NING LU, PhD, is Professor of Engineering at the Colorado School of Mines, where he teaches courses in soil mechanics and geotechnical engineering. He is the author of more than thirty papers published in peer-reviewed journals and serves as an editorial board member for the Journal of Geotechnical and Geoenvironmental Engineering. He is a member of the American Society of Civil Engineers and a lifetime member of the American Geophysical Union. WILLIAM J. LIKOS, PhD, is Assistant Professor of Civil and Environmental Engineering at the University of Missouri—Columbia, where he teaches courses in soil mechanics and soil behavior. He is a former geotechnical engineer with the U.S. Geological Survey. He is the author of numerous papers regarding unsaturated and expansive soil behavior, an editorial board member for the Geotechnical Testing Journal, and a member of ASCE and the Clay Minerals Society.

• FOREWORD xviiPREFACE xixSYMBOLS xxiINTRODUCTION 11 STATE OF UNSATURATED SOIL 31.1 Unsaturated Soil Phenomena 31.1.1 Definition of Unsaturated Soil Mechanics 31.1.2 Interdisciplinary Nature of Unsaturated Soil Mechanics 41.1.3 Classification of Unsaturated Soil Phenomena 61.2 Scope and Organization of Book 81.2.1 Chapter Structure 81.2.2 Geomechanics and Geo-environmental Tracks 111.3 Unsaturated Soil in Nature and Practice 121.3.1 Unsaturated Soil in Hydrologic Cycle 121.3.2 Global Extent of Climatic Factors 121.3.3 Unsaturated Zone and Soil Formation 131.3.4 Unsaturated Soil in Engineering Practice 181.4 Moisture, Pore Pressure, and Stress Profiles 201.4.1 Stress in the Unsaturated State 201.4.2 Saturated Moisture and Stress Profiles: Conceptual Illustration 211.4.3 Unsaturated Moisture and Stress Profiles: Conceptual Illustration 221.4.4 Illustrative Stress Analysis 231.5 State Variables, Material Variables, and Constitutive Laws 261.5.1 Phenomena Prediction 261.5.2 Head as a State Variable 281.5.3 Effective Stress as a State Variable 301.5.4 Net Normal Stresses as State Variables 331.6 Suction and Potential of Soil Water 341.6.1 Total Soil Suction 341.6.2 Pore Water Potential 351.6.3 Units of Soil Suction 381.6.4 Suction Regimes and the Soil-Water Characteristic Curve 39Problems 43I FUNDAMENTAL PRINCIPLES 452 MATERIAL VARIABLES 472.1 Physical Properties of Air and Water 472.1.1 Unsaturated Soil as a Multiphase System 472.1.2 Density of Dry Air 482.1.3 Density of Water 502.1.4 Viscosity of Air and Water 532.1.5 Flow Regimes 552.2 Partial Pressure and Relative Humidity 572.2.1 Relative Humidity in Unsaturated Soil Mechanics 572.2.2 Composition and Partial Pressure of Air 572.2.3 Equilibrium between Free Water and Air 592.2.4 Equilibrium between Pore Water and Air 622.2.5 Relative Humidity 632.2.6 Dew Point 642.3 Density of Moist Air 652.3.1 Effect of Water Vapor on Density of Air 652.3.2 Formulation for Moist Air Density 662.4 Surface Tension 732.4.1 Origin of Surface Tension 732.4.2 Pressure Drop across an Air-Water Interface 762.5 Cavitation of Water 802.5.1 Cavitation and Boiling 802.5.2 Hydrostatic Atmospheric Pressure 822.5.3 Cavitation Pressure 84Problems 863 INTERFACIAL EQUILIBRIUM 893.1 Solubility of Air in Water 893.1.1 Henry’s Law 893.1.2 Temperature Dependence 913.1.3 Volumetric Coefficient of Solubility 923.1.4 Henry’s Law Constant and Volumetric Coefficient of Solubility 933.1.5 Vapor Component Correction 943.1.6 Mass Coefficient of Solubility 953.2 Air-Water-Solid Interface 963.2.1 Equilibrium between Two Water Drops 963.2.2 Equilibrium at an Air-Water-Solid Interface 973.2.3 Contact Angle 993.2.4 Air-Water-Solid Interface in Unsaturated Soil 1013.3 Vapor Pressure Lowering 1043.3.1 Implications of Kelvin’s Equation 1043.3.2 Derivation of Kelvin’s Equation 1063.3.3 Capillary Condensation 1113.4 Soil-Water Characteristic Curve 1143.4.1 Soil Suction and Soil Water 1143.4.2 Capillary Tube Model 1153.4.3 Contacting Sphere Model 1183.4.4 Concluding Remarks 124Problems 1244 CAPILLARITY 1284.1 Young-Laplace Equation 1284.1.1 Three-Dimensional Meniscus 1284.1.2 Hydrostatic Equilibrium in a Capillary Tube 1314.2 Height of Capillary Rise 1334.2.1 Capillary Rise in a Tube 1334.2.2 Capillary Finger Model 1364.2.3 Capillary Rise in Idealized Soil 1374.2.4 Capillary Rise in Soil 1394.3 Rate of Capillary Rise 1404.3.1 Saturated Hydraulic Conductivity Formulation 1404.3.2 Unsaturated Hydraulic Conductivity Formulation 1424.3.3 