Unsaturated Soil Mechanics

FOREWORD xvii

PREFACE xix

SYMBOLS xxi

INTRODUCTION 1

1 STATE OF UNSATURATED SOIL 3

1.1 Unsaturated Soil Phenomena 3

1.1.1 Definition of Unsaturated Soil Mechanics 3

1.1.2 Interdisciplinary Nature of Unsaturated Soil Mechanics 4

1.1.3 Classification of Unsaturated Soil Phenomena 6

1.2 Scope and Organization of Book 8

1.2.1 Chapter Structure 8

1.2.2 Geomechanics and Geo-environmental Tracks 11

1.3 Unsaturated Soil in Nature and Practice 12

1.3.1 Unsaturated Soil in Hydrologic Cycle 12

1.3.2 Global Extent of Climatic Factors 12

1.3.3 Unsaturated Zone and Soil Formation 13

1.3.4 Unsaturated Soil in Engineering Practice 18

1.4 Moisture, Pore Pressure, and Stress Profiles 20

1.4.1 Stress in the Unsaturated State 20

1.4.2 Saturated Moisture and Stress Profiles: Conceptual Illustration 21

1.4.3 Unsaturated Moisture and Stress Profiles: Conceptual Illustration 22

1.4.4 Illustrative Stress Analysis 23

1.5 State Variables, Material Variables, and Constitutive Laws 26

1.5.1 Phenomena Prediction 26

1.5.2 Head as a State Variable 28

1.5.3 Effective Stress as a State Variable 30

1.5.4 Net Normal Stresses as State Variables 33

1.6 Suction and Potential of Soil Water 34

1.6.1 Total Soil Suction 34

1.6.2 Pore Water Potential 35

1.6.3 Units of Soil Suction 38

1.6.4 Suction Regimes and the Soil-Water Characteristic Curve 39

Problems 43

I FUNDAMENTAL PRINCIPLES 45

2 MATERIAL VARIABLES 47

2.1 Physical Properties of Air and Water 47

2.1.1 Unsaturated Soil as a Multiphase System 47

2.1.2 Density of Dry Air 48

2.1.3 Density of Water 50

2.1.4 Viscosity of Air and Water 53

2.1.5 Flow Regimes 55

2.2 Partial Pressure and Relative Humidity 57

2.2.1 Relative Humidity in Unsaturated Soil Mechanics 57

2.2.2 Composition and Partial Pressure of Air 57

2.2.3 Equilibrium between Free Water and Air 59

2.2.4 Equilibrium between Pore Water and Air 62

2.2.5 Relative Humidity 63

2.2.6 Dew Point 64

2.3 Density of Moist Air 65

2.3.1 Effect of Water Vapor on Density of Air 65

2.3.2 Formulation for Moist Air Density 66

2.4 Surface Tension 73

2.4.1 Origin of Surface Tension 73

2.4.2 Pressure Drop across an Air-Water Interface 76

2.5 Cavitation of Water 80

2.5.1 Cavitation and Boiling 80

2.5.2 Hydrostatic Atmospheric Pressure 82

2.5.3 Cavitation Pressure 84

Problems 86

3 INTERFACIAL EQUILIBRIUM 89

3.1 Solubility of Air in Water 89

3.1.1 Henry’s Law 89

3.1.2 Temperature Dependence 91

3.1.3 Volumetric Coefficient of Solubility 92

3.1.4 Henry’s Law Constant and Volumetric Coefficient of Solubility 93

3.1.5 Vapor Component Correction 94

3.1.6 Mass Coefficient of Solubility 95

3.2 Air-Water-Solid Interface 96

3.2.1 Equilibrium between Two Water Drops 96

3.2.2 Equilibrium at an Air-Water-Solid Interface 97

3.2.3 Contact Angle 99

3.2.4 Air-Water-Solid Interface in Unsaturated Soil 101

3.3 Vapor Pressure Lowering 104

3.3.1 Implications of Kelvin’s Equation 104

3.3.2 Derivation of Kelvin’s Equation 106

3.3.3 Capillary Condensation 111

3.4 Soil-Water Characteristic Curve 114

3.4.1 Soil Suction and Soil Water 114

3.4.2 Capillary Tube Model 115

3.4.3 Contacting Sphere Model 118

3.4.4 Concluding Remarks 124

Problems 124

4 CAPILLARITY 128

4.1 Young-Laplace Equation 128

4.1.1 Three-Dimensional Meniscus 128

4.1.2 Hydrostatic Equilibrium in a Capillary Tube 131

4.2 Height of Capillary Rise 133

4.2.1 Capillary Rise in a Tube 133

4.2.2 Capillary Finger Model 136

4.2.3 Capillary Rise in Idealized Soil 137

4.2.4 Capillary Rise in Soil 139

4.3 Rate of Capillary Rise 140

4.3.1 Saturated Hydraulic Conductivity Formulation 140

4.3.2 Unsaturated Hydraulic Conductivity Formulation 142

4.3.3 Experimental Verification 145

4.4 Capillary Pore Size Distribution 147

4.4.1 Theoretical Basis 147

4.4.2 Pore Geometry 150

4.4.3 Computational Procedures 153

4.5 Suction Stress 160

4.5.1 Forces between Two Spherical Particles 160

4.5.2 Pressure in the Water Lens 162

