Computational Geomechanics

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<p>Computational Geomechanicswith special Reference to Earthquake Engineering</p> <p>0 C Zienkiewicz, Institute for Numerical Methods in Engineering,Swansea, Wales</p> <p>A H C Chan, University of Birmingham, England</p> <p>M Pastor, CEDEX* and ETS de Ingenieros de Caminos, Madrid, Spain B A Schrefler, University of Padua, Italy</p> <p>T Shiomi, Takenaka Corporation, Japan</p> <p>*</p> <p>Centro de E s t ~ i ~ x f i &amp; I &amp; i d n / e Obras Publicas</p> <p>Chichester New York</p> <p>.</p> <p>JOHN WILEY &amp; SONSWeinheim Brisbane Singapore Toronto</p> <p>.</p> <p>.</p> <p>Copyright</p> <p>1999 John Wiley &amp; Sons Ltd, Baffins Lane, Chichester, West Sussex PO19 IUD, England National 01243 779777 International (+44) 1243 779777 e-mail (for orders and customer service enquiries): Visit our Home Page on http:l/ or</p> <p>All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London, UK WIP 9HE, without the permission in writing of the publisher.Other Wiley Editorial Offices</p> <p>John Wiley &amp; Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, USA WILEY-VCH Verlag GmbH, Pappelallee 3, D-69469 Weinheim, Germany Jacaranda Wiley Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley &amp; Sons (Asia) Pte Ltd. 2 Clementi Loop # 02-01. Jin Xing Distripark, Singapore 129809 John Wiley &amp; Sons (Canada) Ltd, 22 Worcester Road, Rexdale, Ontario M9W ILI, Canada</p> <p>Library of Congress Cataloging-in-Publication Data Computational geomechanics with special reference to earthquake engineering1 O.C. Zienkiewicz . . . [et al.]. p. cm. Includes bibliographical references and index. ISBN0471-98285-7 1. Earthquake engineering 2. Mathematics. I. Zienkiewicz, O.C. TA705.C625 1998 624.1 ' 7 6 2 6 ~ 2 1 98-8795 CIP British Library Cataloguing in Publication Data</p> <p>A catalogue record for this book is available from the British Library ISBN 0-471-98285-7 Typeset in 10/12.25pt Times from the author's disks by Pure Tech India Ltd, Pondicherry Printed and bound in Great Britain by Bookcraft (Bath) Ltd, Midsomer Norton, Somerset This book is printed on acid-free paper responsibly manufactured from sustainable forestry, in which at least two trees are planted for each one used for paper production.</p> <p>Contents</p> <p>Preface</p> <p>1 Introduction and the Concept of Effective Stress1.1 Preliminary Remarks 1.2 The Nature of Soils and Other Porous Media: Why a Full Deformation Analysis is the Only Viable Approach for Prediction 1.3 Concepts of Effective Stress in Saturated or Partially Saturated Media 1.3.1 A single fluid present in the pores-historical note 1.3.2 An alternative approach to effective stress 1.3.3 Effective stress in the presence of two (or more) pore fluids. Partially saturated media References</p> <p>2 Equations Governing the Dynamic, Soil-Pore Fluid, Interaction2.1 General Remarks on the Presentation 2.2 Fully Saturated Behaviour With A Single Pore Fluid (Water) 2.2.1 Equilibrium and Mass Balance Relationship (u, w and p) 2.2.2 Simplified equation sets (u-p form) 2.2.3 Limits of validity of the various approximations , 2.3 Partially Saturated Behaviour with Air Pressure Neglected @ = 0) 2.3.1 Why is inclusion of semi-saturation required in practical analysis? 2.3.2 The modification of equations necessary for partially saturated conditions 2.4 Partially Saturated Behaviour with Air Flow Considered (pa 0) 2.4.1 The governing equations including air flow 2.4.2 The governing equation 2.5 Alternative derivation of the governing equations of sections 2.1-2.4, based on the hybrid mixture theory 2.5.1 Kinematic equations 2.5.2 Microscopic balance equations 2.5.3 Macroscopic balance equations 2.5.4 Constitutive equations 2.5.5 General field equations 2.5.6 Nomenclature 2.6 Concluding Remarks References</p> <p>&gt;</p> <p>vi</p> <p>CONTENTS</p> <p>3 Finite Element Discretization and Solution of the Governing Equations3.1 The Procedure of Discretization by the Finite Element Method 3.2 u-p Discretization for a General Geomechanics Finite Element Code 3.2.1 Summary of the general governing equations 3.2.2 Discretization of the governing equation in space 3.2.3 Discretization in time 3.2.4 General applicability of transient solution (consolidation, static solution, drained uncoupled, undrained) Time step length The consolidation equation Static problems-undrained and fully drained behaviour 3.2.5 The Structure of the numerical equations illustrated by their Linear equivalent 3.2.6 Damping matrices 3.3 The u-U Discretization and its Explicit Solution 3.3.1 The governing equation 3.3.2 Discretized equation and the explicit scheme 3.3.3 The structure of the numerical equations in linear equivalent 3.4 Theory: Tensorial Form of the Equations 3.5 Conclusions References</p> <p>4 Constitutive Relations-Plasticity4.1 Introduction 4.2 The general Framework of Plasticity 4.2.1 Phenomenological aspects 4.2.2 Generalized