Experimental Verification 1454.4 Capillary Pore Size Distribution 1474.4.1 Theoretical Basis 1474.4.2 Pore Geometry 1504.4.3 Computational Procedures 1534.5 Suction Stress 1604.5.1 Forces between Two Spherical Particles 1604.5.2 Pressure in the Water Lens 1624.5.3 Effective Stress due to Capillarity 1634.5.4 Effective Stress Parameter and Water Content 165Problems 168II STRESS PHENOMENA 1715 STATE OF STRESS 1735.1 Effective Stress in Unsaturated Soil 1735.1.1 Macromechanical Conceptualization 1735.1.2 Micromechanical Conceptualization 1745.1.3 Stress between Two Spherical Particles with Nonzero Contact Angle 1755.1.4 Pore Pressure Regimes 1815.2 Hysteresis 1825.2.1 Hysteresis Mechanisms 1825.2.2 Ink-Bottle Hysteresis 1845.2.3 Contact Angle Hysteresis 1865.2.4 Hysteresis in the Soil-Water Characteristic Curve 1875.2.5 Hysteresis in the Effective Stress Parameter 1875.2.6 Hysteresis in the Suction Stress Characteristic Curve 1915.3 Stress Tensor Representation 1915.3.1 Net Normal Stress, Matric Suction, and Suction Stress Tensors 1915.3.2 Stress Tensors in Unsaturated Soil: Conceptual Illustration 1955.4 Stress Control by Axis Translation 2015.4.1 Rationale for Axis Translation 2015.4.2 Equilibrium for an Air-Water-HAE System 2025.4.3 Equilibrium for an Air-Water-HAE-Soil System 2035.4.4 Characteristic Curve for HAE Material 2045.4.5 Controlled Stress Variable Testing 2045.5 Graphical Representation of Stress 2075.5.1 Net Normal Stress and Matric Suction Representation 2075.5.2 Effective Stress Representation 213Problems 2186 SHEAR STRENGTH 2206.1 Extended Mohr-Coulomb (M-C) Criterion 2206.1.1 M-C for Saturated Soil 2206.1.2 Experimental Observations of Unsaturated Shear Strength 2216.1.3 Extended M-C Criterion 2296.1.4 Extended M-C Criterion in Terms of Principal Stresses 2326.2 Shear Strength Parameters for the Extended M-C Criterion 2336.2.1 Interpretation of Triaxial Testing Results 2336.2.2 Interpretation of Direct Shear Testing Results 2366.3 Effective Stress and the M-C Criterion 2386.3.1 Nonlinearity in the Extended M-C Envelope 2386.3.2 Effective Stress Approach 2416.3.3 Measurements of _ at Failure 2426.3.4 Reconciliation between _b and _f 2446.3.5 Validity of Effective Stress as a State Variable for Strength 2476.4 Shear Strength Parameters for the M-C Criterion 2486.4.1 Interpretation of Direct Shear Testing Results 2486.4.2 Interpretation of Triaxial Testing Results 2506.5 Unified Representation of Failure Envelope 2526.5.1 Capillary Cohesion as a Characteristic Function for Unsaturated Soil 2526.5.2 Determining the Magnitude of Capillary Cohesion 2566.5.3 Concluding Remarks 261Problems 2657 SUCTION AND EARTH PRESSURE PROFILES 2677.1 Steady Suction and Water Content Profiles 2677.1.1 Suction Regimes in Unsaturated Soil 2677.1.2 Analytical Solutions for Profiles of Matric Suction 2707.1.3 Hydrologic Parameters for Representative Soil Types 2727.1.4 Profiles of Matric Suction for Representative Soil Types 2737.1.5 Profiles of Water Content for Representative Soil Types 2757.2 Steady Effective Stress Parameter and Stress Profiles 2807.2.1 Profiles of the Effective Stress Parameter _  2807.2.2 Profiles of Suction Stress and Their Solution Regimes 2827.2.3 Profiles of Suction Stress for Representative Soil Types 2897.2.4 Concluding Remarks 2927.3 Earth Pressure at Rest 2947.3.1 Extended Hooke’s Law 2947.3.2 Profiles of Coefficient of Earth Pressure at Rest 2967.3.3 Depth of Cracking 2977.4 Active Earth Pressure 3017.4.1 Mohr-Coulomb Failure Criteria for Unsaturated Soil 3017.4.2 Rankine’s Active State of Failure 3027.4.3 Active Earth Pressure Profiles for Constant Suction Stress 3067.4.4 Active Earth Pressure Profiles for Variable Suction Stress 3087.4.5 Active Earth Pressure Profiles with Tension Cracks 3107.5 Passive Earth Pressure  3127.5.1 Rankine’s Passive State of Failure 3127.5.2 Passive Earth Pressure Profiles for Constant Suction Stress 3157.5.3 Passive Earth Pressure Profiles for Variable Suction Stress 3187.5.4 Concluding Remarks 320Problems 322III FLOW PHENOMENA 3238 STEADY FLOWS 3258.1 Driving Mechanisms for Water and Airflow 3258.1.1 Potential for Water Flow 3258.1.2 Mechanisms for Airflow 3268.1.3 Regimes for Pore Water Flow and Pore Airflow 3268.1.4 Steady-State Flow Law for Water 3288.2 Permeability and Hydraulic Conductivity 3298.2.1 Permeability versus Conductivity 3298.2.2 Magnitude, Variability, and