Granular flow down an inclined plane: Bagnold scaling and rheology

We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow $v_x\mathrm{}\left(z\right)\mathrm{}$ scales with height of the pile H, according to $v_x\mathrm{}\left(z\right)\mathrm{}\propto H^{\alpha }$, with $\alpha =1.52\mathrm{}\pm 0.05$. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.