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boundary element methods for soil structure interaction
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Boundary Element Methods for Soil-Structure Interaction
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Boundary Element Methods for
Soil-Structure Interaction
Edited by
W.S. HALL
University of Teesside,
Middlesbrough, United Kingdom
and
G. OLIVETO
University of Catania,
Catania, Italy
KLUWER ACADEMIC PUBLISHERS
NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN: 0-306-48387-4
Print ISBN: 1-4020-1300-0
©2004 Kluwer Academic Publishers
New York, Boston, Dordrecht, London, Moscow
Print ©2003 Kluwer Academic Publishers
All rights reserved
No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,
mechanical, recording, or otherwise, without written consent from the Publisher
Created in the United States of America
Visit Kluwer Online at: http://kluweronline.com
and Kluwer's eBookstore at: http://ebooks.kluweronline.com
Dordrecht
CONTENTS
INTRODUCTION
W S Hall (Teesside), G Oliveto (Catania)
xvii
PART 1. SOIL-STRUCTURE INTERACTION
1. TWENTY FIVE YEARS OF BOUNDARY ELEMENTS FOR
DYNAMIC SOIL-STRUCTURE INTERACTION
J Dominguez (Seville)
1
9
13
16
20
24
28
31
34
35
36
37
38
39
42
1.
2.
Introduction
Dynamic Stiffness of Foundations
2.1.
2.2.
2.3.
2.4.
THREE-DIMENSIONAL FOUNDATIONS
3.
4.
Seismic Response of Foundations
Dynamic Soil-Water-Structure Interaction. Seismic
Response of Dams
4.1 FLUID-SOLID INTERFACES
5. Gravity Dams
5.1.
5.2.
5.3
5.4.
5.5.
DAM ON A RIGID FOUNDATION.
EMPTY RESERVOIR
DAM ON A RIGID FOUNDATION.
RESERVOIR FULL OF WATER
DAM ON A FLEXIBLE FOUNDATION.
EMPTY RESERVOIR
DAM ON A FLEXIBLE FOUNDATION.
RESERVOIR FULL OF WATER
BOTTOM SEDIMENT EFFECTS
STRIP FOUNDATIONS
AXISYMMETRIC FOUNDATIONS
FOUNDATIONS ON SATURATED
POROELASTIC SOILS
vi
44
45
46
49
51
56
57
61
61
62
63
64
65
65
66
66
66
67
68
68
68
69
69
69
69
70
70
71
73
74
74
74
6. Arch Dams
6.1.
6.2.
6.3.
6.4.
6.5
DAM ON A RIGID FOUNDATION.
EMPTY RESERVOIR
DAM ON A FLEXIBLE FOUNDATION.
EMPTY RESERVOIR
DAM ON A FLEXIBLE FOUNDATION.
RESERVOIR FULL OF WATER
TRAVELLING WAVE EFFECTS
POROELASTIC SEDIMENT EFFECTS
7. References
2. COMPUTATIONAL SOIL-STRUCTURE INTERACTION
D Clouteau (Paris), D Aubry (Paris)
1. Introduction
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
PHYSICAL MODELS
NUMERICAL MODELS
HETEROGENEITIES IN THE BEM
TIME DOMAIN BEM/ FREQUENCY
DOMAIN BEM
STOCHASTIC APPROACH
UNBOUNDED STRUCTURES
GUIDELINES
2. Physical and Mathematical Models
2.1.
2.2.
2.3.
GEOMETRY
THE UNKNOWN FIELDS
LOADS
2.3.1.
2.3.2.
2.3.3.
Incident Fields
Initial Conditions
Applied Forces and Tractions
2.4. LINEAR EQUATIONS
2.4.1.
2.4.2.
Field Equations
Coupling Equations
2.5. VARIABILITY ON THE PARAMETERS
2.5.1.
2.5.2.
Stochastic Model of the Soil Parameters
Stochastic Model for the Applied Loads
2.6. SUMMARY OF MODELLING SECTION
2.6.1. Wellposedness and Approximation
3. Domain Decomposition
3.1. COUPLING FIELDS
3.2.
