Stochastic Flow Rule

This work describes a multi-scale approach for granular flow, where the flow is viewed as a sequence of many localized collective grain displacements. Clustered grain displacements are dictated by the motion of meso-sized "spots", which perform a random walk through the material packing. The Spot Model was first proposed by Professor Bazant in 2000 to model granular flow through a silo apparatus. However, the original model lacks of any mechanics, thereby constricting general applicability to other flow environments. The Stochastic Flow Rule (SFR) attempts to generalize the Spot Model by deriving spot parameters directly from the material stresses. This extends the spot concept beyond silo flow to any geometry with a computable stress field. To approximate the stress profile in a slow flowing granular assembly, we utilize the Slip-Line Theory of solid mechanics. The SFR then describes quantitatively how to convert the slip-line field and stresses into the necessary parameters to fully characterize a spot's random trajectory through the material and generate a steady flow profile.