Granular Matter

, Volume 14, Issue 4, pp 457–468 | Cite as

Effect of grain roughness on strength, volume changes, elastic and dissipated energies during quasi-static homogeneous triaxial compression using DEM

  • J. Kozicki
  • J. TejchmanEmail author
  • Z. Mróz
Open Access
Original Paper


A quasi-static homogeneous drained triaxial compression test on cohesionless sand under constant lateral pressure was simulated using a three-dimensional DEM model. Grain roughness was modelled by means of symmetric clusters composed of rigid spheres imitating irregular particle shapes. The effect of grain roughness on shear strength, dilatancy, kinetic, elastic and dissipated energies was numerically analyzed. Some numerical results were compared with available experimental results.


Triaxial test Granular material Discrete element method Grain roughness Energy Dissipation 



Scientific work has been carried out by the first two authors as a part of the Project: “Innovative resources and effective methods of safety improvement and durability of buildings and transport infrastructure in the sustainable development” financed by the European Union (POIG.01.01.02-10-106/09-01).

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


  1. 1.
    Alonso-Marroquin F., Vardoulakis I., Herrmann H., Weatherley D., Mora P.: Effect of rolling on dissipation in fault gouges. Phys. Rev. E 74, 031306 (2006)ADSCrossRefGoogle Scholar
  2. 2.
    Alonso-Marroquin F., Mühlhaus H.B., Herrmann H.: Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles. Particuology 6, 390–403 (2008)CrossRefGoogle Scholar
  3. 3.
    Alonso-Marroquin F., Wang Y.: An efficient algorithm for granular dynamics simulations with complex-shaped objects. Granul. Matter 11(5), 317–329 (2009)CrossRefGoogle Scholar
  4. 4.
    Bardet J.P.: Introduction to computational granular mechanics. In: Cambou, B. (ed) Behaviour of Granular Materials, CISM 385, pp. 99–171. Springer, Udine (1998)Google Scholar
  5. 5.
    Belheine N., Plassiard J.P., Donze F.V., Darve F., Seridi A.: Numerical simulations of drained triaxial test using 3D discrete element modeling. Comput. Geotech. 36(1–2), 320–331 (2009)CrossRefGoogle Scholar
  6. 6.
    Bi Z., Sun Q., Jin F., Zhang M.: Numerical study on energy transformation in granular matter under biaxial compression. Granul. Matter 13, 503–510 (2011)CrossRefGoogle Scholar
  7. 7.
    Brinkgreve, R.: Geomaterial models and numerical analysis of softening. Dissertation, Delft University, pp. 1–153. (1994)Google Scholar
  8. 8.
    Collins I.F.: The concept of stored plastic work or frozen elastic energy in soil mechanics. Geotechnique 55, 373–382 (2005)CrossRefGoogle Scholar
  9. 9.
    Collins I.F., Houlsby G.T.: Application of thermomechanical principles to the modelling of geotechnical materials. Proc. R. Soc. Lond. Ser. A 453, 1975–2001 (1997)ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    Cundall P.A., Strack O.D.L.: The distinct numerical model for granular assemblies. Geotechnique 29, 47–65 (1979)CrossRefGoogle Scholar
  11. 11.
    Cundall P.A., Hart R.: Numerical modeling of discontinua. J. Eng. Comput. 9, 101–113 (1992)CrossRefGoogle Scholar
  12. 12.
    Ferellec J.F., McDowell G.R.: A method to model realistic particle shape and inertia in DEM. Granul. Matter 12, 459–467 (2010)CrossRefGoogle Scholar
  13. 13.
