An Introduction to Soil Dynamics

by Arnold Verruijt

Overview

to Soil Dynamics Arnold Verruijt Delft University of Technology, Delft, The Netherlands Arnold Verruijt Delft University of Technology 2628 CN Delft Netherlands [e-mail] A CD-ROM accompanies this book containing programs for waves in piles, propagation of earthquakes in soils, waves in a half space generated by a line load, a point load, a strip load, or a moving load, and the propagation of a shock wave in a saturated elastic porous material. Computer programs are also available from the website http://geo.verruijt.net ISBN 978-90-481-3440-3 e-ISBN 978-90-481-3441-0 DOI 10.1007/978-90-481-3441-0 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009940507 © Springer Science+Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, phoopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface This book gives the material for an introductory course on Soil Dynamics, as given for about 10 years at the Delft University of Technology for students of civil en- neering, and updated continuously since 1994.

Product Details

ISBN-13:	9789048134403
Publisher:	Springer Netherlands
Publication date:	01/22/2010
Series:	Theory and Applications of Transport in Porous Media , #24
Edition description:	2010
Pages:	433
Product dimensions:	6.30(w) x 9.30(h) x 1.00(d)

Table of Contents

1 Vibrating Systems 1

1.1 Single Mass System 1

1.2 Characterization of Viscosity 2

1.3 Free Vibrations 3

Small Damping 4

Critical Damping 5

Large Damping 6

1.4 Forced Vibrations 6

Dissipation of Work 9

1.5 Equivalent Spring and Damping 10

1.6 Solution by Laplace Transform Method 11

1.7 Hysteretic Damping 13

2 Waves in Piles 17

2.1 One-Dimensional Wave Equation 17

2.2 Solution by Laplace Transform Method 18

2.2.1 Pile of Infinite Length 18

2.2.2 Pile of Finite Length 20

2.3 Separation of Variables 21

2.3.1 Shock Wave in Finite Pile 22

2.3.2 Periodic Load 24

2.4 Solution by Characteristics 26

2.5 Reflection and Transmission of Waves 29

2.6 The Influence of Friction 34

Infinitely Long Pile 37

2.7 Numerical Solution 38

Example 39

2.8 A Simple Model for a Pile with Friction 42

Problems 43

3 Earthquakes in Soft Layers 45

3.1 Earthquake Parameters 46

3.2 Horizontal Vibrations 47

3.2.1 Unloaded Soil Layer 48

3.2.2 Soil Layer with Surface Load 50

3.3 Shear Waves in a Gibson Material 52

3.4 Hysteretic Damping 54

3.4.1 Basic Equations 54

3.4.2 Unloaded Soil Layer 56

3.4.3 Soil Layer with Surface Load 58

3.5 Numerical Solution 60

Basic Equations 60

Problems 63

4 Theory of Consolidation 65

4.1 Consolidation 65

4.1.1 Undrained Compression of a Porous Medium 66

4.1.2 The Principle of Effective Stress 67

4.2 Conservation of Mass 68

4.3 Darcy's Law 71

4.4 Equilibrium Equations 72

4.5 Drained Deformations 75

4.6 Undrained Deformations 76

4.7 Cryer's Problem 78

Basic Equations 78

Boundary Conditions 79

Initial Response 80

Solution of the Problem 80

Inverse Laplace Transformation 81

Results 81

4.8 Uncoupled Consolidation 82

Constant Isotropic Total Stress 83

Horizontally Confined Deformations 84

4.9 Terzaghi's Problem 85

Solution 86

Settlement 87

Problems 90

5 Dynamics of Porous Media 91

5.1 Basic Differential Equations 91

5.1.1 Conservation of Mass 91

5.1.2 Conservation of Momentum 93

5.1.3 Constitutive Equations 94

5.2 Propagation of Plane Waves 95

5.3 Special Cases 96

5.3.1 Undrained Waves 96

5.3.2 Rigid Solid Matrix 97

5.4 Analytical Solution 99

5.4.1 Periodic Solution 99

5.4.2 Response to a Sinusoidal Load 103

5.4.3 Approximation of the Solution 104

5.4.4 Numerical Verification 107

5.4.5 Response to a Block Wave 108

5.5 Numerical Solution 109

5.6 Conclusion 111

6 Cylindrical Waves 113

6.1 Static Problems 113

6.1.1 Basic Equations 113

6.1.2 General Solution 115

6.1.3 Examples 115

6.2 Dynamic Problems 120

6.2.1 Sinusoidal Vibrations at the Cavity Boundary 120

6.2.2 Equivalent Spring and Damping 125

6.3 Propagation of a Shock Wave 127

6.3.1 Solution by Laplace Transform 127

6.3.2 Solution by Fourier Series 129

6.4 Radial Propagation of Shear Waves 131

6.4.1 Sinusoidal Vibrations at the Cavity Boundary 132

Problems 134

Spherical Waves 137

7.1 Static Problems 137

7.1.1 Basic Equations 137

7.1.2 General Solution 139

7.1.3 Examples 139

7.2 Dynamic Problems 143

7.2.1 Propagation of Waves 144

7.2.2 Sinusoidal Vibrations at the Cavity Boundary 145

