5.1 INTRODUCTION

As has been indicated in Chapter 1, a complete elastic-plastic analysis of stress and strain in a mass of soil as the footing load is increased to failure is almost always complicated, and limit analysis is one of the methods that furnishes the load-carrying capacity of a footing on a soil in a more direct manner. Before we move on to apply the techniques of limit analysis developed in the preceding two Chapters to various stability problems in soil mechanics, we shall first, in this Chapter, present some typical elastic-plastic responses of soils to footing loads so that physical insight for this class of problems is obtained.

We present here the numerical results of a detailed study of plane strain and axisymmetric flat rigid footings bearing on an elastic-perfectly plastic soil (except section 5.8). Complete load displacement histories are presented from zero-load to failure, encompassing initial elastic behavior, contained plastic flow and collapse. We show stress distributions and zones of yielding at various load levels during continued loading. We show also velocity fields at the collapse state. Particular attention is given to the effect of the changing soil geometry on the response of the soil stratum to the footing loads. The finite element method and an incremental integration scheme are used to numerically solve the governing equations. Details of this finite element formulation are given in Chapter 12.

The finite element formulation was developed originally for structural analysis and it has been used for solving many complex...