Viscoplastic modeling of granular column collapse with pressure-dependent rheology

Abstract

A mechanical and numerical model of dry granular flows is proposed that quantitatively reproduce laboratory experiments of granular column collapse over inclined planes. The rheological parameters are directly derived from the experiments. The so-called μ(I) rheology is reformulated in the framework of Drucker–Prager plasticity with the yield stress and viscosity η(‖D‖,p) depending on both the pressure p and the norm of the strain rate tensor ‖D‖.The granular domain, velocities, stress deviator and pressure fields are calculated using a finite element method based on an iterative decomposition–coordination formulation coupled with the augmented Lagrangian method.2-D simulations using this model well reproduce the dynamics and deposits of collapsing granular columns. The flow is essentially located in a surface layer behind the front, whereas it is distributed over the whole depth near the front where basal sliding occurs. The computed runout distances and slopes of the deposits agree very well with the values found in the experiments.Using an easily calculated order of magnitude approximation of the mean viscosity during the flow (η=1Pas here), we show that a Drucker–Prager rheology with a constant viscosity gives results very similar to the μ(I) rheology and agrees with experimental height profiles, while significantly reducing the computational cost. Within the range of viscosities 0.1<η<1Pas, the dynamics and deposits are very similar. The observed slumping behavior therefore appears to be mainly due to the flow/no-flow criterion and to the associated strain-independent part of the “flowing constitutive relation” (i.e. related to plastic effects). However, the results are very different when an unrealistically large value of viscosity (10Pas) is used.