    Gudehus G., Nübel K.: Evolution of shear bands in sand. Geotechnique 54(3), 187–201 (2004)CrossRefGoogle Scholar
  14. 14.
    Herrmann H.J., Luding S.: Modeling granular media on the computer. Continuum Mech. Thermodyn. 10(4), 189–231 (1998)MathSciNetADSCrossRefzbMATHGoogle Scholar
  15. 15.
    Hertz H.: On the contact of elastic solids. J. Reine Angew. Math. 92, 156–171 (1882)zbMATHGoogle Scholar
  16. 16.
    Iwashita K., Oda M.: Rolling resistance at contacts in simulation of shear band development by DEM. ASCE J. Eng. Mech. 124(3), 285–292 (1998)CrossRefGoogle Scholar
  17. 17.
    Jerier J.F., Richefeu V., Imbault D., Donze F.V.: Packing spherical discrete elements for large scale simulations. Comput. Methods Appl. Mech. Eng. 199, 1668–1676 (2010)ADSCrossRefzbMATHGoogle Scholar
  18. 18.
    Jiang M.J., Yu H.S., Harris D.: A novel discrete model for granular material incorporating rolling resistance. Comput. Geotech. 32, 340–357 (2005)CrossRefGoogle Scholar
  19. 19.
    Ketterhagen W.R., Amende M.T., Hancock B.C.: Process modeling in the pharmaceutical industry using the discrete element method. Pharm. Res. Dev. 98, 442–470 (2009)Google Scholar
  20. 20.
    Kolymbas D., Wu W.: Recent results of triaxial tests with granular materials. Powder Technol. 60(2), 99–119 (1990)CrossRefGoogle Scholar
  21. 21.
    Kozicki J., Donze F.V.: A new open-source software developed for numerical simulations using discrete modelling methods. Comput. Methods Appl. Mech. Eng. 197, 4429–4443 (2008)ADSCrossRefzbMATHGoogle Scholar
  22. 22.
    Kozicki J., Donze F.V.: Yade-open DEM: an open-source software using a discrete element merhod to simulate granular material. Eng. Comput. 26(7), 786–805 (2009)CrossRefGoogle Scholar
  23. 23.
    Kruyt N.P., Rothenburg L.: Shear strength, dilatancy, energy and dissipation in quasi-static deformation of granular materials. J. Stat. Mech. P07021, 1–10 (2006)Google Scholar
  24. 24.
    Luding S.: Cohesive, frictional powders: contact models for tension. Granul. Matter. 10(4), 235–246 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Maeda K., Sakai H., Kondo A., Yamaguchi T., Fukuma M., Nukudani E.: Stress-chain based micromechanics of sand with grain shape effect. Granul. Matter 12, 499–505 (2010)CrossRefGoogle Scholar
  26. 26.
    Matsushima T., Chang C.S.: Quantitative evolution of the effect of irregularly shaped particles in sheared granular assemblies. Granul. Matter 13, 269–276 (2011)CrossRefGoogle Scholar
  27. 27.
    Mindlin R.D., Deresiewicz H.: Elastic spheres in contact under varying oblique forces. J. Appl. Mech. Trans. ASME 75, 327–344 (1953)MathSciNetGoogle Scholar
  28. 28.
    Mohamed A., Gutierrez M.: Comprehensive study of the effects of rolling resistance on the stress-strain and strain localization behavior of granular materials. Granul. Matter 12(5), 527–541 (2010)CrossRefGoogle Scholar
  29. 29.
    Ng T.T.: Particle shape effect on macro- and micro-behaviors of monodisperse ellipsoids. Int. J. Numer. Anal. Methods Geomech. 33, 511–552 (2009)CrossRefGoogle Scholar
  30. 30.
    Oda M., Kazama H.: Micro-structure of shear band and its relation to the mechanism of dilatancy and failure of granular soils. Geotechnique 48(4), 465–481 (1998)CrossRefGoogle Scholar
  31. 31.
    Ord A., Hibbs B., Regenauer-Lieb K.: Shear band emergence in granular materials—a numerical study. Int. J. Numer. Anal. Methods Geomech. 31, 373–393 (2007)CrossRefzbMATHGoogle Scholar
