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Pré-Publication, Document De Travail Année : 2014

A shallow model including static-flowing transition for viscoplastic Drucker-Prager materials

Résumé

Observed avalanche flows of dense granular material have the prop-erty to present two possible behaviors: static (solid) or flowing (fluid). In such situation, an important challenge is to describe mathemati-cally the evolution of the physical interface between the two phases. In this work we derive a set of equations that is able to manage the dynamics of such interface, in the so-called shallow regime where the flow is supposed to be thin compared to its downslope extension. It is obtained via a shallow asymptotics starting from the Drucker-Prager model for viscoplastic materials, in which we have to make several assumptions. Additionally to the classical ones that are that the cur-vature of the topography, the width of the layer of material, and the viscosity are small, we assume that the internal friction angle is close to the slope angle, the velocity is small, and the pressure is convex with respect to the normal variable. The assumption that the inter-nal friction angle has to be close to the slope angle is necessary for the velocity to remain small, and the convexity of the pressure is an assumption of stability of the double layer static-flowing configura-tion. We present here the resulting model, that takes the form of 1 an overdetermined initial-boundary problem in the variable normal to the topography. It handles arbitrary velocity profiles, and is there-fore more general than previous models such as the BCRE model. It includes a new non-hydrostatic nonlinear coupling term. It has the property to be numerically solvable, at least in the uncoupled case, with or without viscosity.
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Dates et versions

hal-01081213 , version 1 (07-11-2014)
hal-01081213 , version 2 (25-03-2015)
hal-01081213 , version 3 (26-01-2016)

Identifiants

  • HAL Id : hal-01081213 , version 1

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François Bouchut, Ioan Ionescu, Anne Mangeney. A shallow model including static-flowing transition for viscoplastic Drucker-Prager materials. 2014. ⟨hal-01081213v1⟩
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