Quasiperiodic compaction events in a two-dimensional frictional model

Avalanche precursors are small, quasiperiodic surface displacements observed experimentally during the slow inclination of a granular bed. In spite of being studied experimentally since the mid-2000s, they have eluded numerical models. One recent contribution is a one-dimensional model where a line of sliders linked by springs is placed on a slowly inclined frictional plane. In this paper, we present a two-dimensional model that stands between this one-dimensional model and the three-dimensional experimental setup. In our model, disks are placed on a frictional plane, and interact with their neighbors and boundaries with typical granular molecular dynamics interactions. The model robustly produces quasiperiodic compaction events. The angular period (change in inclination between two events) is proportional to the difference between the static and dynamic friction coefficients. The first event occurs systematically earlier than predicted by the coefficient of static friction: The inclination can be predicted by subtracting the angular period from the static friction angle. The inclination at the initial event and the angular period decrease for large systems. When the inclination is varied cyclically, longer sequences of events can be observed, as in recent experiments. Finally, the relation between the observed compaction events and avalanches and avalanche precursors are discussed.