Modelling particle breakage in unsaturated granular assemblies

In this paper we use a thermomechanical approach to study inelastic processes in unsaturated granular matter. The paper extends the breakage mechanics theory to unsaturated conditions, investigates the physical roots of hydro-mechanical coupling and elucidates the interplay between yielding locus and degree of saturation. For this purpose, energy storage mechanisms are hypothesized to consist of the sum of an elastic energy potential and a hydraulic contribution inspired by the capillary theory. Microscopic arguments are then used to define suitable grainsize scaling laws. These assumptions are finally combined with a statistical homogenization procedure, thus deriving a macroscopic Helmholtz free energy. The paper shows that such procedure, together with the breakage dissipation, is able to capture salient couplings between mechanics and hydraulics. The results provide a novel theoretical explanation for the approaches commonly used in plasticity models for unsaturated porous media.