Skip to main content
SpringerLink
Log in

The influence of particle-size distribution on critical state behavior of spherical and non-spherical particle assemblies

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

Abstract

This paper presents an investigation into the effects of particle-size distribution on the critical state behavior of granular materials using discrete element method (DEM) simulations on both spherical and non-spherical particle assemblies. A series of triaxial test DEM simulations examine the influence of particle-size distribution (PSD) and particle shape, which were independently assessed in the analyses presented. Samples were composed of particles with varying shapes characterized by overall regularity (OR) and different PSDs. The samples were subjected to the axial compression through different loading schemes: constant volume, constant mean effective stress, and constant lateral stress. All samples were sheared to large strains to ensure that a critical state was reached. Both the macroscopic and microscopic behaviors in these tests are discussed here within the framework of the anisotropic critical state theory. It is shown that both OR and PSD may affect the response of the granular assemblies in terms of the stress–strain relations, dilatancy, and critical state behaviors. For a given PSD, both the shear strength and fabric norm decrease with an increase in OR. The critical state angle of shearing resistance is highly dependent on particle shape. In terms of PSD, uniformly distributed assemblies mobilize higher shear strength and experience more dilative responses than specimens with a greater variation of particle sizes. The position of the critical state line in the e–p′ space is also affected by PSD. However, the effects of PSD on critical strength and evolution of fabric are negligible. These findings highlight the importance of particle shape and PSD that should be included in the development of constitutive models for granular materials.

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

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
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Roscoe, K.H., Schofield, A.N., Wroth, C.P.: On the yielding of soils. Géotechnique 8(1), 22–53 (1958)

    Article  Google Scholar 

  2. Schofield, A., Wroth, P.: Critical State Soil Mechanics. McGraw–Hill, New York (1968)

    Google Scholar 

  3. Li, X.S., Dafalias, Y.F.: Anisotropic critical state theory: role of fabric. J. Eng. Mech. 138(3), 263–275 (2012)

    Article  Google Scholar 

  4. Dafalias, Y.F., Taiebat, M.: SANISAND-Z: zero elastic range sand plasticity model. Géotechnique 66(12), 999–1013 (2016)

    Article  Google Scholar 

  5. Chen, Y.N., Yang, Z.X.: A family of improved yield surfaces and their application in modeling of isotropically over-consolidated clays. Comput. Geotech. 90, 133–143 (2017)

    Article  Google Scholar 

  6. Yin, Z.Y., Wu, Z.X., Hicher, P.Y.: Modeling monotonic and cyclic behavior of granular materials by exponential constitutive function. J. Eng. Mech. 144(4), 04018014 (2018)

    Article  Google Scholar 

  7. Yang, Z.X., Xu, T.T., Chen, Y.N.: J2-deformation type model coupled with state dependent dilatancy. Comput. Geotech. 105, 129–141 (2019)

    Article  Google Scholar 

  8. Zhao, J., Guo, N.: A new definition on critical state of granular media accounting for fabric anisotropy. In: AIP Conference Proceedings, vol. 1542. pp. 229–232. AIP Publishing LLC (2013)

  9. Yang, Z.X., Wu, Y.: Critical state for anisotropic granular materials: a discrete element perspective. Int. J. Geomech. 17(2), 04016054 (2017)

    Article  Google Scholar 

  10. Li, X.S., Dafalias, Y.F.: Dissipation consistent fabric tensor definition from DEM to continuum for granular media. J. Mech. Phys. Solids 78, 141–153 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  11. Xie, Y.H., Yang, Z.X., Barreto, D., Jiang, M.D.: The influence of particle geometry and the intermediate stress ratio on the shear behavior of granular materials. Granul. Matter 19(2), 35 (2017)

    Article  Google Scholar 

  12. Thornton, C.: Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1), 43–53 (2000)

    Article  Google Scholar 

  13. Taylor, D.W.: Fundamentals of Soil Mechanics. Wiley, New York (1948)

    Google Scholar 

  14. Santamarina, J.C.: Soil Behaviour: The Role of Particle Shape. Thomas Telford, London (2004)

    Google Scholar 

  15. Cho, G.C., Dodds, J., Santamarina, J.C.: Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J. Geotech. Geoenviron. Eng. 133(11), 591–602 (2006)

    Article  Google Scholar 

  16. Yang, J., Luo, X.D.: Exploring the relationship between critical state and particle shape for granular materials. J. Mech. Phys. Solids 84, 196–213 (2015)

