Skip to main content
SpringerLink
Log in

A SPH approach for large deformation analysis with hypoplastic constitutive model

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

A hypoplastic constitutive model is implemented in a smoothed particle hydrodynamics code for the first time. An improved wall boundary treatment is presented for better performance. The proposed approach is first validated by comparing the numerical results with the analytical solutions for oedometer test. Two more problems involving large deformation, i.e., the collapse of sand between two parallel plates and the failure of a homogeneous slope, are analyzed to demonstrate the performance of the proposed method.

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

Access this article

Log in via an institution

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
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Bathe KJ, Ramm E, Wilson EL (1975) Finite element formulations for large deformation dynamic analysis. Int J Numer Meth Eng 9(2):353–386

    Article  MATH  Google Scholar 

  2. Bui HH, Fukagawa R, Sako K, Ohno S (2008) Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model. Int J Numer Anal Meth Geomech 32(12):1537–1570

    Article  MATH  Google Scholar 

  3. Bui HH, Fukagawa Ryoichi, Sako Kazunari, Wells JC (2010) Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics (SPH). Geotechnique 61(7):565–574

    Article  Google Scholar 

  4. 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 Meth Geomech 37(1):31–50

    Article  Google Scholar 

  5. 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 

  6. Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191(2):448–475

    Article  MATH  Google Scholar 

  7. Fang C, Wu W (2014) On the weak turbulent motions of an isothermal dry granular dense flow with incompressible grains: part II. Complete closure models and numerical simulations. Acta Geotech 9(5):739–752

    Article  Google Scholar 

  8. Foster CD, Nejad TM (2013) Embedded discontinuity finite element modeling of fluid flow in fractured porous media. Acta Geotech 8(1):49–57

    Article  Google Scholar 

  9. Ghosh S, Kikuchi N (1991) An arbitrary lagrangian-eulerian finite element method for large deformation analysis of elastic-viscoplastic solids. Comput Methods Appl Mech Eng 86(2):127–188

    Article  MATH  Google Scholar 

  10. Gomez-Gesteira M, Rogers BD, Dalrymple RA, Crespo AJC (2010) State-of-the-art of classical SPH for free-surface flows. J Hydraul Res 48(S1):6–27

    Article  Google Scholar 

  11. Gray JP, Monaghan JJJ, Swift RP (2001) SPH elastic dynamics. Comput Methods Appl Mech Eng 190(49):6641–6662

    Article  MATH  Google Scholar 

  12. Griffiths DV, Lane PA (1999) Slope stability analysis by finite elements. Geotechnique 49(3):387–403

    Article  Google Scholar 

  13. Gudenhus G (1996) A comprehensive equation for granular materials. Soil Found 36(1):1–12

    Article  Google Scholar 

  14. Gylland AS, Jostad HP, Nordal S (2014) Experimental study of strain localization in sensitive clays. Acta Geotech 9(2):227–240

    Article  Google Scholar 

  15. Hleibieh J, Wegener D, Herle I (2014) Numerical simulation of a tunnel surrounded by sand under earthquake using a hypoplastic model. Acta Geotech 9(4):631–640

    Article  Google Scholar 

  16. Hu Y, Randolph MF (1998) A practical numerical approach for large deformation problems in soil. Int J Numer Anal Meth Geomech 22(5):327–350

    Article  MATH  Google Scholar 

  17. Johnson GR, Stryk RA, Beissel SR (1996) SPH for high velocity impact computations. Comput Methods Appl Mech Eng 139(1):347–373

    Article  MATH  Google Scholar 

  18. Khoei AR, Tabarraie AR, Gharehbaghi SA (2005) H-adaptive mesh refinement for shear band localization in elasto-plasticity cosserat continuum. Commun Nonlinear Sci Numer Simul 10(3):253–286

    Article  MATH  Google Scholar 

  19. Kolymbas D (1991) An outline of hypoplasticity. Arch Appl Mech 61(3):143–151

    MATH  Google Scholar 

  20. Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahdadi FA (1993) High strain lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J Comput Phys 109(1):67–75

    Article  MATH  Google Scholar 

  21. Liu MB, Liu GR, Zong Z, Lam KY (2003) Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology. Comput Fluids 32(3):305–322

    Article  MATH  Google Scholar 

  22. Lube G, Huppert HE, Sparks RSJ, Hallworth MA (2004) Axisymmetric collapses of granular columns. J Fluid Mech 508:175–199

    Article  MATH  Google Scholar 

  23. Lube G, Huppert HE, Sparks RSJ, Freundt A (2005) Collapses of two-dimensional granular columns. Phys Rev E 72(4):041301

    Article  Google Scholar 

  24. Mašín D (2005) A hypoplastic constitutive model for clays. Int J Numer Anal Meth Geomech 29(4):311–336

    Article  MATH  Google Scholar 

  25. Mast CM, Arduino P, Mackenzie-Helnwein P, Miller GR (2015) Simulating granular column collapse using the material point method. Acta Geotech 10:101–116

    Article  Google Scholar 

  26. Mayne PW, Kulhawy FH (1982) K0-OCR relationships in soil. J Geotech Eng Div 108(6):851–872

    Google Scholar 

  27. Monaghan JJ (1988) An introduction to SPH. Comput Phys Commun 48(1):89–96

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  30. Osinov VA, Chrisopoulos S, Triantafyllidis T (2013) Numerical study of the deformation of saturated soil in the vicinity of a vibrating pile. Acta Geotech 8(4):439–446

