Stochastic and deterministic models for dense granular flow

Abstract

Granular materials such as sand or gravel surround us everyday and yet remain poorly understood. In this thesis, two models are developed for dense granular flow, each capable of predicting flows with accuracy in multiple environments. The models are based on differing perspectives of grain-level dynamics, with one deriving flow from a stochastic mechanism and the other from a deterministic deformation law. The Stochastic Flow Rule (SFR): This work models granular flow as a sequence of localized collective grain displacements. As in the Spot Model for drainage (Bazant 2001), grain clusters move as dictated by "spots" which travel through the material as biased random-walkers. The SFR derives spot motion directly from the material stresses, thus generalizing and extending the Spot Model beyond drainage to any quasi-2D geometry with a computable stress field. Limit-State Mohr-Coulomb Plasticity is used to approximate the stress profile in a slow flowing granular assembly. The SFR then describes quantitatively how to convert the slip-line field and stresses into the necessary parameters to fully define a spot's random trajectory through the material and generate a steady flow profile. Results are compared to known flow data. Nonlinear Granular Elasto-Plasticity: This work models granular deformation at the meso-scale as a deterministic consequence of the local stresses and state parameters. Recently proposed models for granular elasticity (Jiang and Liu 2003) and plastic flow (Jop et al. 2006) are combined into one universal granular continuum law, capable of predicting both flowing regions and stagnant zones simultaneously in any arbitrary 3D flow geometry.

(cont.) The unification is performed by first motivating physically, and then implementing a Kroner-Lee elasto-plastic decomposition. The model is then numerically solved in multiple geometries and results are compared to experiments and discrete simulations.