A Novel Mathematical Approach for Gravity-Driven Granular Flows in Block Caving

This study presents a novel mathematical model aimed at elucidating the distinctive behavior observed in the flow of flat-bottom silos. A scheme analogous to the spot model proposed by Bazant is adopted, in which groups of particles move in relation to a static medium. However, we assume that the movement of the particles is driven by the local change in the tensional state instead of the increment of interstitial space through the diffusion of spots. We propose that the tensional state and gravity might induce a driving force with a larger magnitude than the friction exerted at the boundary of the group of mobilized particles. Thus, the dynamics of the flow is controlled by the driving and frictional force. Finally, we have introduced a dimensionless number (Y) corresponding to the ratio of driving to frictional force to characterize the movement of particles. By assuming that frictional force at the interface has a viscous component proportional to the relative speed of the mobilized particles, we have writen an equation analogous to Darcy s law for the flow of a Bingham fluid in a porous medium. The finite element method is utilized to solve the model, and the numerical findings demonstrate a strong correspondence with experimental results achieved in flat-bottom silos featuring one or two openings. Comparatively, the results of the kinematic model are surpassed, with a notable enhancement in the depiction of the velocity field. © 2023 Elsevier Inc.