Lecture Notes in Engineering

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Lecture Notes in Engineering

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P Silvester

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College of Engineering

Dept. of Civil Engg. and Engg. Mechanics The University of Arizona

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School of Engineering, Dept. of Civil Engg.

Princeton University Princeton, NJ 08544 (USA) Laser Fusion - Plasma:

R. McCrory

Lab. for Laser Energetics, University of Rochester Rochester, NY 14627 (USA)

S.AOrszag

Applied and Computational Mathematics 218 Fine Hall

Princeton, NJ 08544 (USA)

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Dept. of Nuclear Engg., MIT Cambridge, MA 02139 (USA) Mechanics of Materials:

FA Leckie

Dept. of Mechanical Engineering Univ. of California

Santa Barbara, CA 93106 (USA) A R. S. Ponter

Dept. of Engineering, The University Leicester LE1 7RH (UK)

Fluid Mechanics:

K.-P Holz

Inst. fOr Stromungsmechanik, Universitat Hannover, Callinstr. 32 D-3000 Hannover 1 (FRG) Nonlinear Mechanics:

K.-J. Bathe

Dept. of Mechanical Engg., MIT Cambridge, MA 02139 (USA) Structural Engineering:

J. Connor

Dept. of Civil Engineering, MIT Cambridge, MA 02139 (USA)

w.

Wunderlich

Inst. fOr Konstruktiven Ingenieurbau Ruhr-Universitat Bochum

Universitatsstr.150,

D·4639 Bochum-Ouerenburg (FRG) Structural Engineering, Fluids and Thermodynamics:

J. Argyris

Inst. fUr Statik und Dynamik der Luft- und Raumfahrtkonstruktion Pfaffenwaldring 27

D-7000 Stuttgart 80 (FRG)

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Lecture Notes in Engineering

Edited by C. A. Brebbia and S. A. Orszag

52 Y. S. Jiang

Slope Analysis

Using Boundary Elements

Springer-Verlag

Berlin Heidelberg New York

London Paris Tokyo Hong Kong

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Series Editors

C. A. Brebbia . S. A. Orszag

Consulting Editors

J. Argyris . K -J. Bathe· A. S. Cakmak . J. Connor· R. McCrory C. S. Desai· K-P. Holz . F. A. Leckie· G. Pinder· A. R. S. Pont J. H. Seinfeld . P. Silvester· P. Spanos· W. Wunderlich· S. Yip

Author

Yansheng Jiang

Laboratoire de Geologie de L'lngenieur,

d'Hydrogeologie et de Prospection geophysique Batiment B 19

Universite de Liege au Sart Tilman 4000 Liege

BELGIUM

Series Editors

C. A. Brebbia . S. A. Orszag

Consulting Editors

J. Argyris . K -J. Bathe· A. S. Cakmak . J. Connor· R. McCrory C. S. Desai· K-P. Holz . F. A. Leckie· G. Pinder· A. R. S. Pont J. H. Seinfeld . P. Silvester· P. Spanos· W. Wunderlich· S. Yip

Author

Yansheng Jiang

Laboratoire de Geologie de L'lngenieur,

d'Hydrogeologie et de Prospection geophysique Batiment B 19

Universite de Liege au Sart Tilman 4000 Liege

BELGIUM

ISBN 978-3-540-51625-5 ISBN 978-3-642-83918-4 (eBook) DOI 10.1007/978-3-642-83918-4

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its version of June 24, 1985, and a copyright fee must always be paid.

Violations fall under the prosecution act of the German Copyright Law.

The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its version of June 24, 1985, and a copyright fee must always be paid.

Violations fall under the prosecution act of the German Copyright Law.

The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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CHAPTER 1 1.2 1.1 1.3 1.4

CHAPTER 2

2. I 2.3 2.2

2.4

CHAPTER 3

3.1 3.2 3.3 3.4

CHAPTER 4

4.1 4.2 4.3 4.4 4.5

4.6 4.7 CHAPTER 5

5.1 5.2 5.3 5.4

CONTENTS

INTRODUCTION ... 1

Statement of the problem ... 1

Limit equilibrium methods ... 3

Fini te element method ... 5

Boundary element method ... 9

BASIC THEORY AND TECHNIQUES OF BOUNDARY ELEMENT METHOD ... 11

Governing equations ... 11

Integral equations ... 13

Fundamental solutions ... 14

2.3.1 Kelvin's solution(2D) ... 15

2.3.2 Melan's solution ... 16

Implementation of the boundary element method ... 19

2.4.1 Boundary integral equations ... 19

2.4.2 Numerical implementation ... 20

2.4.3 Subregions ... 23

GALERKIN TENSOR AND TRANSFORMATION OF BODY FORCE INTEGRAL ... 24

Transformat ion of body force integral ... 24

Galerkin tensor ... 36

Gravitational force integral for the half plane ... 27

Examples ... 33

3.4.1 Shallow tunnel ... 34

3.4.2 Vertical slope ... 41

DIRECT BOUNDARY ELEMENT APPROACHES FOR SLOPE STABILITY ANALYSIS ... 47

Formulations of the plastic ratio method ... 47

Calculations of the excess stresses ... 51

Implementation ... 54

Plastic ratio ... 55

Examples ... 59

4.5.] Slope in homogeneous cohesive soil ... 59

4.5.2 Vertical slope in soil with friction ... 68

Slope analysis using the joint elements ... 71

Elastoplastic analysis of slope stability ... 74

INDIRECT BOUNDARY ELEMENT ALGORITHM FOR SLOPE STABILITY ANALySIS ... 82

Introduction ... 82

Constant quadrupole element ... 83

Indirect boundary element algorithm ... 87

About redistributions of excess stresses ... 89

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IV

5.5 Slope stability analysis ... 93

Example 5-1 ... 95

Example 5-2 ... 95

Example 5-3 ... 97

CHAPTER 6 GENERAL CONCLUSIONS ... 98

REFERENCES ... 100

APPENDIX A DISPLACEMENTS OF MELAN'S SOLUTION DEDUCED FROM THE CORRESPONDING AIRY'S FUNCTIONS ... 107

APPENDIX B DEVELOPMENTS OF GALERKIN TENSOR CORRESPONDING TO MELAN'S SOLUTION ... 143