Stochastic Model for Time-Dependent Compression of Particulate Media

The volumetric creep of loose granular materials, in absence of pore fluid pressure, is modeled as a stochastic process of diffusion-convection for excess porosity under sustained, applied loading. The analogy of the underlying concepts, with the theory of sedimentation in Brownian motion, and differences with the earlier contribution of Marsal (1965) are discussed. The analytical formulation and numerical solution are presented for a 1D compression with finite strain and moving boundary surface. The results represent the time evolution of the spatial distribution of the material porosity and the rate of settlement. The compression versus time relationship is normalized in dimensionless form to facilitate the determination of the governing equation coefficients from test data. Examples of determination and comparisons with the model response are presented. According to the model, final settlement is reached asymptotically with equilibrium porosity. At transient states, the spatial distribution of porosity is not necessarily uniform, even when both initial and final distribution are uniform.