Skip to main content
SpringerLink
Log in

Fourier–Voronoi-based generation of realistic samples for discrete modelling of granular materials

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

This paper presents a novel method to generate realistic packings for discrete modelling of granular materials. To generate a packing of 2D dense sample in a container of arbitrary shape, a number of key particle properties are identified as the targeted ones to reproduce, including the grain size distribution, density, particles orientations as well as specific shape characteristics of the particles. Four descriptors, including elongation, circularity, roundness, regularity, are chosen to characterize the particle shape. The considered container is discretized by a Voronoi tessellation with prescribed cell size and orientation distributions. Each Voronoi cell is then filled with a particle with prescribed shape characteristics. Several algorithms are proposed and are compared in terms of their computational efficiency and accuracy to define the particle contours, to constrain the Voronoi tessellation and to fill the Voronoi cells with particles. Two examples are further employed to demonstrate the accuracy and the potential usefulness of the proposed method for a wide range of applications where discrete modelling of granular media is important.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Desrues J., Viggiani G.: Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Methods Geomech. 28(4), 279–321 (2001)

    Article  Google Scholar 

  2. Hall S.A., Bornert M., Desrues J., Pannier Y., Lenoir N., Viggiani G., Béuelle P.: Discrete and continuum analysis of localised deformation in sand using X-ray μCT and volumetric digital image correlation. Géotechnique 60(5), 315–322 (2010)

    Article  Google Scholar 

  3. Cavaretta I., Coop M., O’Sullivan C.: The influence of particle characteristics on the behavior of coarse grained soils. Géotechnique 60(6), 413–423 (2010)

    Article  Google Scholar 

  4. Cundall P.A., Strack O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29, 47–65 (1979)

    Article  Google Scholar 

  5. Blott S.J., Pye K.: Particle shape: a review and new methods of characterization and classification. Sedimentology 55, 31–63 (2008)

    Google Scholar 

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

    Article  Google Scholar 

  7. Jiang M.J., Yu H.-S., Harris D.: A novel discrete model for granular material incorporating rolling resistance. Comput. Geotech. 32(5), 340–357 (2005)

    Article  Google Scholar 

  8. Thomas P.A., Bray J.D.: Capturing nonspherical shape of granular media with disk clusters. J. Geotech. Geoenviron. Eng. 125, 169–178 (1999)

    Article  Google Scholar 

  9. Jensen R.P., Edil T.B., Bosscher P.J., Plesha M.E., Ben Kahla N.: Effect of particle shape on interface behavior of DEM-simulated granular materials. Int. J. Geomech. 1(1), 1–19 (2011)

    Article  Google Scholar 

  10. Salot C., Gotteland P., Villard P.: Influence of relative density on granular materials behavior: DEM simulation of triaxial tests. Granul. Matter 11, 221–236 (2009)

    Article  Google Scholar 

  11. Stahl M., Konietzky H.: Discrete element simulation of ballast and gravel under special consideration of grain-shape, grain-size and relative density. Granul. Matter 13, 417–428 (2011)

    Article  Google Scholar 

  12. Katagiri J., Matsushima T., Yamada Y.: Simple shear simulation of 3D irregularly-shaped particles by image-based DEM. Granul. Matter 12, 491–497 (2010)

    Article  Google Scholar 

  13. Matsushima T., Katagiri J., Uesugi K., Tsuchiyama A., Nakano T.: 3D shape characterization and image-based DEM simulation of the Lunar soil simulant FJS-1. J. Aerosp. Eng. 22(1), 15–23 (2009)

    Article  Google Scholar 

  14. McDowel G., Li H., Lowndes I.: The importance of particle shape in discrete-element modelling of particle flow in a chute. Géotech. Lett. 1(3), 59–64 (2011)

    Article  Google Scholar 

  15. Ng T.-T.: Particle shape effect on macro- and micro-behavior of monodisperse ellipsoids. Int. J. Numer. Anal. Methods Geomech. 33, 511–527 (2009)

    Article  Google Scholar 

  16. Ouadfel H., Rothenburg L.: “Stress-force fabric” relationship for assemblies of ellipsoids. Mech. Mater. 33, 201–221 (2001)

    Article  Google Scholar 

  17. Lin X., Ng T.T.: A three-dimensional discrete element model using arrays of ellipsoids. Géotechnique 47(2), 319–329 (1997)

    Article  Google Scholar 

  18. Azema E., Radjai F., Peyroux R., Saussine G.: Force transmission in a packing of pentagonal particles. Phys. Rev. E 76, 011301 (2007)

    Article  ADS  Google Scholar 

  19. Azema E., Radjai F.: Stress-strain behavior and geometrical properties of packings of elongated particles. Phys. Rev. E. 81, 051304 (2010)

    Article  ADS  Google Scholar 

  20. Fu P., Dafalias Y.: Fabric evolution within shear bands of granular materials and its relation to critical state theory. Int. J. Numer. Anal. Methods Geomech. 35(18), 1918–1948 (2011)

    Article  Google Scholar 

  21. Pournin L., Weber M., Tsukahara M., Ferrez J.-A., Ramaioli M., Liebling Th.M.: Three-dimensional distinct element simulation of spherocylinder crystallization. Granul. Matter 7(2–3), 119–126 (2005)

