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Granular Matter

, Volume 13, Issue 3, pp 255–260 | Cite as

Failure mechanisms in granular media: a discrete element analysis

  • François NicotEmail author
  • Nejib Hadda
  • Franck Bourrier
  • Luc Sibille
  • Félix Darve
Original Paper

Abstract

This paper attempts to numerically validate the concept of diffuse failure using a discrete element method. First, the theoretical background is reviewed, and it is shown how the kinetic energy of a system, initially at rest after a loading history, is likely to abruptly increase under the effect of disturbances. The vanishing of the second-order work thus constitutes a basic ingredient, related to both the pioneering work of Hill (J Mech Phys Solids (6):236–249, 1958) and the notion of bifurcation applied to geomechanics (Vardoulakis and Sulem in Bifurcation analysis in geomechanics, Chapman & Hall Publisher, London, 1995). Discrete numerical simulations were performed on homogeneous three-dimensional specimens, and the three basic conditions that must be satisfied in order to observe a failure mechanism are numerically checked. Finally, this work illustrates the phenomena that are likely to affect in situ slopes, for instance, when the loading (due to weather conditions or human activities) meets the three basic conditions for a failure mechanism to develop.

Keywords

Bifurcation Sustainability Second-order work Loading parameters Discrete element method Diffuse failure Collapse 

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References

  1. 1.
    Bazant Z., Cedolin L.: Stability of Structures. Dover Edition Publ, USA (2003)Google Scholar
  2. 2.
    Challamel N., Nicot F., Lerbet J., Darve F.: On the stability of non-conservative elastic systems under mixed perturbations. Eur. J. Env. Civil Eng. 13(3), 347–367 (2009)Google Scholar
  3. 3.
    Challamel N., Nicot F., Lerbet J., Darve F.: Stability of non-conservative elastic structures under additional kinematics constraints. Eng. Struct. 32(10), 3086–3092 (2010)CrossRefGoogle Scholar
  4. 4.
    Cundall P.A., Strack O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  5. 5.
    Darve F., Vardoulakis I.: Degradations and Instabilities in Geomaterials. Springer, Berlin (2004)Google Scholar
  6. 6.
    Gudehus, G.: A comparison of some constitutive laws for soils under radially symmetric loading and unloading. In: Aachen, Wittke, W. (eds.) 3rd International Conference on Numerical Methods in Geomechanics, vol. 4, pp. 1309–1324. Balkema Publisher, (1979)Google Scholar
  7. 7.
    Hill R.: A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids 6, 236–249 (1958)ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    Kozicki J., Donze F.V.: A new open-source software developed for numerical simulations using discrete modeling methods. Comp. Meth. Appl. Mech. Eng 197(49-50), 4429–4443 (2008)zbMATHCrossRefGoogle Scholar
  9. 9.
    Laouafa F., Darve F.: Modelling of slope failure by a material instability mechanism. Comp. Geotech. 29(4), 301–325 (2002)CrossRefGoogle Scholar
  10. 10.
    Nicot F., Darve F.: A micro-mechanical investigation of bifurcation in granular materials. Int. J. Solids Struct. 44, 6630–6652 (2007)zbMATHCrossRefGoogle Scholar
  11. 11.
    Nicot, F., Challamel, N., Lerbet, J., Darve, F.: Mixed loading conditions, revisiting the question of stability in geomechanics. Int. J. Num. Anal. Methods Geomech. Article first published online: 2 SEP 2010. doi: 10.1002/nag.959 (2010)
  12. 12.
    Nicot F., Darve F., Khoa H.D.V.: Bifurcation and second-order work in geomaterials. Int. J. Num. Anal. Methods Geomechanics 31, 1007–1032 (2007)ADSzbMATHCrossRefGoogle Scholar
  13. 13.
    Nicot F., Sibille L., Darve F.: Bifurcation in granular materials: an attempt at a unified framework. Int. J. Solids Struct. 46, 3938–3947 (2009)zbMATHCrossRefGoogle Scholar
  14. 14.
    Radjai, F., Roux, S., Moreau, J.J.: Contact forces in a granular packing. Chaos, 9, (n°3), 544–550 (1999)Google Scholar
  15. 15.
    Sibille L., Donzé F., Nicot F., Chareyre B., Darve F.: Bifurcation detection and catastrophic failure. Acta Geotecnica 3(1), 14–24 (2008)Google Scholar
  16. 16.
    Sibille L., Nicot F., Donzé F., Darve F.: Analysis of failure occurrence from direct simulations. Eur. J. Environ. Civil Eng. 13(2), 187–202 (2009)Google Scholar
  17. 17.
    Thom R.: Stabilité Structurelle et Morphogénèse. Interéditions Paris Publ, Paris (1972)Google Scholar
  18. 18.
    Vardoulakis I., Goldscheider M., Gudehus G.: Formation of shear bands in sand bodies as a bifurcation problem. Int. J. Numer. Anal. Meth. Geomech. 2(n°2), 99–128 (1978)CrossRefGoogle Scholar
  19. 19.
    Vardoulakis I.: Shear band inclination and shear modulus of sand in biaxial tests. Int. J. Numer. Anal. Meth. Geomech. 4(2), 103–119 (1980)zbMATHCrossRefGoogle Scholar
  20. 20.
    Vardoulakis I., Sulem J.: Bifurcation Analysis in Geomechanics. Chapman & Hall Publisher, London (1995)Google Scholar
  21. 21.
    Wang Y., Alonso-Marroquin F.: A finite deformation method for discrete modeling, particle rotation and parameter calibration. Granular Matter 11(5), 331–343 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • François Nicot
    • 1
    Email author
  • Nejib Hadda
    • 1
  • Franck Bourrier
    • 1
  • Luc Sibille
    • 2
  • Félix Darve
    • 3
  1. 1.CEMAGREFGrenobleFrance
  2. 2.Institut de Recherche en Génie Civil et Mécanique, Université de Nantes, ECN-CNRSNantesFrance
  3. 3.UJF-INPG-CNRS, Laboratoire Sols Solides Structures RisquesGrenobleFrance

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