4.5.3 Effective Stress due to Capillarity 163

4.5.4 Effective Stress Parameter and Water Content 165

Problems 168

II STRESS PHENOMENA 171

5 STATE OF STRESS 173

5.1 Effective Stress in Unsaturated Soil 173

5.1.1 Macromechanical Conceptualization 173

5.1.2 Micromechanical Conceptualization 174

5.1.3 Stress between Two Spherical Particles with Nonzero Contact Angle 175

5.1.4 Pore Pressure Regimes 181

5.2 Hysteresis 182

5.2.1 Hysteresis Mechanisms 182

5.2.2 Ink-Bottle Hysteresis 184

5.2.3 Contact Angle Hysteresis 186

5.2.4 Hysteresis in the Soil-Water Characteristic Curve 187

5.2.5 Hysteresis in the Effective Stress Parameter 187

5.2.6 Hysteresis in the Suction Stress Characteristic Curve 191

5.3 Stress Tensor Representation 191

5.3.1 Net Normal Stress, Matric Suction, and Suction Stress Tensors 191

5.3.2 Stress Tensors in Unsaturated Soil: Conceptual Illustration 195

5.4 Stress Control by Axis Translation 201

5.4.1 Rationale for Axis Translation 201

5.4.2 Equilibrium for an Air-Water-HAE System 202

5.4.3 Equilibrium for an Air-Water-HAE-Soil System 203

5.4.4 Characteristic Curve for HAE Material 204

5.4.5 Controlled Stress Variable Testing 204

5.5 Graphical Representation of Stress 207

5.5.1 Net Normal Stress and Matric Suction Representation 207

5.5.2 Effective Stress Representation 213

Problems 218

6 SHEAR STRENGTH 220

6.1 Extended Mohr-Coulomb (M-C) Criterion 220

6.1.1 M-C for Saturated Soil 220

6.1.2 Experimental Observations of Unsaturated Shear Strength 221

6.1.3 Extended M-C Criterion 229

6.1.4 Extended M-C Criterion in Terms of Principal Stresses 232

6.2 Shear Strength Parameters for the Extended M-C Criterion 233

6.2.1 Interpretation of Triaxial Testing Results 233

6.2.2 Interpretation of Direct Shear Testing Results 236

6.3 Effective Stress and the M-C Criterion 238

6.3.1 Nonlinearity in the Extended M-C Envelope 238

6.3.2 Effective Stress Approach 241

6.3.3 Measurements of _ at Failure 242

6.3.4 Reconciliation between _b and _f 244

6.3.5 Validity of Effective Stress as a State Variable for Strength 247

6.4 Shear Strength Parameters for the M-C Criterion 248

6.4.1 Interpretation of Direct Shear Testing Results 248

6.4.2 Interpretation of Triaxial Testing Results 250

6.5 Unified Representation of Failure Envelope 252

6.5.1 Capillary Cohesion as a Characteristic Function for Unsaturated Soil 252

6.5.2 Determining the Magnitude of Capillary Cohesion 256

6.5.3 Concluding Remarks 261

Problems 265

7 SUCTION AND EARTH PRESSURE PROFILES 267

7.1 Steady Suction and Water Content Profiles 267

7.1.1 Suction Regimes in Unsaturated Soil 267

7.1.2 Analytical Solutions for Profiles of Matric Suction 270

7.1.3 Hydrologic Parameters for Representative Soil Types 272

7.1.4 Profiles of Matric Suction for Representative Soil Types 273

7.1.5 Profiles of Water Content for Representative Soil Types 275

7.2 Steady Effective Stress Parameter and Stress Profiles 280

7.2.1 Profiles of the Effective Stress Parameter _  280

7.2.2 Profiles of Suction Stress and Their Solution Regimes 282

7.2.3 Profiles of Suction Stress for Representative Soil Types 289

7.2.4 Concluding Remarks 292

7.3 Earth Pressure at Rest 294

7.3.1 Extended Hooke’s Law 294

7.3.2 Profiles of Coefficient of Earth Pressure at Rest 296

7.3.3 Depth of Cracking 297

7.4 Active Earth Pressure 301

7.4.1 Mohr-Coulomb Failure Criteria for Unsaturated Soil 301

7.4.2 Rankine’s Active State of Failure 302

7.4.3 Active Earth Pressure Profiles for Constant Suction Stress 306

7.4.4 Active Earth Pressure Profiles for Variable Suction Stress 308

7.4.5 Active Earth Pressure Profiles with Tension Cracks 310

7.5 Passive Earth Pressure  312

7.5.1 Rankine’s Passive State of Failure 312

7.5.2 Passive Earth Pressure Profiles for Constant Suction Stress 315

7.5.3 Passive Earth Pressure Profiles for Variable Suction Stress 318

7.5.4 Concluding Remarks 320

Problems 322

III FLOW PHENOMENA 323

8 STEADY FLOWS 325

8.1 Driving Mechanisms for Water and Airflow 325

