Skip to main content
Log in

A new SPH-based approach to simulation of granular flows using viscous damping and stress regularisation

  • Original Paper
  • Published:
Landslides Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

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)

    Article  Google Scholar 

  • Balmforth NJ, Kerswell RR (2005) Granular collapse in two dimensions. J Fluid Mech 538:399–428

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Borja RI (2013) Plasticity modelling and computation. Springer, Berlin

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191:448–475

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Crosta GB, Imposimato S, Roddeman D (2015) Granular flows on erodible and non-erodible inclines. Granul Matter 17(5):667–685

    Article  Google Scholar 

  • Dilts AG (1999) Moving-least-squares-particle hydrodynamics consistency and stability. Int J Numer Methods Eng 44(8):1115–1155

    Article  Google Scholar 

  • Dyka CT, Randles PW, Ingel RP (1997) Stress points for tension instability in SPH. Int J Numer Methods Eng 40(13):2325–2341

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Forterre Y, Pouliquen O (2008) Flows of dense granular media. Annu Rev Fluid Mech 40:1–24

    Article  Google Scholar 

  • Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181(2):375–389

    Article  Google Scholar 

  • Gingold RA, Monaghan JJ (1982) Kernel estimates as a basis for general particle methods in hydrodynamics. J Comput Phys 46(3):429–453

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Gray JP, Monaghan JJ, Swift RP (2001) SPH elastic dynamics. Comput Methods Appl Mech Eng 190:6641–6662

    Article  Google Scholar 

  • Guo Y, Curtis JS (2014) Discrete element method simulations for complex granular flows. Annu Rev Fluid Mech 47:21–46

    Article  Google Scholar 

  • Herrmann HJ, Luding S (1998) Modeling granular media on the computer. Contin Mech Thermodyn 10:189–231

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Holsapple KA (2013) Modeling granular material flows: the angle of repose, fluidization and the cliff collapse problem. Planet Space Sci 82:11–26

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Krabbenhoft K, Lyamin AV, Huang J, da Silva MV (2012) Granular contact dynamics using mathematical programming methods. Comput Geotech 43:165–176

    Article  Google Scholar 

  • Kumar K, Soga K, Delenne JY (2013) Multi-scale modelling of granular avalanches. AIP Conf Proc 1542:1250–1253

    Article  Google Scholar 

  • Lacaze L, Phillips JC, Kerswell RR (2008) Planar collapse of a granular column: experiments and discrete element simulations. Phys Fluids 20(6):063302

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Lajeunesse E, Mangeney-Castelnau A, Vilotte JP (2004) Spreading of a granular mass on a horizontal plane. Phys Fluids 16(7):2371–2381

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Lube G, Huppert HE, Sparks RSJ, Freundt A (2005) Collapses of two-dimensional granular columns. Phys Rev E 72:041301

    Google Scholar 

  • Lube G, Huppert HE, Sparks RSJ, Freundt A (2011) Granular column collapses down rough, inclined channels. J Fluid Mech 675:347–368

    Article  Google Scholar 

  • Lucy L (1977) A numerical approach to testing the fission hypothesis. Astron J 82:1013–1024

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • MiDi GDR (2004) On dense granular flows. Eur Phys J E14.4:341–365

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30:543–574

    Article  Google Scholar 

  • Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110(2):399–406

    Article  Google Scholar 

  • Monaghan JJ (2012) Smoothed particle hydrodynamics and its diverse applications. Annu Rev Fluid Mech 44:323–346

    Article  Google Scholar 

  • Monaghan JJ, Gingold RA (1983) Shock simulation by the particle method SPH. J Comput Phys 52(2):374–389

    Article  Google Scholar 

  • Monaghan JJ, Lattanzio JC (1985) A refined particle method for astrophysical problems. Astron Astrophys 149(1):135–143

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Nguyen CT, Bui HH, Bui Fukagawa R (2015) Failure mechanism of 2D granular flows: experiment. J Chem Eng Jpn 48(6):395–402

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comput Methods Appl Mech Eng 139(1):375–408

    Article  Google Scholar 

  • Rondon L, Pouliquen O, Aussillous P (2011) Granular collapse in a fluid: role of the initial volume fraction. Phys Fluids 23(7):073301

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Sołowski WT, Sloan SW (2015) Evaluation of material point method for use in geotechnics. Int J Numer Anal Methods Geomech 39(7):685–701

    Article  Google Scholar 

  • Staron L, Hinch EJ (2005) Study of the collapse of granular columns using two-dimensional discrete-grain simulation. J Fluid Mech 545:1–27

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Thompson EL, Huppert HE (2007) Granular column collapses: further experimental results. J Fluid Mech 575:177–186

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Zenit R (2005) Computer simulations of the collapse of a granular column. Phys Fluids 17(3):031703

    Article  Google Scholar 

  • Zhang X, Krabbenhoft K, Sheng D (2014) Particle finite element analysis of the granular column collapse problem. Granul Matter 16(4):609–619

    Article  Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to Ha H. Bui.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10346-016-0681-y

Keywords

Navigation