    Article  ADS  Google Scholar 

  17. Kokusho, T., Hara, T., Hiraoka, R.: Undrained shear strength of granular soils with different particle gradations. J. Geotech. Geoenviron. Eng. 130(6), 621–629 (2004)

    Article  Google Scholar 

  18. Simoni, A., Houlsby, G.T.: The direct shear strength and dilatancy of sand–gravel mixtures. Geotech. Geol. Eng. 24(3), 523–549 (2006)

    Article  Google Scholar 

  19. Yang, J., Luo, X.D.: The critical state friction angle of granular materials: Does it depend on grading? Acta Geotech. 2, 1–13 (2017)

    ADS  Google Scholar 

  20. Azéma, E., Linero, S., Estrada, N., Lizcano, A.: Does modifying the particle size distribution of a granular material (i.e., material scalping) alters its shear strength? In: The European Physical Journal Conferences, vol. 140, p. 06001 (2017)

    Article  Google Scholar 

  21. Wood, D.M., Maeda, K.: Changing grading of soil: effect on critical states. Acta Geotech. 3(1), 3–14 (2008)

    Article  Google Scholar 

  22. Muir, W.D.: Modelling mechanical consequences of erosion. Géotechnique 60(6), 447–457 (2010)

    Article  Google Scholar 

  23. Carrera, A., Coop, M., Lancellotta, R.: Influence of grading on the mechanical behaviour of Stava tailings. Géotechnique 61(11), 935–946 (2011)

    Article  Google Scholar 

  24. Bandini, V., Coop, M.R.: The influence of particle breakage on the location of the critical state line of sands. S. Atl. Q. 51(4), 591–600 (2011)

    Google Scholar 

  25. Ghafghazi, M., Shuttle, D.A., Dejong, J.T.: Particle breakage and the critical state of sand. Soils Found. 54(3), 451–461 (2014)

    Article  Google Scholar 

  26. Xiao, Y., Liu, H., Ding, X., Chen, Y., Jiang, J., Zhang, W.: Influence of particle breakage on critical state line of rockfill material. Int. J. Geomech. 16(1), 04015031 (2016)

    Article  Google Scholar 

  27. Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 30(30), 331–336 (1979)

    Google Scholar 

  28. Williams, J.R., Hocking, G., Mustoe, G.G.W.: Theoretical basis of the discrete element method. In: Numerical Method in Engineering, Theory and Applications. Proceedings of International Conference on Numerical Methods in Engineering, pp. 897–906. A. A.Balkema, Rotterdam (1985)

  29. Thornton, C., Antony, S.J.: Quasi-static shear deformation of a soft particle system. Powder Technol. 109(1–3), 179–191 (2000)

    Article  Google Scholar 

  30. Combe, G.L., Roux, J.L.: Discrete numerical simulation, quasistatic deformation and the origins of strain in granular materials. In: Third International Symposium on Deformation Characteristics of Geomaterials, Lyon, France (2003)

    Google Scholar 

  31. O’Sullivan, C.: Particulate Discrete Element Modelling: A Geomechanics Perspective. Applied Geotechnics. Spon Press, London (2011)

    Google Scholar 

  32. Nouguier-Lehon, C., Cambou, B., Vincens, E.: Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis. Int. J. Numer. Anal. Methods Geomech. 27(14), 1207–1226 (2010)

    Article  Google Scholar 

  33. Alonso-Marroquín, F.: Role of anisotropy in the elastoplastic response of a polygonal packing. Phys. Rev. E 71(1), 051304 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  34. Peña, A.A., Lizcano, A., Alonso-Marroquin, F., Herrmann, H.J.: Biaxial test simulations using a packing of polygonal particles. Int. J. Numer. Anal. Methods Geomech. 32(2), 143–160 (2010)

    Article  Google Scholar 

  35. Ng, T.T.: Fabric evolution of ellipsoidal arrays with different particle shapes. J. Eng. Mech. 127(10), 994–999 (2001)

    Article  Google Scholar 

  36. Ng, T.T.: Behavior of ellipsoids of two sizes. J. Geotech. Geoenviron. Eng. 130(10), 1077–1083 (2004)

    Article  Google Scholar 

  37. Yan, W.M., Dong, J.: Effect of particle grading on the response of an idealized granular assemblage. Int. J. Geomech. 11(4), 276–285 (2011)

    Article  Google Scholar 

  38. Azéma, E., Radjai, F., Dubois, F.: Packings of irregular polyhedral particles: strength, structure, and effects of angularity. Phys. Rev. E 87(6), 062203 (2013)

