4.1 INTRODUCTION

The lower-bound method of limit analysis is different from the upper-bound method in that the equilibrium equation and yield condition instead of the work equation and failure mechanism are considered. Moreover, whereas the development of the work equation from an assumed collapse mechanism is always clear, many engineers find the construction of a plastic equilibrium stress field to be quite unrelated to physical intuition. Without physical insight there is trouble in finding effective ways to alter the stress fields when they do not give a close bound on the collapse or limit load. Often the user employs the existing stress fields from well-known texts or the more recent technical literature as a magic handbook and tries to fit his problem to the particular solutions he finds. Intuition and innovation seem discouraged by unfamiliarity and apparent complexity. Although the discontinuous fields of stress which will be drawn and discussed in this Chapter are simpler to visualize, they too are not often employed in an original manner by the design engineer. Yet, in fact, the concepts are familiar to the civil engineer in his terms and can be utilized by the designer as a working tool. In this Chapter, it is hoped that the following discussion of the stress field in plane strain problems will make this lower-bound technique of limit analysis more readily accessible to engineers.

Most of the early work on the construction of a stress field is concerned with the pure cohesive soil or Tresca...