Granular Matter

, 20:12 | Cite as

The influence of rolling resistance on the stress-dilatancy and fabric anisotropy of granular materials

  • Yiming Liu
  • Huabei Liu
  • Haijun Mao
Original Paper


The effects of rolling resistance on the stress-dilatancy behavior and fabric anisotropy of granular materials were investigated through a three-dimensional discrete element method (DEM). A rolling resistance model was incorporated into the DEM code PFC3D and triaxial DEM simulations under simulated drained and undrained conditions were carried out. The results show that there existed a threshold value of the rolling friction. When the rolling friction was smaller than this value, the mechanical behavior of granular materials under both drained and undrained conditions were substantially influenced by the rolling friction, but the influence diminished when it was larger than the threshold value. A linear relationship has been observed between the dilatancy coefficient and the natural logarithm of the rolling-friction coefficient when it was smaller than the threshold value. An increase in the rolling friction led to an increase in the fabric anisotropy of all strong contacts under both testing conditions until the threshold value was attained. The investigation on the effect of rolling friction on the microstructure of granular materials revealed that the rolling friction enhanced the stability of force chains, which resulted in the difference in the stress-dilatancy behavior. Finally, the relationship between the stress ratio q/p\(^{\prime }\) and the fabric measure at strong contacts \(\hbox {H}_{\mathrm{d}}^{\mathrm{s}} /\hbox {H}_{\mathrm{m}}^{\mathrm{s}}\) was found independent of the inter-particle friction, rolling friction and testing conditions.


Discrete element method Rolling resistance Dilatancy Fabric anisotropy Granular materials 