Scaling Effects 3318.3 Hydraulic Conductivity Function 3338.3.1 Conceptual Model for the Hydraulic Conductivity Function 3338.3.2 Hysteresis in the Hydraulic Conductivity Function 3368.3.3 Relative Conductivity 3368.3.4 Effects of Soil Type 3388.4 Capillary Barriers 3418.4.1 Natural and Engineered Capillary Barriers 3418.4.2 Flat Capillary Barriers 3428.4.3 Dipping Capillary Barriers 3458.5 Steady Infiltration and Evaporation 3498.5.1 Horizontal Infiltration 3498.5.2 Vertical Infiltration and Evaporation 3528.6 Steady Vapor Flow 3598.6.1 Fick’s Law for Vapor Flow 3598.6.2 Temperature and Vapor Pressure Variation 3598.6.3 Vapor Density Gradient 3618.7 Steady Air Diffusion in Water 3638.7.1 Theoretical Basis 3638.7.2 Air Diffusion in an Axis Translation System 366Problems 3679 TRANSIENT FLOWS 3699.1 Principles for Pore Liquid Flow 3699.1.1 Principle of Mass Conservation 3699.1.2 Transient Saturated Flow 3719.1.3 Transient Unsaturated Flow 3729.2 Rate of Infiltration 3769.2.1 Transient Horizontal Infiltration 3769.2.2 Transient Vertical Infiltration 3809.2.3 Transient Moisture Profile for Vertical Infiltration 3849.3 Transient Suction and Moisture Profiles 3869.3.1 Importance of Transient Soil Suction and Moisture 3869.3.2 Analytical Solution of Transient Unsaturated Flow 3869.3.3 Numerical Modeling of Transient Unsaturated Flow 3899.4 Principles for Pore Gas Flow 3969.4.1 Principle of Mass Conservation for Compressible Gas 3969.4.2 Governing Equation for Pore Airflow 3979.4.3 Linearization of the Airflow Equation 3989.4.4 Sinusoidal Barometric Pressure Fluctuation 4009.5 Barometric Pumping Analysis 4029.5.1 Barometric Pumping 4029.5.2 Theoretical Framework 4039.5.3 Time Series Analysis 4049.5.4 Determining Air Permeability 407Problems 412IV MATERIAL VARIABLE MEASUREMENT AND MODELING 41510 SUCTION MEASUREMENT 41710.1 Overview of Measurement Techniques 41710.2 Tensiometers 42010.2.1 Properties of High-Air-Entry Materials 42010.2.2 Tensiometer Measurement Principles 42110.3 Axis Translation Techniques 42410.3.1 Null Tests and Pore Water Extraction Tests 42410.3.2 Pressure Plates 42510.3.3 Tempe Pressure Cells 42710.4 ElectricalThermal Conductivity Sensors 42910.5 Humidity Measurement Techniques 43110.5.1 Total Suction and Relative Humidity 43110.5.2 Thermocouple Psychrometers 43210.5.3 Chilled-Mirror Hygrometers 43810.5.4 Polymer Resistance Capacitance Sensors 44110.6 Humidity Control Techniques 44310.6.1 Isopiestic Humidity Control 44410.6.2 Two-Pressure Humidity Control 44510.7 Filter Paper Techniques 44910.7.1 Filter Paper Measurement Principles 44910.7.2 Calibration and Testing Procedures 45110.7.3 Accuracy, Precision, and Performance 452Problems 45911 HYDRAULIC CONDUCTIVITY MEASUREMENT 46211.1 Overview of Measurement Techniques 46211.2 Steady-State Measurement Techniques 46311.2.1 Constant-Head Method 46311.2.2 Constant-Flow Method 46611.2.3 Centrifuge Method 47211.3 Transient Measurement Techniques 47611.3.1 Hydraulic Diffusivity 47611.3.2 Horizontal Infiltration Method 47711.3.3 Outflow Methods 48011.3.4 Instantaneous Profile Methods 484Problems 49312 SUCTION AND HYDRAULIC CONDUCTIVITY MODELS 49412.1 Soil-Water Characteristic Curve Models 49412.1.1 SWCC Modeling Parameters 49512.1.2 Brooks and Corey (BC) Model 49712.1.3 van Genuchten (VG) Model 49912.1.4 Fredlund and Xing (FX) Model 50512.2 Hydraulic Conductivity Models 50612.2.1 Empirical and Macroscopic Models 50912.2.2 Statistical Models 516Problems 527REFERENCES 531INDEX 547

NING LU, PhD, is Professor of Engineering at the Colorado School of Mines, where he teaches courses in soil mechanics and geotechnical engineering. He is the author of more than thirty papers published in peer-reviewed journals and serves as an editorial board member for the Journal of Geotechnical and Geoenvironmental Engineering. He is a member of the American Society of Civil Engineers and a lifetime member of the American Geophysical Union. WILLIAM J. LIKOS, PhD, is Assistant Professor of Civil and Environmental Engineering at the University of Missouri—Columbia, where he teaches courses in soil mechanics and soil behavior. He is a former geotechnical engineer with the U.S. Geological Survey. He is the author of numerous papers regarding unsaturated and expansive soil behavior, an editorial board member for the Geotechnical Testing Journal, and a member of ASCE and the Clay Minerals Society.

