Limit Analysis and Limit Equilibrium Solutions in Soil Mechanics

Abstract

Idealizations in soil mechanics are usually necessary in order to obtain solutions and to have these solutions in a readily applicable form. Limit equilibrium has been a method of solving various soil stability problems. One weakness of the limit equilibrium method has been the neglect of the stress-strain relationship of the soil. According to the mechanics of solids, this condition must be satisfied for a complete solution. Limit analysis, through the concept of a yield criterion and its associated flow rule, considers the stress-strain relationship. However, a soil with cohesion and internal friction is not modeled accurately by a theory of perfect plasticity. Nevertheless, indications are that the stability problems in soil mechanics will, in time, be computed on the basis of the limit theorems of plasticity. A discussion is given, therefore, of the significance of the limit analysis in terms of the real behavior of soils and their idealizations. With this background the meaning of existing limit equilibrium solutions is discussed, and the power and simplicity of application of the limit analysis method is demonstrated.