· Numerical Methods in Geomechanics

NATO ADVANCED STUDY INSTITUTES SERIES

Proceedings of the Advanced Study Institute Programme, which aims

at the dissemination of advanced knowledge and the formation of contacts among scientists from different countries

The series is published by an international board of publishers in conjunction with NATO Scientific Affairs Division

A Life Sciences Plenum Publishing Corporation

B Physics London and New York

C Mathematical D. Reidel Publishing Company and Physical Dordrecht, Boston and London Sciences

D Behavioural and Social Sciences Martinus Nijhoff Publishers

E Engineering and The Hague, London and Boston

Materials Sciences

F Computer and Springer Verlag

Systems Sciences Heidelberg

G Ecological Sciences

Series C - Mathematical and Physical Sciences

Volume 92 - Numerical Methods in Geomechanics

Numerical Methods

in Geomechanics Proceedings of the NATO Advanced Study Institute, University of Minho, Braga, Portugal, held at Vimeiro, August 24 - September 4, 1981

edited by

J. B. MARTINS School of Engineering, University of Minho, Braga, Portugal

D. Reidel Publishing Company

Dordrecht: Holland / Bo~ton: U.S.A. / London: England

Publbhed in cooperation with NATO Scientific Affair~ Divi~ion

library of Congress Cataloging in Publication Data

NATO Advanced Study Institute (1981 : Vimeiro, Lisbon, Portugal) Numerical methods in geomechanics.

(NATO advanced study institutes series. Series C, Mathematical and physical sciences; v. 92)

Includes bibliographical references and index. 1. Soil mechanics-Mathematics-Congresses. 2. Rock mechanics­

Mathematics-Congresses. 3. Numerical calculations-Congresses. I. Martins, J. B. (J. Barreiros) II. Title. III. Series. TA710.AIN37 1981 624.1'513 82-13263 ISBN-13: 978-94-009-7897-3 e-ISBN-13: 978-94-009-7895-9 001: 10.1007/978-94-009-7895-9

Published by D. Reidel Publishing Company P.O. Box 17, 3300 AA Dordrecht, Holland

Sold and distributed in the U.S.A. and Canada by Kluwer Boston Inc., 190 Old Derby Street, Hingham, MA 02043, U.S.A.

In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322,3300 AH Dordrecht, Holland

D. Reidel Publishing Company is a member of the Kluwer Group

All Rights Reserved Copyright (C) 1982 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover 1st edition 1982 No part of ttie material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any informational storage and retrieval system, without written permission from the copyright owner

