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

Abstract

We 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.

Modeling Two‐Phase Debris Flows With Grain‐Fluid Separation Over Rugged Topography: Application to the 2009 Hsiaolin Event, Taiwan

“…Although the results have shown the general applicability of the present two-phase model and offered an insight into the influences of the topography and parameters with the distinct constituents, some important effects or phenomena are still missing. For example, the nonhydrostatic pressure with enhanced gravity (Denlinger & Iverson, 2004) or due to nonuniform velocity distribution (e.g., Castro-Orgaz et al, 2015;Kaitna et al, 2016), as well as the excess pore fluid pressure induced by granular dilatancy (e.g., Bouchut et al, 2016Bouchut et al, , 2017Iverson, 2005;Kaitna et al, 2016), is not taken into account. This partly explains the small angle of basal friction b for the solid constituent in simulating the large-scale event by Hsiaolin village.…”

“…Pudasaini () and Meng and Wang () improved the two‐fluid model of Pitman and Le () by including the impacts of viscous fluid behavior and using distinct momentum interaction behavior. In addition, the dilatancy effects are taken into account in the two‐phase model of Bouchut et al (, ), in which the individual velocities of each constituent are determined.…”

The relation between dilatancy, effective stress and dispersive pressure in granular avalanches

“…In the terminology of Bagnold, they always remain at the limit of static dilation. This is the fundamental problem in avalanche and debris flow physics, that is only recently earning attention [6,14]. At present, dispersive pressures are used within the framework of Terzaghi's effective stress principle, but are not directly associated with the energy fluxes required to change the configuration of the flow volume.…”

Microseismic Emissions During Pneumatic Fracturing: A Numerical Model to Explain the Experiments

“…Fluid flow inside granular media is a very common phenomenon in nature and in industrial applications. Particularly, if the fluid flow is pressurized, it can induce rapid porosity changes inside the porous medium which is in contact with the fluid, like fracturing and channeling (Benson et al, ; Bouchut et al, ; J. A. Eriksen, Toussaint, et al, ; Farquharson et al, , ; Galland et al, ; Gidaspow, ; Goren et al, , ; Johnsen, Chevalier, et al, ; Johnsen et al, ; Johnsen, Toussaint, et al, ; Kunii & Levenspiel, ; Trulsson et al, ; Vinningland et al, , , , ).…”

“…Fluid flow inside granular media is a very common phenomenon in nature and in industrial applications. Particularly, if the fluid flow is pressurized, it can induce rapid porosity changes inside the porous medium which is in contact with the fluid, like fracturing and channeling (Benson et al, 2008;Bouchut et al, 2016;Farquharson et al, 2016Farquharson et al, , 2015Gidaspow, 1994;Goren et al, 2010Goren et al, , 2011Johnsen, Chevalier, et al, 2008;Johnsen et al, 2006;Kunii & Levenspiel, 1991;Trulsson et al, 2012;Vinningland et al, 2007aVinningland et al, , 2007bVinningland et al, , 2010Vinningland et al, , 2012. This type of brittle deformation is visible in nature (e.g., volcanic activities and tremors), and in engineering (ground improvements, CO 2 sequestration, and fracturing applications; Agency, 1994;Aochi et al, 2011;Charléty et al, 2007;Cuenot et al, 2008;Dorbath et al, 2009;Gao et al, 2014;Schuring et al, 1996).…”