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

¹ Laboratoire d’Analyse et de Mathématiques Appliquées, Université Gustave Eiffel, CNRS-UMR 8050, F-77454, Marne-la-Vallée, France
² Departamento Matemática Aplicada I, Universidad de Sevilla. E.T.S. Arquitectura. Avda, Reina Mercedes, s/n. 41012 Sevilla, Spain
³ Institut de Physique du Globe de Paris, Université Paris Cité, CNRS-UMR 7154, 1 rue Jussieu, 75005 Paris, France

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Published online: 1 December 2025

Abstract

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