Acta Mechanica Solida Sinica

, Volume 27, Issue 1, pp 1–14 | Cite as

Rotational Resistance and Shear-Induced Anisotropy in Granular Media

  • Jidong Zhao
  • Ning Guo


This paper presents a micromechanical study on the behavior of granular materials under confined shear using a three-dimensional Discrete Element Method (DEM). We consider rotational resistance among spherical particles in the DEM code as an approximate way to account for the effect of particle shape. Under undrained shear, it is found rotational resistance may help to increase the shear strength of a granular system and to enhance its resistance to liquefaction. The evolution of internal structure and anisotropy in granular systems with different initial conditions depict a clear bimodal character which distinguishes two contact subnetworks. In the presence of rotational resistance, a good correlation is found between an analytical stress-force-fabric relation and the DEM results, in which the normal force anisotropy plays a dominant role. The unique properties of critical state and liquefaction state in relation to granular anisotropy are also explored and discussed.

Key Words

granular media anisotropy discrete element method (DEM) rotational resistance liquefaction critical state 


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  1. 1.
    Been, K. and Jefferies, M., Soil Liquefaction: A Critical State Approach. Taylor & Francis, New York, 2006.Google Scholar
  2. 2.
    Roscoe, K.H., Schofield, A.N. and Wroth, C.P., On the yielding of soils. Géotechnique, 1958, 8(1): 22–53.CrossRefGoogle Scholar
  3. 3.
    Rowe, P.W., The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proceedings of the Royal Society A, 1962. 269(1339): 500–527.CrossRefGoogle Scholar
  4. 4.
    McDowell, G.R., Bolton, M.D. and Robertson, D., The fractal crushing of granular materials. Journal of the Mechanics and Physics of Solids, 1996, 44(12): 2079–2102.CrossRefGoogle Scholar
  5. 5.
    Li, X.S. and Dafalias, Y.F., Dilatancy for cohesionless soils. Géotechnique, 2000, 50(4): 449–460.CrossRefGoogle Scholar
  6. 6.
    Gutierrez, M. and Ishihara, K., Non-coaxiality and energy dissipation in granular materials. Soils and Foundations, 2000, 40(2): 49–59.CrossRefGoogle Scholar
  7. 7.
    Collins, I.F. and Muhunthan, B., On the relationship between stress-dilatancy, anisotropy, and plastic dissipation for granular materials. Géotechnique, 2003, 53(7): 611–618.CrossRefGoogle Scholar
  8. 8.
    Yu, H.S. and Yuan, X., On a class of non-coaxial plasticity models for granular soils. Proceedings of the Royal Society A, 2006, 462(2067): 725–748.CrossRefGoogle Scholar
  9. 9.
    Chandler, H.W. and Sands, C.M., The role of a realistic volume constraint in modelling a two dimensional granular assembly. Journal of the Mechanics and Physics of Solids, 2007, 55(7): 1341–1356.CrossRefGoogle Scholar
  10. 10.
    Mueth, D.M., Debregeas, G.F., Karczmar, G.S., Eng, P.J., Nagel, S.R. and Jaeger, H.M., Signatures of granular mcirostructure in dense shear flows. Nature, 2000, 406: 385–389.CrossRefGoogle Scholar
  11. 11.
    Behringer, R.P., Daniels, K.E., Majmudar, T.S. and Sperl, M., Fluctuations, correlations and transitions in granular materials: statistical mechanics for a non-conventional system. Philosophical Transactions of the Royal Society A, 2008, 366(1865): 493–504.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Guo, N. and Zhao, J., Bimodal character of induced anisotropy in granular materials under undrained shear. In: Jiang, M., Liu, F. and Bolton, M. (eds.) Geomechanics and Geotechnics: from Micro to Macro. Taylor & Francis, Shanghai, China, 2011: 513–517.Google Scholar
  13. 13.
    Zhao, J. and Guo, N., Signature of anisotropy in liquefiable sand under undrained shear. In: Bonelli, S., Dascalu, C. and Nicot, F. (eds.) 9th International Workshop on Bifurcation and Degradation in Geomaterials. Springer, Porquerolles, France, 2011: 45–51.CrossRefGoogle Scholar