• FOREWORD xviiPREFACE xixSYMBOLS xxiINTRODUCTION 11 STATE OF UNSATURATED SOIL 31.1 Unsaturated Soil Phenomena 31.1.1 Definition of Unsaturated Soil Mechanics 31.1.2 Interdisciplinary Nature of Unsaturated Soil Mechanics 41.1.3 Classification of Unsaturated Soil Phenomena 61.2 Scope and Organization of Book 81.2.1 Chapter Structure 81.2.2 Geomechanics and Geo-environmental Tracks 111.3 Unsaturated Soil in Nature and Practice 121.3.1 Unsaturated Soil in Hydrologic Cycle 121.3.2 Global Extent of Climatic Factors 121.3.3 Unsaturated Zone and Soil Formation 131.3.4 Unsaturated Soil in Engineering Practice 181.4 Moisture, Pore Pressure, and Stress Profiles 201.4.1 Stress in the Unsaturated State 201.4.2 Saturated Moisture and Stress Profiles: Conceptual Illustration 211.4.3 Unsaturated Moisture and Stress Profiles: Conceptual Illustration 221.4.4 Illustrative Stress Analysis 231.5 State Variables, Material Variables, and Constitutive Laws 261.5.1 Phenomena Prediction 261.5.2 Head as a State Variable 281.5.3 Effective Stress as a State Variable 301.5.4 Net Normal Stresses as State Variables 331.6 Suction and Potential of Soil Water 341.6.1 Total Soil Suction 341.6.2 Pore Water Potential 351.6.3 Units of Soil Suction 381.6.4 Suction Regimes and the Soil-Water Characteristic Curve 39Problems 43I FUNDAMENTAL PRINCIPLES 452 MATERIAL VARIABLES 472.1 Physical Properties of Air and Water 472.1.1 Unsaturated Soil as a Multiphase System 472.1.2 Density of Dry Air 482.1.3 Density of Water 502.1.4 Viscosity of Air and Water 532.1.5 Flow Regimes 552.2 Partial Pressure and Relative Humidity 572.2.1 Relative Humidity in Unsaturated Soil Mechanics 572.2.2 Composition and Partial Pressure of Air 572.2.3 Equilibrium between Free Water and Air 592.2.4 Equilibrium between Pore Water and Air 622.2.5 Relative Humidity 632.2.6 Dew Point 642.3 Density of Moist Air 652.3.1 Effect of Water Vapor on Density of Air 652.3.2 Formulation for Moist Air Density 662.4 Surface Tension 732.4.1 Origin of Surface Tension 732.4.2 Pressure Drop across an Air-Water Interface 762.5 Cavitation of Water 802.5.1 Cavitation and Boiling 802.5.2 Hydrostatic Atmospheric Pressure 822.5.3 Cavitation Pressure 84Problems 863 INTERFACIAL EQUILIBRIUM 893.1 Solubility of Air in Water 893.1.1 Henry’s Law 893.1.2 Temperature Dependence 913.1.3 Volumetric Coefficient of Solubility 923.1.4 Henry’s Law Constant and Volumetric Coefficient of Solubility 933.1.5 Vapor Component Correction 943.1.6 Mass Coefficient of Solubility 953.2 Air-Water-Solid Interface 963.2.1 Equilibrium between Two Water Drops 963.2.2 Equilibrium at an Air-Water-Solid Interface 973.2.3 Contact Angle 993.2.4 Air-Water-Solid Interface in Unsaturated Soil 1013.3 Vapor Pressure Lowering 1043.3.1 Implications of Kelvin’s Equation 1043.3.2 Derivation of Kelvin’s Equation 1063.3.3 Capillary Condensation 1113.4 Soil-Water Characteristic Curve 1143.4.1 Soil Suction and Soil Water 1143.4.2 Capillary Tube Model 1153.4.3 Contacting Sphere Model 1183.4.4 Concluding Remarks 124Problems 1244 CAPILLARITY 1284.1 Young-Laplace Equation 1284.1.1 Three-Dimensional Meniscus 1284.1.2 Hydrostatic Equilibrium in a Capillary Tube 1314.2 Height of Capillary Rise 1334.2.1 Capillary Rise in a Tube 1334.2.2 Capillary Finger Model 1364.2.3 Capillary Rise in Idealized Soil 1374.2.4 Capillary Rise in Soil 1394.3 Rate of Capillary Rise 1404.3.1 Saturated Hydraulic Conductivity Formulation 1404.3.2 Unsaturated Hydraulic Conductivity Formulation 1424.3.3 Experimental Verification 1454.4 Capillary Pore Size Distribution 1474.4.1 Theoretical Basis 1474.4.2 Pore Geometry 1504.4.3 Computational Procedures 1534.5 Suction Stress 1604.5.1 Forces between Two Spherical Particles 1604.5.2 Pressure in the Water Lens 1624.5.3 Effective Stress due to Capillarity 1634.5.4 Effective Stress Parameter and Water Content 165Problems 168II STRESS PHENOMENA 1715 STATE OF STRESS 1735.1 Effective Stress in Unsaturated Soil 1735.1.1 Macromechanical Conceptualization 1735.1.2 Micromechanical Conceptualization 1745.1.3 Stress between Two Spherical Particles with Nonzero Contact Angle 1755.1.4 Pore Pressure Regimes 1815.2 Hysteresis 1825.2.1 Hysteresis Mechanisms 1825.2.2 Ink-Bottle Hysteresis 1845.2.3 Contact Angle Hysteresis 1865.2.4 Hysteresis in the Soil-Water Characteristic Curve 1875.2.5 Hysteresis in the Effective Stress Parameter 1875.2.6 Hysteresis in the Suction Stress Characteristic Curve 1915.3 Stress Tensor Representation 1915.3.1 Net Normal Stress, Matric Suction, and Suction Stress Tensors 1915.3.2 Stress Tensors in Unsaturated Soil: Conceptual Illustration 1955.4 Stress Control by Axis Translation 2015.4.1 Rationale for Axis Translation 2015.4.2 Equilibrium for an Air-Water-HAE System 