COITEITS

Preface List of Participants Lecture Program

CHAPTER I - FUNDAMENTALS

1 Field Equations

ix xi xv

E.R. Arantes e Oliveira 3

2 Basic Formulation of Static and Dynamic Behaviour of Soil and Other Porous Media

O. C. ZienkieuJicz 39

3 Generalized Plasticity and Some Models for Geomechanics

O.C. Zienkiewicz 57

4 Constitutive Equations for Soil Media Jean H. Proevost 79

5 Constitutive Modeling and Soil-Structure Interaction

C.S. Desai 103

6 Rock Mass Behaviour and Its Mathematical Modelling

K. KovaY'i 145

CHAPTER II - FINITE ELEMENTS TECHNIQUES

1 Numerical Analysis of Shallow Foundations I.M. Smith

2 Numerical Analysis of Deep Foundations I.M. Smith

165

167

187

3 Finite Element Analysis of Coupled Deformation and Fluid Flow in Porous Media

Ranbir S. Sandhu

4 Finite Elements and Slope Stability D.J. Naylor

CONTENTS

203

229

CHAPTER III - MATHEMATICAL PROGRAMMING METHODS 245

1 Plastic Analysis in Geomechanics by Mathematical Programming

John MUnro 247

2 Optimization Methods for Parametric Identification of Geotechnical Systems

G. Maier and G. Gioda 273

3 Embankments and Slopes by Mathematical Programming

J.B. Martins

CHAPTER IV - BOUNDARY ELEMENT TECHNIQUES

1 Fundamentals of Boundary Elements

305

335

C.A. Brebbia 337

2 Boundary Elements in Groundwater Flow Problems L.C. Wrobel and C.A. Brebbia 355

3 Boundary Element Formulation to Solve No-Tension Problems in Geomechanics

W.S. Venturini and C.A. Brebbia 375

4 Elastoplastic Analysis Using Boundary Elements J.C.F. Telles and C.A. Brebbia 389

CHAPTER V - SEISMIC PROBLEMS

1 Seismic Site and Soil-Structure Interaction Analysis

John Lysmer

407

409

CONTENTS

2 Liquefaction of Sandy Soils Jose FoZque

CHAPTER VI - STATISTICAL METHODS

Statistical and Probabilistic Methods in Geomechanics

A. HaZdar

APENDICES

LECTURE - Liquefaction of Soils During Earthquakes

I.M. IdriS8

RESEARCH PRESENTATIONS* IN PANELS 1 Dynamic, Cyclic and Transient Aspects in

Soil Engineering M.P. Luong

2 Buried Structures-S~rounding Soil Interac tion

M.P. Luong

3 Bearing Capacity and Shape Factors for Shallow Foundations

M.P. Luong

4 Coefficient of Potential Rupture for Earth Structures

M.P. Luong

NAME INDEX

SUBJECT INDEX

* written papers

vii

455

471

473

505

507

531

541

547

557

567

573

PREFACE

This volume contains the edited texts of the lectures and written discussions prepared for the NATO sponsored Advanced Study Institute (ASI) on "Numerical Methods in Geomechanics" promoted by the University of Minho, Braga, Portugal and held at Vimeiro Hotel (Torres Vedras) - August 24 to September 4, 1981.

The object of the NATO-AS I has been to gather, as lecturers ,a wide range of scientists and engineers specialized on the above branch of knwoledgement in order to cover the whole variety of approaches for the solution of the set of problems concerning Geomechanics. In this way we could make available to the students, most of them researchers in this field, a large number of concepts, views and techniques for the solution of the problems they are concerned with. At the same time it was possible to disclose relationships between apparently different techniques for the solution of the same problem. For example some plasticity problems may be solved either by the usual finite elements technique or by mathematical programming or by the boundary elements method. Therefore, a link exi s ts amongs t thos e me thods. However, there has been in the pas t lack of effort to spring out these links, since there is a tendency for the researchers to stress the method they are working with and to forget about other methods, at least in what concerns their fundamentals.

Bringing together scientists from distinct schools of thought, this ASI has provided a forum for an interchange of views and of experiences amongst the lecturers and panelists themselves.lnthis way a stimulating and rewarding experience was given to each participant, mainly to the students,mostof them preparing their doctoral theses.

Therefore, we hope these proceedings will be a way of reV1 v1ng the "spirit of Vimeiro" giving an opportunity to the students to apply some important new concepts put forward at this ASI, and to the lecturers and panelists to try, in their new experiments, to apply each others concepts and methods in order to make a correct comparison and to find the reasons for agreement or disagreement between results.

ix I

J. B. Mtutin. (ed.). Numerlctll Method. in GeomeclumicB. ix-x. Copyright e 1982 by D. Reidel Publishing Company.

x PREFACE

We hope further that the Proceedings will give to all professionals an up-to-date and broad view of the methods available to solve geomechanical problems and a forward looking for future developments.

In fact many lecturers have brought to this Advanced Institute a number of quite new ideas for the solution of geomechanical problems which are particularly difficult, since they concern materials made bv Nature and not bv Man. with a most complex constitution and dealing with rather intrincated geometric shapes.

So, we wish to express our appreciation to those lecturers who put so great interest in this ASI.

In organizing the Chapters of these proceedings we have found some difficulties due to the fact that some lecturers have written their lectures in one final paper covering a somewhat large range of subjects. Therefore, the chapters do not follow exactly the order of the lectures and probably some people may feel that a better arrangement could be done.

We are greatfull to my Colleague Carlos Bernardo from U .M. who from the very begining was a full-time organizer of this Advanced Institute and to the staff of the University of Minho whose dedication allowed to overcome the many difficulties that always arrive in organizations such as this one.

Thanks are also due to the Vice-Chancelor of the U .M. for the facilities made available for the Institute.

Finally we extend our deep appreciation to the NATO Division of Scientific Affairs whose generous financial support made possible this NATO-ASI and the publication of these Proceedings.

