This paper presents a method to assign soft-sphere contact model parameters in a discrete-element simulation with which we can reproduce the experimentally measured avalanche dynamics of finite dry granular mass down a flume. We adopt the simplest linear model in which interaction force is decomposed along or tangent to the contact normal. The model parameters are chosen uniquely to satisfy theoretical models or to meet experimental evidences at either the particle or the bulk size level. The normal mode parameters are chosen specifically to ensure Hertzian contact time (but not its force-displacement history) and the resulting loss of particle kinetic energy, characterized by a measured coefficient of restitution, for each pair of colliding surfaces. We follow the literature to assign the tangential spring constant according to an elasticity model but propose a method to assign the friction coefficient using a measured bulk property that characterizes the bulk discharge volume flow rate. The linear contact model with the assigned parameters are evaluated by comparing the simulated bulk avalanche dynamics down three slopes to the experimental data, including instantaneous particle trajectories and bulk unsteady velocity profile. Satisfying quantitative agreement can be obtained except at the free surface and the early-time front propagation velocity.
REFERENCES
1.
J.
Jenkins
and S.
Savage
, “A theory for the rapid flow of identical, smooth, nearly elastic particles
,” J. Fluid Mech.
130
, 187
–202
(1983
).2.
C. K. K.
Lun
, S.
Savage
, D.
Jeffrey
, and N.
Chepurniy
, “Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field
,” J. Fluid Mech.
140
, 223
–256
(1984
).3.
S. B.
Savage
, “Analyses of slow high-concentration flows of granular materials
,” J. Fluid Mech.
377
, 1
(1998
).4.
P.
Johnson
and R.
Jackson
, “Frictional-collisional constitutive relations for granular materials with applications to plane shearing
,” J. Fluid Mech.
176
, 67
–93
(1987
).5.
P.
Johnson
, P.
Nott
, and R.
Jackson
, “Frictional-collisional equations of motion for particulate flows and their applications to plane shearing
,” J. Fluid Mech.
210
, 501
–535
(1990
).6.
M.
Babic
, H. H.
Shen
, and H. T.
Shen
, “The stress tensor in granular shear flows of uniform, deformable disks at high solids concentrations
,” J. Fluid Mech.
219
, 81
–118
(1990
).7.
P.
Mills
, M.
Tixier
, and D.
Loggia
, “Model for stationary dense granular flow along an inclined wall
,” Europhys. Lett.
45
, 733
–738
(1999
).8.
C.
Ancey
and P.
Evesque
, “Frictional-collisional regime for granular suspension flow down an inclined channel
,” Phys. Rev. E
62
, 8349
–8360
(2000
).9.
M. Y.
Louge
, “Model for dense granular flows down bumpy inclines
,” Phys. Rev. E
67
, 061303
(2003
).10.
I. S.
Aranson
and L.
Tsimring
, “Continuum theory of partially fluidized granular flows
,” Phys. Rev. E
65
, 061303
(2002
).11.
J. B.
Knight
, E. E.
Ehrichs
, V. Y.
Kuperman
, J. K.
Flint
, H. M.
Jaeger
, and S. R.
Nagel
, “Experimental study of granular convection
,” Phys. Rev. E
54
, 5726
–5738
(1996
).12.
O.
Pouliquen
, “Scaling laws in granular flows down a bumpy inclined plane
,” Phys. Fluids
11
, 542
–548
(1999
).13.
D.
Howell
, R.
Behringer
, and C.
Veje
, “Stress fluctuations in a 2D granular Couette experiment: A continuum transition
,” Phys. Rev. Lett.
82
, 5241
–5244
(1999
).14.
C.
Ancey
, “Dry granular flows down an inclined channel: Experimental investigations on the frictional-collisional regime
,” Phys. Rev. E
65
, 011304
(2001
).15.
D.
Khakhar
, A. V.
Orpe
, P.
Andersen
, and J. M.
Ottino
, “Surface flows of granular materials: Model and experiments in heap formation
,” J. Fluid Mech.
441
, 255
–264
(2001
).16.
Y.
Forterre
and O.
Pouliquen
, “Flows of dense granular media
,” Annu. Rev. Fluid Mech.
40
, 1
–24
(2008
).17.
L. E.
Silbert
, “Granular flow down an inclined plane: Bagnold scaling and rheology
,” Phys. Rev. E
64
, 051302
(2001
).18.
D.
Volfson
, L.
Tsimring
, and I. S.
Aranson
, “Partially fluidized shear granular flows: Continuum theory and MD simulations
,” Phys. Rev. E
68
, 021301
(2003
).19.
G.