2025.4.3 Equilibrium for an Air-Water-HAE-Soil System 2035.4.4 Characteristic Curve for HAE Material 2045.4.5 Controlled Stress Variable Testing 2045.5 Graphical Representation of Stress 2075.5.1 Net Normal Stress and Matric Suction Representation 2075.5.2 Effective Stress Representation 213Problems 2186 SHEAR STRENGTH 2206.1 Extended Mohr-Coulomb (M-C) Criterion 2206.1.1 M-C for Saturated Soil 2206.1.2 Experimental Observations of Unsaturated Shear Strength 2216.1.3 Extended M-C Criterion 2296.1.4 Extended M-C Criterion in Terms of Principal Stresses 2326.2 Shear Strength Parameters for the Extended M-C Criterion 2336.2.1 Interpretation of Triaxial Testing Results 2336.2.2 Interpretation of Direct Shear Testing Results 2366.3 Effective Stress and the M-C Criterion 2386.3.1 Nonlinearity in the Extended M-C Envelope 2386.3.2 Effective Stress Approach 2416.3.3 Measurements of _ at Failure 2426.3.4 Reconciliation between _b and _f 2446.3.5 Validity of Effective Stress as a State Variable for Strength 2476.4 Shear Strength Parameters for the M-C Criterion 2486.4.1 Interpretation of Direct Shear Testing Results 2486.4.2 Interpretation of Triaxial Testing Results 2506.5 Unified Representation of Failure Envelope 2526.5.1 Capillary Cohesion as a Characteristic Function for Unsaturated Soil 2526.5.2 Determining the Magnitude of Capillary Cohesion 2566.5.3 Concluding Remarks 261Problems 2657 SUCTION AND EARTH PRESSURE PROFILES 2677.1 Steady Suction and Water Content Profiles 2677.1.1 Suction Regimes in Unsaturated Soil 2677.1.2 Analytical Solutions for Profiles of Matric Suction 2707.1.3 Hydrologic Parameters for Representative Soil Types 2727.1.4 Profiles of Matric Suction for Representative Soil Types 2737.1.5 Profiles of Water Content for Representative Soil Types 2757.2 Steady Effective Stress Parameter and Stress Profiles 2807.2.1 Profiles of the Effective Stress Parameter _  2807.2.2 Profiles of Suction Stress and Their Solution Regimes 2827.2.3 Profiles of Suction Stress for Representative Soil Types 2897.2.4 Concluding Remarks 2927.3 Earth Pressure at Rest 2947.3.1 Extended Hooke’s Law 2947.3.2 Profiles of Coefficient of Earth Pressure at Rest 2967.3.3 Depth of Cracking 2977.4 Active Earth Pressure 3017.4.1 Mohr-Coulomb Failure Criteria for Unsaturated Soil 3017.4.2 Rankine’s Active State of Failure 3027.4.3 Active Earth Pressure Profiles for Constant Suction Stress 3067.4.4 Active Earth Pressure Profiles for Variable Suction Stress 3087.4.5 Active Earth Pressure Profiles with Tension Cracks 3107.5 Passive Earth Pressure  3127.5.1 Rankine’s Passive State of Failure 3127.5.2 Passive Earth Pressure Profiles for Constant Suction Stress 3157.5.3 Passive Earth Pressure Profiles for Variable Suction Stress 3187.5.4 Concluding Remarks 320Problems 322III FLOW PHENOMENA 3238 STEADY FLOWS 3258.1 Driving Mechanisms for Water and Airflow 3258.1.1 Potential for Water Flow 3258.1.2 Mechanisms for Airflow 3268.1.3 Regimes for Pore Water Flow and Pore Airflow 3268.1.4 Steady-State Flow Law for Water 3288.2 Permeability and Hydraulic Conductivity 3298.2.1 Permeability versus Conductivity 3298.2.2 Magnitude, Variability, and Scaling Effects 3318.3 Hydraulic Conductivity Function 3338.3.1 Conceptual Model for the Hydraulic Conductivity Function 3338.3.2 Hysteresis in the Hydraulic Conductivity Function 3368.3.3 Relative Conductivity 3368.3.4 Effects of Soil Type 3388.4 Capillary Barriers 3418.4.1 Natural and Engineered Capillary Barriers 3418.4.2 Flat Capillary Barriers 3428.4.3 Dipping Capillary Barriers 3458.5 Steady Infiltration and Evaporation 3498.5.1 Horizontal Infiltration 3498.5.2 Vertical Infiltration and Evaporation 3528.6 Steady Vapor Flow 3598.6.1 Fick’s Law for Vapor Flow 3598.6.2 Temperature and Vapor Pressure Variation 3598.6.3 Vapor Density Gradient 3618.7 Steady Air Diffusion in Water 3638.7.1 Theoretical Basis 3638.7.2 Air Diffusion in an Axis Translation System 366Problems 3679 TRANSIENT FLOWS 3699.1 Principles for Pore Liquid Flow 3699.1.1 Principle of Mass Conservation 3699.1.2 Transient Saturated Flow 3719.1.3 Transient Unsaturated Flow 3729.2 Rate of Infiltration 3769.2.1 Transient Horizontal Infiltration 3769.2.2 Transient Vertical Infiltration 3809.2.3 Transient Moisture Profile for Vertical Infiltration 3849.3 Transient Suction and Moisture Profiles 3869.3.1 Importance of Transient Soil Suction and Moisture 3869.3.2 Analytical Solution of Transient Unsaturated Flow 3869.3.3 Numerical Modeling of Transient Unsaturated Flow 3899.4 Principles for Pore Gas Flow 3969.4.1 Principle of Mass Conservation for Compressible Gas 3969.4.2 Governing Equation for Pore Airflow 3979.4.3 Linearization of the Airflow Equation 3989.4.4 Sinusoidal Barometric Pressure