January 1982 J.B. Martins

LIST OF PARTICIPANTS

Abascal, J.D. Escuela Superior de Ingenieros

Industriales Sevilla-12, Spain

Alarcon, E. Escuela Politecnica Superior de

Ingenieros Industriales Madrid - 6, Spain

Anand, S.C. Department of Civil Engineering Clemson University Clemson, S. Carolina, USA 29631

Barros, M.H.F. Departamento de Engenharia Civil Universidade de Coimbra 3000 Coimbra, Portugal

Barroso, M.J.G. Laboratorio Nacional de Engenharia

Civil 1700 Lisboa, Portugal

Beliveau, J.G. Department of Civil Engineering Universite de Sherbrooke Sherbrooke, Quebec, Canada J1K 2R1

Benitez, F.e. Escuela Politecnica Superior de

Ingenieros Industriales Madrid - 6, Spain

Bolle, A. Institut du Genie Civil- Bat C 2 Universite de Liege B - 4000 Liege, Be Igium

Borm, G. Lersthul fur Fe1smechanik Universitat Fridericiana zu

Karlsruhe D- 7500 Karlsruhe 1, West Germany

Brebbia, C.A. Department of Civil Engineering The University Southampton, England S095NH

Carballo, F .A. Escuela Superior de Ingenieros

Industriales Sevilla - 12, Spain

Cavilhas, J.L.A. Hidrotecnica Portuguesa Ed HP Guine, Prior Ve1ho Lisboa, Portugal

Cerejeira, J.M.G. OMAN - Centro de Estudos e Projectos R. Eugenio de Castro, 8 - 89 Esq9 Almada, Portugal

Chapel, F.M. Laboratoire de Mecanique des Sols Ecole Centrale des Arts et

Manufactures 92290 Chatenay - Ma1abry, France

Civelek, M.B. Department of Civil Engineering Bogazi~i University P.K. 2 Bebek, Istanbul, Turkey

Cividini, A. 1st. di Scienza e Tecnica delle

Construzioni Politecnico 20133 Milano, Italy

Cormeau, I. Consultant Control Data Belgium

N.V.-S.A. Leopold III Lan III 1130 Brussels, Belgium

Correia, A.G. lnstituto Superior Tecnico 1000 Lisboa, Portugal

xi

xii

Cozzarelli, F.A. Department of Civil Engineering State University of New York at

Buffalo Buffalo, N.Y., USA 14214

Cruz, J.M.L. Hidrotecnica Portuguesa Ed HP Guine, Prior Velho Lisboa, Portugal

Cunha, A.J.V.P. Laboratorio Nacional de Engenharia

Civil 1700 Lisboa, Portugal

Davies, T.G. Department of Civil Engineering State University of New York at

Buffalo Buffalo, N.Y., USA 14214

Desai, C.S. Department of Civil Engineering Virginia Polytechnic Institute and

State University Blacksburg, Virginia, USA 24061

Doblare, M. Escuela Politecnica Superior de

Ingenieros Industriales Madrid - 6, Spain

Durgunoglu, T. Earthquake Engineering Research

Institute Bogazi~i University P.K. 2 Bebek, Istanbul, Turkey

Ferreira, A.M.S. Geotecnia Universidade Nova de Lisboa 1800 Lisboa, Portugal

Figueiras, J.A. University College of Swansea Swansea, England SA2 8PP

Fonseca, A.M.A. CECUP - Centro de Engenharia Ci vii Universidade do Porto R. dos Bragas 4000 Porto, Portugal

Gaspar, J.E.T. Cubiertas Y MZOV S.A. Ayala 42 Madrid 1, Spain

Georgiou, P. Computational Mechanics Centre Southampton, Englang SOl OAA

LIST OF PARTICIPANTS

Gioda, G. 1st. di Scienza e Tecnica delle

Construzioni Po Ii tecnico 20133 Milano, Italy

Gonzalez, J.M.V. Instituto Superior Tecnico 1000 Lisboa, Portugal

Grossmann, N. Laboratorio Nacional de Engenharia

civil 1700 Lisboa, Portugal

Gumusoglu, M.C. Department of Engineering Geology

and Rock Mechanics Tesvikiye, Istanbul, Turkey

Gus smann, P. Institut fur Grundbau und

Bodenmechanik Pfaffernwaldring 35 7 Stuttgart 80, West Germany

Haahr, F. Soil Mechanics and Foundation

Engineering Technical University of Denmark Maglebjergvej 1 DK - 2800 Lingby, Denmark

Haldar, A. Georgia Institute of Technology Atlanta, Georgia, USA 30332

Halonen, O. Technical Research Centre of

Finland Geotechnical Laboratory Lampomiehenkuja 2 B SF - 02150, Espoo 15, Finland

Heuze, F.E. Lawrence Li vermore National Lab. University of California Livermore, Calif., USA 94550

