Stochastic Stress Models with Horizontal Forces

Previous work on stochastic models of stress distributions in granular half-spaces is extended to include the presence of horizontal as well as vertical surface forces. The resulting model is that of a standard stochastic process with a preferential drift in the direction of the horizontal surface force. The linear elastic stress distributions can be fitted into the general framework of this model. The theory is incomplete in the sense that certain quantities are indeterminate, particularly in the three-dimensional case. However, with the help of certain assumptions, stress distributions can be derived that possess the following realistic physical features: they fall off more sharply than the elastic distributions in a horizontal direction; and the diagonal components do not become tensile, in contrast to the elastic case. Finally, it is indicated how the theory may be generalized to the multilayer case.