  32. 32.
    Pena A.A., Lizcano A., Alonso-Mattoquin F., Herrmann H.J.: Biaxial test simulations using a packing of polygonal particles. Int. J. Numer. Anal. Methods Geomech. 32, 143–160 (2008)CrossRefGoogle Scholar
  33. 33.
    Rojek J.: Discrete element modelling of rock cutting. Comput. Methods Mater. Sci. 7(2), 224–230 (2007)Google Scholar
  34. 34.
    Rothenburg L., Bathurst R.J.: Micromechanical features of granular materials with planar elliptical particles. Geotechnique 42, 79–7995 (1992)CrossRefGoogle Scholar
  35. 35.
    Salot C., Gotteland P., Villard P.: Influence of relative density on granular materials behaviour: DEM simulations of triaxial tests. Granul. Matter 11(4), 221–236 (2009)CrossRefGoogle Scholar
  36. 36.
    Šmilauer, V., Chareyre, B.: Yade DEM Formulation. Manual (2011)Google Scholar
  37. 37.
    Tillemans H.J., Herrmann H.J.: Simulating deformations of granular solids under shear. Phys. A 217(3–4), 261–288 (1995)Google Scholar
  38. 38.
    Tejchman J., Wu W.: Numerical study on shear band patterning in a Cosserat continuum. Acta Mech. 99, 61–74 (1993)CrossRefzbMATHGoogle Scholar
  39. 39.
    Tejchman J.: Influence of a characteristic length on shear zone formation in hypoplasticity with different enhancements. Comput. Geotech. 31(8), 595–611 (2004)CrossRefGoogle Scholar
  40. 40.
    Tejchman J.: FE modeling of shear localization in granular bodies with micro-polar hypoplasticity. In: Wu, W., Borja, R.I. (eds) Springer Series in Geomechanics and Geoengineering, Springer, Berlin (2008)Google Scholar
  41. 41.
    Tejchman J., Gorski J.: Computations of size effects in granular bodies within micro-polar hypoplasticity during plane strain compression. Int. J. Solids Struct. 45(6), 1546–1569 (2008)CrossRefzbMATHGoogle Scholar
  42. 42.
    Thornton C., Yin K.K., Adams M.J.: Numerical simulation of the impact fracture and fragmentation of agglomerates. J. Phys. D 29, 424–435 (1996)ADSCrossRefGoogle Scholar
  43. 43.
    Widulinski L., Kozicki J., Tejchman J.: Numerical simulation of a triaxial test with sand using DEM. Arch. Hydro Eng. Environ. Mech. 56(3–4), 3–26 (2009)Google Scholar
  44. 44.
    Widulinski L., Tejchman J., Kozicki J., Leśniewska D.: Discrete simulations of shear zone patterning in sand in earth pressure problems of a retaining wall. Int. J. Solids Struct. 48(7–8), 1191–1209 (2011)CrossRefzbMATHGoogle Scholar
  45. 45.
    Wu, W.: Hypoplastizität als Mathematisches Modell zum Mechanischen Verhalten granularer Stoffe. Heft 129, Institute for Soil- and Rock-Mechanics, University of Karlsruhe (1992)Google Scholar
  46. 46.
    Zhao, Z., Liu, C.S.: Energy dissipation and dispersion effects in granular media. Phys. Rev. E 78(031307), (2008)Google Scholar
  47. 47.
    Zhu H.P., Zhou Z.Y., Yang R.Y., Yu A.B.: Discrete particle simulation of particulate systems: theoretical developments. Chem. Eng. Sci. 62, 3378–3396 (2007)CrossRefGoogle Scholar
  48. 48.
    Yan Y., Ji S.: Discrete element modelling of direct shear tests for a granular material. Int. J. Numer. Anal. Methods Geomech. 34, 978–990 (2010)Google Scholar

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© The Author(s) 2012

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland
  2. 2.Polish Academy of SciencesInstitute of Fundamental Technological ResearchWarsawPoland

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