## CONTENTS

PREFACE xiii

1 PROPERTIES OF SOIL 1

1.1 Soil Formation / 1

1.2 Physical Parameters of Soils / 3

1.2.1 Relative Density / 7

1.3 Mechanical Properties of Soil / 8

1.3.1 Sieve Analysis / 8

1.3.2 Hydrometer Analysis / 10

1.4 Soil Consistency / 11

1.4.1 Liquid Limit / 12

1.4.2 Plastic Limit / 12

1.4.3 Shrinkage Limit / 12

1.5 Plasticity Chart / 13

1.6 Classification Systems / 14

1.7 Compaction / 16

2 ELASTICITY AND PLASTICITY 21

2.1 Introduction / 21

2.2 Stress Matrix / 22

2.3 Elasticity / 23

2.3.1 Three-Dimensional Stress Condition / 23

2.3.2 Uniaxial Stress Condition / 24

2.3.3 Plane Strain Condition / 25

2.3.4 Plane Stress Condition / 27

2.4 Plasticity / 28

2.5 Modified Cam Clay Model / 28

2.5.1 Normal Consolidation Line and Unloading–Reloading

Lines / 30

2.5.2 Critical-State Line / 33

2.5.3 Yield Function / 36

2.5.4 Hardening and Softening Behavior / 36

2.5.5 Elastic Moduli for Soil / 38

2.5.6 Summary of Modified Cam Clay Model Parameters / 39

2.5.7 Incremental Plastic Strains / 40

2.5.8 Calculations of the Consolidated–Drained Stress–Strain

Behavior of a Normally Consolidated Clay Using the Modified

Cam Clay Model / 42

2.5.9 Step-by-Step Calculation Procedure for a CD Triaxial Test on

NC Clays / 44

2.5.10 Calculations of the Consolidated–Undrained Stress–Strain

Behavior of a Normally Consolidated Clay Using the Modified

Cam Clay Model / 47

2.5.11 Step-by-Step Calculation Procedure for a CU Triaxial Test on

NC Clays / 49

2.5.12 Comments on the Modified Cam Clay Model / 53

2.6 Stress Invariants / 53

2.6.1 Decomposition of Stresses / 55

2.7 Strain Invariants / 57

2.7.1 Decomposition of Strains / 57

2.8 Extended Cam Clay Model / 58

2.9 Modified Drucker–Prager/Cap Model / 61

2.9.1 Flow Rule / 63

2.9.2 Model Parameters / 64

2.10 Lade’s Single Hardening Model / 68

2.10.1 Elastic Behavior / 68

2.10.2 Failure Criterion / 68

2.10.3 Plastic Potential and Flow Rule / 69

2.10.4 Yield Criterion / 72

2.10.5 Predicting Soil’s Behavior Using Lade’s Model: CD Triaxial

Test Conditions / 82

3 STRESSES IN SOIL 90

3.1 Introduction / 90

3.2 In Situ Soil Stresses / 90

3.2.1 No-Seepage Condition / 93

3.2.2 Upward-Seepage Conditions / 97

3.2.3 Capillary Rise / 99

3.3 Stress Increase in a Semi-Infinite Soil Mass Caused by External

Loading / 101

3.3.1 Stresses Caused by a Point Load (Boussinesq Solution) / 102

3.3.2 Stresses Caused by a Line Load / 104

3.3.3 Stresses Under the Center of a Uniformly Loaded Circular

Area / 109

3.3.4 Stresses Caused by a Strip Load (B/L ≈ 0) / 114

3.3.5 Stresses Caused by a Uniformly Loaded Rectangular

Area / 116

4 CONSOLIDATION 124

4.1 Introduction / 124

4.2 One-Dimensional Consolidation Theory / 125

4.2.1 Drainage Path Length / 127

4.2.2 One-Dimensional Consolidation Test / 127

4.3 Calculation of the Ultimate Consolidation Settlement / 131

4.4 Finite Element Analysis of Consolidation Problems / 132

4.4.1 One-Dimensional Consolidation Problems / 133

4.4.2 Two-Dimensional Consolidation Problems / 147

5 SHEAR STRENGTH OF SOIL 162

5.1 Introduction / 162

5.2 Direct Shear Test / 163

5.3 Triaxial Compression Test / 170

5.3.1 Consolidated–Drained Triaxial Test / 172

5.3.2 Consolidated–Undrained Triaxial Test / 180

5.3.3 Unconsolidated–Undrained Triaxial Test / 185

5.3.4 Unconfined Compression Test / 186

5.4 Field Tests / 186

5.4.1 Field Vane Shear Test / 187

5.4.2 Cone Penetration Test / 187

5.4.3 Standard Penetration Test / 187

5.5 Drained and Undrained Loading Conditions via FEM / 188

6 SHALLOW FOUNDATIONS 209

6.1 Introduction / 209

6.2 Modes of Failure / 209

6.3 Terzaghi’s Bearing Capacity Equation / 211

6.4 Meyerhof’s General Bearing Capacity Equation / 224

6.5 Effects of the Water Table Level on Bearing Capacity / 229

7 LATERAL EARTH PRESSURE AND RETAINING WALLS 233

7.1 Introduction / 233

7.2 At-Rest Earth Pressure / 236

7.3 Active Earth Pressure / 241

7.3.1 Rankine Theory / 242

7.3.2 Coulomb Theory / 246

7.4 Passive Earth Pressure / 249

7.4.1 Rankine Theory / 249

7.4.2 Coulomb Theory / 252

7.5 Retaining Wall Design / 253

7.5.1 Factors of Safety / 256

7.5.2 Proportioning Walls / 256

7.5.3 Safety Factor for Sliding / 257

7.5.4 Safety Factor for Overturning / 258

7.5.5 Safety Factor for Bearing Capacity / 258

7.6 Geosynthetic-Reinforced Soil Retaining Walls / 271

7.6.1 Internal Stability of GRS Walls / 272

7.6.2 External Stability of GRS Walls / 275

8 PILES AND PILE GROUPS 286

8.1 Introduction / 286

8.2 Drained and Undrained Loading Conditions / 286

8.3 Estimating the Load Capacity of Piles / 291

8.3.1 α-Method / 291

8.3.2 β-method / 297

8.4 Pile Groups / 301

8.4.1 α-Method / 304

8.4.2 β-Method / 304

8.5 Settlements of Single Piles and Pile Groups / 312

8.6 Laterally Loaded Piles and Pile Groups / 313

8.6.1 Broms’ Method / 314

8.6.2 Finite Element Analysis of Laterally Loaded Piles / 317

9 PERMEABILITY AND SEEPAGE 332

9.1 Introduction / 332

9.2 Bernoulli’s Equation / 333

9.3 Darcy’s Law / 337

9.4 Laboratory Determination of Permeability / 338

