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SUBSTNUCTUNE TWO

Finite Element Analysis of Gravity Dams using SubstructureTechnique

Dr S S Saini, FellowS K Garg, Non-member

A dam-foundation system can be modelled and analysed with great-accuracy using finite element method(FEM) while considering the effect of various materials involved. But as the size of the dam-foundation systemincreases, this method requires large computer memory and hard disc space. Substructuring of large damfoundation systems provides a solution to the problem faced in one-stagefmite element analysis. Avo-dimen-sional analysis of a proposed concrete gravity dam has been carried out here, using substructure technique. Acomparison of execution time and hard disc storage requirement has been given. It has been concluded thatthe substructure technique leads to a significant reduction in both computer time and hard disc spacerequirements without any compromise in the accuracy of the solution.

Keywords : FEM; Substructure; Reduced stiffness matrix; Iterative approach; Analysis; Dam; Foundation

INTRODUCTION

Several dams are proposed to be constructed in regionshaving relatively geologically less sound rocks. Detailedanalysis of dams along with foundation is necessary for suchsites, which is not possible by the conventional methods ofdam analysis. Problems often faced in the analysis of highdams, dams with powerhouse cavity, allied undergroundstructures and arch dams cannot be solved reliably using con-ventional methods. Hence, for economy and reliability indam design, other sophisticated methods like fmite elementmethod are to be used.

Finite element method can take into account the actual valleyshaper as well as different properties of concrete andheterogeneous foundation materials. Using this method, anygeometry of the dam-foundation system can be modelledwith great accuracy while considering the various materialproperties involved 2. But as the size of the dam-foundationsystem increases, this method requires large computermemory and hard disc space. Hence, very large dam-foun-dation systems cannot be modelled even on large computersthus limiting the use of finite element analysis. Substructur-ing of large dam-foundation systems provides a solution tothe problems faced in one-stage finite element analysis.

In this paper, a proposed concrete gravity dam, founded onweak rocks has been analysed using substructure approach.It has been found that considerable saving in computer tuneand storage requirement is obtained while using substructuretechnique, without any loss in the accuracy of results. The ex-ample demonstrates the effectiveness of the substructure ap-proach for analysing large dam-foundation systems and can alsobe extended for carrying out the three-dimensional analysis.

SUBSTRUCTURE TECHNIQUE

In substructure approach, the structure is divided into smallerparts known as substructures. Each substructure is of suchsize that it can be handled easily while considering one at a

Dr S S Saini and S K Garg are with Department of Civil EngineeringUniversity of Rourke., Roorkee 247 667.'Ibis paper (revised) was received on December 5, 1996. Written discussionon the paper will be entertained until June 30, 1997.

Vol 78, May 1997

time. Common boundary between the two substructures istermed as interface. Representation of a typical dam-founda-tion system into two substructures is indicated in Fig 1. Solu-tion by substructure approach can be obtained either usingiterative approach3 4 or reduced stiffness matrix approach", 6

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Fig 1 Partitioning Into two substructures

Iterative Approach

Iterative approach is aimed at obtaining the deformations bycarrying out several iterations. Initially, substructure-I is as-sumed to be fixed at the interface and analysed. Reactionsobtained at the interface are applied (with reversed signs) onsubstructure-II as loads. The second substructure is analysedto get the displacements at the interface. Now, these displace-ments are used as prescribed displacements at the interfaceof the substructure-I which is analysed again to obtain newreactions at the interface. In this way, the process is carriedout till the convergence is achieved. Convergence is con-sidered to occur when the difference between the reactionsobtained at the interface in the current iteration and in theprevious iteration, calculated as fraction of reactions in thepresent iteration on vector-norm basis, is less than theprescribed permissible error (adopted as 0.02 in this study).Knowing deformations, strains and stresses in the substruc-tures can also be computed.

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