• Phan, Minh
• Dubois, Thierry
• Roche, Olivier
• Chupin, Laurent

Abstract

In an effort to model dry and dense granular flows, two viscoplastic models with constant viscosity and pressure-dependent thresholds are investigated through numerical simulations of the collapse of columns of glass beads over a horizontal plane. The yield stress in the Drucker-Prager model is proportional to the dynamic pressure, while that of the hydrostatic pressure model depends on the flow height. Unlike the Drucker-Prager model, which may lead to small-scale instabilities, the hydrostatic pressure model is well-posed. Both models are used to simulate the spreading of granular columns, with aspect ratios equal to 0.7 and 2, and comparison with experiments are presented. A level-set formulation for the Navier-Stokes equations is used, so that the interface between the granular material and the ambient air is tracked. The rheology is formulated as a projection, allowing for an efficient computation of the plastic part of the stress tensor. Coulomb friction conditions are applied on the walls. The dynamics of the collapse and the final deposit are accurately simulated with the Drucker-Prager model while the hydrostatic pressure model produces non-physically relevant solutions. The sensitivity of the results, with respect to the resolution, the viscosity, and the basal friction coefficient, is studied. During the collapse, the granular material consists of a basal deposit overlain by a flowing layer, which are separated by an interface that migrates upwards until the flowing layer is consumed. The time evolution of this static-mobile interface is quantified and a good agreement is found with experiments.

Topics

• impedance spectroscopy
• polymer
• experiment
• simulation
• glass
• glass
• viscosity