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Granular Matter

, Volume 15, Issue 2, pp 139–147 | Cite as

A discrete element analysis of elastic properties of granular materials

  • X. Q. Gu
  • J. YangEmail author
Original Paper

Abstract

The elastic properties of a regular packing of spheres with different tolerances were evaluated using the discrete element method to elucidate the mechanisms behind the discrepancies between laboratory experiments and theoretical predictions of the classic Hertz-Mindlin contact law. The simulations indicate that the elastic modulus of the packing is highly dependent on the coordination number and the magnitude and distribution of contact normal forces, and this dependence is macroscopically reflected as the influence of confining pressure and void ratio. The increase of coordination number and the uniformity of contact normal forces distribution with increasing confining pressure results in the stress exponent \(n\) for elastic modulus being higher than 1/3 as predicted by the Hertz-Mindlin law. Furthermore, the simulations show that Poisson’s ratio of a granular packing is not a constant as commonly assumed, but rather it decreases as confining pressure increases. The variation of Poisson’s ratio appears to be a consequence of the increase of the coordination number rather than the increase of contact normal forces with confining pressure.

Keywords

Elastic moduli Granular material  Poisson’s ratio Pressure dependence 

Notes

Acknowledgments

The work presented in this paper was supported by the University of Hong Kong through the Seed Funding for Basic Research scheme (11159098) and the Outstanding Young Researcher Award scheme (2006–2007). This support is gratefully acknowledged.

References

  1. 1.
    Hardin, B.O., Richart, F.E.: Elastic wave velocities in granular soils. J. Soil Mech. Found. Eng. Div. 89(SM1), 39–56 (1963)Google Scholar
  2. 2.
    Richart, F.E., Hall, J.R., Woods, R.D.: Vibrations of Soils and Foundations. Prentice-Hall, Englewood Cliffs (1970)Google Scholar
  3. 3.
    Hardin, B.O., Drnevich, V.P.: Shear modulus and damping in soil: Measurement and parameter effects. J. Soil Mech. Found. Div. 98(7), 603–624 (1972)Google Scholar
  4. 4.
    Iwasaki, T., Tatsuoka, F.: Effect of grain size and grading on dynamic shear moduli of sand. Soils Found. 17(3), 19–35 (1977)CrossRefGoogle Scholar
  5. 5.
    Kokusho, T.: Cyclic triaxial test of dynamic soil properties for wide strain range. Soils Found. 20(2), 45–60 (1980)CrossRefGoogle Scholar
  6. 6.
    Stokoe, K.H.I.I., Hwang, S.K., Lee, J.N.-K.: Effects of various parameters on the stiffness and damping of soils at small to medium strains. Proc. First Int. Conf. Prefail. Deformat. Charact. Geomater. 2, 785–816 (1995)Google Scholar
  7. 7.
    Wichtmann, T., Triantafyllidis, T.: On the influence of the grain size distribution curve on P-wave velocity, constrained elastic modulus \(M_{\rm max}\) and Poisson’s ratio of quartz sands. Soil Dyn. Earthq. Eng. 30, 757–766 (2010)CrossRefGoogle Scholar
  8. 8.
    Yang, J., Gu, X.Q.: Shear stiffness of granular material at small strain: does it depend on grain size? Géotechnique 63(2), 165–179 (2013)CrossRefGoogle Scholar
  9. 9.
    Duffy, J., Mindlin, R.D.: Stress-strain relations and vibrations of a granular medium. J. Appl. Mech. 24, 585–593 (1956)MathSciNetGoogle Scholar
  10. 10.
    Petrakis, E., Dobry, R.: Micromechanical Modeling of Granular Soil at Small Strain by Arrays of Elastic Spheres. Report CE-87-02, Dept. Civil Eng., Rensselaer Polytechnic Institute, Troy, NY (1987)Google Scholar
  11. 11.
    Wichtmann, T., Triantafyllidis, Th: Influence of the grain-size distribution curve of quartz sand on small strain shear modulus \(G_{\rm max}\). J. Geotech. Geoenviron. Eng. 135(10), 1404–1418 (2009)CrossRefGoogle Scholar
  12. 12.
    Yang, J., Gu, X.Q.: Dynamic shear modulus of dry sand: effect of test method. In: Proceedings of the 14th European Conference on Earthquake Engineering, Ohrid, Macedonia (2010)Google Scholar
  13. 13.
    Goddard, J.D.: Nonlinear elasticity and pressure-dependent wave speeds in granular media. Proc. R. Soc. Lond. 430, 105–131 (1990)ADSzbMATHCrossRefGoogle Scholar
  14. 14.
    Chen, Y.-C., Ishibashi, I., Jenkins, J.T.: Dynamic shear modulus and fabric: Part I, depositional and induced anisotropy. Géotechnique 38(1), 25–32 (1988)CrossRefGoogle Scholar
  15. 15.
    Santamarina, J.C., Cascante, G.: Effect of surface roughness on the wave propagation parameters. Géotechnique 48(1), 129–136 (1998) Google Scholar
  16. 16.
    Yimsiri, S., Soga, K.: Effect of surface roughness on small-strain modulus: Micromechanics view. Proc. 2nd Int. Symp. Prefail. Deform. Charact. Geomater. 1, 597–602 (1999)Google Scholar
  17. 17.
    Kumar, J., Madhusudhan, B.N.: Effect of relative density and confining pressure on Poisson ratio from bender-extender element tests. Géotechnique 60(7), 561–567 (2010)CrossRefGoogle Scholar
  18. 18.
    Gu, X.Q.: Dynamic Properties of Granular Materials at the Macro and Micro Scales. PhD thesis, The University of Hong Kong, Hong Kong (2012)Google Scholar
  19. 19.
    McDowell, G.R., Bolton, M.D.: Micro mechanics of elastic soil. Soils Found. 41(6), 147–152 (2001)CrossRefGoogle Scholar
  20. 20.
    Chang, C.S., Misra, A., Sundaram, S.S.: Properties of granular packing under low amplitude cyclic loading. Soil Dyn. Earthq. Eng. 10(4), 201–211 (1991)CrossRefGoogle Scholar
  21. 21.
    Itasca: User’s manual for PFC\(^{2D}\). Itasca Consulting Group, Inc., Minneapolis (2005)Google Scholar
  22. 22.
    Hoque, E., Tatsuoka, F.: Effects of stress ratio on small-strain stiffness during triaxial shearing. Géotechnique 54(7), 429–439 (2004)CrossRefGoogle Scholar
  23. 23.
    Thornton, C.: Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1), 43–53 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Geotechnical EngineeringTongji UniversityShanghaiChina
  2. 2.Department of Civil EngineeringThe University of Hong KongPokfulamHong Kong

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