9.5 Permeability of Stratified Soils / 340

9.6 Seepage Velocity / 342

9.7 Stresses in Soils Due to Flow / 343

9.8 Seepage / 346

9.9 Graphical Solution: Flow Nets / 349

9.9.1 Calculation of Flow / 350

9.9.2 Flow Net Construction / 351

9.10 Flow Nets for Anisotropic Soils / 354

9.11 Flow Through Embankments / 355

9.12 Finite Element Solution / 356

REFERENCES 377

INDEX 381

## PREFACE

The purpose of this book is to provide civil engineering students and practitioners

with simple basic knowledge on how to apply the finite element method to soil

mechanics problems. This is essentially a soil mechanics book that includes traditional

soil mechanics topics and applications. The book differs from traditional soil

mechanics books in that it provides a simple and more flexible alternative using

the finite element method to solve traditional soil mechanics problems that have

closed-form solutions. The book also shows how to apply the finite element method

to solve more complex geotechnical engineering problems of practical nature that

do not have closed-form solutions.

In short, the book is written mainly for undergraduate students, to encourage

them to solve geotechnical engineering problems using both traditional engineering

solutions and the more versatile finite element solutions. This approach not only

teaches the concepts but also provides means to gain more insight into geotechnical

engineering applications that reinforce the concepts in a very profound manner.

The concepts are presented in a basic form so that the book can serve as a valuable

learning aid for students with no background in soil mechanics. The main prerequisite

would be strength of materials (or equivalent), which is a prerequisite for

soil mechanics in most universities.

General soil mechanics principles are presented for each topic, followed by traditional

applications of these principles with longhand solutions, which are followed

in turn by finite element solutions for the same applications, and then both solutions

are compared. Further, more complex applications are presented and solved using

the finite element method.

The book consist of nine chapters, eight of which deal with traditional soil

mechanics topics, including stresses in semi-infinite soil mass, consolidation, shear

strength, shallow foundations, lateral earth pressure, deep foundations (piles), and

seepage. The book includes one chapter (Chapter 2) that describes several elastic

and elastoplastic material models, some of which are used within the framework of

the finite element method to simulate soil behavior, and that includes a generalized

three-dimensional linear elastic model, the Cam clay model, the cap model and

Lade’s model. For undergraduate teaching, one can include a brief description of

the essential characteristics and parameters of the Cam clay model and the cap

model without much emphasis on their mathematical derivations.

Over 60 solved examples appear throughout the book. Most are solved longhand

to illustrate the concepts and then solved using the finite element method embodied

in a computer program: ABAQUS. All finite element examples are solved using

ABAQUS. This computer program is used worldwide by educators and engineers to

solve various types of civil engineering and engineering mechanics problems. One

of the major advantages of using this program is that it is capable of solving most

geotechnical engineering problems. The program can be used to tackle geotechnical

engineering problems involving two- and three-dimensional configurations that may

include soil and structural elements, total and effective stress analysis, consolidation

analysis, seepage analysis, static and dynamic (implicit and explicit) analysis,

failure and post-failure analysis, and a lot more. Nevertheless, other popular finite

element or finite difference computer programs specialized in soil mechanics can be

used in conjunction with this book in lieu of ABAQUS—obviously, this depends

on the instructor’s preference.

The PC Education Version of ABAQUS can be obtained via the internet so

that the student and practitioner can use it to rework the examples of the book

and to solve the homework assignments, which can be chosen from those end-ofchapter

problems provided. Furthermore, the input data for all examples can be

downloaded from the book’s website (www.wiley.com/college/helwany). This can

be very useful for the student and practitioner, since they can see how the input

should be for a certain problem, then can modify the input data to solve more

complex problems of the same class.

I express my deepest appreciation to the staff at John Wiley & Sons Publishing

Company, especially Mr. J. Harper, Miss K. Nasdeo, and Miss M. Torres for their

assistance in producing the book. I am also sincerely grateful to Melody Clair for

her editing parts of the manuscript.

Finally, a very special thank you to my family, Alba, Eyad, and Omar, and my

brothers and sisters for their many sacrifices during the development of the book.