The study was partly supported by the National Natural Foundation of China (Grant No. 51778259), which is gratefully acknowledged.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Aboul Hosn, R., Sibille, L., Benahmed, N., Chareyre, B.: Discrete numerical modeling of loose soil with spherical particles and interparticle rolling friction. Granul. Matter 19(1), 1–12 (2017)CrossRefGoogle Scholar
  2. 2.
    Ai, J., Chen, J.F., Rotter, J.M., Ooi, J.Y.: Assessment of rolling resistance models in discrete element simulations. Powder Technol. 206(3), 269–282 (2011). CrossRefGoogle Scholar
  3. 3.
    Antony, S.J.: Evolution of force distribution in three-dimensional granular media. Phys. Rev. E 63(1), 011302 (2000)ADSCrossRefGoogle Scholar
  4. 4.
    Antony, S.J., Kuhn, M.R.: Influence of particle shape on granular contact signatures and shear strength: new insights from simulations. Int. J. Solids Struct. 41(21), 5863–5870 (2004)CrossRefMATHGoogle Scholar
  5. 5.
    ASTM: ASTM D7181: method for consolidated drained triaxial compression test for soils. In: Astm ASTM International (2011)Google Scholar
  6. 6.
    Azéma, E., Radjai, F., Saussine, G.: Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mech. Mater. 41(6), 729–741 (2009)CrossRefGoogle Scholar
  7. 7.
    Bardet, J., Huang, Q.: Rotational stiffness of cylindrical particle contacts. Powders Grains 93, 39–43 (1993)Google Scholar
  8. 8.
    Barreto, D., O’Sullivan, C.: The influence of inter-particle friction and the intermediate stress ratio on soil response under generalised stress conditions. Granul. Matter. 14(4), 505–521 (2012)CrossRefGoogle Scholar
  9. 9.
    Belheine, N., Plasslard, J.P., Donze, F.V., Darve, F., Seridi, A.: Numerical simulation of drained triaxial test using 3D discrete element modeling. Comput. Geotech. 36(1–2), 320–331 (2009). CrossRefGoogle Scholar
  10. 10.
    Bolton, M.: The strength and dilatancy of sands. Geotechnique 36(1), 65–78 (1986). CrossRefGoogle Scholar
  11. 11.
    Camusso, M., Barla, M.: Microparameters calibration for loose and cemented soil when using particle methods. Int. J. Geomech. 9(5), 217–229 (2009)CrossRefGoogle Scholar
  12. 12.
    Cavarretta, I., Coop, M., O’sullivan, C.: The influence of particle characteristics on the behaviour of coarse grained soils. Géotechnique 60(6), 413–423 (2010)CrossRefGoogle Scholar
  13. 13.
    Chakraborty, T., Salgado, R.: Dilatancy and shear strength of sand at low confining pressures. J. Geotech. Geoenviron. 136(3), 527–532 (2010)CrossRefGoogle Scholar
  14. 14.
    Chen, X., Zhang, J.: Influence of relative density on dilatancy of clayey sand-fouled aggregates in large-scale triaxial tests. J. Geotech. Geoenviron. Eng. 142(10), 06016011 (2016). CrossRefGoogle Scholar
  15. 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. 132(5), 591–602 (2006)CrossRefGoogle Scholar
  16. 16.
    Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  17. 17.
    Dai, B.B., Yang, J., Zhou, C.Y.: Observed effects of interparticle friction and particle size on shear behavior of granular materials. Int. J. Geomech. 16(1), 04015011 (2015)CrossRefGoogle Scholar
  18. 18.
    Esposito III, M.P., Andrus, R.D.: Peak shear strength and dilatancy of a pleistocene age sand. J. Geotech. Geoenviron. 143, 04016079 (2016)CrossRefGoogle Scholar
  19. 19.
    Estrada, N., Azéma, E., Radjai, F., Taboada, A.: Identification of rolling resistance as a shape parameter in sheared granular media. Phys. Rev. E 84(1), 011306 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    Estrada, N., Azema, E., Radjai, F., Taboada, A.: Comparison of the effects of rolling resistance and angularity in sheared granular media. AIP Conf. Proc. 1542, 891–894 (2013). ADSCrossRefGoogle Scholar
  21. 21.
    Fityus, S., Giacomini, A., Buzzi, O.: The significance of geology for the morphology of potentially unstable rocks. Eng. Geol. 162, 43–52 (2013)CrossRefGoogle Scholar
  22. 22.
    Guo, N., Zhao, J.: The signature of shear-induced anisotropy in granular media. Comput. Geotech. 47, 1–15 (2013)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Guo, P., Su, X.: Shear strength, interparticle locking, and dilatancy of granular materials. Can. Geotech. J. 44(5), 579–591 (2007)CrossRefGoogle Scholar