plasticity 4.2.3 Classical theory of plasticity 4.3 Critical State Models 4.3.1 Introduction 4.3.2 Critical state models for normally consolidated clay 4.3.3 Extension to sands 4.4 Advanced Models 4.4.1 Introduction 4.4.2 A generalized plasticity model for clays 4.4.3 A generalized plasticity model for sands 4.4.4 Anisotropy 4.5 Modified Densification Model 4.5.1 Densification model for cyclic mobility References</p> <p>5 Examples for Static, Consolidation and Partially Saturated Dynamic Problems5.1 Introduction 5.2 Static Problems 5.2.1 Example (a): Unconfined situation-small constraint -Embankment -Footing 5.2.2 Example (b): Problems with medium (intermediate) constraint on deformation 5.2.3 Example (c): Strong constraints-undrained behaviour 5.2.4 Example (d): The effect of the K section of the yield criterion</p> <p>CONTENTSIsothermal Drainage of Water from a Vertical Column of Sand Modelling of Subsidence due to Pumping from a Phreatic Aquifer Air storage Modelling in an Aquifer Flexible Footing Resting on a Partially Saturated Soil Comparison of Consolidation and Dynamic Results Between Small strain and Finite Deformation Formulation 5.7.1 Consolidation of fully saturated soil column 5.7.2 Consolidation of fully and partially saturated soil column 5.7.3 Consolidation of two-dimensional soil layer under fully and partially saturated conditions 5.7.4 Fully saturated soil column under earthquake loading 5.7.5 Elasto-plastic large-strain behaviour of an initially saturated vertical slope under a gravitational loading and horizontal earthquake followed by a partially saturated consolidation phase 5.8 Conclusions References 5.3 5.4 5.5 5.6 5.7</p> <p>vii</p> <p>6 Validation of Prediction by Centrifuge6.1 Introduction 6.2 Scaling Laws of Centrifuge Modelling 6.3 Centrifuge Test of a Dyke Similar to a Prototype Retaining Dyke in Venezuela 6.4 The VELACS Project 6.4.1 General analysing procedure 6.4.2 Description of the precise method of determination of each coefficient in the numerical model 6.4.3 Modelling of the laminar box 6.4.4 Parameters identified for the Pastor-Zienkiewicz Mark 111 model 6.5 Comparison with the VELACS Centrifuge Experiment 6.5.1 Description of the models Model No. 1 Model No. 3 Model No. I I 6.5.2 Comparison of experiment and prediction 6.6 Centrifuge test of a Retaining Wall 6.7 Conclusions References</p> <p>7 Prediction Applications and Back Analysis7.1 Introduction 7.2 Example 1: Simulation of Port Island Liquefaction-Effect of Multi-dimensional Loading 7.2.1 Introductory remarks 7.2.2 Multi-directional loading observed and its numerical modelling-simulation of liquefaction phenomena observed at Port Island -Conditions and modelling -Results of simulation -Effects of multi-directional loading 7.3 Simulation of Liquefaction Behaviour During Niigita Earthquake to Illustrate the Effect of Initial (shear) Stress</p> <p>viiiInfluence of initial shear stress -Significance of ISS component to the responses -Theoretical considerations 7.4 Quay Wall Failure and a Countermeasure 7.4.1 Conditions and modelling -Configuration -Soil layers and properties -Input Motion 7.4.2 Results and remarks 7.5 Lower San Fernando D a m Failure 7.6 Mechanism of Liquefaction Failure o n a n Earth D a m (the N Dam) 7.6.1 Objective of the analysis 7.6.2 Input motion 7.6.3 Conditions and modelling -Soil properties -Parameters for liquefaction -Initial stress 7.6.4 Results of calculations 7.6.5 Remarks 7.7 Liquefaction Damage in the Niigata Earthquake of 1964 7.7.1 Results 7.8 Interaction Between Ordinary Soil and Improved Soil Layer 7.8.1 Input motions -Earth pressure due to liquefaction 7.8.2 Safety for seismic loading -External safety -Internal safety 7.8.3 Remarks References 7.3.1</p> <p>CONTENTS</p> <p>8 Some Special Aspects of Analysis and Formulation: Radiation Boundaries, Adaptive Finite Element Requirement and Incompressible Behaviour8.1 Introduction 8.2 Input for Earthquake Analysis and Radiation Boundary 8.2.1 Specified earthquake motion: absolute and relative displacements 8.2.2 The radiation boundary condition: formulation of a one-dimensional problem 8.2.3 The radiation boundary condition: treatment of two- dimensional problem 8.2.4 Earthquake input and the radiation boundary condition-concluding remarks 8.3 Adaptive Refinement for Improved Accuracy and the Capture of Localized Phenomena 8.3.1 Introduction to adaptive refinement 8.3.2 Localization and strain softening: possible non-uniqueness of numerical solutions 8.4 Stabilization of Computation for Nearly Incompressible Behaviour with Mixed Interpolation 8.4.1 The problem of incompressible behaviour under undrained conditions 8.4.2 The velocity correction, stabilization process 8.4.3 Examples illustrating the effectiveness of the operator split procedure 8.4.4 The reason for the success of the stabilizing algorithm References</p> <p>CONTENTS</p> <p>9 Computer Procedures for Static and Dynamic Saturated Porous Media finite element