3.3.
3.4.
3.5.
LOCAL BOUNDARY VALUE PROBLEMS
VARIATIONAL FORMULATIONS
THE SFSI EQUATION
FEM AND REDUCTION TECHNIQUES
3.5.1.
3.5.2.
Component Mode Synthesis
Principal Directions
4. Boundary Integral Equations and BEM
4.1.
4.2.
4.3.
4.4.
4.5.
REGULARIZED BOUNDARY INTEGRAL
EQUATION IN A LAYERED HALF-SPACE
REGULARIZING TENSORS
BOUNDARY ELEMENTS
COUPLING WITH OTHER NUMERICAL
TECHNIQUES
FEM-BEM COUPLING INSIDE A VOLUME
5. Unbounded Interfaces
5.1.
5.2.
5.3.
5.4.
5.5.
GENERAL SPACE-WAVENUMBER
TRANSFORM
INVARIANT OPERATORS
DOMAIN DECOMPOSITION ON INVARIANT
DOMAINS
BEM ON INVARIANT DOMAINS
NON INVARIANT UNBOUNDED
INTERFACES
5.5.1.
5.5.2.
5.5.3.
Statistically Homogeneous Random
Medium
Weakly Perturbed Invariant Domains
Truncated Invariant Domain
6. Green’s Functions of a Layered Half-Space
6.1.
6.2.
6.3.
SOLUTION IN THE SLOWNESS SPACE
FAST INVERSE HANKEL TRANSFORM
SINGULARITIES
7. Applications
7.1.
7.2.
SOIL-FLUID-STRUCTURE INTERACTION
MODAL REDUCTION FOR SSI
7.2.1.
7.2.2.
Selecting Dynamic Interface Modes
Selecting Input Shapes for Static
Correction
7.3.
7.4.
SSI ON A RANDOM SOIL
SFSI FOR PERIODIC SHEET-PILES
vii
74
75
76
77
78
79
80
80
81
82
83
84
87
87
89
89
90
92
92
92
92
93
94
95
95
96
96
96
98
99
100
103
viii
7.5.
7.6.
TOPOGRAPHIC SITE EFFECTS USING SSI
FRAMEWORK
THE CITY-SITE EFFECT
7.6.1. Spectral Ratios
7.7. SSI IN BOREHOLE GEOPHYSICS
8.
9.
Conclusion
References
10.Appendix: Mathematical Results and Formulae
10.1. MATHEMATICAL PROPERTIES OF
VARIATIONAL BIE
10.1.1. Coupling on a Volume
10.2.
10.3.
10.4.
10.5.
PROPER NORM FOR RESIDUAL FORCES
MATRICES FOR THE REFLECTIONTRANSMISSION SCHEME
HANKEL TRANSFORM
RECONSTRUCTION FORMULAE
3. THE SEMI-ANALYTICAL FUNDAMENTAL-SOLUTIONLESS SCALED BOUNDARY FINITE-ELEMENT METHOD
TO MODEL UNBOUNDED SOIL
J P Wolf (Lausanne), C Song (Sydney)
1.
2.
3.
4.
Introduction
Objective of Dynamic Soil-Structure Interaction Analysis
SalientConcept
Scaled-Boundary-Transformation-Based Derivation
4.1.
4.2.
4.3.
4.4.
4.5.
4.6.
GOVERNING EQUATIONS OF
ELASTODYNAMICS
BOUNDARY DISCRETISATION WITH FINITE
ELEMENTS
DYNAMIC STIFFNESS MATRIX
HIGH-FREQUENCY ASYMPTOTIC EXPANSION
OF DYNAMIC STIFFNESS MATRIX
MATERIAL DAMPING
UNIT-IMPULSE RESPONSE MATRIX
5.
6.
7.
8.
Mechanically Based Derivation
Analytic Solution in Frequency Domain
Numerical Solution in Frequency and Time Domains
Extensions
8.1. INCOMPRESSIBLE ELASTICITY
107
107
109
112
112
114
122
122
123
124
124
125
125
127
129
130
134
134
135
136
137
139
140
141
144
148
149
149
8.2.
