UNSATURATED SOIL MECHANICS NING LU

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UNSATURATED SOIL MECHANICS NING LU

PREFACE

The principal aim of this book is to provide a thorough grounding in unsaturated
soil mechanics principles from three fundamental perspectives: thermodynamics,
mechanics, and hydrology. The book is written to guide a first
course on the subject and is primarily intended for undergraduate seniors,
graduate students, and researchers with backgrounds in the more general fields
of geotechnical engineering, soil science, environmental engineering, and
groundwater hydrology.
In formulating this book, we have maintained the opinion that a first course
in any branch of mechanics should emphasize the fundamental principles that
govern the phenomena of interest. A principles-based approach to learning is
most beneficial to the general reader and is particularly appropriate for the
subject of unsaturated soil mechanics as it remains a young, dynamic, and
rapidly emerging field of research and practice. Our general viewpoint towards
the pursuit of understanding is reflected by Thomas Henry Huxley’s
(1825–1895) statement: ‘‘The known is finite, the unknown infinite; intellectually
we stand on an islet in the midst of an illimitable ocean of inexplicability.
Our business in every generation is to reclaim a little more land.’’ We
hope that this book will provide the necessary background and motivation for
those who desire to explore and reclaim the ocean of unsaturated soil mechanics
problems that nature and society continue to present.
A comprehensive introductory account of unsaturated soil mechanics is
presented in Chapter 1 to provide readers with a road map for the remainder
of the book. This includes a general introduction to unsaturated soil phenomena
(Section 1.1), a formulation for the scope of the book (Section 1.2), a
discussion of the role of unsaturated soil mechanics in nature and engineering
practice (Section 1.3), a discussion of some essential differences between
Copyrighted Material
Copyright © 2004 John Wiley & Sons Retrieved from: www.knovel.com
unsaturated soil mechanics and classical (saturated) soil mechanics (Section
1.4), an introduction to the state and material variables and constitutive laws
forming the language of unsaturated soil mechanics (Section 1.5), and an
introduction to suction and pore water potential concepts for unsaturated soil
(Section 1.6).
The remainder of the book is presented as four progressive and interrelated
parts. Part I examines the fundamental principles applicable to unsaturated
soil mechanics. Parts II and III illustrate application of these principles to
stress and flow phenomena in unsaturated soil, respectively. Finally, Part IV
describes, illustrates, and evaluates the major measurement and modeling
techniques used to quantify the state and material variables required to describe
these stress and flow phenomena.
In formulating the first three parts of the text, we offer a perspective that
unites the microscopic physical basis and the macroscopic thermodynamic
framework for pore water retention and the state of stress in unsaturated soil.
Two constitutive relationships are needed to describe unsaturated flow phenomena,
namely, the soil-water characteristic curve and the hydraulic conductivity
characteristic curve. For unsaturated stress phenomena, we contend
that an additional relationship referred to as the suction stress characteristic
curve is required.
The materials covered in this book have been an outgrowth of unsaturated
soil mechanics courses taught at the Colorado School of Mines and University
of Missouri–Columbia for graduating seniors and graduate students over
the past four years. The book contains sufficient material for a one-semester,
laboratory-supplemented course tailored along either a geomechanics or geoenvironmental
track. Problems are provided at the end of each chapter with
solutions available from the publisher’s web site at www.wiley.com.
While many colleagues have been helpful in making the book possible in
its present form, any error, bias, or inaccuracy remains ours. We are grateful
to the following people who generously provided insightful reviews for at
least one chapter: Jiny Carrera, Mandar M. Dewoolkar, Susan Eustes, Shemin
Ge, Jonathan W. Godt, D. Vaughan Griffiths, Laureano R. Hoyos, Jr., Nasser
Khalili, K.K. (Muralee) Muraleetharan, Harold W. Olsen, Paul M. Santi,
Charles D. Shackelford, Radhey S. Sharma, Alexandra Wayllace, and
Changfu Wei.

CONTENTS

FOREWORD xvii
PREFACE xix
SYMBOLS xxi
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 Electrical/Thermal 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