Development of a practical methodology for the analysis of gravity dams using the non-linear finite element method

Abstract

For many decades the ‘classical’ method has been used to design gravity dams. This method is based on the Bernoulli shallow beam theory. The finite element method (FEM) has become a powerful tool for the dam design engineer. The FEM can deal with material properties, temperatures and dynamic load conditions, which the classical method cannot analyse. The FEM facilitates the design and optimisation of new dams and the back analysis of existing dams. However, the linear elastic FEM has a limitation in that computed stresses are sensitive to mesh density at ‘singularity points’. Various methods have been proposed to deal with this problem. In this paper the Drucker-Prager non-linear finite element method (DP NL FEM) yield model is presented as a method to overcome the problem of the stress peaks at singularity points, and to produce more realistic stresses at the base of the dam wall. The fundamentals of the DP NL FEM are presented. Benchmark studies of this method demonstrate the method’s viability to deal with zones in a structure with stresses beyond the elastic limit where yielding of the material occurs. A case study of a completed gravity dam is analysed, comparing several analysis techniques. The service and extreme load cases are investigated. Different material properties for the concrete and rock, including weathered material along the base of the wall, are considered. The application and merits of the DP NL FEM are presented. The calculation of the critical factor of safety against sliding is done with a more realistic determination of the conditions along the base of the wall.