Granular flow down a rough inclined plane: transition between thin and thick piles

Abstract

The rheology of granular particles in an inclined plane geometry is studied using molecular dynamics simulations. The flow--no-flow boundary is determined for piles of varying heights over a range of inclination angles $θ$. Three angles determine the phase diagram: $θ_{r}$, the angle of repose, is the angle at which a flowing system comes to rest; $θ_{m}$, the maximum angle of stability, is the inclination required to induce flow in a static system; and $θ_{max}$ is the maximum angle for which stable, steady state flow is observed. In the stable flow region $θ_{r}<θ<θ_{max}$, three flow regimes can be distinguished that depend on how close $θ$ is to $θ_{r}$: i) $θ>>θ_{r}$: Bagnold rheology, characterized by a mean particle velocity $v_{x}$ in the direction of flow that scales as $v_{x}\propto h^{3/2}$, for a pile of height $h$, ii) $θ\gtrsimθ_{r}$: the slow flow regime, characterized by a linear velocity profile with depth, and iii) $θ\approxθ_{r}$: avalanche flow characterized by a slow underlying creep motion combined with occasional free surface events and large energy fluctuations. We also probe the physics of the initiation and cessation of flow. The results are compared to several recent experimental studies on chute flows and suggest that differences between measured velocity profiles in these experiments may simply be a consequence of how far the system is from jamming.