## CONTENTS

Foreword xiii

Preface xv

Acknowledgments xvii

CHAPTER 1 Theory to Practice of Unsaturated Soil Mechanics 1

1.1 Introduction 1

1.2 Moisture and Thermal Flux Boundary Conditions 6

1.3 Determination of Unsaturated Soil Properties 8

1.4 Stages in Moving Toward Implementation 9

1.5 Need for Unsaturated Soil Mechanics 11

1.6 Partial Differential Equations in Soil Mechanics 17

1.7 Engineering Protocols for Unsaturated Soils 26

CHAPTER 2 Nature and Phase Properties of Unsaturated Soil 29

2.1 Introduction 29

2.2 Soil Classification 34

2.3 Phase Properties 48

2.4 Volume-Mass Variables 66

2.5 Soil Compaction 73

2.6 Volume-Mass Relations When Mass Is Lost from

System 76

CHAPTER 3 State Variables for Unsaturated Soils 80

3.1 Introduction 80

3.2 Basis for Stress State Variables 84

3.3 Stress State Variables for Unsaturated Soils 87

3.4 Representation of Stress States 94

3.5 Equations for Mohr Circle 98

3.6 Role of Osmotic Suction 105

CHAPTER 4 Measurement and Estimation of State Variables 109

4.1 Introduction 109

4.2 Measurement of Soil Suction 109

4.3 Measurement of Total Suction 149

4.4 Measurement of Osmotic Suction 164

4.5 Measurement of In Situ Water Content 165

4.6 Estimation of Soil Suction 169

CHAPTER 5 Soil-Water Characteristic Curves for Unsaturated Soils 184

5.1 Introduction 184

5.2 Volume-Mass Constitutive Relations 190

5.3 Equations for SWCC 200

5.4 Regression Analysis on SWCC Equations 214

5.5 Hysteresis, Initialization, and Interpretation

of SWCC 217

5.6 Pham and Fredlund (2011) Equation for Entire

SWCC 224

5.7 Gitirana and Fredlund (2004) SWCC 231

5.8 Measurement of SWCC Using Pressure Plate

Devices 234

5.9 Single-Specimen Pressure Plate Devices

for Geotechnical Engineering 242

5.10 Vacuum Desiccators for High Suctions 249

5.11 Use of Chilled-Mirror or Dew-Point Method 251

5.12 Estimation of SWCC 253

5.13 Two-Point Method of Estimating SWCC 263

5.14 Correlation of Fitting Parameters to Soil Properties 265

5.15 Application of SWCC 269

5.16 Guidelines and Recommendations for Engineering

Practice 271

CHAPTER 6 Ground Surface Moisture Flux Boundary Conditions 273

6.1 Introduction 273

6.2 Climatic Classification for a Site 274

6.3 Boundary Value Framework for Near-Ground-

Surface Design 278

6.4 Challenges of Numerical Modeling Ground

Surface Moisture Flux Conditions 321

CHAPTER 7 Theory of Water Flow through Unsaturated Soils 327

7.1 Introduction 327

7.2 Theory of Flow of Water 327

7.3 Darcy’s Law for Unsaturated Soils 331

7.4 Partial Differential Equations for Steady-State

Water Flow 344

7.5 Partial Differential Equations for Transient

Seepage 351

7.6 Direct Measurement of Water Flow Properties 354

CHAPTER 8 Solving Saturated/Unsaturated Water Flow Problems 375

8.1 Introduction 375

8.2 Estimation of Permeability Function 375

8.3 Application to Saturated-Unsaturated Water Flow

Problems 397

8.4 Conditions under Which Matric Suction Can Be

Maintained 437

CHAPTER 9 Air Flow through Unsaturated Soils 450

9.1 Introduction 450

9.2 Theory of Free Air Flow 450

9.3 Fick’s Law and Darcy’s Law for Air Flow 451

9.4 Diffusion of Air through Water 458

9.5 Other Components of Air Flow 460

9.6 Partial Differential Equations for Air Flow through

Unsaturated Soils 461

9.7 Direct Measurement of Air Coefficient

of Permeability 465

9.8 Direct Measurement of Air Diffusion through

Water 467

9.9 Indirect Estimation of Air Flow Properties 472

9.10 Applications to Saturated-Unsaturated Air Flow

Problems 480

CHAPTER 10 Heat Flow Analysis for Unsaturated Soils 487

10.1 Introduction 487

10.2 Theory of Heat Flow 488

10.3 Theory of Freezing and Thawing Soils 492

10.4 Formulation of Partial Differential Equations for

Conductive Heat Flow 495

10.5 Direct Measurement of Thermal Properties 500

10.6 Estimation Procedures for Thermal Properties 505

10.7 Applications to Thermal Problems 510

10.8 One-Dimensional Heat Flow in Unfrozen and

Frozen Soils 511

10.9 Two-Dimensional Heat Flow Example Involving

Chilled Pipeline 511

10.10 Two-Dimensional Heat Flow Example with

Surface Temperatures above and below Freezing 512

10.11 Aldrich (1956) Example of Vertical Column 516

CHAPTER 11 Shear Strength of Unsaturated Soils 520

11.1 Introduction 520

