Rarefaction wave propagation in tapered granular columns

The study of stress waves in granular materials is of some importance in several industrial bulk materials handling systems. In particular, the growth in the magnitude of rarefaction waves due to friction has been thought to play an important role in the silo quaking phenomenon. To this end, this paper examines the propagation of rarefaction waves in granular columns subject to Coulomb wall friction, focusing on the effect of geometry by examining converging and diverging tapered columns. A one-dimensional dynamic model of these systems is developed and analytical solutions of this model are compared to a numerical model based on the Arbitrary Lagrangian-Eulerian formulation in a finite element analysis. This numerical model was first validated using the known behaviour of cylindrical columns. In all cases, the rarefaction waves examined in this work grew with the distance travelled up the column; however, the rate was shown to depend on the half-angle of the taper. Over a range of small angles, the analytical model was found to accurately predict this behaviour.