Fluctuation 4009.5 Barometric Pumping Analysis 4029.5.1 Barometric Pumping 4029.5.2 Theoretical Framework 4039.5.3 Time Series Analysis 4049.5.4 Determining Air Permeability 407Problems 412IV MATERIAL VARIABLE MEASUREMENT AND MODELING 41510 SUCTION MEASUREMENT 41710.1 Overview of Measurement Techniques 41710.2 Tensiometers 42010.2.1 Properties of High-Air-Entry Materials 42010.2.2 Tensiometer Measurement Principles 42110.3 Axis Translation Techniques 42410.3.1 Null Tests and Pore Water Extraction Tests 42410.3.2 Pressure Plates 42510.3.3 Tempe Pressure Cells 42710.4 ElectricalThermal Conductivity Sensors 42910.5 Humidity Measurement Techniques 43110.5.1 Total Suction and Relative Humidity 43110.5.2 Thermocouple Psychrometers 43210.5.3 Chilled-Mirror Hygrometers 43810.5.4 Polymer Resistance Capacitance Sensors 44110.6 Humidity Control Techniques 44310.6.1 Isopiestic Humidity Control 44410.6.2 Two-Pressure Humidity Control 44510.7 Filter Paper Techniques 44910.7.1 Filter Paper Measurement Principles 44910.7.2 Calibration and Testing Procedures 45110.7.3 Accuracy, Precision, and Performance 452Problems 45911 HYDRAULIC CONDUCTIVITY MEASUREMENT 46211.1 Overview of Measurement Techniques 46211.2 Steady-State Measurement Techniques 46311.2.1 Constant-Head Method 46311.2.2 Constant-Flow Method 46611.2.3 Centrifuge Method 47211.3 Transient Measurement Techniques 47611.3.1 Hydraulic Diffusivity 47611.3.2 Horizontal Infiltration Method 47711.3.3 Outflow Methods 48011.3.4 Instantaneous Profile Methods 484Problems 49312 SUCTION AND HYDRAULIC CONDUCTIVITY MODELS 49412.1 Soil-Water Characteristic Curve Models 49412.1.1 SWCC Modeling Parameters 49512.1.2 Brooks and Corey (BC) Model 49712.1.3 van Genuchten (VG) Model 49912.1.4 Fredlund and Xing (FX) Model 50512.2 Hydraulic Conductivity Models 50612.2.1 Empirical and Macroscopic Models 50912.2.2 Statistical Models 516Problems 527REFERENCES 531INDEX 547

NING LU, PhD, is Professor of Engineering at the Colorado School of Mines, where he teaches courses in soil mechanics and geotechnical engineering. He is the author of more than thirty papers published in peer-reviewed journals and serves as an editorial board member for the Journal of Geotechnical and Geoenvironmental Engineering. He is a member of the American Society of Civil Engineers and a lifetime member of the American Geophysical Union. WILLIAM J. LIKOS, PhD, is Assistant Professor of Civil and Environmental Engineering at the University of Missouri—Columbia, where he teaches courses in soil mechanics and soil behavior. He is a former geotechnical engineer with the U.S. Geological Survey. He is the author of numerous papers regarding unsaturated and expansive soil behavior, an editorial board member for the Geotechnical Testing Journal, and a member of ASCE and the Clay Minerals Society.

• FOREWORD xviiPREFACE xixSYMBOLS xxiINTRODUCTION 11 STATE OF UNSATURATED SOIL 31.1 Unsaturated Soil Phenomena 31.1.1 Definition of Unsaturated Soil Mechanics 31.1.2 Interdisciplinary Nature of Unsaturated Soil Mechanics 41.1.3 Classification of Unsaturated Soil Phenomena 61.2 Scope and Organization of Book 81.2.1 Chapter Structure 81.2.2 Geomechanics and Geo-environmental Tracks 111.3 Unsaturated Soil in Nature and Practice 121.3.1 Unsaturated Soil in Hydrologic Cycle 121.3.2 Global Extent of Climatic Factors 121.3.3 Unsaturated Zone and Soil Formation 131.3.4 Unsaturated Soil in Engineering Practice 181.4 Moisture, Pore Pressure, and Stress Profiles 201.4.1 Stress in the Unsaturated State 201.4.2 Saturated Moisture and Stress Profiles: Conceptual Illustration 211.4.3 Unsaturated Moisture and Stress Profiles: Conceptual Illustration 221.4.4 Illustrative Stress Analysis 231.5 State Variables, Material Variables, and Constitutive Laws 261.5.1 Phenomena Prediction 261.5.2 Head as a State Variable 281.5.3 Effective Stress as a State Variable 301.5.4 Net Normal Stresses as State Variables 331.6 Suction and Potential of Soil Water 341.6.1 Total Soil Suction 341.6.2 Pore Water Potential 351.6.3 Units of Soil Suction 381.6.4 Suction Regimes and the Soil-Water Characteristic Curve 39Problems 43I FUNDAMENTAL PRINCIPLES 452 MATERIAL VARIABLES 472.1 Physical Properties of Air and Water 472.1.1 Unsaturated Soil as a Multiphase System 472.1.2 Density of Dry Air 482.1.3 Density of Water 502.1.4 Viscosity of Air and Water 532.1.5 Flow Regimes 552.2 Partial Pressure and Relative Humidity 572.2.1 Relative Humidity in Unsaturated Soil Mechanics 572.2.2 Composition and Partial Pressure of Air 572.2.3 Equilibrium between Free Water and Air 592.2.4 Equilibrium between Pore Water and Air 622.2.5 Relative Humidity 632.2.6 Dew Point 642.3 Density of Moist Air 652.3.1 Effect of Water Vapor on Density of