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


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.


Elastic moduli Granular material  Poisson’s ratio Pressure dependence 



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.


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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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