Idriss, I.M. Woodward-Clyde Consultants Three Embarcadero Center, S. 700 S. Francisco, Calif., USA 94111

Jaudenes, M.D.R. Cubiertas Y MZOV S.A. Ayala 42 Madrid 1, Spain

Katzir, M. Foundation and Soil Ltd 44 Revivim St, Box 10107 Tel-Aviv 69274, Israel

UST OF PARTICIPANTS

Kausel, E.A.M. Department of Civil Engineering Massachusetts Institute of Technology Cambridge, Mass., USA 02139

Kelly, W.E. Department of Civil Environmental

Engineering University of Rhode Island Kingston, Rhode Island, USA 02881

Kovari, K. Institut fur Strassen-, Eisenbahn-

und Felsbau ETH - Honggerberg CH - 8093 Zurich, Switzerland

Lemoine, M.E. Koninklijke/Shell Exploratie en

Produktie Laboratorium Volmerlaan 6 2288 GD Rijswijk, Holland

Loret, B. Laboratoire de Mecanique des Solides Ecole Poly technique 91128 Palaiseau, France

Luong, M.P. Laboratoire de Mecanique des Solides Ecole Poly technique 91128 Palaiseau, France

Lysmer, L. Department of Civil Engineering University of California Berkeley, Calif., USA 94720

Maier, G. 1st. di Scienza e Tecnica delle

Construzioni Politecnico 20133 Milano, Italy

Marques, J.C. University of Swansea Swansea SA2 8PP, England

Martins, J.B. Unidade Pedagogica de Engenharia Universidade do Minho 4700 Braga, Portugal

Matos,A.B.C. F.E.U.P. Universidade do Porto 4000 Porto, Portugal

Matos, A.C. F.E.U.P. Universidade do Porto 4000 Porto, Portugal

Mohiuddin, G.M. Gesellschaft fur Reaktorsicherhei t Postfach 101650 5000 Koln 1, West Germany

Morancho, A.L.

xiii

Departamento de Geotecnia Universidad Politecnica de Barcelona Barcelona 17, Spain

Mota, C.A.M. Constru~oes Tecnicas SARL Av. 24 de Julho 24 1200 Lisboa, Portugal

Munro, J. Department of Civil Engineering Imperial College London SW7 2BU, England

Natau, O. Lehrstuhl fur Felsmechanick Universitat Fridericiana zu

Karlsruhe D- 7500 Karlsruhe, West Germany

Naylor, D.J. University College of Swansea Swansea SA2 8PP, England

Neves, E.M. Laboratorio Nacional de Engenharia

Civil 1700 Lisboa, Portugal

Neves, M.L.S.O. Constru~oes Tecnicas SARL Av. 24 de Julho 24 1200 Lisboa, Portugal

Nordal, S. Institut fur Geoteknikk og

Fundamenteringslaere N - 7034 Trondheim - NTH, Norway

Oliveira, E.R.A. Universidade Tecnica de Lisboa 1100 Lisboa, Portugal

Ottosen, N.S. Riso National Laboratory Postbox 49 DK - 4000 Roskilde, Denmark

Paixao, J.C.L. F.E.U.P. Universidade do Porto 4000 Porto, Portugal

Prater, E.G. Institut fur Strassen-, Eisenbahn­

und Felsbau ETH - Honggerberg CH - 8093 Zurich, Switzerland

xiv

Prevost, J.H. Princeton University Princeton, New Jersey, USA 08544

Quaresma, C.F. Departamento de Engenharia Civil Universidade de Coimbra 3000 Coimbra, Portugal

Quiroga, A.S. Departamento Analisis de las

Estruturas Universidad de Santander Santander, Spain

Ratigan, J.L. Geotechnical Engineering University of California Berkeley, Calif., USA 94720

Reis, E.B. F.E.U.P. Universidade do Porto 4000 Porto, Portugal

Rodrigues, F.M.C.P. Laboratorio Nacional de Engenharia

Civil 1700 Lisboa, Portugal

Rucker, W. Bundesanstalt fur Materialprufung Unter den Eichen 87 1000 Berlin 45, West Germany

Sadgorski, W. Bayer Landesamt fur Wasserwirtschaft Dienstgebande Torring Str. 2 8000 Munchen 80, West Germany

Sandhu, R.S. Department of Civil Engineering The Ohio State University Columbus, Ohio, USA 43210