8.3.
8.4.
8.5.
ix
VARIATION OF MATERIAL PROPERTIES IN
RADIAL DIRECTION
REDUCED SET OF BASE FUNCTIONS
TWO-DIMENSIONAL LAYERED UNBOUNDED
SOIL
SUBSTRUCTURING
9. Numerical Examples
9.1.
9.2.
9.3.
9.4.
9.5.
PRISM FOUNDATION EMBEDDED
IN HALF-SPACE
SPHERICAL CAVITY IN FULL-SPACE WITH
SPHERICAL SYMMETRY
IN-PLANE MOTION OF SEMI-INFINITE WEDGE
IN-PLANE MOTION OF CIRCULAR CAVITY IN
FULL PLANE
10.
11.
12.
Bounded Medium
Concluding Remarks
References
4. BEM ANALYSIS OF SSI PROBLEMS IN RANDOM MEDIA
G D Manolis, C Z Karakostas (Thessaloniki)
1.
2.
Introduction
Review of the Literature
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
2.7.
2.8.
2.9.
2.10.PROBABILISTIC RESPONSE SPECTRA
RANDOM LOADING
MONTE CARLO SIMULATIONS
RANDOM BOUNDARIES
SOIL MODELLING
FOUNDATIONS
SLOPE STABILITY
CONSOLIDATION
SOIL-STRUCTURE INTERACTION
EARTHQUAKE SOURCE MECHANISM
3. IntegralEquation Formulation
3.1.
3.2.
3.3.
THEORETICAL BACKGROUND
FORMAL SOLUTION
CLOSURE APPROXIMATION
4. Vibrations in Random Soil Media
149
150
151
152
153
153
156
159
161
163
165
168
172
175
179
180
180
181
181
182
183
184
184
185
187
187
187
188
190
191
OUT-OF-PLANE MOTION OF CIRCULAR CAVITY
IN FULL PLANE WITH HYSTERETIC DAMPING
x
4.1.
4.2.
4.3.
4.4.
PROBLEM STATEMENT
GROUND RANDOMNESS
ANALYTICAL SOLUTION
APPROXIMATE SOLUTION TECHNIQUE
4.4.1.
4.4.2.
4.4.3.
BEM Approach with Volume Integrals
BEM Approach without Volume Integrals
General Comments
4.5.
4.6.
STOCHASTIC FIELD SIMULATIONS
NUMERICAL EXAMPLE
5. BEM Formulation based on Perturbations
5.1.
5.2.
5.3.
5.4.
BACKGROUND
FORMULATION
FUNDAMENTAL SOLUTIONS
NUMERICAL EXAMPLES
5.4.1.
5.4.2
Circular Unlined Tunnel Enveloped by a
Pressure Wave
Circular Unlined Tunnel in a Half-Plane
under Surface Load
6. BEM Formulation Based on Polynomial Chaos
6.1.
6.2.
6.3.
6.4.
BACKGROUND
FORMULATION
RESPONSE STATISTICS
NUMERICAL EXAMPLE
7.
8.
Conclusions
References
5. SOIL-STRUCTURE INTERACTION IN PRACTICE
C C Spyrakos (Athens)
1. Introduction
1.1.
1.2.
BRIEF REVIEW OF LITERATURE ON
BUILDING STRUCTURES AND SSI
BRIEF REVIEW OF LITERATURE ON
BRIDGES AND SSI
2. Seismic Design of Building Structures Including SSI
2.1.
2.2.
2.3.
2.4.
BRIEF INTRODUCTION
DESIGN PROCEDURE
RESPONSE SPECTRUM ANALYSIS WITH SSI
NUMERICAL EXAMPLE: BUILDING
STRUCTURE
192
192
194
195
195
199
201
201
203
206
207
208
211
213
213
216
216
216
217
222
223
227
228
235
235
238
238
238
239
246
247
2.5. CONCLUSIONS
3. Seismic Analysis of Bridges Including SSI
3.1.
