Elastic and Particulate Media

Constitutive relations for soil are proposed which given rise to a diffusion-like equation for the normal stress component. This partial differential equation includes both particulate media theory and the classical linear theory of elasticity, in the sense that the solutions of concentrated load problems for half-spaces, coincide with those due to Flamant and Boussinesq for special values of the contained parameters. This means that all stress boundary value problems for infinite half-spaces in the classical linear theory of elasticity arise as special cases of the theory described here. On the other hand the particulate media theory arises from probabilistic considerations and the results given present for the first time a formal connection with classical elasticity theory.