Foundation vibration analysis using simple physical models

446 Pages·1994·20.667 MB·English

by  Wolf, John P

Foundation Vibration Analysis
Using Simple Physical Models
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Foundation Vibration Analysis
Using Simple Physical Models
John P. Wolf
Swiss Federal Institute of Technology
PTR Prentice Hall
Upper Saddle River, NJ 07458
Library of Congress Cataloging-In-Publication Data
Wolf, John P.
Foundation vibration analysis using simple physical models / John
P. Wolf
p. cm.
Includes bibliographical references and index.
ISBN 0-13-010711-5
1. Foundations—Vibration—Mathematical models. I. Title.
TA775.W57 1994
624.1'5—dc20 93-41384
CIP
Editorial/production supervision: BooksCraft, Inc., Indianapolis, IN
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© 1994 by PTR Prentice Hall
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Printed in the United States of America
10 9 8 7 6 5 4 3 21
ISBN D-13-01D711-S
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Contents
Foreword xi
Preface xvii
List of Tables for Lumped-Parameter Models xxi
1 Introduction 1
1.1 Statement of Problem 1
1.2 Design of Machine Foundation 3
1.3 Effects of Soil-Structure Interaction 5
1.4 Classification of Analysis Methods 7
1.4.1 Direct method and substructure method 7
1.4.2 Frequency domain and time domain 8
1.4.3 Rigorous boundary-element method and approximate simple physical
models 9
1.5 Physical Modeling of Unbounded Soil 10
1.5.1 Applications 10
1.5.2 Overview 11
1.5.3 Examples 15
1.5.4 Requirements 20
1.6 Organization of Text 24
2 Foundation on Surface of Homogeneous Soil Halfspace 27
2.1 Construction of Cone Model 27
2.1.1 Elastic properties and wave-propagation velocities 27
2.1.2 Aspect ratio 29
2.1.3 High-frequency behavior 35
2.1.4 Nearly incompressible soil 40
2.2 Translational cone 42
2.2.1 Stiffness formulation 42
2.2.2 Flexibility formulation 46
2.2.3 Example for hand calculation 52
2.2.4 Vibration of machine foundation 54
2.3 Rotational Cone 64
2.3.1 Stiffness formulation 64
2.3.2 Flexibility formulation 70
V
2.3.3 Example for hand calculation 74
2.3.4 Vibration of machine foundation 76
2.4 Material Damping 89
2.4.1 Correspondence principle applied for harmonic motion 89
2.4.2 Correspondence principle applied to discrete-element
model 91
2.4.3 Comparison of models with linear-hysteretic damping and voigt
viscoelasticity 94
2.4.4 Frictional material damping 96
2.4.5 Example of seismic analysis 101
2.5 Why a Cone Model Can Represent the Elastic Halfspace 104
2.5.1 Object 104
2.5.2 Strength-of-materials versus rigorous theory of halfspace 104
2.5.3 Neglect of portion of halfspace outside cone 111
2.5.4 Inability of cone to represent rayleigh wave 115
2.6 Simple Lumped-Parameter Models 120
2.6.1 Standard lumped-parameter model 120
2.6.2 Fundamental lumped-parameter model 122
2.6.3 Torsional motion of disk with polar mass moment of inertia on
halfspace 127
2.7 Translational and Rocking Wedges 131
2.7.1 Dynamic-stiffness coefficient 131
2.7.2 Aspect ratio 135
2.7.3 Comparison of dynamic-stiffness coefficients for wedge with exact
solution 137
2.8 Insight on Two-Dimensional Versus Three-Dimensional Foundation
Modeling 138
2.8.1 Object 138
2.8.2 Equivalent slice of two-dimensional strip foundation with same material
properties 140
2.8.3 Alternative equivalent slice of two-dimensional strip foundation
adjusting impedance 141
2.8.4 Dynamic-stiffness coefficients of disk and equivalent slices of
strips 143
2.8.5 Decay of waves 146
2.8.6 Row of point loads 147
2.8.7 Square versus slender rectangular foundations 149
3 Foundation on Surface of Soil Layer on Rigid Rock 163
3.1 Construction of Unfolded Layered Cone Model 164
3.1.1 Layered translational cone 164
3.1.2 Layered rotational cone 169
3.2 Flexibility formulation 171
3.2.1 Unit-impulse response function 171
vi Contents
3.2.2 Static case 174
3.3 Stiffness Formulation 175
3.3.1 Pseudo-echo constants for rotation 175
3.3.2 Stiffness echo constants 177
3.3.3 Resonant case for translation 181
3.3.4 Nearly incompressible soil 182
3.3.5 Dynamic-stiffness coefficient 182
3.4 Alternative Order of Realization 186
3.5 Illustrative Example 187
3.6 Soil Layer on Flexible Rock Halfspace 190
3.6.1 Reflection coefficient for translational cone 190
3.6.2 Reflection coefficient for rotational cone 194
3.6.3 Flexibility and stiffness formulations 197
3.6.4 Accuracy evaluation 199
3.7 Basic Lumped-Parameter Model 204
3.7.1 Introductory example 204