MiDi
, “On dense granular flows
,” Eur. Phys. J. E
14
, 341
–365
(2004
).20.
F.
da Cruz
, S.
Emam
, M.
Prochnow
, J.-N.
Roux
, and F.
Chevoir
, “Rheophysics of dense granular materials: Discrete simulation of plane shear flows
,” Phys. Rev. E
72
, 021309
(2005
).21.
C. S.
Campbell
, “Granular material flows: An overview
,” Powder Technol.
162
, 208
–229
(2006
).22.
C.-H.
Liu
, S. R.
Nagel
, D. A.
Schecter
, S. N.
Coppersmith
, S.
Majumdar
, O.
Narayan
, and T. A.
Witten
, “Force fluctuations in bead packs
,” Science
269
, 513
(1995
).23.
C.
Rycroft
, A.
Orpe
, and A.
Kudrolli
, “Physical test of a particle simulation model in a sheared granular system
,” Phys. Rev. E
80
, 031305
(2009
).24.
E. E.
Ehrichs
, H.
Jaeger
, G.
Karczmar
, J.
Knight
, V.
Kuperman
, and S.
Nagel
, “Granular convection observed by magnetic resonance imaging
,” Science
267
, 1632
–1634
(1995
).25.
V. Y.
Kuperman
, “Nuclear magnetic resonance measurements of diffusion in granular media
,” Phys. Rev. Lett.
77
, 1178
–1181
(1996
).26.
M.
Nakagawa
, S.
Altobelli
, A.
Caprihan
, E.
Fukushima
, and E.
Jeong
, “Non-invasive measurements of granular flow by magnetic resonance imaging
,” Exp. Fluids
16
, 54
–60
(1993
).27.
G.
Baxter
, R.
Behringer
, T.
Fagert
, and G.
Johnson
, “Pattern formation in flowing sand
,” Phys. Rev. Lett.
62
(24
), 2825
–2828
(1989
).28.
S.
Antony
, “Link between single-particle properties and macroscopic properties in particulate assemblies: Role of structures in structures
,” Philos. Trans. R. Soc. London, Ser. A
365
, 2879
–2891
(2007
).29.
P.
Cundall
and O. L.
Strack
, “A discrete numerical model for granular assemblies
,” Geotechnique
29
(1
), 47
–65
(1979
).30.
A.
Stevens
and C.
Hrenya
, “Comparison of soft-sphere models to measurements of collision properties during normal impacts
,” Powder Technol.
154
, 99
–109
(2005
).31.
R.
Mindlin
, “Compliance of elastic bodies in contact
,” J. Appl. Mech. Trans. ASME
16
, 259
–268
(1949
).32.
R. D.
Mindlin
and H.
Deresiewicz
, “Elastic spheres in contact under varying oblique forces
,” J. Appl. Mech.
20
, 327
(1953
).33.
O.
Walton
and R.
Braun
, “Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks
,” J. Rheol.
30
(5
), 949
–980
(1986
).34.
O.
Walton
, “Numerical simulation of inelastic, frictional particle-particle interactions
,” in Particulate Two-Phase Flow
, edited by M.
Roco
(Butterworth-Heinemann
, Boston
, 1993
), pp. 884
–911
.35.
H.
Teufelsbauer
, Y.
Wang
, M.-C.
Chiou
, and W.
Wu
, “Flow-obstacle interaction in rapid granular avalanches, DEM simulation and comparison with experiment
,” Granular Matter
11
, 209
–220
(2009
).36.
H.
Teufelsbauer
, Y.
Wang
, S.
Pudasaini
, R.
Borja
, and W.
Wu
, “DEM simulation of impact force exerted by granular flow on rigid structures
,” Acta Geotechnica
6
(3
), 119
–133
(2011
).37.
R.
Valentino
, G.
Baria
, and L.
Montrasio
, “Experimental analysis and micromechanical modeling of dry granular flow and impacts in laboratory flume tests
,” Rock Mech. Rock Eng.
41
(1
), 153
–177
(2008
).38.
J.
Banton
, P.
Villard
, D.
Jongmans
, and C.
Scavia
, “Two-dimensional discrete element models of debris avalanches: Parameterization and the reproducibility of experimental results
,” J. Geophys. Res.
114
, F04013
, doi: (2009
).39.
K. L.
Johnson
, Contact Mechanics
(Cambridge University Press
, New York
, 1985
).40.
P. A.
Cundall
, “Computer simulations of dense sphere assemblies
,” in Micromechanics of Granular Materials
, edited by M.
Satake
and J. T.
Jenkins
(Elsevier Science Publishers
, Amsterdam
, 1988
), pp. 113
–123
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