Abstract
The smoothed particle hydrodynamics (SPH) method was recently extended to simulate granular materials by the authors and demonstrated to be a powerful continuum numerical method to deal with the post-flow behaviour of granular materials. However, most existing SPH simulations of granular flows suffer from significant stress oscillation during the post-failure process, despite the use of an artificial viscosity to damp out stress fluctuation. In this paper, a new SPH approach combining viscous damping with stress/strain regularisation is proposed for simulations of granular flows. It is shown that the proposed SPH algorithm can improve the overall accuracy of the SPH performance by accurately predicting the smooth stress distribution during the post-failure process. It can also effectively remove the stress oscillation issue in the standard SPH model without having to use the standard SPH artificial viscosity that requires unphysical parameters. The predictions by the proposed SPH approach show very good agreement with experimental and numerical results reported in the literature. This suggests that the proposed method could be considered as a promising continuum alternative for simulations of granular flows.
Similar content being viewed by others
References
Artoni R, Santomaso AC, Gabrieli F, Tono D, Cola S (2014) Collapse of quasi-two-dimensional wet granular columns. Phys Rev E 87:032205 (2013)
Balmforth NJ, Kerswell RR (2005) Granular collapse in two dimensions. J Fluid Mech 538:399–428
Belytschko T, Krongauz Y, Dolbow J, Gerlach C (1998) On the completeness of meshfree particle methods. Int J Numer Methods Eng 43(5):785–819
Blanc T, Pastor M (2012) A stabilized Fractional Step, Runge Kutta Taylor SPH algorithm for coupled problems in geomechanics. Comput Methods Appl Mech Eng 221–222:41–53
Blanc T, Pastor M (2013) A stabilized Smoothed Particle Hydrodynamics, Taylor-Galerkin algorithm for soil dynamics problems. Int J Numer Anal Methods Geomech 37(1):1–30
Borja RI (2013) Plasticity modelling and computation. Springer, Berlin
Bui HH, Fukagawa R (2013) An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: case of hydrostatic pore-water pressure. Int J Numer Anal Methods Geomech 37(1):31–50
Bui HH, Khoa HDV (2011) “Bearing capacity bearing capacity of shallow foundation by smoothed particle hydrodynamics (SPH) analysis”, Proceedings of the 2nd International Symposium on Computational Geomechanics (COMGEO II), pp.457-468
Bui HH, Fukgawa R, Sako K (2006) “Smoothed particle hydrodynamics for soil mechanics”, Proceedings of the 6th European Conference on Numerical Methods in Geotechnical Engineering—Numer Methods Geotech Eng. 278–281
Bui HH, Sako K, Fukgawa R (2007) Numerical simulation of soil-water interaction using smoothed particle hydrodynamics (SPH) method. J Terramech 44(5):339–346
Bui HH, Fukgawa R, Sako K, Ohno S (2008a) Lagrangian mesh-free particle method (SPH) for large deformation and post-failure flows of geomaterial using elastic-plastic soil constitutive model. Int J Numer Anal Methods Geomech 32(12):1537–1570
Bui HH, Sako K, Fukagawa R, Wells JC (2008b) “SPH-based numerical simulations for large deformation of geomaterial considering soil-structure interaction”, 12th International Conference on Computer Methods and Advances in Geomechanics 2008, Goa, India, 570–578
Bui HH, Sako K, Fukagawa R, Wells JC (2009) “Numerical simulation of granular materials based on smoothed particle hydrodynamics (SPH)”, Powders and Grains, AIP Conf. Proc. 1145, 575
Bui HH, Sako K, Fukagawa R, Wells JC (2011) Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics (SPH). Geotechnique 61(7):565–574
Bui HH, Kodikara J, Bouazza A, Haque A, Ranjith PG (2014) A novel computational approached for large deformation and post-failure analyses of segmental retaining wall systems. Int J Numer Anal Methods Geomech 38(13):1321–1340
Carter MM, Arduino P, Mackenzie-Helnwein P, Miller GR (2014) Simulating granular column collapse using the Material Point Method. Acta Geotech 10(1):101–116
Chauchat J, Médale M (2014) A three-dimensional numerical model for dense granular flows based on the μ (I) rheology. J Comput Phys 256:696–712
