Granular avalanches in a two-dimensional rotating drum with imposed vertical vibration

Abstract

We present statistics on granular avalanches in a rotating drum with and without imposed vertical vibration. The experiment consists of a quasi-two-dimensional, vertical drum containing pentagonal particles and rotated at a constant angular velocity. The drum rests on an electromagnetic shaker to allow vibration of the assembly as it rotates. We measure time series of the slope of the interface and find that the critical angle for slope failure θ(c) and the resulting angle of repose θ(r) are broadly distributed with an approximate power-law distribution of avalanches θ(c)-θ(r) for large avalanches. The faceted pentagonal grains used lead to significant interlocking with critical and repose angles (θ(c)≈45° and θ(r)≈39°) larger than experiments using spherical grains, even with vibration, and avalanche magnitudes correlated with the prior build-up and anti-correlated with the prior avalanche. We find that the stability of the assembly increases with small vibrations and is destabilized at vibration amplitudes above a dimensionless acceleration (peak acceleration divided by acceleration due to gravity) of Γ=0.2. We also study history dependence of the avalanches by periodically oscillating the drum to compare the initial avalanche upon reversal of shear to steady-state distributions for avalanches during continuous rotation. We observe history dependence as an initial decrease in critical angle upon reversal of the drum rotation direction, indicating that a texture is induced to resist continued shear such that the surface is weaker to reversals in shear direction. Memory of this history is removed by sufficient external vibration (Γ≥0.8), which leads to compaction and relaxation of the surface layer grains responsible for avalanching dynamics, as initial and steady-state avalanche distributions become indistinguishable.