3.7.2 Achieved accuracy 207
3.7.3 Coefficients of springs, dashpots, and mass 210
3.7.4 Rigid block on layer and on halfspace with partial uplift 211
3.8 Cutoff Frequency 214
3.8.1 General considerations 214
3.8.2 Practical significance of cutoff frequency 216
3.8.3 Bar on elastic foundation 217
3.8.4 Criterion for existence of cutoff frequency 220
4 Embedded Foundation and Pile Foundation 226
4.1 Embedded Disk with Double-Cone Model and its Green's
Function 228
4.1.1 One-sided cone 228
4.1.2 Double cone 228
4.1.3 Embedded disk with anti-symmetric and symmetric mirror disks to
model free surface and fixed boundary of halfspace 232
4.1.4 Embedded disk with anti-symmetric and symmetric mirror disks to
Model Free Surface and Fixed Boundary of Layer 235
4.1.5 Embedded disk with mirror disk to model interface with
halfspace 237
4.2 Matrix Formulation for Harmonic Loading of Foundation Embedded in
halfspace 239
4.2.1 Dynamic-flexibility matrix of free field 239
4.2.2 Dynamic-stiffness matrix 240
4.2.3 Example 242
4.3 Matrix Formulation in Time Domain of Foundation Embedded in
Halfspace 244
Contents vii
4.3.1 Dynamic-flexibility matrix of free field 244
4.3.2 Interaction force-displacement relationship 247
4.3.3 Example 250
4.4 Foundation Embedded in Layer 252
4.5 Limitation of Single Cone Model 255
4.6 Fundamental Lumped-Parameter Model for Foundation Embedded in
Halfspace 258
4.6.1 Coupled horizontal and rocking motions 258
4.6.2 Coefficients of spring, dashpots, and mass 261
4.6.3 Hammer foundation with partial uplift of anvil 262
4.7 Basic Lumped-Parameter Model for Foundation Embedded in
Layer 267
4.7.1 Coupled horizontal and rocking motions 267
4.7.2 Achieved accuracy 270
4.7.3 Coefficients of springs, dashpots, and mass 273
4.7.4 Hammer foundation with partial uplift of anvil 273
4.8 Single Pile 276
4.8.1 Analogy to embedded foundation 276
4.8.2 Matrix formulation for harmonic loading of pile embedded in
halfspace 276
4.8.3 Example of single floating pile 278
4.9 Pile Group 279
4.9.1 Group behavior 279
4.9.2 Dynamic-interaction factor 280
4.9.3 Matrix formulation for dynamic-stiffness matrix 283
4.9.4 Example of floating 3x3 pile group 286
5 Simple Vertical Dynamic Green's Function 294
5.1 Green's Function of Point Load on Surface of Halfspace 295
5.1.1 Static case 295
5.1.2 Dynamic case 295
5.2 Solutions Derived via Point-load Green's Function 298
5.2.1 Ring of point loads 298
5.2.2 Rigid disk in vertical motion 299
5.3 Approximate Green's Function of Disk 300
5.3.1 Illustrative example 300
5.3.2 Summary of equations 301
5.4 Matrix Formulation of Surface Foundation with Arbitrary Shape Modeled with
Subdisks 303
5.5 Example of Square Surface Foundation 304
5.6 Through-Soil Coupling of Surface Foundations 304
viii Contents
6 Seismic Excitation 308
6.1 Basic Equation of Motion of Substructure Method 309
6.1.1 Formulation in total displacements for harmonic excitation 309
6.1.2 Formulation in total displacements in time domain 314
6.1.3 Kinematic and inertial interactions 316
6.2 Free-Field Response of Site 318
6.3 Effective Foundation Input Motion 320
6.3.1 Vertical and rocking components of rigid surface foundation modeled
with subdisks 320
6.3.2 Rigid surface foundation subjected to horizontally propagating
waves 321
6.3.3 Embedded foundation modeled with stack of disks 325
6.4 Surface Foundation Modeled with Cones and Unfolded Cones 327
6.4.1 Homogeneous soil halfspace 327
6.4.2 Soil layer on rigid rock 331
6.5 Foundation Modeled with Lumped-Parameter Model 333
6.6 Basic Equation of Motion of Direct Method 336
7 Dynamic Soil-Structure Interaction 341
7.1 Coupled Structure-Soil System For Horizontal and Rocking
Motions 342
7.1.1 Simplest dynamic model 342
7.1.2 Equations of motion 344
7.1.3 Effect of interaction with soil on response of structure 345
7.2 Equivalent One-Degree-of-Freedom System 346
7.2.1 Material damping of soil 346
7.2.2 Equivalent natural frequency, damping ratio and input
motion 347
7.2.3 Parametric study 351
7.3 Other Equivalent Systems 354
7.3.1 Dynamic model for vertical motion 354
7.3.2 Redundant coupled structure-soil system for horizontal and rocking
motions 356
7.3.3 Coupled rigid block-soil system 358
A Interaction Force-Displacement Relationship and Green's
Function of Cone Model 362
Al Translational Cone 363
A1.1 Equation of motion 363
A1.2 Interaction force-displacement relationship 364
A1.3 Displacement-interaction force relationship 365
A1.4 Green's function 366
A2 Rotational Cone 368
Contents ix