7.2.3 Propagation of a Shock Wave 149

Problems 154

Elastostatics of a Half Space 157

8.1 Basic Equations of Elastostatics 158

8.2 Boussinesq Problems 160

8.2.1 Concentrated Force 162

8.2.2 Uniform Load on a Circular Area 163

8.3 Fourier Transforms 164

8.3.1 Line Load 165

8.3.2 Strip Load 168

8.4 Axially Symmetric Problems 169

8.4.1 Uniform Load on a Circular Area 170

8.5 Mixed Boundary Value Problems 172

8.5.1 Rigid Circular Plate 173

8.5.2 Penny Shaped Crack 177

8.6 Confined Elastostatics 180

8.6.1 An Axially Symmetric Problem 181

8.6.2 A Plane Strain Problem 184

9 Elastodynamics of a Half Space 187

9.1 Basic Equations of Elastodynamics 188

9.2 Compression Waves 189

9.3 Shear Waves 189

9.4 Rayleigh Waves 190

9.5 Love Waves 194

9.5.1 A Practical Implication 198

10 Confined Elastodynamics 201

10.1 Line Load on Half Space 202

10.2 Line Pulse on Half Space 206

10.3 Strip Load on Half Space 207

10.3.1 Strip Pulse 207

10.3.2 Inversion by De Hoop's Method 208

10.3.3 Constant Strip Load 212

10.4 Point Load on Half Space 217

10.5 Periodic Load on a Half Space 219

Displacement of the Origin 222

Vibrating Point Load 224

Problems 224

11 Line Load on Elastic Half Space 225

11.1 Line Pulse 225

11.1.1 Description of the Problem 225

11.1.2 Solution by Integral Transform Method 227

11.1.3 The Vertical Displacement 230

11.1.4 The Vertical Displacement of the Surface 244

11.1.5 The Horizontal Displacement 249

11.1.6 The Horizontal Displacement of the Surface 255

11.2 Constant Line Load 260

11.2.1 Isotropic Stress 262

11.2.2 The Vertical Normal Stress 271

11.2.3 The Horizontal Normal Stress 278

11.2.4 The Shear Stress 284

Conclusion 289

Problems 290

12 Strip Load on Elastic Half Space 291

12.1 Strip Pulse 292

12.1.1 The Isotropic Stress 293

12.1.2 The Vertical Normal Stress 299

12.1.3 The Horizontal Normal Stress 305

12.1.4 The Shear Stress 308

12.2 Strip Load 312

12.2.1 The Isotropic Stress 313

12.2.2 The Vertical Normal Stress 320

12.2.3 The Horizontal Normal Stress 326

12.2.4 The Shear Stress 335

Conclusion 342

Problems 342

13 Point Load on an Elastic Half Space 345

13.1 Problem 345

13.1.1 Basic Equations 345

13.2 Solution 347

13.2.1 Vertical Displacement of the Surface 349

13.2.2 The Pekeris Procedure 350

13.2.3 Numerical Evaluation of the Integrals 355

13.2.4 Computer Program POINTLOAD 358

13.2.5 Results 359

14 Moving Loads on an Elastic Half Plane 361

14.1 Moving Wave 361

14.1.1 Basic Equations 361

14.1.2 Solutions 363

14.1.3 Solution 1 365

14.1.4 Solution 2 367

14.1.5 Completion of the Solution 369

14.1.6 First Boundary Condition 370

14.1.7 Second Boundary Condition 370

14.1.8 The Two Constants 372

14.1.9 Final Solution 372

14.1.l0 The Displacement of the Origin 373

14.2 Moving Strip Load 374

14.2.1 Vertical Displacement of the Surface 375

14.2.2 Vertical Normal Stress 376

14.2.3 Isotropic Stress 380

14.2.4 Horizontal Normal Stress 381

14.2.5 Shear Stress 382

15 Foundation Vibrations 385

15.1 Foundation Response 385

Circular Footing 386

15.2 Equivalent Spring and Damping 389

15.3 Soil Properties 391

15.4 Propagation of Vibrations 392

15.5 Design Criteria 392

Appendix A Integral Transforms 395

A.1 Laplace Transforms 395

A.1.1 Definitions 395

A.1.2 Example 396

A.l.3 Heaviside's Expansion Theorem 397

A.2 Fourier Transforms 398

A.2.1 Fourier Series 398

A.2.2 From Fourier Series to Fourier Integral 400

A.2.3 Application 401

A.2.4 List of Fourier Transforms 403

A.3 Hankel Transforms 406

A.3.1 Definitions 406

A.3.2 List of Hankel Transforms 407

A.4 De Hoop's Inversion Method 409

A.4.1 Introduction 409

A.4.2 Example 410

Appendix B Dual Integral Equations 417

Appendix C Bateman-Pekeris Theorem 419

References 423

Author Index 427

Index 431

Editorial Reviews

From the reviews:

 “Verruijt (Delft Univ. of Technology, Netherlands) begins this 15-chapter work by discussing the basic properties of dynamic systems including various forms of damping, defined using an elementary system of mass linear spring and damper. … The author … focuses on the basics of dynamic problems in elastic continua for different types of waves, and provides solutions for more difficult mixed boundary values. … Summing Up: Recommended. Graduate students, researchers, and faculty.” (R. P. Khera, Choice, Vol. 47 (11), August, 2010)

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