Stochastic Modeling of Load-Induced Settlement in Loose Granular Materials

Abstract

The response of loose cohesionless granular material to surface applied loads is investigated from the viewpoint of probabilistic mechanics of particulate media. A model is proposed that is based on the combined propagation of intergranular forces and an excess volume of voids. In this regard, it provides a bridge between earlier theories developed independently for the diffusion of stresses and for the propagation of settlements. In its general formulation, the theory can model three-dimensional, transient effects. However, the model is believed to be limited to normally consolidated or noncompacted, fully drained or dry, granular materials that do not exhibit dilatancy effects. The derived numerical modeling of steady state deflection patterns under a rigid footing is found to be in good agreement with x-ray images of laboratory model tests using noncompacted silt. The proposed theory recognizes the discrete and inherently random nature of natural granular materials such as cohesionless soils and builds upon these fundamental characteristics to predict responses of such materials to boundary applied load. This is achieved by modeling intergranular force and excess pore volume propagation as Markovian diffusion-advection processes. This approach, which departs from traditional continuum mechanics models, seems to have potential for addressing some of the challenging aspects of granular material mechanics in lunar or Martian environments.