Kinematic model for quasi static granular displacements in block caving: Dilatancy effects on drawbody shapes

A generalized purely kinematic model is proposed for the description of the displacement field in a granular material slowly discharging from a hopper. In addition to the diffusion constant of the well-known kinematic model, our generalized version includes a new parameter accounting for the dilatancy effect that takes place at early stages of the flow. Experimental measurements of particle tracers displacements were made in a “quasi two-dimensional” hopper and a promising agreement with the model was found. Applications to quasi static flows occurring in underground mining are discussed. It is shown that the effect of a small dilation on drawbody shapes can be introduced by taking a slightly larger diffusion constant DPDP in the kinematic model. As a consequence, the drawbody width WW links to the drawbody height HH as W2∝DPHW2∝DPH, with DPDP being a linear function of granulate size. This result that is valid in two and three dimensions, captures the main features of independent laboratory measurements as well as observations performed in operating mines.