For many problems of practical interest, it is necessary to estimate settlements under

conditions in which the induced stress varies spatially. The first steps in the analyses of

such problems usually involve estimations of the initial states of stress in the soil and of the

changes in these stresses during loading and as the soil again approaches equilibrium. Two

methods of analysis have commonly been followed. The first may be termed the method of limiting equilibrium. In this method, the stresses that would cause failure are calculated and the applied stresses are compared with the failure stresses to determine a factor of safety against complete failure. The method provides no information about deformations or states of stress within the soil mass. This method of analysis is used to determine the bearing capacity of a foundation or the stability of a slope.