Diffusion Analogy for Some Stress Computations

Abstract

Although soil is an assemblage of discrete particles of varying sizes, shapes, and mineral composition, the classical basis for the computation of stresses in soil mechanics is the Boussinesq theory of elastic potentials in which the soil is assumed to be a homogeneous, linearly elastic isotropic continuum, and a normal point load is applied on the surface of an infinite half-space as in Fig. I (a). Many researchers have sought to establish a statistical or probabilistic theory for stress computation in soils and most recently Harr (1) and Endley, et. al (2) have developed such a theory. The diffusion analogy presented in this note has strictly speaking already been presented by Harr (1) and indeed Harr's work in some respects goes beyond this note. However, at the time the work in this note was done the writers were unaware of the work in Refs. 1 and 2. This note is therefore offered as a different exposition of a very important subject. In particular the diffusion analogy constant C(related to Harr's coefficient of lateral stress v by 2C = v) is calculated in a novel way. It is hoped that this exposition will stimulate thinking and further work in this area.