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After extensive quasi-static shearing, dense dry granular flows attain asteady-state condition of porosity and deviatoric stress, even as particles arecontinually rearranged. The paper considers two-dimensional flow and derivesthe probability distributions of two topological measures of particlearrangement---coordination number and void valence---that maximize topologicalentropy. By only considering topological dispersion, the method closelypredicts the distribution of void valences, as measured in discrete element(DEM) simulations. Distributions of coordination number are also derived byconsidering packings that are geometrically and kinetically consistent with theparticle sizes and friction coefficient. A cross-entropy principle results in adistribution of coordination numbers that closely fits DEM simulations.

Dense granular flow at the critical state: maximum entropy and topological disorder