11.2 Theory of Shear Strength 520

11.3 Measurement of Shear Strength 536

11.4 Special Equipment Design Considerations 541

11.5 Triaxial Test Procedures for Unsaturated Soils 551

11.6 Interpretation of Triaxial Test Results 554

11.7 Direct Shear Tests 565

11.8 Typical Laboratory Test Results 567

11.9 Selection of Strain Rate 578

CHAPTER 12 Shear Strength Applications in Plastic and Limit

Equilibrium 588

12.1 Introduction 588

12.2 Estimation of Shear Strength Functions for

Unsaturated Soils 588

12.3 Application to Practical Shear Strength Problems

in Geotechnical Engineering 612

12.4 Bearing Capacity 626

12.5 Slope Stability 632

12.6 Optimization Procedures to Solve for Factor of

Safety 642

12.7 Application of Slope Stability Analyses 651

12.8 Hazard Assessment and Decision Analysis Related

to Slope Instability 662

CHAPTER 13 Stress-Deformation Analysis for Unsaturated Soils 666

13.1 Introduction 666

13.2 Concepts of Volume Change and Deformation 670

13.3 Volume-Mass Constitutive Relations 673

13.4 Compressibility Form for Unsaturated Soil Constitutive

Relations 679

13.5 Relationship Among Volumetric Deformation

Coefficients 685

13.6 Pham-Fredlund Volume-Mass Constitutive Model

(2011a) 693

13.7 Formulation of Partial Differential Equations for

Stress-Deformation in Unsaturated Soils 713

13.8 Measurement of Stress-Deformation Properties for

Unsaturated Soils 721

CHAPTER 14 Solving Stress-Deformation Problems with Unsaturated

Soils 731

14.1 Introduction 731

14.2 Estimation of Stress-Deformation Properties 731

14.3 Application to Practical Stress-Deformation

Problems 735

14.4 Evaluation of Stress History in Unsaturated Soils 738

14.5 One-Dimensional Formulations for Deformation

Analysis for Unsaturated Soil 756

14.6 Swelling Theory Formulated in Terms of Incremental

Elasticity Parameters 768

14.7 Evaluation of Elasticity Parameter Functions from

Volume Change Indices 771

14.8 One-Dimensional Solution Using Incremental

Elasticity Formulation 775

14.9 Two-Dimensional Solution Using Incremental

Elasticity Formulation 778

14.10 Challenges in Numerically Modeling of Expansive

Soil Problems 778

CHAPTER 15 Compressibility and Pore Pressure Parameters 783

15.1 Introduction 783

15.2 Coupled and Uncoupled Solutions 784

15.3 Uncoupled Undrained Loading 786

15.4 Derivation of Pore Pressure Parameters 794

15.5 Drained and Undrained Loading 796

15.6 Solutions of Pore Pressure Equations and

Comparisons with Experimental Results 802

15.7 Rheological Model to Represent Relative

Compressibilities of Unsaturated Soil 807

CHAPTER 16 Consolidation and Swelling Processes in Unsaturated

Soils 809

16.1 Introduction 809

16.2 Stress and Seepage Uncoupled and Coupled

Systems 809

16.3 Solution of Consolidation Equations Using Finite

Difference Technique 817

16.4 Typical Consolidation Test Results on Unsaturated

Soils 819

16.5 Dimensionless Consolidation Parameters 823

16.6 Coupled Formulations and Three-Dimensional

Consolidation 825

16.7 Water, Air Flow, and Nonisothermal Systems 829

16.8 Two-Dimensional Stress-Deformation and

Saturated-Unsaturated Seepage Analysis 831

16.9 Computer Simulation of Edge Lift and Edge Drop

of Slabs-on-Ground 845

16.10 Theory for Simulation of Swelling Pressure

Development 848

16.11 Rheological Model for Unsaturated Soils 851

APPENDIX Units and Symbols 858

References 864

Index 911

## PREFACE

Soil mechanics is a relatively young applied science. Karl Terzaghi published his English version of Theoretical Soil Mechanics

in 1943. The book provided a science-based context for analyzing the physical behavior of saturated soils.

Geotechnical engineering has changed in many ways since the 1940s. The procedures for performing subsurface investigations

have undergone some changes, but the investigative procedures remain quite similar. Boreholes are still drilled with

disturbed and undisturbed soil samples taken at intervals for later laboratory testing. However, the manner in which we obtain

our geotechnical engineering solutions has changed dramatically. Terzaghi and his contemporaries assembled the context for

soil mechanics at a time when the tools for solving mathematical problems were significantly different from the tools that are

available today.

