Chute flows of dry granular media: Numerical simulations by a well-posed multilayer model and comparisons with experiments

¹ Chair of Fluid Dynamics, Dept. of Mechanical Engineering, Technical University of Darmstadt, 64287 Darmstadt, Germany
² Laboratory of Environmental and Maritime Hydraulics, Dept. of Civil Engineering, University of Salerno, 84084 Fisciano, Italy
¹ Dept. of Hydraulic and Ocean Engineering, National Cheng-Kung University, 70101 Tainan, Taiwan

^* Corresponding author: sarno@fdy.tu-darmstadt.de

Abstract

Debris flows and avalanches are dangerous natural phenomena, characterized by the gravity-driven motion of granular media immersed in a fluid. For an appropriate hazard assessment or disaster mitigation by scenario investigation, it is crucial to capture the underlying dynamics of the granular solid phase. For this purpose, a multilayer depth-averaged approach represents a promising and computationally efficient tool over fully three-dimensional models. Here we use a mathematically well-posed multilayer model, which implements the µ(I)-rheology and a dilatancy law depending on the inertial number, I, and compare the numerical results of the model with laboratory experiments of steady uniform chute flows over an erodible bed. The well-posedness of the model for any value of I, which is essential to get convergent numerical solutions, is achieved by considering an approximation of the in-plane stress gradients, directly emerging from the µ(I)-rheology. The predicted velocity profiles show a very good agreement with the experimental ones, measured by particle image velocimetry (PIV). The volume fraction profiles by the multilayer model are also in good qualitative agreement with those measured by using the stochastic-optical method (SOM), while they tend to overestimate the volume fraction measurements in the more dilute upper region, closer to the free surface.