    Article  ADS  Google Scholar 

  39. Azéma, E., Radjai, F.: Force chains and contact network topology in sheared packings of elongated particles. Phys. Rev. E 85(3), 031303 (2012)

    Article  ADS  Google Scholar 

  40. Boton, M., Azéma, E., Estrada, N., Radjai, F., Lizcano, A.: Quasistatic rheology and microstructural description of sheared granular materials composed of platy particles. Phys. Rev. E 87(3), 032206 (2013)

    Article  ADS  Google Scholar 

  41. Voivret, C., Radjaï, F., Delenne, J.Y., El Youssoufi, M.S.: Multiscale force networks in highly polydisperse granular media. Phys. Rev. Lett. 102(17), 178001 (2009)

    Article  ADS  Google Scholar 

  42. Estrada, N.: Effects of grain size distribution on the packing fraction and shear strength of frictionless disk packings. Phys. Rev. E 94(6), 062903 (2016)

    Article  ADS  Google Scholar 

  43. Nguyen, D.H., Azéma, E., Sornay, P., Radjai, F.: Effects of shape and size polydispersity on strength properties of granular materials. Phys. Rev. E 91(3), 032203 (2015)

    Article  ADS  Google Scholar 

  44. Azéma, E., Linero, S., Estrada, N., Lizcano, A.: Shear strength and microstructure of polydisperse packings: the effect of size span and shape of particle size distribution. Phys. Rev. E 96(2), 022902 (2017)

    Article  ADS  Google Scholar 

  45. Miao, G., Airey, D.: Breakage and ultimate states for a carbonate sand. Géotechnique 63(14), 1221–1229 (2013)

    Article  Google Scholar 

  46. Yu, F.: Particle breakage and the critical state of sands. Géotechnique 68(8), 713–719 (2017)

    Article  Google Scholar 

  47. Jensen, R.P., Bosscher, P.J., Plesha, M.E., Edil, T.B.: DEM simulation of granular media–structure interface: effects of surface roughness and particle shape. Int. J. Numer. Anal. Methods Geomech. 23(6), 531–547 (2015)

    Article  Google Scholar 

  48. Potticary, M., Zervos, A., Harkness, J.: The effect of particle elongation on the strength of granular materials. In: 24th Conference on Computational Mechanics, UK, pp. 239–242 (2016)

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

    Article  ADS  Google Scholar 

  50. Kozicki, J., Donzé, F.V.: A new open-source software developed for numerical simulations using discrete modeling methods. Comput. Methods Appl. Mech. Eng. 197(49–50), 4429–4443 (2008)

    Article  ADS  Google Scholar 

  51. Yang, Z.X., Yang, J., Wang, L.Z.: Micro-scale modeling of anisotropy effects on undrained behavior of granular soils. Granul. Matter 15(5), 557–572 (2013)

    Article  Google Scholar 

  52. Li, X., Yu, H.S., Li, X.S.: A virtual experiment technique on the elementary behaviour of granular materials with discrete element method. Int. J. Numer. Anal. Methods Geomech. 37(1), 75–96 (2013)

    Article  ADS  Google Scholar 

  53. Gu, X., Huang, M., Qian, J.: DEM investigation on the evolution of microstructure in granular soils under shearing. Granul. Matter 16(1), 91–106 (2014)

    Article  Google Scholar 

  54. Kuhn, M.R., Renken, H.E., Mixsell, A.D., Kramer, S.L.: Investigation of cyclic liquefaction with discrete element simulations. J. Geotech. Geoenviron. Eng. 140(12), 04014075 (2014)

    Article  Google Scholar 

  55. Oda, M., Nakayama, H.: Introduction of inherent anisotropy of soils in the yield function. Stud. Appl. Mech. 20, 81–90 (1988)

    Article  Google Scholar 

  56. Yang, Z.X., Xu, T.T., Chen, Y.N.: Unified modeling of the influence of consolidation conditions on monotonic soil response considering fabric evolution. J. Eng. Mech. 144(8), 04018073 (2018)

    Article  Google Scholar 

  57. Thornton, C., Antony, S.J.: Quasi-static deformation of particulate media. Philos. Trans. Math. Phys. Eng. Sci. 356(1747), 2763–2782 (1998)

    Article  ADS  Google Scholar 

  58. Oda, M.: Co-ordination number and its relation to shear strength of granular material. Soils Found. 17(2), 29–42 (1977)

    Article  Google Scholar 

  59. Ravishankar, B.V., Vinod, J.S., Sitharam, T.G.: Post-liquefaction undrained monotonie behaviour of sands: experiments and DEM simulations. Géotechnique 59(9), 739–749 (2009)

