Inter-event Time Analysis of Avalanches on a Conical Pile Characterized by Mass and Spatial Extent

A conical bead pile is used as a model system for critical behavior in granular systems. The pile is a critical system of roughly 20,000 steel beads atop a circular base; each bead is 3 mm in diameter. The pile is driven by adding one bead at a time to the pile apex. Any bead drop could trigger an avalanche in which beads leave the pile. Changes in pile mass are recorded over the course of tens of thousands of bead drops to characterize the distribution of avalanche sizes, as defined by the number of beads which leave the pile. A camera above the bead pile records video of the dynamic behavior for all medium to large avalanches (involving at least 42 beads); the video is then analyzed with particle image velocimetry (PIV) to yield the surface speed with spatial and temporal resolution. With the PIV result, we find which region of the pile and what fraction of the pile were in the avalanche. Our goal is to broaden our definition of avalanche size or significance from mass-only to an analysis combining mass and active area. This new analysis of the active area for avalanches expands our capabilities for analyzing the time between avalanches and gives us new tracking of pile activity on the pile. Here we have divided the pile into quadrants and tracked which quadrants participated in events. We show that selecting avalanches only by active region and not mass produces similar inter-event time analysis as an analysis with mass-based size only.