Entropy and Granular Materials: Model

Abstract

The macrostructure of a granular material is treated as an ensemble of microstates of like spheres where each microstate is identified by a coordination number and a corresponding porosity. The probability of occurrence of these finite numbers of microstates is constrained by measurable information concerning the macrostate and described by maximizing the information entropy subject to these constraints and the axioms of probability theory. The macrostate behavior is then deduced from the probabilities of occurrence of the microstates and their mechanical performance. Existing observations of phenomena in granular media as related to soils and liquids are discussed and explained in light of the proposed entropy maximization scheme. Critical tests to examine the viability of the entropy model are proposed.