C. Ancey, Plasticity and geophysical flows: A review, Journal of Non-Newtonian Fluid Mechanics, vol.142, issue.1-3, pp.4-35, 2007.
DOI : 10.1016/j.jnnfm.2006.05.005

URL : http://infoscience.epfl.ch/record/111472

B. Andreotti, Y. Forterre, and O. Pouliquen, Les milieux granulaires, entre fluide et solide, EDP sciences, 2011.

N. Balmforth and R. , Granular collapse in two dimensions, Journal of Fluid Mechanics, vol.538, issue.-1, pp.399-428, 2005.
DOI : 10.1017/S0022112005005537

T. Barker, D. G. Schaeffer, P. Bohorquez, and J. M. Gray, Well-posed and ill-posed behaviour of the -rheology for granular flow, Journal of Fluid Mechanics, vol.91, pp.779-794, 2015.
DOI : 10.1146/annurev-fluid-122109-160705

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.
DOI : 10.1016/0021-9991(80)90163-1

F. Bouchut, R. Eymard, and A. Prignet, Convergence of conforming approximations for inviscid incompressible Bingham fluid flows and related problems, Journal of Evolution Equations, vol.34, issue.5, pp.635-669, 2014.
DOI : 10.1007/s00028-014-0231-9

URL : https://hal.archives-ouvertes.fr/hal-00859700

F. Bouchut, E. Fernandez-nieto, A. Mangeney, and P. Lagrée, On new erosion models of Savage???Hutter type for avalanches, Acta Mechanica, vol.392, issue.B9, pp.181-208, 2008.
DOI : 10.1007/s00707-007-0534-9

URL : https://hal.archives-ouvertes.fr/hal-00369433

F. Bouchut, I. R. Ionescu, and A. Mangeney, An analytic approach for the evolution of the static/flowing interface in viscoplastic granular flows, Communications in Mathematical Sciences, vol.14, issue.8, pp.2101-2126, 2016.
DOI : 10.4310/CMS.2016.v14.n8.a2

URL : https://hal.archives-ouvertes.fr/hal-01081213

D. Bresch, E. D. Fernandez-nieto, I. Ionescu, and P. Vigneaux, Augmented Lagrangian method and compressible visco-plastic flows: applications to shallow dense avalanches, Advances in Mathematical Fluid Mechanics, New Directions in Mathematical Fluid Mechanics, pp.57-89, 2010.
DOI : 10.1007/978-3-0346-0152-8_4

C. J. Cawthorn, Several applications of a model for dense granular flows, 1810.

J. Chauchat and M. Médale, A three-dimensional numerical model for dense granular flows based on the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>??</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>I</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> rheology, Journal of Computational Physics, vol.256, pp.696-712, 2014.
DOI : 10.1016/j.jcp.2013.09.004

G. B. Crosta, S. Imposimato, and D. Roddeman, Numerical modeling entrainment/deposition in rock and debris avalanches, Geol, vol.109, pp.135-145, 2009.
DOI : 10.1016/j.enggeo.2008.10.004

G. B. Crosta, S. Imposimato, and D. Roddeman, Numerical modeling of 2-D granular step collapse on erodible and nonerodible surface, Journal of Geophysical Research, vol.17, issue.33, p.3020, 2009.
DOI : 10.1029/2008JF001186

F. Da-cruz, S. Emam, M. Prochnow, J. Roux, and F. Chevoir, Rheophysics of dense granular materials: Discrete simulation of plane shear flows, Physical Review E, vol.72, issue.2, p.21309, 2005.
DOI : 10.1103/PhysRevE.72.021309

P. G. De-gennes, Reflections on the mechanics of granular matter, Physica A: Statistical Mechanics and its Applications, vol.261, issue.3-4, pp.267-293, 1998.
DOI : 10.1016/S0378-4371(98)00438-5

R. Delannay, A. Valance, A. Mangeney, O. Roche, and P. Richard, Granular and particleladen flows: from laboratory experiments to field observations, to appear in, J. Phys. D: Appl. Phys, 2016.

J. C. De-los-reyes and S. G. Andrade, Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods, Journal of Computational and Applied Mathematics, vol.235, issue.1, pp.11-32, 2010.
DOI : 10.1016/j.cam.2010.02.026

B. Domnik, S. P. Pudasaini, R. Katzenbach, and S. A. Miller, Coupling of full two-dimensional and depth-averaged models for granular flows, Journal of Non-Newtonian Fluid Mechanics, vol.201, pp.56-68, 2013.
DOI : 10.1016/j.jnnfm.2013.07.005

D. C. Drucker and W. Prager, Soil mechanics and plastic analysis or limit design, Quarterly of Applied Mathematics, vol.10, issue.2, pp.157-165, 1952.
DOI : 10.1090/qam/48291

