1.1 INTRODUCTION

Partly for simplicity in practice and partly because of the historical development of mechanics of deformable solids, the problems of soil mechanics are often divided into two distinct groups the stability problems and the elasticity problems. They are then treated in two separate and unrelated ways. The stability problems deal with the conditions of ultimate failure of a mass of soil. Problems of earth pressure, bearing capacity, and stability of slopes most often are considered in this category. The most important feature of such problems is the determination of the loads which will cause failure of the soil mass. Solutions to these problems are often obtained using the theory of perfect plasticity. The elasticity problems on the other hand deal with stress or deformation of the soil when no failure of the soil is involved. Stresses at points in a soil mass under a footing, or behind a retaining wall, deformations around tunnels or excavations, and all settlement problems belong in this category. Solutions to these problems are often obtained by using the theory of linear elasticity.

The theory of linear elasticity is based on Hooke's law which establishes a linear relation between stress and strain. The theory of perfect plasticity takes account of the fact that real soil exhibits the mechanical behavior stipulated by Hooke's law only as long as the stress intensity remains sufficiently small. When the stress intensity first reaches a certain critical value, which is called the yield value