Avalanche dynamics in model two-dimensional grain piles

Abstract

We report particle dynamical simulations of a two-dimensional grain pile in a box with the base being slowly tilted from horizontal to ${\ensuremath{\Theta}}_{\mathrm{aval}}$ angle at which the pile undergoes a large layer sliding event. When dissipation between the grains is negligible, the distribution $D(s)$ of displacements $s$ of the surface grains shows decays that are consistent with ${s}^{\ensuremath{-}\ensuremath{\tau}}$ with $\ensuremath{\tau}\ensuremath{\approx}2$ for $0<\ensuremath{\Theta}<{\ensuremath{\Theta}}_{\mathrm{aval}}.$ At time $t>{t}_{\mathrm{aval}}$ at ${\ensuremath{\Theta}}_{\mathrm{aval}}$ we find a crossover in \ensuremath{\tau} to $\ensuremath{\tau}\ensuremath{\approx}3/2.$ Dissipation appears to play a key role in the system dynamics only when $\ensuremath{\Theta}<{\ensuremath{\Theta}}_{\mathrm{aval}}.$ We find that the time for the onset of avalanches, ${t}_{\mathrm{aval}}>~{t}_{W},$ where ${t}_{W}$ is the time when the surface roughness of the sliding pile is minimized.