Chen W, Qiu T (2011) Numerical simulations for large deformation of granular materials using smoothed particle hydrodynamics method. Int J Geomech 12(2):127–135
Cleary PW, Sawley ML (2002) DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl Math Model 26(2):89–111
Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191:448–475
Crosta GB, Imposimato S, Roddeman D (2009) Numerical modeling of 2D granular step collapse on erodible and non-erodible surface. J Geophys Res Earth Surf 114:F03020
Crosta GB, Imposimato S, Roddeman D (2015) Granular flows on erodible and non-erodible inclines. Granul Matter 17(5):667–685
Dilts AG (1999) Moving-least-squares-particle hydrodynamics consistency and stability. Int J Numer Methods Eng 44(8):1115–1155
Dyka CT, Randles PW, Ingel RP (1997) Stress points for tension instability in SPH. Int J Numer Methods Eng 40(13):2325–2341
Farin M, Mangeney A, Roche O (2014) Fundamental changes of granular flow dynamics, deposition, and erosion processes at high slope angles: insights from laboratory experiments. J Geophys Res Earth Surf 119(3):504–532
Forterre Y, Pouliquen O (2008) Flows of dense granular media. Annu Rev Fluid Mech 40:1–24
Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181(2):375–389
Gingold RA, Monaghan JJ (1982) Kernel estimates as a basis for general particle methods in hydrodynamics. J Comput Phys 46(3):429–453
Girolami L, Hergault V, Vinay G, Wachs A (2012) A three-dimensional discrete-grain model for the simulation of dam-break rectangular collapses: comparison between numerical results and experiments. Granul Matter 14(3):381–392
Gray JP, Monaghan JJ, Swift RP (2001) SPH elastic dynamics. Comput Methods Appl Mech Eng 190:6641–6662
Guo Y, Curtis JS (2014) Discrete element method simulations for complex granular flows. Annu Rev Fluid Mech 47:21–46
Herrmann HJ, Luding S (1998) Modeling granular media on the computer. Contin Mech Thermodyn 10:189–231
Hiraoka N, Oya A, Bui HH, Rajeev P, Fukagawa R (2013) Seismic slope failure modelling using the mesh-free SPH method. Int J Geomate 5(1):660–665
Holsapple KA (2013) Modeling granular material flows: the angle of repose, fluidization and the cliff collapse problem. Planet Space Sci 82:11–26
Ionescu IR, Mangeney A, Bouchut F, Roche O (2015) Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J Non-Newtonian Fluid Mech 219:1–18
Jop P, Forterre Y, Pouliquen O (2006) A constitutive law for dense granular flows. Nature 441(727)
Kermani E, Qiu T, Li T (2015) Simulation of collapse of granular columns using the discrete element method. Int J Geomech 04015004
Kerswell RR (2005) Dam break with coulomb friction: a model for granular slumping. Phys Fluids 17:057101
Krabbenhoft K, Lyamin AV, Huang J, da Silva MV (2012) Granular contact dynamics using mathematical programming methods. Comput Geotech 43:165–176
Kumar K, Soga K, Delenne JY (2013) Multi-scale modelling of granular avalanches. AIP Conf Proc 1542:1250–1253
Lacaze L, Phillips JC, Kerswell RR (2008) Planar collapse of a granular column: experiments and discrete element simulations. Phys Fluids 20(6):063302
Lagree PY, Staron L, Popinet S (2011) The granular column collapse as a continuum: validity of a two-dimensional Navier-Stokes model with a μ(I)-rheology. J Fluid Mech 686:378–408
Lajeunesse E, Mangeney-Castelnau A, Vilotte JP (2004) Spreading of a granular mass on a horizontal plane. Phys Fluids 16(7):2371–2381
Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahady FA (1993) High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J Comput Phys 109(1):67–75
Liu GR, Liu MB (2004) Smoothed particle hydrodynamics: a meshfree particle method, World Scientific, Singapore
Lube G, Huppert HE, Sparks RSJ, Hallworth MA (2004) Axisymmetric collapses of granular columns. J Fluid Mech 508:175–199
Lube G, Huppert HE, Sparks RSJ, Freundt A (2005) Collapses of two-dimensional granular columns. Phys Rev E 72:041301
Lube G, Huppert HE, Sparks RSJ, Freundt A (2011) Granular column collapses down rough, inclined channels. J Fluid Mech 675:347–368
Lucy L (1977) A numerical approach to testing the fission hypothesis. Astron J 82:1013–1024
