Interval-based parameters for stress diffusion in granular medium

According to Bourdeau (1986), diffusion of stresses in a granular medium can be described using a probabilistic approach. A point load applied on the surface of a granular media will follow an erratic path, depending on the probability of transition between the grains. The diffusion of the expected vertical stress in the granular medium can be described by a Fokker-Planck type equation. In terms of expected vertical stresses, an equation of diffusion is obtained and the parameter of diffusion is shown to approximate the coefficient of lateral pressure of the material at a given depth z. The coefficient of lateral pressure of the material can be expressed in terms of intervals with upper and lower values to account for uncertainty. In the present approach, we propose to solve the diffusion equation using interval-based parameters to account for uncertainty. Uncertain parameters are considered as discretized fuzzy numbers; they are combined with finite difference method to solve the diffusion equation. Comparisons are made with experimental and available data.