  24. 24.
    Guo, P.J.: Capillary interaction-induced rolling resistance between elliptical particles and its influence on grain column length at pendular state. Acta Geotech. 10(4), 435–447 (2015). CrossRefGoogle Scholar
  25. 25.
    Huang, J., Xu, S., Hu, S.: Effects of grain size and gradation on the dynamic responses of quartz sands. Int. J. Impact Eng. 59, 1–10 (2013)CrossRefGoogle Scholar
  26. 26.
    Ishihara, K., Tatsuoka, F., Yasuda, S.: Undrained deformation and liquefaction of sand under cyclic stresses. Soils Found. 15(1), 15 (1975)Google Scholar
  27. 27.
    Itasca Consulting Group Inc: Particle Flow Code in 3 Dimensions, User’s Guide. (1999)Google Scholar
  28. 28.
    Iwashita, K., Oda, M.: Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technol. 109(1–3), 192–205 (2000). CrossRefGoogle Scholar
  29. 29.
    Iwashita, K., Oda, M.: Rolling resistance at contacts in simulation of shear band development by DEM. J. Eng. Mech. Asce 124(3), 285–292 (1998). CrossRefGoogle Scholar
  30. 30.
    Jiang, M., Li, T., Shen, Z.: Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study. Granul. Matter 18(3), 1–14 (2016)Google Scholar
  31. 31.
    Jiang, M., Harris, D., Yu, H.: A unified two-dimensional contact model to capture the roughness of granular materials by rolling resistance. In: Geomechanics and Geotechnics of Particulate Media: Proceedings of the International Symposium on Geomechanics and Geotechnics of Particulate Media, Ube, Japan, 12–14 September 2006, p.  181. CRC Press (2006)Google Scholar
  32. 32.
    Jiang, M.J., Shen, Z.F., Wang, J.F.: A novel three-dimensional contact model for granulates incorporating rolling and twisting resistances. Comput. Geotech. 65, 147–163 (2015). CrossRefGoogle Scholar
  33. 33.
    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). CrossRefGoogle Scholar
  34. 34.
    Kuhn, M.R.: OVAL and OVALPLOT: Programs for analyzing dense particle assemblies with the discrete element method (2006)Google Scholar
  35. 35.
    Kuhn, M.R., Sun, W., Wang, Q.: Stress-induced anisotropy in granular materials: fabric, stiffness, and permeability. Acta Geotech. 10(4), 399–419 (2015)CrossRefGoogle Scholar
  36. 36.
    Mahmud Sazzad, M., Suzuki, K., Modaressi-Farahmand-Razavi, A.: Macro–micro responses of granular materials under different b values using DEM. Int. J. Geomech. 12(3), 220–228 (2012)CrossRefGoogle Scholar
  37. 37.
    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). CrossRefMATHGoogle Scholar
  38. 38.
    Ng, T.T.: Input parameters of discrete element methods. J. Eng. Mech. 132(7), 723–729 (2006)CrossRefGoogle Scholar
  39. 39.
    Ng, T.-T.: Macro-and micro-behaviors of granular materials under different sample preparation methods and stress paths. Int. J. Solids Struct. 41(21), 5871–5884 (2004)CrossRefMATHGoogle Scholar
  40. 40.
    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)ADSCrossRefGoogle Scholar
  41. 41.
    Oda, M., Iwashita, K.: Study on couple stress and shear band development in granular media based on numerical simulation analyses. Int. J. Eng. Sci. 38(15), 1713–1740 (2000). CrossRefGoogle Scholar
  42. 42.
    Pena, A., Garcia-Rojo, R., Herrmann, H.: Influence of particle shape on sheared dense granular media. Granul. Matter 9(3–4), 279–291 (2007)CrossRefMATHGoogle Scholar
  43. 43.
    Phusing, D., Suzuki, K., Zaman, M.: Mechanical behavior of granular materials under continuously varying b values using DEM. Int. J. Geomech. 16(1), 04015027 (2015)CrossRefGoogle Scholar
  44. 44.
    Plassiard, J.-P., Belheine, N., Donzé, F.-V.: A spherical discrete element model: calibration procedure and incremental response. Granul. Matter 11(5), 293–306 (2009)CrossRefMATHGoogle Scholar
  45. 45.
    Radjai, F., Wolf, D.E., Jean, M., Moreau, J.-J.: Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80(1), 61 (1998)ADSCrossRefGoogle Scholar
  46. 46.
    Rothenburg, L., Bathurst, R.J.: Analytical study of induced anisotropy in idealized granular materials. Géotechnique 39(39), 601–14 (1990)Google Scholar
  47. 47.
