A Nonlinear Constitutive Model for Granular Materials: Application to Gravity Flow

The form of the dissipative part of the stress in flowing granular materials is motivated by considering momentum exchange due to intergranular collisions. Both shear and normal stresses are predicted that are quadratic in the rate of deformation. The equilibrium part of the stress is assumed to include a thermodynamic pressure and a term compatible with the Coulomb failure criterion in the limit of vanishing deformation. Solutions for the volume fraction and velocity fields in steady gravity flow down a slope are found. The volume fraction increases linearly downward through the shearing layer at a rate that decreases with increasing slope. The velocity profile develops an inflection near the lower boundary at smaller slopes, and becomes fully convex downstream as it approaches a critical maximum slope for steady flow. The results are in qualitative agreement with available experimental measurements.