Numerical modelling of a foundation in three dimensions

Abstract

NUMERICAL MODELLING OF A FOUNDATION IN THREE DIMENSIONS ABSTRACT Numerical Modelling has gained increasing importance in solving practical problems in geotechnical engineering. With the help of developments in hardware and software industry, it is possible to solve more complex problems. These developments enable the geotechnical engineer to perform advanced numerical analysis. Finite element method is a useful tool in numerical analysis, it has been widely used in soil mechanics in the last twenty years. To increase the accuracy and quality of numerical computer based calculations, verifications should be performed and results of benchmarks should be compared with results from different software. This document outlines the finite element analysis of a shallow foundation in two and three dimensions. A shallow foundation was placed near to a slope and this model was calculated by using CESAR finite element software. The community of soil mechanics and geotechnical engineering of France has proposed this benchmark to some research institutes and universities. One of these calculations was performed in Ecole Centrale de Nantes by the department of Civil Engineering. The problem has been chosen so that it can be regarded as a simplified analysis of real construction site. One of the basic aims of the research was to observe calculation errors which are caused by discretization, element types, tolerance limits and by the number of increments. By this way, four different models were prepared in both two and three dimensions. These models were then calculated in elastic and elastoplastic conditions. Settlement values were compared with the results of other research institutes and finite element programs to observe the degree of error which is caused xmby discretization. The models were prepared separately with both linear and quadratic elements. Then a correlation was made between these elements. Finally a sensitivity analysis was performed to observe the effects of tolerance limits and the number of increments on calculation errors. Three dimensional models were calculated with different numbers of increments to arrive at a solution of the decision of the number of increments at the beginning of the calculations. Then the influence of tolerance limits on the accuracy of results was researched. In the meantime, it was aimed to make a reference in the selection of mesh density in three dimensional models. As the finite element users are used to make calculations in two dimensions, it is possible to observe the calculation error which is caused by the mesh density and element types. It will therefore be possible to make a correlation with three dimensions in determination of the discretization parameters. Numerical studies require the solving of different problems and the comparison of their results in order to increase the reliability and accuracy of these methods. This research will be a reference for the next researchers to make verifications for finite element programs. xiv