Role of inertia in the starting and stopping mechanisms of granular flows

It is well known that a pile of grains starts and stops flowing at different angles of repose. It is also known that such starting and stopping angles exhibit thickness-dependent behavior, with deeper layers beginning to flow more readily and arresting at lower angles than shallower materials. These considerations have motivated various rheological assumptions in granular constitutive laws. This paper demonstrates that such observations can instead be partly attributed to inertial effects. In particular, we examine the roles of two control parameters characterizing conventional chute flow experiments: the rate of inclination of the chute, and the threshold surface velocity associated with identification of the flow. Both of these parameters control the system's momentum at different instances. We perform two-dimensional discrete element simulations and also develop a one-dimensional analytic model based on the standard $\ensuremath{\mu}(I)$ rheology. Results indeed indicate a difference between the starting and stopping angles as well as a thickness dependency, despite the absence of any hysteresis or material length scale in the underlying rheological model. Higher threshold velocities are shown to produce higher angles at which flow begins. In addition, the starting (stopping) angle increases (decreases) with the applied inclination rate. For thick enough granular layers, no matter how small the rate is, critical angles are shown to deviate from the quasistatic limit. Therefore, inertial effects should not a priori be neglected. To finalize our argument, we show the effect of the inclination rate and the threshold velocity in a laboratory setup, using small-scale experiments of an inclined chute.