    Satake, M.: Fabric tensor in granular materials. In: Proceedings of the IUTAM Symposium on Deformation and Failure of Granular materials, Delft, The Netherlands (1982)Google Scholar
  48. 48.
    Sazzad, M.M., Suzuki, K.: Density dependent macro–micro behavior of granular materials in general triaxial loading for varying intermediate principal stress using DEM. Granul. Matter 15(5), 583–593 (2013)CrossRefGoogle Scholar
  49. 49.
    Shen, Z., Jiang, M., Thornton, C.: DEM simulation of bonded granular material. Part I: contact model and application to cemented sand. Comput. Geotech. 75, 192–209 (2016)CrossRefGoogle Scholar
  50. 50.
    Sukumaran, B., Ashmawy, A.: Quantitative characterisation of the geometry of discret particles. Geotechnique 51(7), 619–627 (2001)CrossRefGoogle Scholar
  51. 51.
    Tang, H., Dong, Y., Chu, X., Zhang, X.: The influence of particle rolling and imperfections on the formation of shear bands in granular material. Granul. Matter 18(1), 1–12 (2016)CrossRefGoogle Scholar
  52. 52.
    Thornton, C.: Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1), 43–53 (2000)CrossRefGoogle Scholar
  53. 53.
    Thornton, C., Antony, S.: Quasi-static deformation of particulate media. Philos. Trans. R. Soc. London Ser. A Math. Phys. Eng. Sci. 356(1747), 2763–2782 (1998)MATHGoogle Scholar
  54. 54.
    Tordesillas, A., Walsh, D.S.: Incorporating rolling resistance and contact anisotropy in micromechanical models of granular media. Powder Technol. 124(1), 106–111 (2002). CrossRefGoogle Scholar
  55. 55.
    Tsomokos, A., Georgiannou, V.: Effect of grain shape and angularity on the undrained response of fine sands. Can. Geotech. J. 47(5), 539–551 (2010)CrossRefGoogle Scholar
  56. 56.
    Vaid, Y., Sasitharan, S.: The strength and dilatancy of sand. Can. Geotech. J. 29(3), 522–526 (1992)CrossRefGoogle Scholar
  57. 57.
    Vermeer, P.A., De Borst, R.: Non-associated plasticity for soils, concrete and rock. HERON 29(3), 1984 (1984)Google Scholar
  58. 58.
    Wang, J., Gutierrez, M.: Discrete element simulations of direct shear specimen scale effects. Géotechnique 60(5), 395–409 (2010)CrossRefGoogle Scholar
  59. 59.
    Wensrich, C., Katterfeld, A.: Rolling friction as a technique for modelling particle shape in DEM. Powder Technol. 217, 409–417 (2012)CrossRefGoogle Scholar
  60. 60.
    Wensrich, C.M., Katterfeld, A., Sugo, D.: Characterisation of the effects of particle shape using a normalised contact eccentricity. Granul. Matter 16(3), 327–337 (2014). CrossRefGoogle Scholar
  61. 61.
    Yang, J., Luo, X.: Exploring the relationship between critical state and particle shape for granular materials. J. Mech. Phys. Solids 84, 196–213 (2015)ADSCrossRefGoogle Scholar
  62. 62.
    Yimsiri, S., Soga, K.: DEM analysis of soil fabric effects on behaviour of sand. Géotechnique 60(6), 483–495 (2010)CrossRefGoogle Scholar
  63. 63.
    Zhang, W.C., Wang, J.F., Jiang, M.J.: DEM-aided discovery of the relationship between energy dissipation and shear band formation considering the effects of particle rolling resistance. J. Geotech. Geoenviron. 139(9), 1512–1527 (2013). CrossRefGoogle Scholar
  64. 64.
    Zhao, J.D., Guo, N.: Rotational resistance and shear-induced anisotropy in granular media. Acta Mech. Solida Sin. 27(1), 1–14 (2014)MathSciNetCrossRefGoogle Scholar
  65. 65.
    Zhou, B., Huang, R.Q., Wang, H.B., Wang, J.F.: DEM investigation of particle anti-rotation effects on the micromechanical response of granular materials. Granul. Matter 15(3), 315–26 (2013)ADSCrossRefGoogle Scholar
  66. 66.
    Zhou, W., Liu, J., Ma, G., Yuan, W., Chang, X.: Macroscopic and microscopic behaviors of granular materials under proportional strain path: a DEM study. Int. J. Numer. Anal. Met. 40(18), 2450–2467 (2016). CrossRefGoogle Scholar
  67. 67.
    Zhou, Y.C., Wright, B.D., Yang, R.Y., Xu, B.H., Yu, A.B.: Rolling friction in the dynamic simulation of sandpile formation. Phys. A 269(2–4), 536–553 (1999). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Civil Engineering and MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Institute of Rock and Soil MechanicsChinese Academy of SciencesWuhanChina

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