Skip to main content

Effects of grain morphology on critical state: a computational analysis


We introduce a new DEM scheme (LS-DEM) that takes advantage of level sets to enable the inclusion of real grain shapes into a classical discrete element method. Then, LS-DEM is validated and calibrated with respect to real experimental results. Finally, we exploit part of LS-DEM potentiality by using it to study the dependency of critical state (CS) parameters such as critical state line (CSL) slope \(\lambda \), CSL intercept \(\varGamma \), and CS friction angle \(\varPhi _{\mathrm{CS}}\) on the grain’s morphology, i.e., sphericity, roundness, and regularity. This study is carried out in three steps. First, LS-DEM is used to capture and simulate the shape of five different two-dimensional cross sections of real grains, which have been previously classified according to the aforementioned morphological features. Second, the same LS-DEM simulations are carried out for idealized/simplified grains, which are morphologically equivalent to their real counterparts. Third, the results of real and idealized grains are compared, so the effect of “imperfections” on real particles is isolated. Finally, trends for the CS parameters (CSP) dependency on sphericity, roundness, and regularity are obtained as well as analyzed. The main observations and remarks connecting particle’s morphology, particle’s idealization, and CSP are summarized in a table that is attempted to help in keeping a general picture of the analysis, results, and corresponding implications.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. 1.

    Alonso-Marroquin F, Herrmann HJ (2002) Calculation of the incremental stress–strain relation of a polygonal packing. Phys Rev E 66:021301

    Article  Google Scholar 

  2. 2.

    Andrade JE, Lim K-W, Avila CF, Vlahinich I (2012) Granular element method for computational particle mechanics. Comput Methods Appl Mech Eng 241–244:262–274

    Article  Google Scholar 

  3. 3.

    Ashmawy AK, Sukumaran B, Hoang AV (2003) Evaluating the influence of particle shape on liquefaction behavior using discrete element method. In: Proceedings of the thirteenth international offshore and polar engineering conference (ISOPE 2003) Honolulu, Hawaii

  4. 4.

    Barrett PJ (1980) The shape of rock particles, a critical review. Sedimentology 27(3):291–303

    Article  Google Scholar 

  5. 5.

    Cho GC, Dodds J, Santamarina JC (2006) Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J Geotech Geoenviron Eng 132(5):591–602

    Article  Google Scholar 

  6. 6.

    Cundall PA (1988) Formulation of a three-dimensional distinct element model—Part I: a scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mech Min Sci 25(3):107–116

    Article  Google Scholar 

  7. 7.

    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29:47–65

    Article  Google Scholar 

  8. 8.

    Galindo-Torres SA, Pedroso DM, Williams DJ, Li L (2012) Breaking processes in three-dimensional bounded granular materials with general shapes. Comput Phys Commun 183:266–277

    Article  Google Scholar 

  9. 9.

    Garcia X, Latham J-P, Xiang J, Harrison JP (2009) A clustered overlapping sphere algorithm to represent real particles in discrete element modelling. Geotechnique 59:779–784

    Article  Google Scholar 

  10. 10.

    Krumbein WC (1941) Measurement and geological significance of shape and roundness of sedimentary particles. J Sediment Res 11(2):64–72

    Google Scholar 

  11. 11.

    Krumbein WC, Sloss LL (1963) Stratigraphy and sedimentation, 2nd edn. Freeman and Company, San Francisco

    Google Scholar 

  12. 12.

    Laursen TA (2002) Computational contact and impact mechanics: fundamentals of modeling interfacial phenomena in nonlinear finite element analysis. Springer, Berlin

    MATH  Google Scholar 

  13. 13.

    Lee X, Dass WC, Manzione CW (1993) Characterization of the internal microstructure of granular materials using computerized tomography. In: Thompson DO, Chimenti DE (eds) Review of progress in quantitative nondestructive evaluation, vol 12. Plenum Press, New York, pp 1675–1680

    Chapter  Google Scholar 

  14. 14.

    Lim K-W, Krabbenhoft K, Andrade JE (2014) On the contact treatment of non-convex particles in the granular elemnt method. Comput Part Mech 1(3):257–275

    Article  Google Scholar 

  15. 15.

    Matsushima T, Chang CS (2011) Quantitative evaluation of the effect of irregularly shaped particles in sheared granular assemblies. Granul Matter 13(3):269–276

    Article  Google Scholar 

  16. 16.

    Miller T, Rognon P, Metzger B, Einav I (2013) Eddy viscosity in dense granular flows. Phys Rev Lett 111:058002

    Article  Google Scholar 

  17. 17.

    Miura K, Maeda K, Furukawa M, Toki S (1997) Physical characteristics of sands with different primary properties. Soils Found 37(3):53–64

    Article  Google Scholar 

  18. 18.

    Miura K, Maeda K, Furukawa M, Toki S (1998) Mechanical characteristics of sands with different primary properties. Soils Found 38(4):159–172

    Article  Google Scholar 

  19. 19.

    Oda M, Iwashita K, Kakiuchi T (1997) Importance of particle rotation in the mechanics of granular materials. In: Behringer RP, Jenkins JT (eds) Powders and grains. A. A. Balkema, Rotterdam, pp 207–210

    Google Scholar 

  20. 20.

    Osher S, Fedkiw R (2003) Level set methods and dynamic implicit surfaces. Springer, Berlin

    Book  MATH  Google Scholar 

  21. 21.

    Peña AA, Lizcano A, Alonso-Marroquin F, Herrmann HJ (2008) Biaxial test simulations using a packing of polygonal particles. Int J Numer Anal Methods Geomech 32:143–160

    Article  MATH  Google Scholar 

  22. 22.

    Powers MC (1953) A new roundness scale for sedimentary particles. J Sediment Res 23(2):117–119

    Google Scholar 

  23. 23.

    Rothenburg L, Bathurst RJ (1992) Micromechanical features of granular assemblies with planar elliptical particles. Geotechnique 42(1):79–95

    Article  Google Scholar 

  24. 24.

    Santamarina JC, Cho GC (2004) Soil behaviour: the role of particle shape. In: Jardine RJ, Potts DM, Higgins KG (eds) Advances in geotechnical engineering: the Skempton vonference, vol 1. Thomas Telford Ltd., London, pp 604–617

    Google Scholar 

  25. 25.

    Skinner A (1969) A note on the influence of interparticle frction on the shearing strength of a random assembly of spherical particles. Geotechnique 19(1):150–157

    Article  Google Scholar 

  26. 26.

    Vlahinic I, Ando E, Viggiani G, Andrade JE (2013) Towards a more accurate characterization of granular media: extracting quantitative descriptors from tomographic images. Granul Matter. doi:10.1007/s10035-013-0460-6

    Google Scholar 

  27. 27.

    Wadell H (1932) Volume, shape, and roundness of rock particles. J Geol 40(5):443–451

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to José E. Andrade.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jerves, A.X., Kawamoto, R.Y. & Andrade, J.E. Effects of grain morphology on critical state: a computational analysis. Acta Geotech. 11, 493–503 (2016).

Download citation


  • Critical state parameters
  • Discrete element method
  • Grain’s morphology
  • Level sets
  • Real grain shapes