A depth-averaged grain-fluid model with dilatancy and an upper-solid layer

To effectively assess the growing hazard related to debris flows, it is crucial to simulate these naturalgrain-fluid flows at a reasonable computational cost. To complement existing depth-averaged grain-fluid flowmodels with an upper-fluid layer, we propose here a model with an upper-solid layer, as a first step towards thedevelopment of unified models describing all possible configurations. This model accounts for granular massdilatancy and pore fluid pressure feedback and solves for solid and fluid velocity in the mixture and for theupper-solid velocity. Simulation in uniform configurations reveals the rich behaviour of the flow and shows thatthe upper-solid and upper-fluid models may predict very different behaviour. Our work highlights the need ofdeveloping two-layer models accounting for dilatancy and unifying upper-solid and upper-fluid configurationsin the same framework.