# A free interface model for static/flowing dynamics in thin-layer flows of granular materials with yield: simple shear simulations and comparison to experiments

3 ANGE - Numerical Analysis, Geophysics and Ecology
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : Flows of dense granular materials involve regions where the material is flowing, and regions where it is static. Describing the dynamics of the interface between these two regions is a key issue to understand the erosion and deposition processes in natural environment. A free interface simplified model for non-averaged thin-layer flows of granular materials has been proposed in Lusso, Bouchut, Ern, Mangeney (2016). It is a coordinate-decoupled version of a model derived by asymptotic expansion by Bouchut, Ionescu, Mangeney (2016) from an incompressible viscoplastic model with Drucker-Prager yield stress. The free interface model describes the evolution of the velocity profile as well as the position of the transition between static and flowing material. It is formulated in the coordinate $Z$ in the direction normal to the topography, and contains a source term that represents the opposite of the net force acting on the flow, including gravity, pressure gradient, and internal friction. We evaluate here the respective role of yield and viscosity in this model in the case of constant source term, which corresponds to simple shear viscoplastic flows. We compare both the analytical solution for the inviscid case and the numerical solution for the viscous case (with a constant viscosity or the variable viscosity of the $\mu(I)$ rheology), with experimental data. Although the model does not describe variations in the flow direction, it is able to reproduce the essential features of granular flow experiments over an inclined static layer of grains, including the stopping time and the erosion of the initial static bed, which is shown to be closely related to the viscosity.
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Cited literature [38 references]

https://hal-upec-upem.archives-ouvertes.fr/hal-00992309
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Submitted on : Thursday, December 22, 2016 - 6:40:52 PM
Last modification on : Monday, March 30, 2020 - 12:04:02 PM
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• HAL Id : hal-00992309, version 3

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Christelle Lusso, François Bouchut, Alexandre Ern, Anne Mangeney. A free interface model for static/flowing dynamics in thin-layer flows of granular materials with yield: simple shear simulations and comparison to experiments. 2016. ⟨hal-00992309v3⟩

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