  14. 14.
    Zhao, J. and Guo, N., Unique critical state characteristics in granular media considering fabric anisotropy. Géotechnique, 2013, 63(8): 695–704.CrossRefGoogle Scholar
  15. 15.
    Ishihara, K., Liquefaction and flow failure during earthquakes. Géotechnique, 1993, 43(3): 351–415.CrossRefGoogle Scholar
  16. 16.
    Li, X.S. and Dafalias, Y.F., Anisotropic critical state theory: role of fabric. Journal of Engineering Mechanics, 2012, 138(3): 263–275.CrossRefGoogle Scholar
  17. 17.
    Zhao, J. and Guo, N., A new definition on critical state of granular media accounting for fabric anisotropy. In: Powders and Grains 2013: AIP Conference Proceedings, 2013, 1542: 229–232.Google Scholar
  18. 18.
    Zhao, J., Guo, N. and Li, X.S., Unique quantification of critical state in granular media considering fabric anisotropy. In Yang, Q., Zhang, J.M., Zheng, H. and Yao, Y.P. (eds.) Constitutive Modeling of Geomaterials: Advances and New Application, Proceedings of the Second International Symposium on Constitutive Modeling of Geomaterials. Springer, Beijing, China, 2013: 247–252.Google Scholar
  19. 19.
    Radjaï, F., Troadec, H. and Roux, S., Key features of granular plasticity. In: Antony, S.J., Hoyle, W. and Ding, Y. (eds.) Granular Materials: Fundamentals and Applications. The Royal Society of Chemistry. Cambridge, UK, 2004.Google Scholar
  20. 20.
    Rothenburg, L. and Bathurst, R.J., Analytical study of induced anisotropy in idealized granular materials. Géotechnique, 1989, 39(4): 601–614.CrossRefGoogle Scholar
  21. 21.
    Chang, C.S., Chao, S.J. and Chang, Y., Estimates of elastic moduli for granular material with anisotropic random packing structure. International Journal of Solids and Structures, 1995, 32(14): 1989–2008.CrossRefGoogle Scholar
  22. 22.
    Radjaï, F., Wolf, D.E., Jean, M. and Moreau, J.J., Bimodal character of stress transmission in granular packings. Physical Review Letters, 1998, 80(1): 61–64.CrossRefGoogle Scholar
  23. 23.
    Rothenburg, L. and Kruyt, N.P., Critical state and evolution of coordination number in simulated granular materials. International Journal of Solids and Structures, 2004, 41(21): 5763–5774.CrossRefGoogle Scholar
  24. 24.
    Kruyt, N.P. and Antony, S.J., Force, relative-displacement, and work networks in granular materials subjected to quasistatic deformation. Physical Review E, 2007, 75(5): 051308.CrossRefGoogle Scholar
  25. 25.
    Antony, S.J. and Kruyt, N.P., Role of interparticle friction and particle-scale elasticity in the shear-strength mechanism of three-dimensional granular media. Physical Review E, 2009, 79(3): 031308.CrossRefGoogle Scholar
  26. 26.
    Cundall, P.A. and Strack, O.D.L., A discrete numerical model for granular assemblies. Géotechnique, 1979, 29(1): 47–65.CrossRefGoogle Scholar
  27. 27.
    Blott, S.J. and Pye, K., Particle shape: a review and new methods of characterization and classification. Sedimentology, 2008, 55(1): 31–63.Google Scholar
  28. 28.
    Mollon, G. and Zhao, J., Fourier-Voronoi-based generation of realistic samples for discrete modeling of granular materials. Granular Matter, 2012, 14(5): 621–638.CrossRefGoogle Scholar
  29. 29.
    Mollon, G. and Zhao, J., Generating realistic 3D sand particles using Fourier descriptors. Granular Matter, 2013, 15(1): 95–108.CrossRefGoogle Scholar
  30. 30.
    Ng, T.-T., Discrete element method simulations of the critical state of a granular material. International Journal of Geomechanics, 2009, 9(5): 209–216.CrossRefGoogle Scholar
  31. 31.
    Abe, S., Place, D. and Mora, P., A parallel implementation of the lattice solid model for the simulation of rock mechanics and earthquake dynamics. Pure and Applied Geophysics, 2004, 161(11–12): 2265–2277.Google Scholar
  32. 32.