Air 652.3.2 Formulation for Moist Air Density 662.4 Surface Tension 732.4.1 Origin of Surface Tension 732.4.2 Pressure Drop across an Air-Water Interface 762.5 Cavitation of Water 802.5.1 Cavitation and Boiling 802.5.2 Hydrostatic Atmospheric Pressure 822.5.3 Cavitation Pressure 84Problems 863 INTERFACIAL EQUILIBRIUM 893.1 Solubility of Air in Water 893.1.1 Henry’s Law 893.1.2 Temperature Dependence 913.1.3 Volumetric Coefficient of Solubility 923.1.4 Henry’s Law Constant and Volumetric Coefficient of Solubility 933.1.5 Vapor Component Correction 943.1.6 Mass Coefficient of Solubility 953.2 Air-Water-Solid Interface 963.2.1 Equilibrium between Two Water Drops 963.2.2 Equilibrium at an Air-Water-Solid Interface 973.2.3 Contact Angle 993.2.4 Air-Water-Solid Interface in Unsaturated Soil 1013.3 Vapor Pressure Lowering 1043.3.1 Implications of Kelvin’s Equation 1043.3.2 Derivation of Kelvin’s Equation 1063.3.3 Capillary Condensation 1113.4 Soil-Water Characteristic Curve 1143.4.1 Soil Suction and Soil Water 1143.4.2 Capillary Tube Model 1153.4.3 Contacting Sphere Model 1183.4.4 Concluding Remarks 124Problems 1244 CAPILLARITY 1284.1 Young-Laplace Equation 1284.1.1 Three-Dimensional Meniscus 1284.1.2 Hydrostatic Equilibrium in a Capillary Tube 1314.2 Height of Capillary Rise 1334.2.1 Capillary Rise in a Tube 1334.2.2 Capillary Finger Model 1364.2.3 Capillary Rise in Idealized Soil 1374.2.4 Capillary Rise in Soil 1394.3 Rate of Capillary Rise 1404.3.1 Saturated Hydraulic Conductivity Formulation 1404.3.2 Unsaturated Hydraulic Conductivity Formulation 1424.3.3 Experimental Verification 1454.4 Capillary Pore Size Distribution 1474.4.1 Theoretical Basis 1474.4.2 Pore Geometry 1504.4.3 Computational Procedures 1534.5 Suction Stress 1604.5.1 Forces between Two Spherical Particles 1604.5.2 Pressure in the Water Lens 1624.5.3 Effective Stress due to Capillarity 1634.5.4 Effective Stress Parameter and Water Content 165Problems 168II STRESS PHENOMENA 1715 STATE OF STRESS 1735.1 Effective Stress in Unsaturated Soil 1735.1.1 Macromechanical Conceptualization 1735.1.2 Micromechanical Conceptualization 1745.1.3 Stress between Two Spherical Particles with Nonzero Contact Angle 1755.1.4 Pore Pressure Regimes 1815.2 Hysteresis 1825.2.1 Hysteresis Mechanisms 1825.2.2 Ink-Bottle Hysteresis 1845.2.3 Contact Angle Hysteresis 1865.2.4 Hysteresis in the Soil-Water Characteristic Curve 1875.2.5 Hysteresis in the Effective Stress Parameter 1875.2.6 Hysteresis in the Suction Stress Characteristic Curve 1915.3 Stress Tensor Representation 1915.3.1 Net Normal Stress, Matric Suction, and Suction Stress Tensors 1915.3.2 Stress Tensors in Unsaturated Soil: Conceptual Illustration 1955.4 Stress Control by Axis Translation 2015.4.1 Rationale for Axis Translation 2015.4.2 Equilibrium for an Air-Water-HAE System 2025.4.3 Equilibrium for an Air-Water-HAE-Soil System 2035.4.4 Characteristic Curve for HAE Material 2045.4.5 Controlled Stress Variable Testing 2045.5 Graphical Representation of Stress 2075.5.1 Net Normal Stress and Matric Suction Representation 2075.5.2 Effective Stress Representation 213Problems 2186 SHEAR STRENGTH 2206.1 Extended Mohr-Coulomb (M-C) Criterion 2206.1.1 M-C for Saturated Soil 2206.1.2 Experimental Observations of Unsaturated Shear Strength 2216.1.3 Extended M-C Criterion 2296.1.4 Extended M-C Criterion in Terms of Principal Stresses 2326.2 Shear Strength Parameters for the Extended M-C Criterion 2336.2.1 Interpretation of Triaxial Testing Results 2336.2.2 Interpretation of Direct Shear Testing Results 2366.3 Effective Stress and the M-C Criterion 2386.3.1 Nonlinearity in the Extended M-C Envelope 2386.3.2 Effective Stress Approach 2416.3.3 Measurements of _ at Failure 2426.3.4 Reconciliation between _b and _f 2446.3.5 Validity of Effective Stress as a State Variable for Strength 2476.4 Shear Strength Parameters for the M-C Criterion 2486.4.1 Interpretation of Direct Shear Testing Results 2486.4.2 Interpretation of Triaxial Testing Results 2506.5 Unified Representation of Failure Envelope 2526.5.1 Capillary Cohesion as a Characteristic Function for Unsaturated Soil 2526.5.2 Determining the Magnitude of Capillary Cohesion 2566.5.3 Concluding Remarks 261Problems 2657 SUCTION AND EARTH PRESSURE PROFILES 2677.1 Steady Suction and Water Content Profiles 2677.1.1 Suction Regimes in Unsaturated Soil 2677.1.2 Analytical Solutions for Profiles of Matric Suction 2707.1.3 Hydrologic Parameters for Representative Soil Types 2727.1.4 Profiles of Matric Suction for Representative Soil Types 2737.1.5 Profiles of Water Content for Representative Soil Types 2757.2 Steady Effective Stress Parameter and Stress Profiles 2807.2.1 Profiles of the Effective Stress Parameter _  2807.2.2 