The collapse of a cylindrical cavity in a granular medium

A cylindrical cavity in a noncohesive granular medium will collapse under gravity, leaving a circular crater in the surface of the material. We study this process through experiment and numerical modeling. Experimentally, we determine the shape and dimensions of craters formed by the collapse of a cylindrical cavity in a bed of small glass beads. Using a depth-averaged continuum model with cylindrical symmetry, we calculate the shape of the free surface both during and after the collapse. We use the model to study the energetics of the collapse process and investigate the dependence of the final crater on the initial shape of the cavity and the initial velocity field. While the shapes of the final craters are not identical in model and experiment, we find good qualitative agreement in aspect ratio and slope.