Quantitative Simulation of Granular Collapse Experiments with Visco-Plastic Models

Abstract:

One of the key issues in landslide modeling is to define the appropriate rheological behavior of these natural granular flows. In particular the description of the static and of the flowing states of granular media is still an open issue. This plays a crucial role in erosion/deposition processes. A first step to address this issue is to derive models able to reproduce laboratory experiments of granular flows.

We propose here a mechanical and numerical model of dry granular flows that quantitatively well reproduces granular column collapse over inclined planes, with rheological parameters directly derived from the laboratory experiments. We reformulate the so-called μ(I) rheology proposed by Jop et al. (2006) where I is the so-called inertial number in the framework of Drucker-Prager plasticity with yield stress and a viscosity η(||D||, p) depending on both the pressure p and the norm of the strain rate tensor ||D||. The resulting dynamic viscosity varies from very small values near the free surface and near the front to 1.5 Pa.s within the quasi-static zone. We show that taking into account a constant mean viscosity during the flow (η = 1 Pa.s here) provides results very similar to those obtained with the variable viscosity deduced from the μ(I) rheology, while significantly reducing the computational cost. This has important implication for application to real landslides and rock avalanches.

The numerical results show that the flow is essentially located in a surface layer behind the front, while the whole granular material is flowing near the front where basal sliding occurs. The static/flowing interface changes as a function of space and time, in good agreement with experimental observations. Heterogeneities are observed within the flow with low and high pressure zones, localized small upward velocity zones and vortices near the transition between the flowing and static grains. These instabilities create 'sucking zones' and have some characteristics similar to experimental observations. They may play a crucial role in erosion processes by helping extracting material from erodible beds.

P. Jop, Y. Forterre, and O. Pouliquen, 2006, Nature 441, 727-730.