Displacements in a column-reinforced granular medium: a probabilistic approach

A probabilistic approach was proposed by Harr [1] to account for diffusion of stresses in a granular medium. It considers that 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 obeys a similar equation as the known Fokker-Planck equation. Bourdeau [2] extended this approach to the diffusion of vertical displacements in a cohesionless granular medium. An equation of diffusion is obtained and the parameter of diffusion is shown to approximate the mean diameter of the material grains. We revisited the formulation of displacements diffusion to account for a gravel column-reinforced soil submitted to foundation loading. A numerical approach based on finite elements method is used to account for a gravel column-reinforced soil submitted to loadings of a building foundation. The obtained results show that the diffusion of displacements in the granular medium is influenced by the grain size distribution and it helps using the method as a valuable tool to calculate settlements. Comparisons are shown when the soil (granular medium) is reinforced with gravel columns.