A. Dufresne, Granular flow experiments on the interaction with stationary runout path materials and comparison to rock avalanche events, Earth Surface Processes and Landforms, vol.105, issue.3, pp.1527-1541, 2012.
DOI : 10.1002/esp.3296

G. Duvaut and J. Lions, Inequalities in mechanics and physic, Translated from the French by, 1976.

N. Khouja, N. Roquet, and B. Cazacliu, Analysis of a Regularized Bingham Model with Pressure-Dependent Yield Stress, Journal of Mathematical Fluid Mechanics, vol.124, issue.1-2, pp.723-739, 2015.
DOI : 10.1007/s00021-015-0230-9

A. Ern and J. Guermond, Theory and practice of finite elements, Applied Mathematical Sciences, vol.159, 2004.
DOI : 10.1007/978-1-4757-4355-5

M. Farin, A. Mangeney, and O. Roche, Fundamental changes of granular flow dynamics, deposition, and erosion processes at high slope angles: Insights from laboratory experiments, Journal of Geophysical Research: Earth Surface, vol.111, issue.10, pp.504-532, 2014.
DOI : 10.1029/2005JF000391

URL : https://hal.archives-ouvertes.fr/hal-01133676

Y. Forterre and O. Pouliquen, Flows of Dense Granular Media, Annual Review of Fluid Mechanics, vol.40, issue.1, pp.1-24, 2008.
DOI : 10.1146/annurev.fluid.40.111406.102142

URL : https://hal.archives-ouvertes.fr/hal-01432132

M. Fortin, Calcul numérique des écoulements des fluides de Bingham et des fluides newtoniens incompressibles par la méthode des éléments finis, 1972.

I. A. Frigaard and C. Nouar, On the usage of viscosity regularisation methods for visco-plastic fluid flow computation, Journal of Non-Newtonian Fluid Mechanics, vol.127, issue.1, pp.1-26, 2005.
DOI : 10.1016/j.jnnfm.2005.01.003

G. Midi, On dense granular flows, Eur. Phys, J, pp.14-341, 2004.

L. Girolami, V. Hergault, G. Vinay, and A. Wachs, A three-dimensional discrete-grain model for the simulation of dam-break rectangular collapses: comparison between numerical results and experiments, Granular Matter, vol.269, issue.5, pp.381-392, 2012.
DOI : 10.1007/s10035-012-0342-3

R. Glowinski and P. L. Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM Stud. Appl. Math, vol.9, 1989.
DOI : 10.1137/1.9781611970838

R. Glowinski, J. Lions, and R. Trémolières, Numerical analysis of variational inequalities, Studies in Mathematics and its Applications, 1981.

F. Hecht, New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, pp.251-265, 2012.
DOI : 10.1515/jnum-2012-0013

I. R. Ionescu, A. Mangeney, F. Bouchut, and O. Roche, Viscoplastic modeling of granular column collapse with pressure-dependent rheology, Journal of Non-Newtonian Fluid Mechanics, vol.219, pp.1-18, 2015.
DOI : 10.1016/j.jnnfm.2015.02.006

URL : https://hal.archives-ouvertes.fr/hal-01080456

I. R. Ionescu, Augmented Lagrangian for shallow viscoplastic flow with topography, Journal of Computational Physics, vol.242, pp.544-560, 2013.
DOI : 10.1016/j.jcp.2013.02.029

R. M. Iverson, M. Reid, M. Logan, R. Lahusen, J. W. Godt et al., Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment, Nature Geoscience, vol.352, issue.2, pp.116-121, 2011.
DOI : 10.1038/ngeo1040

R. M. Iverson, Elementary theory of bed-sediment entrainment by debris flows and avalanches, Journal of Geophysical Research: Earth Surface, vol.69, issue.F3, p.3006, 2012.
DOI : 10.1016/S0013-7952(02)00289-2

R. M. Iverson and C. Ouyang, Entrainment of bed material by Earth-surface mass flows: Review and reformulation of depth-integrated theory, Reviews of Geophysics, vol.46, issue.2, pp.27-58, 2015.
DOI : 10.1007/s11069-012-0395-y

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, issue.-1, pp.167-192, 2005.
DOI : 10.1017/S0022112005005987

URL : https://hal.archives-ouvertes.fr/hal-01432190

P. Jop, Y. Forterre, and O. Pouliquen, A constitutive law for dense granular flows, Nature, vol.94, issue.7094, pp.727-730, 2006.
DOI : 10.1038/nature04801

URL : https://hal.archives-ouvertes.fr/hal-01432178

P. Lagrée, L. Staron, and S. Popinet, The granular column collapse as a continuum: validity of a two-dimensional Navier???Stokes model with a ??(I)-rheology, Journal of Fluid Mechanics, vol.4, pp.378-408, 2011.
DOI : 10.1088/0169-5983/41/6/065001