    Article  Google Scholar 

  60. Edwards, S.F.: The equations of stress in a granular material. Physica A 249(1), 226–231 (1998)

    Article  ADS  Google Scholar 

  61. Fannin, R.J., Shuttle, D.A., Rousé, P.C.: Influence of roundness on the void ratio and strength of uniform sand. Géotechnique 58(58), 227–231 (2008)

    Google Scholar 

  62. Murthy, T.G., Loukidis, D., Carraro, J.A.H., Prezzi, M., Salgado, R.: Undrained monotonic response of clean and silty sands. Géotechnique 57(3), 273–288 (2007)

    Article  Google Scholar 

  63. Li, G., Liu, Y.J., Dano, C., Hicher, P.Y.: Grading-dependent behavior of granular materials: from discrete to continuous modeling. J. Eng. Mech. 141(6), 04014172 (2017)

    Article  Google Scholar 

  64. Kuhn, M.R.: The critical state of granular media: convergence, stationarity and disorder. Géotechnique 66(11), 1–8 (2016)

    Article  Google Scholar 

  65. Zhou, W., Yang, L., Ma, G., Chang, X., Cheng, Y., Li, D.: Macro–micro responses of crushable granular materials in simulated true triaxial tests. Granul. Matter 17(4), 497–509 (2015)

    Article  Google Scholar 

  66. Thornton, C., Zhang, L.: On the evolution of stress and microstructure during general 3D deviatoric straining of granular media. Géotechnique 60(5), 333–341 (2010)

    Article  Google Scholar 

  67. Sadrekarimi, A., Olson, S.M.: Critical state friction angle of sands. Géotechnique 61(9), 771–783 (2011)

    Article  Google Scholar 

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

    Article  Google Scholar 

  69. Li, X.S., Wang, Y.: Linear representation of steady-state line for sand. J. Geotech. Geoenviron. Eng. 124(12), 1215–1217 (1998)

    Article  Google Scholar 

  70. Russell, A.R., Khalili, N.: A bounding surface plasticity model for sands exhibiting particle crus. Can. Geotech. J. 41(6), 1179–1192 (2004)

    Article  Google Scholar 

  71. Biarez, J., Hicher, P.: Influence de la granulométrie et de son évolution par ruptures de grains sur le comportement mécanique de matériaux granulaires. Revue Française De Génie Civil 1(4), 607–631 (1997)

    Article  Google Scholar 

  72. Imseeh, W.H., Druckrey, A.M., Alshibli, K.A.: 3D experimental quantification of fabric and fabric evolution of sheared granular materials using synchrotron micro-computed tomography. Granul. Matter 20(2), 24 (2018)

    Article  Google Scholar 

  73. Cavarretta, I.: The influence of particle characteristics on the engineering behaviour of granular materials. Doctoral dissertation, Imperial College London (2010)

  74. Galindo-Torres, S.A., Muñoz, J.D., Alonso-Marroquín, F.: Minkowski–Voronoi diagrams as a method to generate random packings of spheropolygons for the simulation of soils. Phys. Rev. E 82(5), 056713 (2010)

    Article  ADS  Google Scholar 

  75. Thevanayagam, S., Shenthan, T., Mohan, S., Liang, J.: Undrained fragility of clean sands, silty sands, and sandy silts. J. Geotech. Geoenviron. Eng. 128(10), 849–859 (2002)

    Article  Google Scholar 

Download references

Acknowledgements

The research was funded by the National Key Research and Development Program of China (No. 2016YFC0800200) and Natural Science Foundation of China (Grant Nos. 51578499, 51761130078 and 51825803).

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Zhejiang University, Hangzhou, 310058, Zhejiang, China

    M. D. Jiang, Z. X. Yang & Y. H. Xie

  2. School of Engineering and the Built Environment, Edinburgh Napier University, Merchiston Campus, Edinburgh, EH10 5DT, Scotland, UK

    D. Barreto

  3. Changjiang Institute of Survey, Plan, Design, and Research, Wuhan, 430010, Hubei, China

    Y. H. Xie

Authors
  1. M. D. Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. X. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Barreto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. H. Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Z. X. Yang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, M.D., Yang, Z.X., Barreto, D. et al. The influence of particle-size distribution on critical state behavior of spherical and non-spherical particle assemblies. Granular Matter 20, 80 (2018). https://doi.org/10.1007/s10035-018-0850-x

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-018-0850-x

Keywords

Search

Navigation