    Article  Google Scholar 

  31. 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 Meth Geomech 33(2):143–172

    Article  MATH  Google Scholar 

  32. Peng C, Wu W, Zhang BY (2015) Three-dimensional simulations of tensile cracks in geomaterials by coupling meshless and finite element method. Int J Numer Anal Meth Geomech 39(2):135–154

    Article  Google Scholar 

  33. Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng 196(29):2777–2799

    Article  MATH  MathSciNet  Google Scholar 

  34. Springel V (2010) Smoothed particle hydrodynamics in astrophysics. Ann Rev Astron Astrophys 48:391–430

    Article  Google Scholar 

  35. Sun WC, Kuhn MR, Rudnicki JW (2013) A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band. Acta Geotech 8(5):465–480

    Article  MATH  Google Scholar 

  36. Tejchman J, Bauer E (1996) Numerical simulation of shear band formation with a polar hypoplastic constitutive model. Comput Geotech 19(3):221–244

    Article  Google Scholar 

  37. Tejchman J, Wu W (1997) Dynamic patterning of shear bands in Cosserat continuum. J Eng Mech 123(2):123–133

    Article  Google Scholar 

  38. von Wolffersdorff PA (1996) A hypoplastic relation for granular materials with a predefined limit state surface. Mech Cohesive Frict Mater 1(3):251–271

    Article  Google Scholar 

  39. Wang XT (2009) An updated hypoplastic model, its implementation, and its application in tunnelling. PhD thesis, University of Natural Resources and applied life sciences, Vienna

  40. Wang XT, Wu W (2011) An update hypoplastic constitutive model, its implementation and application. In: Wan R, Alsaleh A, Nghiem L (eds) Bifurcations, instabilities and degradations in geomaterials. Springer, Berlin, pp 133–143

    Chapter  Google Scholar 

  41. Wang J, Chan D (2014) Frictional contact algorithms in SPH for the simulation of soil–structure interaction. Int J Numer Anal Meth Geomech 38(7):747–770

    Article  Google Scholar 

  42. Wu W, Bauer E, Kolymbas D (1996) Hypoplastic constitutive model with critical state for granular materials. Mech Mater 23(1):45–69

    Article  Google Scholar 

  43. Wu CT, Chen JS, Chi L, Huck F (2001) Lagrangian meshfree formulation for analysis of geotechnical materials. J Eng Mech 127(5):440–449

    Article  Google Scholar 

  44. Wu W, Bauer E (1994) A simple hypoplastic constitutive model for sand. Int J Numer Anal Meth Geomech 18(12):833–862

    Article  MATH  Google Scholar 

  45. Wu W, Kolymbas D (2000) Hypoplasticity then and now. In: Kolymbas D (ed) Constitutive modelling of granular materials. Springer, Berlin, pp 57–105

    Chapter  Google Scholar 

  46. Wu W, Kolymbas D (1990) Numerical testing of the stability criterion for hypoplastic constitutive equations. Mech Mater 9(3):245–253

    Article  Google Scholar 

  47. Wu W, Niemunis A (1996) Failure criterion, flow rule and dissipation function derived from hypoplasticity. Mech Cohesive Frict Mater 1(2):145–163

    Article  Google Scholar 

  48. Xu XY, Ouyang J, Yang BX, Liu ZJ (2013) SPH simulations of three-dimensional non-newtonian free surface flows. Comput Methods Appl Mech Eng 256:101–116

    Article  MathSciNet  Google Scholar 

  49. Zbib HM, Aifantis EC (1988) On the structure and width of shear bands. Scr Metall 22(5):703–708

    Article  Google Scholar 

  50. Zhu H, Martys NS, Ferraris C, Kee DD (2010) A numerical study of the flow of bingham-like fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method. J Nonnewton Fluid Mech 165(7):362–375

    Article  MATH  Google Scholar 

  51. Zhuang L, Nakata Y, Kim U, Kim D (2014) Influence of relative density, particle shape, and stress path on the plane strain compression behavior of granular materials. Acta Geotech 9(2):241–255

    Article  Google Scholar 

Download references

Acknowledgments

The authors acknowledge the funding from the European Commission under its People Programme (Marie Curie Actions) of the Seventh Framework Programme FP7/2007-2013/ under Research Executive Agency Grant Agreement No. 289911 under title: Multiscale Modelling of Landslides and Debris Flows. The first author wishes to acknowledge the financial support from the Otto Pregl Foundation for Fundamental Geotechnical Research in Vienna.

Author information

Authors and Affiliations

  1. Nottingham Center for Geomechanics, University of Nottingham, Nottingham, NG7 2RD, UK

    Chong Peng & Hai-sui Yu

  2. Institut für Geotechnik, Universität für Bodenkultur, Feistmantelstrasse 4, 1180, Vienna, Austria

    Chong Peng & Wei Wu

  3. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Chun Wang

Authors
  1. Chong Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hai-sui Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chong Peng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Peng, C., Wu, W., Yu, Hs. et al. A SPH approach for large deformation analysis with hypoplastic constitutive model. Acta Geotech. 10, 703–717 (2015). https://doi.org/10.1007/s11440-015-0399-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-015-0399-3

Keywords

Search

Navigation