Limit Analysis of Soil Structure by Rigid Plastic Finite Element Method

Abstract

We investigate a numerical approach to analyze the limit state of soil structures, assuming that the mechanical property of the soil is rigid plastic. It is well known that the collapse analysis of frame structures can be formulated as the linear programming problem through the upper bound theorem of plasticity. Recently this method was extended to continuum. Since the nonlinear programming problem must be treated in this case, no well-established technique is found out in the literature. There also is a little theoretical confusion concerning the constraint conditions and the indeterminate pressure (total mean stress).In this paper, we firstly formulate the problem by using the upper bound theorem and secondly show that the minimization of the upper bound is equivalent to finding out the equilibrium state with the indeterminate pressure. The present numerical procedure is illustrated by typical problems, i. e., bearing capacity of shallow foundation and slope stability. Good agreement between the present results and well-known solutions confirms that our approach can be used as a general method for the limit analysis of soil structures.