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.
Return to personal page