    Ishihara, K. and Oda, M., Rolling resistance at contacts in simulation of shear band development by DEM. Journal of Engineering Mechanics, 1998, 124(3): 285–292.CrossRefGoogle Scholar
  33. 33.
    Estrada, N., Taboada, A. and Radjaï, F., Shear strength and force transmission in granular media with rolling resistance. Physical Review E, 2008, 78(2): 021301.CrossRefGoogle Scholar
  34. 34.
    Jiang, M.J., Yu, H.-S. and Harris, D., A novel discrete model for granular material incorporating rolling resistance. Computers and Geotechnics, 2005, 32(5): 340–357.CrossRefGoogle Scholar
  35. 35.
    Jiang, M.J., Yu, H.-S. and Harris, D., Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(8): 723–761.CrossRefGoogle Scholar
  36. 36.
    Mair, K. and Hazzard, J.F., Nature of stress accommodation in sheared granular material: Insights from 3D numerical modeling. Earth and Planetary Science Letters, 2007, 259(3–4): 469–485.CrossRefGoogle Scholar
  37. 37.
    Yimsiri, S. and Soga, K., DEM analysis of soil fabric effects on behaviour of sand. Géotechnique, 2010, 60(6): 483–495.CrossRefGoogle Scholar
  38. 38.
    Christoffersen, J., Mehrabadi, M.M. and Nemat-Nasser, S., A micromechanical description of granular material behavior. Journal of Applied Mechanics, 1981, 48(2): 339–344.CrossRefGoogle Scholar
  39. 39.
    Cambou, B., Dubujet, P. and Nouguier-Lehon, C., Anisotropy in granular materials at different scales. Mechanics of Materials, 2004, 36(12): 1185–1194.CrossRefGoogle Scholar
  40. 40.
    Satake, M., The role of the characteristic line in static soil behavior. In: IUTAM symposium on Deformation and Failure of Granular Materials. A. A. Balkema, Delft, 1982: 63–68.Google Scholar
  41. 41.
    Oda, M., Fabric tensor for discontinuous geological materials. Soils and Foundations, 1982, 22(4): 96–108.CrossRefGoogle Scholar
  42. 42.
    Ouadfel, H. and Rothenburg, L., ‘Stress-force-fabric’ relationship for assemblies of ellipsoids. Mechanics of Materials, 2001, 33(4): 201–221.CrossRefGoogle Scholar
  43. 43.
    Sitharam, T.G., Vinod, J.S. and Ravishankar, B.V., Post-liquefaction undrained monotonic behaviour of sands: experiments and DEM simulations. Géotechnique, 2009, 59(9): 739–749.CrossRefGoogle Scholar
  44. 44.
    Gao, Z., Zhao, J. and Yao, Y., A generalized anisotropic failure criterion for geomaterials. International Journal of Solids and Structures, 2010, 47(22–23): 3166–3185.CrossRefGoogle Scholar
  45. 45.
    Guo, N. and Zhao, J., The signature of shear-induced anisotropy in granular media. Computers and Geotechnics, 2013, 47: 1–15.MathSciNetCrossRefGoogle Scholar
  46. 46.
    Rothenburg, L., Micromechanics of Idealized Granular Systems. Ph.D. thesis, Carleton University, 1980.Google Scholar
  47. 47.
    Chantawarungal, K., Numerical Simulations of Three Dimensional Granular Assemblies. Ph.D. thesis, University of Waterloo, 1993.Google Scholar
  48. 48.
    Voivret, C., Radjaï, F., Delenne, J.Y. and El Youssoufi, M.S., Multiscale force networks in highly polydisperse granular media. Physical Review Letters, 2009, 102(17): 178001.CrossRefGoogle Scholar
  49. 49.
    Tordesillas, A. and Muthuswamy, M., On the modeling of confined buckling of force chains. Journal of the Mechanics and Physics of Solids, 2009, 57(4): 706–727.MathSciNetCrossRefGoogle Scholar
  50. 50.
    Johnson, K., Contact Mechanics. Cambridge University Press, London, 1985.CrossRefGoogle Scholar
  51. 51.
    Thornton, C., Numerical simulations of deviatoric shear deformation of granular media. Géotechnique, 2000, 50(1): 43–53.CrossRefGoogle Scholar
  52. 52.
    Been, K., Jefferies, M.G. and Hachey, J., The critical state of sands. Géotechnique, 1991, 41(3): 365–381.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringThe Hong Kong University of Science and Technology, Clearwater BayKowloonHong Kong, China

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