A micromechanics model for consolidated granular solids

The porosity and micro-structure have a significant influence on the stress-strain behavior of solids formed by consolidation of granular material, such as sedimentary rocks and sintered solids. In this paper, a stress-strain model for consolidated granular solids is presented accounting for the effects of internal structure. The granular solid is envisioned to be composed of polyhedral micro-cells containing a single grain and the associated void space. Such a physical model of granular solid is especially useful for representing the effect of heterogeneity due to the randomness of micro-structure. An equivalent local stiffness tensor is derived for the micro-cell by considering the stress and strain fields in the micro-cell. A ‘self consistent’ effective medium methodology is employed to obtain the overall property of a representative volume element (RVE). First order approximation of the derived relationship is presented that explicitly relates the micro-structure to the stiffness tensor of such solids.