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A two-phase two-layer model for fluidized granular flows with dilatancy effects

By François Bouchut, Enrique D. Fernandez-Nieto, Anne Mangeney and Gladys Narbona-Reina

Abstract

International audienceWe propose a two-phase two-thin-layer model for fluidized debris flows that takes into account dilatancy effects, based on the closure relation proposed by Roux and Radjai (1998). This relation implies that the occurrence of dilation or contraction of the granular material depends on whether the solid volume fraction is respectively higher or lower than a critical value. When dilation occurs, the fluid is sucked into the granular material, the pore pressure decreases and the friction force on the granular phase increases. On the contrary, in the case of contraction, the fluid is expelled from the mixture, the pore pressure increases and the friction force diminishes. To account for this transfer of fluid into and out of the mixture, a two-layer model is proposed with a fluid layer on top of the two-phase mixture layer. Mass and momentum conservation are satisfied for the two phases, and mass and momentum are transferred between the two layers. A thin-layer approximation is used to derive average equations, with accurate asymptotic expansions. Special attention is paid to the drag friction terms that are responsible for the transfer of momentum between the two phases and for the appearance of an excess pore pressure with respect to the hydrostatic pressure. For an appropriate form of dilatancy law we obtain a depth-averaged model with a dissipative energy balance in accordance with the corresponding 3D initial system

Topics: Fluidized granular flows, two-phase, dilatancy, two-layer, depth-averaged model, critical volume fraction, excess pore pressure, [ SDU.STU.GP ] Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [ SPI.MECA.MEFL ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]
Publisher: Cambridge University Press (CUP)
Year: 2016
DOI identifier: 10.1017/jfm.2016.417
OAI identifier: oai:HAL:hal-01161930v3
Provided by: Hal-Diderot

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