Particle finite element analysis of the granular column collapse problem

The problem of granular column collapse is investigated by means of an axisymmetric version of the particle finite element method (PFEM). The granular medium is represented by a simple rate-independent plasticity model and the frictional contact between the granular flow and its rigid basal surface is accounted for. In the version of the PFEM developed for this study, the governing equations of the boundary value problem are cast in terms of an optimization problem and solved using mathematical programming tools. The agreement between model and experiment is generally satisfactory, quantitatively as well as qualitatively. However, the friction angle of the granular material, as well as the exact interface conditions between the base and granular material, are shown to have a relatively significant influence on the results.

[1]  Y. Forterre,et al.  Flows of Dense Granular Media , 2008 .

[2]  Wei Chen,et al.  Numerical Simulations for Large Deformation of Granular Materials Using Smoothed Particle Hydrodynamics Method , 2012 .

[3]  Eric Lajeunesse,et al.  Granular slumping on a horizontal surface , 2005 .

[4]  A. Hogg,et al.  Two-dimensional granular slumps down slopes , 2007 .

[5]  N. Balmforth,et al.  Granular collapse in two dimensions , 2005, Journal of Fluid Mechanics.

[6]  P. Wriggers,et al.  An interior‐point algorithm for elastoplasticity , 2007 .

[7]  Giovanni B. Crosta,et al.  Numerical modeling of 2‐D granular step collapse on erodible and nonerodible surface , 2009 .

[8]  Scott W. Sloan,et al.  Associated computational plasticity schemes for nonassociated frictional materials , 2012 .

[9]  Kristian Krabbenhoft,et al.  A general non‐linear optimization algorithm for lower bound limit analysis , 2003 .

[10]  Paul W. Cleary,et al.  Quasi-static fall of planar granular columns: comparison of 2D and 3D discrete element modelling with laboratory experiments , 2009 .

[11]  Andrei V. Lyamin,et al.  Computational Cam clay plasticity using second-order cone programming , 2012 .

[12]  Herbert E. Huppert,et al.  Granular column collapses: further experimental results , 2007, Journal of Fluid Mechanics.

[13]  R. Kerswell,et al.  Dam break with Coulomb friction: a model for granular slumping , 2005 .

[14]  E. J. Hinch,et al.  Study of the collapse of granular columns using two-dimensional discrete-grain simulation , 2005, Journal of Fluid Mechanics.

[15]  S. Sloan,et al.  Formulation and solution of some plasticity problems as conic programs , 2007 .

[16]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1994, ACM Trans. Graph..

[17]  P. Mills,et al.  Model for a stationary dense granular flow along an inclined wall , 1999 .

[18]  H. Huppert,et al.  Granular column collapses down rough, inclined channels , 2011, Journal of Fluid Mechanics.

[19]  Dong Wang,et al.  Particle finite element analysis of large deformation and granular flow problems , 2013 .

[20]  G. Midi,et al.  On dense granular flows , 2003, The European physical journal. E, Soft matter.

[21]  Andrei V. Lyamin,et al.  Granular contact dynamics with particle elasticity , 2012, Granular Matter.

[22]  Two dimensional fall of granular columns controlled by slow horizontal withdrawal of a retaining wall , 2006 .

[23]  Massimiliano Cremonesi,et al.  A Lagrangian finite element approach for the analysis of fluid–structure interaction problems , 2010 .

[24]  Pierre-Yves Lagrée,et al.  The granular column collapse as a continuum: validity of a two-dimensional Navier–Stokes model with a μ(I)-rheology , 2011, Journal of Fluid Mechanics.

[25]  R. Kerswell,et al.  Axisymmetric granular collapse: a transient 3D flow test of viscoplasticity. , 2008, Physical review letters.

[26]  H. Huppert,et al.  Axisymmetric collapses of granular columns , 2004, Journal of Fluid Mechanics.

[27]  O. Pouliquen,et al.  Granular collapse in a fluid: Role of the initial volume fraction , 2010 .

[28]  Kristian Krabbenhoft,et al.  Three-dimensional granular contact dynamics with rolling resistance , 2013 .

[29]  Gert Lube,et al.  Collapses of two-dimensional granular columns. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  N. Mangold,et al.  Erosion and mobility in granular collapse over sloping beds , 2010 .

[31]  Anne Mangeney,et al.  On the run-out distance of geophysical gravitational flows: Insight from fluidized granular collapse experiments , 2011 .

[32]  E. Oñate,et al.  The particle finite element method. An overview , 2004 .

[33]  Erling D. Andersen,et al.  On implementing a primal-dual interior-point method for conic quadratic optimization , 2003, Math. Program..

[34]  Rich R. Kerswell,et al.  Planar collapse of a granular column: Experiments and discrete element simulations , 2008 .

[35]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[36]  Jean-Pierre Vilotte,et al.  On the use of Saint Venant equations to simulate the spreading of a granular mass , 2005 .

[37]  Roberto Zenit,et al.  Computer simulations of the collapse of a granular column , 2005 .

[38]  Andrei V. Lyamin,et al.  Granular contact dynamics using mathematical programming methods , 2012 .

[39]  E. J. Hinch,et al.  The spreading of a granular mass: role of grain properties and initial conditions , 2006 .

[40]  Olivier Pouliquen,et al.  A constitutive law for dense granular flows , 2006, Nature.

[41]  Jean-Pierre Vilotte,et al.  Spreading of a granular mass on a horizontal plane , 2004 .