Profiles of Suction Stress and Their Solution Regimes 2827.2.3 Profiles of Suction Stress for Representative Soil Types 2897.2.4 Concluding Remarks 2927.3 Earth Pressure at Rest 2947.3.1 Extended Hooke’s Law 2947.3.2 Profiles of Coefficient of Earth Pressure at Rest 2967.3.3 Depth of Cracking 2977.4 Active Earth Pressure 3017.4.1 Mohr-Coulomb Failure Criteria for Unsaturated Soil 3017.4.2 Rankine’s Active State of Failure 3027.4.3 Active Earth Pressure Profiles for Constant Suction Stress 3067.4.4 Active Earth Pressure Profiles for Variable Suction Stress 3087.4.5 Active Earth Pressure Profiles with Tension Cracks 3107.5 Passive Earth Pressure  3127.5.1 Rankine’s Passive State of Failure 3127.5.2 Passive Earth Pressure Profiles for Constant Suction Stress 3157.5.3 Passive Earth Pressure Profiles for Variable Suction Stress 3187.5.4 Concluding Remarks 320Problems 322III FLOW PHENOMENA 3238 STEADY FLOWS 3258.1 Driving Mechanisms for Water and Airflow 3258.1.1 Potential for Water Flow 3258.1.2 Mechanisms for Airflow 3268.1.3 Regimes for Pore Water Flow and Pore Airflow 3268.1.4 Steady-State Flow Law for Water 3288.2 Permeability and Hydraulic Conductivity 3298.2.1 Permeability versus Conductivity 3298.2.2 Magnitude, Variability, and Scaling Effects 3318.3 Hydraulic Conductivity Function 3338.3.1 Conceptual Model for the Hydraulic Conductivity Function 3338.3.2 Hysteresis in the Hydraulic Conductivity Function 3368.3.3 Relative Conductivity 3368.3.4 Effects of Soil Type 3388.4 Capillary Barriers 3418.4.1 Natural and Engineered Capillary Barriers 3418.4.2 Flat Capillary Barriers 3428.4.3 Dipping Capillary Barriers 3458.5 Steady Infiltration and Evaporation 3498.5.1 Horizontal Infiltration 3498.5.2 Vertical Infiltration and Evaporation 3528.6 Steady Vapor Flow 3598.6.1 Fick’s Law for Vapor Flow 3598.6.2 Temperature and Vapor Pressure Variation 3598.6.3 Vapor Density Gradient 3618.7 Steady Air Diffusion in Water 3638.7.1 Theoretical Basis 3638.7.2 Air Diffusion in an Axis Translation System 366Problems 3679 TRANSIENT FLOWS 3699.1 Principles for Pore Liquid Flow 3699.1.1 Principle of Mass Conservation 3699.1.2 Transient Saturated Flow 3719.1.3 Transient Unsaturated Flow 3729.2 Rate of Infiltration 3769.2.1 Transient Horizontal Infiltration 3769.2.2 Transient Vertical Infiltration 3809.2.3 Transient Moisture Profile for Vertical Infiltration 3849.3 Transient Suction and Moisture Profiles 3869.3.1 Importance of Transient Soil Suction and Moisture 3869.3.2 Analytical Solution of Transient Unsaturated Flow 3869.3.3 Numerical Modeling of Transient Unsaturated Flow 3899.4 Principles for Pore Gas Flow 3969.4.1 Principle of Mass Conservation for Compressible Gas 3969.4.2 Governing Equation for Pore Airflow 3979.4.3 Linearization of the Airflow Equation 3989.4.4 Sinusoidal Barometric Pressure Fluctuation 4009.5 Barometric Pumping Analysis 4029.5.1 Barometric Pumping 4029.5.2 Theoretical Framework 4039.5.3 Time Series Analysis 4049.5.4 Determining Air Permeability 407Problems 412IV MATERIAL VARIABLE MEASUREMENT AND MODELING 41510 SUCTION MEASUREMENT 41710.1 Overview of Measurement Techniques 41710.2 Tensiometers 42010.2.1 Properties of High-Air-Entry Materials 42010.2.2 Tensiometer Measurement Principles 42110.3 Axis Translation Techniques 42410.3.1 Null Tests and Pore Water Extraction Tests 42410.3.2 Pressure Plates 42510.3.3 Tempe Pressure Cells 42710.4 ElectricalThermal Conductivity Sensors 42910.5 Humidity Measurement Techniques 43110.5.1 Total Suction and Relative Humidity 43110.5.2 Thermocouple Psychrometers 43210.5.3 Chilled-Mirror Hygrometers 43810.5.4 Polymer Resistance Capacitance Sensors 44110.6 Humidity Control Techniques 44310.6.1 Isopiestic Humidity Control 44410.6.2 Two-Pressure Humidity Control 44510.7 Filter Paper Techniques 44910.7.1 Filter Paper Measurement Principles 44910.7.2 Calibration and Testing Procedures 45110.7.3 Accuracy, Precision, and Performance 452Problems 45911 HYDRAULIC CONDUCTIVITY MEASUREMENT 46211.1 Overview of Measurement Techniques 46211.2 Steady-State Measurement Techniques 46311.2.1 Constant-Head Method 46311.2.2 Constant-Flow Method 46611.2.3 Centrifuge Method 47211.3 Transient Measurement Techniques 47611.3.1 Hydraulic Diffusivity 47611.3.2 Horizontal Infiltration Method 47711.3.3 Outflow Methods 48011.3.4 Instantaneous Profile Methods 484Problems 49312 SUCTION AND HYDRAULIC CONDUCTIVITY MODELS 49412.1 Soil-Water Characteristic Curve Models 49412.1.1 SWCC Modeling Parameters 49512.1.2 Brooks and Corey (BC) Model 49712.1.3 van Genuchten (VG) Model 49912.1.4 Fredlund and Xing (FX) Model 50512.2 Hydraulic Conductivity Models 50612.2.1 Empirical and Macroscopic Models 50912.2.2 Statistical Models 516Problems 527REFERENCES 531INDEX 547