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.