Analysis9.1 Introduction 9.2 Outline description of DIANA-SWANDYNE I1 9.3 Description of major routines used in DIANA-SWANDYNE I1 9.3.1 The top level routines 9.3.2 Subroutines for control and material data input 9.3.3 Subroutines for mesh data input 9.3.4 Subroutines called by the main control routine for analysis 9.3.5 Subroutines for the formation of element matrices and residual calculation 9.4 Major service subroutines 9.5 Constitutive model subroutines 9.5.1 Standard constitutive model interfacing subroutine CONSTI 9.5.2 Constitutive models available for general dissemination 9.5.3 Other constitutive models implemented 9.6 System-dependent subroutines References</p> <p>Appendix 9A Implementing New Models into SM2D</p> <p>Author Index Subject Index</p> <p>Preface</p> <p>Although the concept of effective stress in soils is accepted by all soil mechanicians, practical predictions and engineering calculations are traditionally based on total stress approaches. When the senior author began, in the early seventies, the application of numerical approaches to the field of soil mechanics in general and to soil dynamics in particular, it became clear to him that a realistic prediction of the behaviour of soil masses could only be achieved if the total stress approaches were abandoned. The essential model should consider the coupled interaction of the soil skeleton and of the pore fluid. Indeed, the phenomena of weakening and of 'liquefaction' in soil when subjected to repeated loading such as that which occurs in earthquakes, can only be explained by considering this 'two-phase' action and the quantitative analysis and prediction of real behaviour can only be achieved by sophisticated computation. The simple limit methods often applied in statics are no longer useful. It therefore seems necessary at the present time to present, in a single volume, the basis of such computational approaches because a wider audience of practitioners and engineering students will require the knowledge which hitherto has only been available through scientific publications scattered throughout many journals and conferences. The present book is an attempt to provide a rapid answer to this need. The multiple authorship not only ensures a speedy result, it also introduces members of the research team which, during the last decade, have focused attention on the subject which has developed practical computer codes which are now available to both practitioners and researchers. Since 1975 large number of research workers, both students and colleagues, have participated both at Swansea and elsewhere in laying the foundations of numerical predictions which were based largely on concepts introduced in the early forties by Biot. However, the total stress calculation continues to be used by some engineers for earthquake response analysis, often introduced with the linear approximations. Such simplifications are generally not useful and can lead to erroneous predictions. In recent years, centrifuge experiments have permitted the study of some soil problems involving both statics and dynamics. These provide a useful set of benchmark predictions. Here a validation of the two-phase approach was available and close agreement between computation and experiment was found. A very important landmark was a workshop held at the University of California, Davis, in 1993, which</p> <p>PREFACE</p> <p>xi</p> <p>reported results of the VELACS project (Verification of Liquefaction Analysis by Centrifuge Studies)-sponsored by the National Science Foundation of USA. At this workshop a full vindication of the effective stress, two-phase approaches was clearly available and it is evident that these will be the basis of future engineering computations and prediction of behaviour for important soil problems. The book shows some examples of this validation and also indicates examples of practical application of the procedures described. During numerical studies it became clear that the geomaterial-soil, would often be present in a state of incomplete saturation when part of the void was filled with air. Such partial saturation is responsible for the presence of negative pressures which allow some 'apparent' cohesion to be developed in non-cohesive soils. This phenomenon may be present at the outset of loading or may indeed develop during the dynamic process. We have therefore incorporated its presence in the treatment presented in this book and thus achieved wider applicability for the methods described. Despite the large number of authors, we have endeavoured to present a unified approach and have used the same notation, style and spirit throughout. The first three chapters present the theory of porous media in the saturated and unsaturated states and thus establish general backbone to the problem of soil mechanics. Chapter 4, essential before numerical approximation, deals with the very importa...</p>


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