Dynamic Behavior of Slip Avalanches on a Granular Pile Matches Mean-Field Scaling Predictions

A conical bead pile is used as a model system to experimentally investigate slip avalanches. The pile of 3 mm diameter beads is slowly driven by dropping single beads onto the apex; we wait for any resulting motion on the pile to complete before dropping a subsequent bead. Our primary definition of avalanche size is the number of beads which leave the pile during the event, as measured by the change in mass of the pile.

The statistical properties of the avalanches, including avalanche size distribution and the distribution of events in time, have been previously shown to match well with a mean-field model of slip avalanches [Dahmen et al., Nat Phys 7, 554 (2011)]. Using an overhead camera to record the dynamics of individual avalanches, we can now compare additional predictions of the model to this experimental system. We use particle image velocimetry to analyze the slip rate of beads on the pile surface during the avalanche. The time resolution of the slip rate measurements allows us to resolve the overall pile motion from one bead drop into discrete sub-avalanches; what had been defined as a single avalanche is now recognized as an avalanche cluster. Each sub-avalanche is then characterized by a distinct slip size, duration, and temporal profile. We show that the resulting distributions, scaling exponents, and temporal profiles are in quantitative agreement with mean field theory predictions, providing direct experimental evidence that slip avalanches in granular piles show not only scale invariant statistics but also scale invariant dynamics.