The Application of Finite Elements to Problems of Soil

Abstract

The finite element method is now well established as an extremely useful tool for the displacement and stress analysis of problems with complicated boundary conditions. One aim of this thesis is to investigate the suitability of the method in the solution of the range of Civil Engineering problems usually associated with Soil and Rock Mechanics. A further aim has been to extend the method into the analysis of complete structures integral with the foundation material. A suite of programs has been written to carry out finite element analysis in two or three dimensions using the new families of Isoparametric elements. The accuracy and efficiency of these elements has been assessed in relation to a typical foundation problem which can be analysed using more conventional methods. Two important non-linear two dimensional problems have been investigated namely the analysis of the plane strain compression test, involving the idealisation of smooth interfaces, and, crack propagation. In the former an iterative process has been followed to analyse the test and compare results with experimental conclusions, The process of crack propagation has been followed using an incremental method which involves changing compatibility conditions to introduce separations at element boundaries. The major part of this thesis is concerned with a method for analysing complete three dimensional structures together with their foundation materials. With this method it is possible to include the complex interactions of structure and foundation as well as the nonlinear stress-strain response of the soil. In order to assess the accuracy of the method it was necessary to construct a model testing apparatus and conduct a series of experiments.