In the 1940s, the writers of soil mechanics textbooks attempted to take complex three-dimensional, real-world problems

and reduce them to simplified, closed-form solutions. Flownets provided a graphical solution for the movement of water

through an isotropic, homogeneous, two-dimensional porous continuum. Methods of (vertical) slices provided a solution

for calculating the factor of safety of a two-dimensional slope. Methods of (horizontal) layers provided a solution for the

calculation of settlement of a one-dimensional, compressible clay soil. The soil mechanics world contained a series of soil

property constants (e.g., k, c, and φ

), and those soil properties that were not constants were converted to a linear form to be

represented as constants (e.g., Cc and Cs ).

It became clear in the 1960s and 1970s that unsaturated soil properties would need to be defined as nonlinear unsaturated

soil property functions (USPFs). Unsaturated soil mechanics became a vibrant area of geotechnical research, and it was

apparent that we were entering a new era that required a new paradigm for solving saturated-unsaturated soil mechanics

problems. If unsaturated soil mechanics was to find its way into geotechnical engineering practice there needed to be reliable

methodologies for obtaining the unsaturated soil property functions at reasonable cost and effort. Consequently, a wide variety

of estimation procedures emerged from research in many countries. The estimation procedures relied heavily on the saturated

soil properties and an understanding of the soil-water characteristic curve (SWCC), that is, the relationship between water

content and soil suction.

The 1960s and 1970s were decades that witnessed rapid growth in our ability to solve complex mathematical formulations.

The computer could be used to solve new mathematical formulations that described the physical behavior of saturatedunsaturated

soil mechanics problems. Numerical methods of solution emerged for all areas of material behavior, areas that

spanned well beyond classical soil mechanics. Soil mechanics problems were visualized as boundary value problems with

the following conditions defined: (i) geometry and stratigraphy, (ii) initial conditions and boundary conditions, (iii) soil

properties, and (iv) solution techniques. The physics of soil behavior was defined for a referential elemental volume (REV)

of the saturated-unsaturated soil continuum and the mathematical formulation describing the physics of soil behavior took on

the form of a partial differential equation (PDE). Generally the PDEs were found to be nonlinear because of the nonlinear

unsaturated soil property functions required as part of the formulation. The type of equations that many of us disliked as

undergraduate students became the heart of unsaturated soil problem solving. Fortunately, we were able to hide the PDE

solver in advanced computer software tools.

Geotechnical engineers have benefited from research undertaken in two primary areas: (i) soil physics and agronomy and

(ii) computer technology and mathematics. In particular, it was the rapid growth in computing capability (i.e., computer

hardware and software) that made the solution of unsaturated soil problems possible. The stage was set for solving saturatedunsaturated

soil mechanics problems within a boundary value context through use of numerical modeling techniques.

It is an understatement to say that the digital computer has revolutionized the way that soil mechanics is now implemented

in engineering practice. It is safe to say that it would not be possible to model and solve saturated-unsaturated soil mechanics

problems within a science framework without the power of the digital computer. Geotechnical engineering has moved into

a new paradigm, a problem-solving environment involving SWCCs, USPFs, and PDEs. It is a world in which the challenge

becomes the convergence and the uniqueness of the soil mechanics solution. It is a world in which computer software is no

longer a luxury but a necessity for sound engineering practice.

During the course of writing this book, numerous example problems were analyzed using the SVOffice geotechnical software

suite. The examples in this book are freely distributed as resources related to the learning process associated with unsaturated

soil mechanics. Instructions for obtaining these examples may be found at www.soilvision.com/usmep. The examples include

seepage (SVFLUX™), slope stability (SVSLOPE®), freeze/thaw (SVHEAT™), and stress/deformation (SVSOLID™) finite

element numerical models for which the setup and solution information can be examined.

Eduardo Alonso and Antonio Gens (2011) put it well in the Preface to the Fifth International Conference on Unsaturated

Soils, Barcelona, Spain, when they wrote, “The development of unsaturated soil mechanics in recent decades has been

remarkable and it has resulted in momentous advances in fundamental knowledge, testing methods, computational procedures,

prediction methodologies and geotechnical practice.” As authors, we trust that the book Unsaturated Soil Mechanics in

Engineering Practice will further advance the usage of the science of unsaturated soil behavior in engineering practice.

Unsaturated Soil Mechanics in Engineering Practice constitutes a substantial addition and reorganization of information

from what was synthesized in the book Soil Mechanics for Unsaturated Soils by D. G. Fredlund and H. Rahardjo. Unsaturated

Soil Mechanics in Engineering Practice more thoroughly covers our present knowledge of unsaturated soil behavior and better

reflects the manner in which practical unsaturated soil engineering problems are solved. The fundamental physics of unsaturated

soil behavior presented in Soil Mechanics for Unsaturated Soils has been retained in the present edition while greater emphasis

has been placed on the importance of using the SWCC when solving engineering problems. Greater emphasis has also been

placed on the quantification of thermal and moisture boundary conditions based on the use of weather data. In the end, the

reader should find Unsaturated Soil Mechanics in Engineering Practice to be a practical book leading geotechnical engineers

through to the implementation of unsaturated soil mechanics into engineering practice.