8.1.1 Potential for Water Flow 325

8.1.2 Mechanisms for Airflow 326

8.1.3 Regimes for Pore Water Flow and Pore Airflow 326

8.1.4 Steady-State Flow Law for Water 328

8.2 Permeability and Hydraulic Conductivity 329

8.2.1 Permeability versus Conductivity 329

8.2.2 Magnitude, Variability, and Scaling Effects 331

8.3 Hydraulic Conductivity Function 333

8.3.1 Conceptual Model for the Hydraulic Conductivity Function 333

8.3.2 Hysteresis in the Hydraulic Conductivity Function 336

8.3.3 Relative Conductivity 336

8.3.4 Effects of Soil Type 338

8.4 Capillary Barriers 341

8.4.1 Natural and Engineered Capillary Barriers 341

8.4.2 Flat Capillary Barriers 342

8.4.3 Dipping Capillary Barriers 345

8.5 Steady Infiltration and Evaporation 349

8.5.1 Horizontal Infiltration 349

8.5.2 Vertical Infiltration and Evaporation 352

8.6 Steady Vapor Flow 359

8.6.1 Fick’s Law for Vapor Flow 359

8.6.2 Temperature and Vapor Pressure Variation 359

8.6.3 Vapor Density Gradient 361

8.7 Steady Air Diffusion in Water 363

8.7.1 Theoretical Basis 363

8.7.2 Air Diffusion in an Axis Translation System 366

Problems 367

9 TRANSIENT FLOWS 369

9.1 Principles for Pore Liquid Flow 369

9.1.1 Principle of Mass Conservation 369

9.1.2 Transient Saturated Flow 371

9.1.3 Transient Unsaturated Flow 372

9.2 Rate of Infiltration 376

9.2.1 Transient Horizontal Infiltration 376

9.2.2 Transient Vertical Infiltration 380

9.2.3 Transient Moisture Profile for Vertical Infiltration 384

9.3 Transient Suction and Moisture Profiles 386

9.3.1 Importance of Transient Soil Suction and Moisture 386

9.3.2 Analytical Solution of Transient Unsaturated Flow 386

9.3.3 Numerical Modeling of Transient Unsaturated Flow 389

9.4 Principles for Pore Gas Flow 396

9.4.1 Principle of Mass Conservation for Compressible Gas 396

9.4.2 Governing Equation for Pore Airflow 397

9.4.3 Linearization of the Airflow Equation 398

9.4.4 Sinusoidal Barometric Pressure Fluctuation 400

9.5 Barometric Pumping Analysis 402

9.5.1 Barometric Pumping 402

9.5.2 Theoretical Framework 403

9.5.3 Time Series Analysis 404

9.5.4 Determining Air Permeability 407

Problems 412

IV MATERIAL VARIABLE MEASUREMENT AND MODELING 415

10 SUCTION MEASUREMENT 417

10.1 Overview of Measurement Techniques 417

10.2 Tensiometers 420

10.2.1 Properties of High-Air-Entry Materials 420

10.2.2 Tensiometer Measurement Principles 421

10.3 Axis Translation Techniques 424

10.3.1 Null Tests and Pore Water Extraction Tests 424

10.3.2 Pressure Plates 425

10.3.3 Tempe Pressure Cells 427

10.4 ElectricalThermal Conductivity Sensors 429

10.5 Humidity Measurement Techniques 431

10.5.1 Total Suction and Relative Humidity 431

10.5.2 Thermocouple Psychrometers 432

10.5.3 Chilled-Mirror Hygrometers 438

10.5.4 Polymer Resistance Capacitance Sensors 441

10.6 Humidity Control Techniques 443

10.6.1 Isopiestic Humidity Control 444

10.6.2 Two-Pressure Humidity Control 445

10.7 Filter Paper Techniques 449

10.7.1 Filter Paper Measurement Principles 449

10.7.2 Calibration and Testing Procedures 451

10.7.3 Accuracy, Precision, and Performance 452

Problems 459

11 HYDRAULIC CONDUCTIVITY MEASUREMENT 462

11.1 Overview of Measurement Techniques 462

11.2 Steady-State Measurement Techniques 463

11.2.1 Constant-Head Method 463

11.2.2 Constant-Flow Method 466

11.2.3 Centrifuge Method 472

11.3 Transient Measurement Techniques 476

11.3.1 Hydraulic Diffusivity 476

11.3.2 Horizontal Infiltration Method 477

11.3.3 Outflow Methods 480

11.3.4 Instantaneous Profile Methods 484

Problems 493

12 SUCTION AND HYDRAULIC CONDUCTIVITY MODELS 494

12.1 Soil-Water Characteristic Curve Models 494

12.1.1 SWCC Modeling Parameters 495

12.1.2 Brooks and Corey (BC) Model 497

12.1.3 van Genuchten (VG) Model 499

12.1.4 Fredlund and Xing (FX) Model 505

12.2 Hydraulic Conductivity Models 506

12.2.1 Empirical and Macroscopic Models 509

12.2.2 Statistical Models 516

Problems 527

REFERENCES 531

INDEX 547