b)

c)

d)

e)

Page 35 of 37



DraftMean stress, p (kPa)

0 500 1000 1500 2000

Spe

cific

vol

ume,

V

1.4

1.6

1.8

2.0

2.2

2.4

b) Bentonite-sand-buffer

Constant mean stress (CMS)

Constant stiffness (CS)

Constant volume (CV)

Figure 13. Swelling Equilibrium Limit results: a) Retaining wall constructed inexpansive soil illustrating swelling conditions, b) Swelling paths and experiments for bentonite-sand-buffer, and SEL summary plots for c) Bentonite-sand-buffer, d) Bearpaw clay, and e) Lake Agassiz clay (after Lim and Siemens 2016).

a) Retaining wall constructed in expansive soil

Unconfined swelling

SEL

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Draft

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