E. Lajeunesse, A. Mangeney-castelnau, and J. Vilotte, Spreading of a granular mass on a horizontal plane, Physics of Fluids, vol.16, issue.7, pp.2371-2381, 2004.
DOI : 10.1063/1.1736611

B. T. Liu, S. J. Muller, and M. M. Denn, Convergence of a regularization method for creeping flow of a Bingham material about a rigid sphere, Journal of Non-Newtonian Fluid Mechanics, vol.102, issue.2, pp.179-191, 2002.
DOI : 10.1016/S0377-0257(01)00177-X

G. Lube, H. E. Huppert, R. Sparks, and A. Freundt, Collapses of two-dimensional granular columns, Physical Review E, vol.72, issue.4, p.41301, 2005.
DOI : 10.1103/PhysRevE.72.041301

A. Lucas, A. Mangeney, and J. Ampuero, Frictional velocity-weakening in landslides on Earth and on other planetary bodies, Nature Communications, vol.97, p.3417, 2014.
DOI : 10.1038/ncomms4417

URL : https://hal.archives-ouvertes.fr/hal-01207415

C. Lusso, Modélisation numérique des écoulements gravitaires viscoplastiques avec transition fluide/solide, PhD thesis, 2013.

C. Lusso, F. Bouchut, A. Ern, and A. Mangeney, A free interface model for static/flowing dynamics in thin-layer flows of granular materials with yield: simple shear simulations and comparison to experiments, p.992309, 2016.

. Pirulli, On the use of Saint-Venant equations for simulating the spreading of a granular mass, J. Geophys. Res, vol.110, p.9103, 2005.

A. Mangeney, F. Bouchut, N. Thomas, J. P. Vilotte, and M. O. Bristeau, Numerical modeling of self-channeling granular flows and of their levee-channel deposits, Journal of Geophysical Research, vol.55, issue.XXXV, p.2017, 2007.
DOI : 10.1029/2006JF000469

URL : https://hal.archives-ouvertes.fr/hal-00311797

A. Mangeney, O. Roche, O. Hungr, N. Mangold, G. Faccanoni et al., Erosion and mobility in granular collapse over sloping beds, Journal of Geophysical Research, vol.45, issue.11/12, pp.115-03040, 2010.
DOI : 10.1029/2009JF001462

URL : https://hal.archives-ouvertes.fr/hal-00521671

A. Mangeney, L. S. Tsimring, D. Volfson, I. Aranson, and F. Bouchut, Avalanche mobility induced by the presence of an erodible bed and associated entrainment, Geophysical Research Letters, vol.68, issue.2, pp.34-22401, 2007.
DOI : 10.1029/2007GL031348

URL : https://hal.archives-ouvertes.fr/hal-00311802

N. Martin, I. R. Ionescu, A. Mangeney, F. Bouchut, and M. Farin, ) rheology and lateral wall effects, Physics of Fluids, vol.29, issue.1, 2017.
DOI : 10.1063/1.4971320

L. Moretti, A. Mangeney, Y. Capdeville, E. Stutzmann, C. C. Huggel et al., Numerical modeling of the Mount Steller landslide flow history and of the generated long period seismic waves, Geophysical Research Letters, vol.167, issue.3-4, pp.39-16402, 2012.
DOI : 10.1029/2010JF001734

URL : https://hal.archives-ouvertes.fr/hal-00728958

E. Ntovoris and M. , Regis, A solution with free boundary for non-Newtonian fluids with Drucker-Prager plasticity criterion, p.1374181, 2016.

T. C. Papanastasiou, Flows of Materials with Yield, Journal of Rheology, vol.31, issue.5, pp.385-404, 1987.
DOI : 10.1122/1.549926

S. Pudasaini and K. Hutter, Avalanche Dynamics, 2007.

N. Roquet and P. Saramito, An adaptive finite element method for Bingham fluid flows around a cylinder, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.31-32, pp.3317-3341, 2003.
DOI : 10.1016/S0045-7825(03)00262-7

S. B. Savage and K. Hutter, The motion of a finite mass of granular material down a rough incline, Journal of Fluid Mechanics, vol.196, issue.-1, pp.177-215, 1989.
DOI : 10.1007/BF01180101

D. G. Schaeffer, Instability in the evolution equations describing incompressible granular flow, Journal of Differential Equations, vol.66, issue.1, pp.19-50, 1987.
DOI : 10.1016/0022-0396(87)90038-6

B. Sovilla, P. Burlando, and P. Bartelt, Field experiments and numerical modeling of mass entrainment in snow avalanches, Journal of Geophysical Research: Earth Surface, vol.39, issue.7, p.3007, 2006.
DOI : 10.1029/2005JF000391

Y. Wang, Tracking of the yield surfaces of laminar viscoplastic flows in noncircular ducts using an adaptive scheme, Proceedings of the National Science Council, Republic of China, pp.311-318, 1999.