Shaw, R.P. Department of Engineering Science University of New York at

Buffalo New York, USA 14214

Silva, A.J. University of Rhode Island Narragansett Rhode Island, USA 02882

Silva, M.A.G. Gabinete da Area de Sines R. Artilharia 1 1200 Lisboa, Portugal

LIST OF PARTICIPANTS

Smith, I.M. Simon Engineering Laboratories University of Manchester Manchester M13 9PL, England

Soeiro, F.A. Bureau d'Etudes et de Recherches

Geotechniques Engineering 6 Rue des Colonels Renard 75017 Paris, France

Sousa, L.M.R. Laboratorio Nacional de Engenharia

Civil 1700 Lisboa, Portugal

Swoboda, C. Universitat Innsbruck Technikerstrasse 13 A - 6020 Innsbruck, Austria

Taylor, B.B. Department of Civil Engineering University of Waterloo Ontario, Canada N2L 3GL

Veiga, E.V. Universidade do Minho 4700 Braga, Portugal

Vilar, C. Universidade do Minho 4700 Braga, Portugal

Wolfe, W.E. The Ohio State University 2070 Neil Avenue Columbus, Ohio, USA 43210

Wynendaele, H. Katholieke Universiteit te Leuven Celestijnenlaan 200 A 3030 Haverlee, Belgium

Zacas, M. Geomechaniki S.A. 25 Bairaktari Str. Athens (607), Greece

Zeman, A.J. Shore Processes Section Hydraulic Research Division National Water Research Institute P.O. Box 5050 Burlington, Ontario, Canada

Zienkiewicz, O.C. Applied Science Building University College of Wales Swansea SA2 8PP, England

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RA'l'O A S I "IIlIIInICAL MBTIIODS III GEOIIBClWlICS" 24TH AUGUST 'l'O 4TH SEPTEMBER 1981

STIlUCTUIlE OF TIlE DISCUSSION PAlll!LS

PAlll!LISTS SUBJECTS

LECTURERS OTHER Ml!MBERS

Constitutive Laws for Soils C.Desai, Blacksburg, U.S.A. F.A.Cozarelli, Buffalo, U.S.A. (Statics) J.Prevost, Princeton, U.S.A.

Constitutive Laws for Soils O.C.Zienckiewicz, Swansea, U.K. M.P.Luong, Palaiseau, France (Dynamics)

Foundations I.M.Smith, Manchester, U.K. M.P.Luong, Palaiseau, France T.Davies, Buffalo, U.S.A.

Rock Masses Behaviour K.Kovari, Zurich, Switzerland F.E.Heuze, Livermore, calif~U.S.A.1 T • Durgunoglu , Istanbul, Turkey i G. Swoboda, Innsbruck, Austria .1

Underground Openings G.Borm, Karlrsruhe, Germany F.E.Heuze, Livermore, Calif.,U.S.A., O.Natau, Karlrsruhe, Germany S.C.Anand, Clemson, S.Carol.,U.S.A.,

T.Durgunoglu, Istanbul, Turkey

Seepage and Consolidation R. S. Sandhu, Columbus, U. S.A. G.Gioda, Milano, Italy

Identification by Mathem. G.Maier, Milano, Italy G.Gioda, Milano, Italy

Programming

Plastic Analysis by Mathem. J • Munro , London, U.K. G.Gioda, Milano, Italy I Programming

R.P.Shaw, Buffalo, U.S.A. I

H.Winendaele, Haverlee, Belgium I Boundary Element Methods C.Brebbia, Southampton, U.K. E.Alarcon, Madrid, Spain I

J .Dominguez, Sevilla, Spain

I P .Georgiou, Southampton, U.K.

Soil-Structure Interaction M.P.Luong, Palaiseau, France I

(Statics) C.Desai, Blacksburg, U.S.A. M.B.Civelek, Istanbul, Turkey S.C.Anand, Clemson, S.Carol.,U.S.A.

Soil-Structure Interaction Jean-Guy Beliveau, Quebec, Canada

(Dynamics) J .Lysmer, Berkeley, U. S.A. E.Kausel, Massachusetts, U.S.A. M. B.Civelek, Istanbul, Turkey

Seismic Analysis J.Lysmer, Berkeley, U.S.A. I.M.Idriss, S.Franc., Calif.,U.S.A.

Soil Liquefaction I.M.Idriss, S.F.,Calif., U.S.A. J .Folque, Lisbon, Portugal

Statistical and Probabilistic A. Haldar, At lanta, Georgia, U.S.A. Methods in Geomechanics

xvi