We simulate here dry granular flows resulting from the collapse of granular columns on an inclined channel (up to 22 degrees) and compare precisely the results with laboratory experiments.
Incompressibility is assumed despite the dilatancy observed in the experiments (up to 10%). The 2-D model is based on the so-called $\mu(I)$ rheology that induces a Drucker-Prager yield stress and a
variable viscosity. A nonlinear Coulomb friction term, representing the friction on the lateral walls of the channel is added to the model. We demonstrate that this term is crucial to accurately
reproduce granular collapses on slopes larger than 10 degrees whereas it remains of little effect on horizontal slope.
Quantitative comparison between experimental and numerical changes with time of the thickness profiles and front velocity makes it possible to strongly constrain the rheology. In particular, we show that the use of a variable or a constant viscosity does not change significantly the results provided that these viscosities are of the same order. However, only a fine tuning of the constant viscosity (\eta=1 Pa.s) makes it possible to predict the slow propagation phase observed experimentally at large slopes. Finally, we observed that small-scale instabilities develop when refining the mesh (also called ill-posed behavior, characterized in Barker et al. (2015) and in the present work), associated to the mechanical model. The velocity field becomes stratified and bands of high velocity gradient appear. These model instabilities are not avoided by using variable viscosity model such as the $\mu(I)$ rheology. However we show that the velocity range, the static-flowing transition and the thickness profiles are almost not affected by them.
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