Mangeney‐Castelnau A, Bouchut F, Vilotte JP, Lajeunesse E, Aubertin A, Pirulli M (2005) On the use of Saint Venant equations to simulate the spreading of a granular mass. J Geophys Res Solid Earth 110(B9):1978–2012
Mangeney‐Castelnau A, Roche O, Hungr O, Mangold N, Faccanoni G, Lucas A (2010) Erosion and mobility in granular collapse over sloping beds. J Geophys Res Earth Surf 115(F3):2003–2012
MiDi GDR (2004) On dense granular flows. Eur Phys J E14.4:341–365
Minatti L, Paris E (2015) A SPH model for the simulation of free surface granular flows in a dense regime. Appl Math Model 39(1):363–382
Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30:543–574
Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110(2):399–406
Monaghan JJ (2012) Smoothed particle hydrodynamics and its diverse applications. Annu Rev Fluid Mech 44:323–346
Monaghan JJ, Gingold RA (1983) Shock simulation by the particle method SPH. J Comput Phys 52(2):374–389
Monaghan JJ, Lattanzio JC (1985) A refined particle method for astrophysical problems. Astron Astrophys 149(1):135–143
Moriguchi S, Borja RI, Yashima A, Sawada K (2009) Estimating the impact force generated by granular flow on a rigid obstruction. Acta Geotech 4(1):57–71
Morris J, Johnson S (2009) Dynamic simulations of geological materials using combined FEM/DEM/SPH analysis. Geomech Geo Eng An Int J 4(1):91–101
Nguyen CT, Bui HH, Fukagawa R (2013) Two-dimensional numerical modelling of modular-block soil retaining walls collapse using meshfree method. Int J Geomate 5(1):647–652
Nguyen CT, Bui HH, Bui Fukagawa R (2015) Failure mechanism of 2D granular flows: experiment. J Chem Eng Jpn 48(6):395–402
Pastor M, Haddad B, Sorbino G, Cuomo S, Drempetic V (2009) A depth-integrated, coupled SPH model for flow-like landslides and related phenomena. Int J Numer Anal Methods Geomech 33(2):143–172
Pouliquen O, Cassar C, Jop P, Forterre Y, Nicolas M (2006) “Flow of dense granular material: towards simple constitutive laws”, J. Stat. Mech., P07020
Rabczuk T, Eibl J (2003) Simulation of high velocity concrete fragmentation using SPH/MLSPH. Int J Numer Methods Eng 56(10):1421–1444
Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comput Methods Appl Mech Eng 139(1):375–408
Rondon L, Pouliquen O, Aussillous P (2011) Granular collapse in a fluid: role of the initial volume fraction. Phys Fluids 23(7):073301
Shao S, Lo EY (2003) Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv Water Resour 26(7):787–800
Sołowski WT, Sloan SW (2015) Evaluation of material point method for use in geotechnics. Int J Numer Anal Methods Geomech 39(7):685–701
Staron L, Hinch EJ (2005) Study of the collapse of granular columns using two-dimensional discrete-grain simulation. J Fluid Mech 545:1–27
Staron L, Hinch EJ (2007) The spreading of a granular mass: role of grain properties and initial conditions. Granul Matter 9(3–4):205–217
Thompson EL, Huppert HE (2007) Granular column collapses: further experimental results. J Fluid Mech 575:177–186
Utili S, Zhao T, Houlsby GT (2015) 3D DEM investigation of granular column collapse: evaluation of debris motion and its destructive power. Eng Geol 186:3–16
Verghese SJ, Nguyen CT, Bui HH (2013) Evaluation of plasticity-based soil constitutive models in simulation of braced excavation. Int J Geomate 5(2):672–677
Zenit R (2005) Computer simulations of the collapse of a granular column. Phys Fluids 17(3):031703
Zhang X, Krabbenhoft K, Sheng D (2014) Particle finite element analysis of the granular column collapse problem. Granul Matter 16(4):609–619
Acknowledgments
Funding support from the Australian Research Council via projects LP13010088 and DP160100775 (Ha H. Bui), DP140100945 and FT140100408 (Giang D. Nguyen), from Monash Civil Engineering via RTSI project (Ha H. Bui and Chi T. Nguyen) and from the Japan Society for the Promotion of Science (JSPS) via project VNM11010 (Cuong T. Nguyen) is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nguyen, C.T., Nguyen, C.T., Bui, H.H. et al. A new SPH-based approach to simulation of granular flows using viscous damping and stress regularisation. Landslides 14, 69–81 (2017). https://doi.org/10.1007/s10346-016-0681-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10346-016-0681-y