Stochastic model of transient compression in granular media

A particulate mechanics theory for the transient compression of granular media is proposed. The analytic model describes the propagation of the excess volume of voids through the particulate medium as a stochastic diffusion process. The formulation of the model and its numerical solution are presented for the case of one-dimensional compression and constant effective stress. The main results express the evolution in time of the spatial distribution of the material porosity and the rate of settlement. Tests performed in the laboratory show good agreement between the proposed theory and secondary consolidation settlement observed with loose cohesionless soil.