Regularisation and validation of a depth-averaged model for granular flow consistent with the incompressible mu left parenthesis upper I right parenthesis μ ( I ) μ (I) rheology

We present a regularised extension of a three-equation depth-averaged model for granular flows recently derived by Deléage et al. (2025 J. Fluid Mech. , vol. 1009, p. A57). The previous model was obtained consistently with the mu left parenthesis upper I right parenthesis μ ( I ) μ (I) -rheology (where mu μ μ denotes the friction coefficient and upper I I I the inertial number), with an asymptotic expansion of the flow variables near a steady uniform flow. However, the range of slope at which steady uniform granular flows can be observed is limited, and the former model cannot be used outside this range, with a possible loss of hyperbolicity, in particular for the liquid/solid and liquid/gas transitions. We present in this paper an extension of the three-equation model, which is valid for any value of the slope. In order to achieve this, we introduce a regularisation coefficient enabling us to model a transition between various flow regimes. This coefficient is written in a way that preserves the consistency with the mu left parenthesis upper I right parenthesis μ ( I ) μ (I) -rheology in the range of slope admitting steady uniform flows. Outside this range, the model keeps a well-posed hyperbolic structure. The predictions of the regularised model are then validated through comparisons with experimental data in various unsteady and non-uniform regimes. We first study dry fronts, and show that the model successfully predicts the flattening of the profiles when the Froude number increases, while keeping a well-defined front. We then show that the model provides accurate results for the final deposit left after a dam break on low-inclination slopes. Another validation is performed on steep slopes. The regularisation procedure is also discussed. Finally, we reproduce the retrogressive failure experiment.