Nonsmooth simulations of 3D Drucker-Prager granular flows and validation against experimental column collapses

Abstract

In this paper, transient granular flows are examined both numerically and experimentally. Simulations are performed using the 3D nonsmooth numerical granular model introduced in Daviet & Bertails-Descoubes (2016), which represents the granular medium as an inelastic and dilatable continuum subject to the Drucker-Prager yield criterion in the dense regime. One feature of this numerical model is to resolve such a nonsmooth rheology without any regularisation, by leveraging tools from nonsmooth optimisation. We show that this nonsmooth simulator, which relies on a constant friction coefficient, is able to reproduce with high fidelity various experimental granular collapses over inclined erodible beds, provided the friction coefficient is set to the avalanche angle - and not to the stop angle, as generally done. Our results, obtained for two different granular materials and for bed inclinations ranging from 0° to 20°, suggest that a simple constant friction rheology choice remains reasonable for capturing a large variety of granular collapses up to aspect ratios in the order of 10. We further investigate the precise role of the frictional walls by performing experimental and simulated collapses with various channel widths. We find out that, unlike some assumptions formerly made in the literature, the channel width has lower influence on the granular flow. Finally, we extend the constant coefficient model with an hysteretic model, thereby improving the predictions of the early-stage dynamics of the collapse. This illustrates the potential effects of such phenomenology on transient flows, paving the way to more elaborate analysis.