    Article  MATH  Google Scholar 

  22. Azema E., Radjai F., Saussine G.: Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mech. Mater. 41, 729–741 (2009)

    Article  Google Scholar 

  23. Pena A.A., Garcia-Rojo R., Herrmann H.J.: Influence of particle shape on sheared dense granular media. Granul. Matter 9, 279–291 (2007)

    Article  MATH  Google Scholar 

  24. Lu M., McDowell G.R.: The importance of modelling ballast particle shape in DEM. Granul. Matter 9(1–2), 71–82 (2007)

    Google Scholar 

  25. Mollon, G., Richefeu, V., Daudon, D., Villard, P.: Assessment of DEM parameters for rock mass propagation. Second World Landslide Forum, 3–7 October 2011, Roma (2011) (in press)

  26. Mollon, G., Richefeu, V., Villard, P., Daudon, D.: Numerical simulation of rock avalanches: influence of a local dissipative contact model on the collective behavior of granular flows. J. Geophys. Res. 117 (2012). doi:10.1029/2011JF002202

  27. Tillemans H.-J., Herrmann H.-J.: Simulating deformations of granular solids under shear. Phys. A. 217, 261–288 (1995)

    Article  Google Scholar 

  28. Galindo-Torres S.-A., Pedroso D.-M.: Molecular dynamics simulations of complex-shaped particles using Voronoi-based spheropolyhedra. Phys. Rev. E. 81, 061303 (2010)

    Article  ADS  Google Scholar 

  29. Galindo-Torres S.-A., Munoz J.-D., Alonso-Marroquin F.: Minkowski–Voronoi diagrams as a method to generate random packing of spheropolygons for the simulation of soils. Phys. Rev. E. 82, 056713 (2010)

    Article  ADS  Google Scholar 

  30. Houlsby G.T.: Potential particles: a method for modelling non-circular particles in DEM. Comput. Geotech. 36, 953–959 (2009)

    Article  Google Scholar 

  31. Jerier J.-F., Imbault D., Donze F.-V., Doremus P.: A geometric algorithm based on tetrahedral meshes to generate a dense polydisperse sphere packing. Granul. Matter 11, 43–52 (2009)

    Article  Google Scholar 

  32. Bagi K.: An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies. Granul. Matter 7, 31–43 (2005)

    Article  MATH  Google Scholar 

  33. Sahu K.K., Ishihara K.N.: Modelling local voids using an irregular polyhedron based on natural neighbourhood and application to characterize near-dense random packing (DRP). Philos. Mag. 86(36), 5909–5926 (2006)

    Article  ADS  Google Scholar 

  34. Bowman E.T., Soga K., Drummond W.: Particle shape characterization using Fourier descriptor analysis. Geotechnique 51(6), 545–554 (2001)

    Article  Google Scholar 

  35. Garboczi E.J.: Three-dimensional mathematical analysis of particle shape using x-ray tomography and spherical harmonics: application to aggregates used in concrete. Cem. Concr. Res. 32(10), 1621–1638 (2002)

    Article  Google Scholar 

  36. Das, N.: Modeling three-dimensional shape of sand grains using discrete element method. PhD Thesis. University of South Florida. p 149 (2007)

  37. Gross D., Li M.: Constructing microstructures of poly- and nanocrystalline materials for numerical modeling and simulation. Appl. Phys. Lett. 80(5), 746–748 (2002)

    Article  ADS  Google Scholar 

  38. Xu T., Li M.: Topological and statistical properties of a constrained Voronoi tessellation. Philos. Mag. 89(4), 349–374 (2009)

    Article  ADS  Google Scholar 

  39. Masad E., Saadeh S., Al-Rousan T., Garboczi E., Little D.: Computations of particle surface characteristics using optical and X-ray CT images. Comput. Mater. Sci. 34, 406–424 (2005)

    Article  Google Scholar 

  40. Ferellec J.-F., McDowell G.R.: A simple method to create complex particle shapes for DEM. Geomech. Geoeng. 3(3), 211–216 (2008)

    Article  Google Scholar 

  41. Ferellec J.-F., McDowell G.: A method to model realistic particle shape and inertia in DEM. Granul. Matter 12, 459–467 (2010)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  43. Riley N.A.: Projection sphericity. J. Sed. Petrol. 11, 94–97 (1941)

    Google Scholar 

  44. Ehrlich R., Weinberg B.: An exact method for characterization of grain shape. J. Sediment. Petrol. 40(1), 205–212 (1970)

    Google Scholar 

  45. Meloy T.P.: Fast Fourier transform applied to shape analysis of particle silhouettes to obtain morphological data. Powder Technol. 17, 27–35 (1977)

    Article  Google Scholar 

  46. Fortune S.: A sweepline algorithm for Voronoi diagrams. Algorithmica 2(1–4), 153–174 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  47. Halton J.: Algorithm 247: radical-inverse quasi-random point sequence. Com. ACM. 7(12), 701 (1964)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong

    Guilhem Mollon & Jidong Zhao

Authors
  1. Guilhem Mollon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jidong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guilhem Mollon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mollon, G., Zhao, J. Fourier–Voronoi-based generation of realistic samples for discrete modelling of granular materials. Granular Matter 14, 621–638 (2012). https://doi.org/10.1007/s10035-012-0356-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-012-0356-x

Keywords

Search

Navigation