3.2.
BRIEF INTRODUCTION
MODELLING OF THE STRUCTURE AND
THE SOIL
3.2.1.
3.2.2.
3.2.3.
Modelling Backfill Soil Stiffness
Modelling Pile Stiffness
Modelling Abutment Stiffness for Linear
Iterative Analysis
3.3.
3.4.
3.5.
ITERATIVE ANALYSIS PROCEDURE
MODELLING ABUTMENT STIFFNESS FOR
NON-LINEAR ANALYSIS
BRIDGE EXAMPLE
3.5.1.
3.5.2.
Stiffness Computation
Parametric Studies
3.6. REMARKS AND CONCLUSIONS
4.
5.
References
Appendix
PART 2. RELATED TOPICS AND APPLICATIONS
6. BEM TECHNIQUES FOR NONLOCAL ELASTICITY
C Polizzotto (Palermo)
1.
2.
3.
4.
5.
Introduction
Nonlocal Elasticity
Thermodynamic Framework
Boundary-value Problem
Hu-Washizu Principle Extended to Nonlocal Elasticity
5.1.
5.2.
NONLOCAL HYPERELASTIC MATERIAL
LINEAR LOCAL ELASTICITY WITH
CORRECTION STRAIN
6.
7.
8.
9.
10. References
A Boundary/Domain Stationarity Principle
Symmetric Galerkin BEM Technique
Nonsymmetric Collocation BEM Technique
Conclusions
xi
249
251
251
251
251
253
255
257
260
261
264
268
269
270
272
275
277
279
281
284
284
285
287
290
293
294
295
xii
7. BEM FOR CRACK DYNAMICS
M H Aliabadi (London)
Abstract
1.
2.
3.
4.
5.
6.
Introduction
Time Domain Method (TDM)
Laplace Transform Method (LTM)
Dual Reciprocity Method (DRM)
Cauchy and Hadamard Principal-Value Integrals
Numerical Examples
6.1.
6.2.
A CENTRAL INCLINED CRACK
ELLIPTICAL CRACK
7.
8.
Conclusions
References
8. SYMMETRIC GALERKIN BOUNDARY ELEMENT
ANALYSIS IN THREE-DIMENSIONAL LINEAR-ELASTIC
FRACTURE MECHANICS
A Frangi (Milan), G Maier(Milan), G Novati(Trento),
R Springhetti (Trento)
Abstract
1.
2.
3.
Introduction
Formulation
Numerical Evaluation of Weakly Singular Integrals
3.1.
3.2.
3.3.
COINCIDENT ELEMENTS
COMMON EDGE
COMMON VERTEX
4. Numerical Examples
4.1.
4.2.
4.3.
4.4.
FRACTURES IN INFINITE DOMAINS
EDGE CRACKED BAR
CIRCULAR EDGE CRACK IN A PLATE
QUARTER ELLIPTIC CORNER CRACK
IN A PLATE
5.
6.
Concluding Remarks
References
Appendices
7.
8.
9.
Surface Rotors
Transformations and Equivalence of Domains
Equivalence of and
297
297
299
303
305
307
308
308
310
311
312
315
315
316
320
321
324
326
327
328
331
336
339
339
341
342
343
344
xiii
9. NUMERICAL SIMULATION OF SEISMIC WAVE
SCATTERING AND SITE AMPLIFICATION, WITH
APPLICATION TO THE MEXICO CITY VALLEY
L C Wrobel (London), E Reinoso (Mexico City),
H Power (Nottingham)
Abstract
1.
2.
3.
4.
5.
6.
7.
8.
9.
Introduction
Wave Propagation in a Half-Space
2.1. INCIDENT WAVES
BEM Formulation for SH Waves
BEM Formulation for P, SV and Rayleigh Waves
Observed Amplification in the Mexico City Valley
One-dimensional Response in the Mexico City Valley
Two-dimensional Modelling Using the BEM
Conclusions
References
345
345
347
349
351
355
359
364
365
369
373
INDEX 377
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