On Phase Transition and Self-Organized Critical State in Granular Packings

Abstract

We model two-dimensional systems of granular aggregates confined between two planes and demonstrate that at a critical grain volume fraction an abrupt rigidity transition occurs. This transition is observed both in static and shear tests. The grain volume fraction at which the transition occurs, $ν_c$, decreases with increasing friction between the grains. Densely packed grains, with a volume fraction $ν> ν_c$, display an elastic-plastic rheology. Dilute packings, with $ν<ν_c$, display gas-like characteristics. Packings with $ν=ν_c$ display phase coexistance. It is shown that when volume fraction is allowed to change freely (using constant normal stress boundary condition), it evolves spontaneously to $ν_c$ under a wide range of boundary conditions, exhibiting &#39;self-organized criticality&#39;.