  A flow model is developed for dense shear-driven granular flow. As described
in the geomechanics literature, a critical state condition is reached after
sufficient shearing beyond an initial static packing. During further shearing
at the critical state, the stress, fabric, and density remain nearly constant,
even as particles are being continually rearranged. The paper proposes a
predictive framework for critical state flow, viewing it as a condition of
maximum disorder at the micro-scale. The flow model is constructed in a
two-dimensional setting from the probability density of the motions, forces,
and orientations of inter-particle contacts. Constraints are applied to this
probability density: constant mean stress, constant volume, consistency of the
contact dissipation rate with the stress work, and the fraction of sliding
contacts. The differential form of Shannon entropy, a measure of disorder, is
applied to the density, and the Jaynes formalism is used to find the density of
maximum disorder in the underlying phase space. The resulting distributions of
contact force, movement, and orientation are compared with two-dimensional DEM
simulations of biaxial compression. The model favorably predicts anisotropies
of the contact orientations, contact forces, contact movements, and the
orientations of those contacts undergoing slip. The model also predicts the
relationships between contact force magnitude and contact motion. The model is
an alternative to affine-field descriptions of granular flow.
