R. Abgrall and S. Karni, Two-Layer Shallow Water System: A Relaxation Approach, SIAM J. Scientific Computing, vol.31, pp.1603-1627, 2009.

B. Andreotti, Y. Forterre, and O. Pouliquen, Granular Media: Between Fluid and Solid, 2013.

E. Audusse, A multilayer Saint-Venant model: derivation and numerical validation, Discrete and Continuous Dynamical Systems Series B, vol.5, issue.2, pp.189-214, 2005.

M. Bercovier and M. Engelman, A finite-element method for incompressible non-Newtonian flows, Journal of Computational Physics, vol.36, issue.3, pp.313-326, 1980.

F. Bouchut, E. D. Fernández-nieto, A. Mangeney, and G. Narbona-reina, A two-phase shallow debris flow model with energy balance. ESAIM: M2AN, vol.49, pp.101-140, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00860871

F. Bouchut, E. D. Fernández-nieto, A. Mangeney, and G. Narbona-reina, A two-phase twolayer model for fluidized granular flows with dilatancy effects, Journal of Fluid Mechanics, vol.801, pp.166-221, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01161930

F. Bouchut, E. D. Fernández-nieto, E. H. Koné, A. Mangeney, and G. Narbona-reina, A two-phase solid-fluid model for dense granular flows including dilatancy effects: comparison with submarine granular collapse experiments, EPJ Web Conf, vol.140, p.9039, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01631797

H. Capart, C. Hung, and C. P. Stark, Depth-integrated equations for entraining granular flows in narrow channels, Journal of Fluid Mechanics, vol.765, 2015.

A. Chiapolino and R. Saurel, Models and methods for two-layer shallow water flows, Journal of Computational Physics, vol.371, pp.1043-1066, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01809202

E. D. Fernández-nieto, J. Garres-díaz, A. Mangeney, and G. Narbona-reina, A multilayer shallow model for dry granular flows with the µ(I) rheology: Application to granular collapse on erodible beds, Journal of Fluid Mechanics, vol.798, pp.643-681, 2016.

E. D. Fernández-nieto, J. Garres-díaz, A. Mangeney, and G. Narbona-reina, 2D granular flows with the µ(I) rheology and side walls friction: a well-balanced multilayer discretization, Journal of Computational Physics, vol.356, pp.192-219, 2018.

E. D. Fernández-nieto, E. H. Koné, and T. Chacón-rebollo, A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution, Journal of Scientific Computing, vol.60, issue.2, pp.408-437, 2014.

D. L. George and R. M. Iverson, A two-phase debris-flow model that includes coupled evolution of volume fractions, granular dilatancy, and pore-fluid pressure, pp.415-424, 2011.

D. L. George and R. M. Iverson, A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.470, p.20130820, 2014.

I. R. Ionescu, A. Mangeney, F. Bouchut, and R. Roche, Viscoplastic modeling of granular column collapse with pressure-dependent rheology, Journal of Non-Newtonian Fluid Mechanics, vol.219, issue.0, pp.1-18, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01080456

R. M. Iverson, The physics of debris flows, Reviews of Geophysics, vol.35, issue.3, pp.245-296, 1997.

R. M. Iverson and D. L. George, A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.470, p.20130819, 2014.

R. Jackson, The Dynamics of Fluidized Particles. Cambridges Monographs on Mechanics, 2000.

P. Jop, Y. Forterre, and O. Pouliquen, Crucial role of sidewalls in granular surface flows: consequences for the rheology, Journal of Fluid Mechanics, vol.541, pp.167-192, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01432190

P. Jop, Y. Forterre, and O. Pouliquen, A constitutive law for dense granular flows, Nature, vol.441, issue.7094, pp.727-730, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00118375

P. Lagrée, L. Staron, and S. Popinet, The granular column collapse as a continuum: validity of a two-dimensional Navier-Stokes with a µ(I)-rheology, Journal of Fluid Mechanics, vol.686, pp.378-408, 2011.

C. Lusso, A. Ern, F. Bouchut, A. Mangeney, M. Farin et al., Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse, Journal of Computational Physics, vol.333, pp.387-408, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01133786

M. Pelanti, F. Bouchut, and A. Mangeney, A Roe-type scheme for two-phase shallow granular flows over variable topography, ESAIM: M2AN, vol.42, issue.5, pp.851-885, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01342261

N. Martin, I. R. Ionescu, A. Mangeney, F. Bouchut, and M. Farin, Continuum viscoplastic simulation of a granular column collapse on large slopes: µ(I) rheology and lateral wall effects, Physics of Fluids, vol.29, issue.1, p.13301, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01204716

M. Pailha and O. Pouliquen, A two-phase flow description of the initiation of underwater granular avalanches, Journal of Fluid Mechanics, vol.633, pp.115-135, 2009.

T. C. Papanastasiou, Flows of Materials with Yield, Journal of Rheology, vol.31, issue.5, pp.385-404, 1987.

E. B. Pitman and L. Le, A two-fluid model for avalanche and debris flows, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.363, pp.1573-1601, 1832.

S. Roux and F. Radjai, Texture-Dependent Rigid-Plastic Behavior, pp.229-236, 1998.