Failure Mechanics of Geomaterials

  • Florent Prunier
  • François Nicot
  • Richard Wan
  • Jérôme Duriez
  • Félix Darve
Reference work entry


Geomaterials represent an important class of dissipative materials whose mechanical behavior is pressure, density, and fabric dependent. This constitutive characteristic together with the discrete particulate nature of the material leads to the manifestation of a rich variety of failure modes whose precise understanding is elusive within standard failure theories. The present chapter attempts to clarify this issue by invoking plasticity/damage phenomena in geomaterials and exploits their non-associated character in relation to rate-independent irreversible strains. The second-order work criterion provides a basic framework within which failure can be systematically treated as a divergence instability that leads to various forms, including localized and diffuse modes. This new interpretation considers the existence of a bifurcation domain and so-called instability cones whose generators denote the range of loading directions in stress space along which the material response is potentially unstable. As additional important characteristics, macroscopic failure is found to occur with an outburst of kinetic energy with the proper load control parameter in place, as demonstrated in discrete element computations. Finally, the failure analysis of in situ boundary value problems as in a rock and a soil slope is presented using the second-order work.


Discrete Element Method Triaxial Test Rock Slope Rock Joint Stress Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. S.C. Bandis, A.C. Lumsden, N.R. Barton, Fundamentals of rock joint deformation. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 20(6), 249–268 (1983)CrossRefGoogle Scholar
  2. A.W. Bishop, Principle of effective stress. Teknisk. Ukeblad. 106(39), 859–863 (1959)Google Scholar
  3. P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  4. A. Daouadji, H. Al Gali, F. Darve, A. Zeghloul, Instability in granular materials, an experimental evidence of diffuse mode of failure for loose sands. J. Eng. Mech. 136(5), 575–588 (2010)CrossRefGoogle Scholar
  5. A. Daouadji, F. Darve, H. Al-Gali, P.Y. Hicher, F. Laouafa, S. Lignon, F. Nicot, R. Nova, M. Pinheiro, F. Prunier, L. Sibille, R. Wan, Diffuse failure in geomaterials: experiments, theory and modeling. Int. J. Numer. Anal. Methods Geomech. 35(16), 1731–1773 (2011)CrossRefGoogle Scholar
  6. F. Darve, S. Labanieh, Incremental constitutive law for sands and clays: simulations of monotonic and cyclic tests. Int. J. Numer. Anal. Methods Geomech. 6(2), 243–275 (1982)CrossRefMATHGoogle Scholar
  7. F. Darve, E. Flavigny, M. Meghachou, Yield surfaces and principle of superposition revisited by incrementally non-linear constitutive relations. Int. J. Plast. 11(8), 927–948 (1995)CrossRefMATHGoogle Scholar
  8. F. Darve, G. Servant, F. Laouafa, H.D.V. Khoa, Failure in geomaterials: continuous and discrete analyses. Comp. Methods Appl. Mech. Eng. 193, 3057–3085 (2004)CrossRefMATHGoogle Scholar
  9. F. Darve, L. Sibille, A. Daouadji, F. Nicot, Bifurcations in granular media: macro- and micro-mechanics approaches. Comptes Rendus Acad. Sci. Mec. 335, 496–515 (2007)CrossRefMATHGoogle Scholar
  10. J. Duriez, F. Darve, F.V. Donzé, A discrete modeling-based constitutive relation for infilled rock joints. Int. J. Rock Mech. Min. Sci. 48(3), 458–468 (2011a)CrossRefGoogle Scholar
  11. J. Duriez, F. Darve, F.V. Donzé, Incrementally non-linear plasticity applied to rock joint modeling. Int. J. Numer. Anal. Methods Geomech. (2011b). doi:10.1002/nag.1105Google Scholar
  12. J. Duriez, F. Darve, F.V. Donzé, F. Nicot, Material stability analysis of rock joints. Int. J. Numer. Anal. Methods Geomech. (2012). doi:10.1002/nag.2149Google Scholar
  13. G. Gudehus, A comparison of some constitutive laws for soils under radially loading symmetric loading unloading, in Third International Conference on Numerical Methods in Geomechanics, 1979, edn Balkema, pp. 1309–1323Google Scholar
  14. R. Hill, A general theory of uniqueness and stability in elasto-plastic solids. J. Mech. Phys. Solids 6, 236–249 (1958)CrossRefMATHGoogle Scholar
  15. P.V. Lade, Static instability and liquefaction of loose fine sandy slopes. J. Geotech. Eng. Div. Am. Soc. Civ. Eng. 118(1), 51–71 (1992)CrossRefGoogle Scholar
  16. F. Laouafa, F. Prunier, A. Daouadji, H. Al-Gali, F. Darve, Stability in geomechanics, experimental and numerical analyses. Int. J. Numer. Anal. Methods Geomech. 35(2), 112–139 (2011)CrossRefMATHGoogle Scholar
  17. J. Lerbet, M. Aldowadji, N. Challamel, F. Nicot, F. Prunier, F. Darve, P-positive definite matrices and stability of nonconservative systems. J. Appl. Math. Mech. ZAMM 92(5), 409–422 (2012)CrossRefMATHGoogle Scholar
  18. S. Lignon, F. Laouafa, F. Prunier, F. Darve, H.D.V. Khoa, Hydro-mechanical modelling of landslides with a material instability criterion. Geotechnique 59(6), 513–524 (2009)CrossRefGoogle Scholar
  19. A.E.H. Love, A Treatise of Mathematical Theory of Elasticity (Cambridge University Press, Cambridge, 1927)MATHGoogle Scholar
  20. M.M. Mehrabadi, M. Oda, S. Nemat-Nasser, On statistical description of stress and fabric in granular materials. Int. J. Numer. Anal. Methods Geomech. 6, 95–108 (1982)MathSciNetCrossRefMATHGoogle Scholar
  21. V. Merrien-Soukatchoff, J. Duriez, M. Gasc, F. Darve, F.V. Donzé, Mechanical Stability Analyses of Fractured Rock Slopes, in Rockfall Engineering, ed. by S. Lambert, F. Nicot (Wiley/ISTE, New York/London, 2011)Google Scholar
  22. P. Mollema, M. Antonellini, Compaction bands: a structural analog for anti-mode I cracks in aeolian sandstone. Tectonophysics 267, 209–228 (1996)CrossRefGoogle Scholar
  23. F. Nicot, F. Darve, A micro-mechanical investigation of bifurcation in granular materials. Int. J. Solids Struct. 44, 6630–6652 (2007)CrossRefMATHGoogle Scholar
  24. F. Nicot, F. Darve, Diffuse and localized failure modes: two competing mechanisms. Int. J. Numer. Anal. Methods Geomech. 35(5), 586–601 (2011)CrossRefMATHGoogle Scholar
  25. F. Nicot, F. Darve, H.D.V. Khoa, Bifurcation and second-order work in geomaterials. Int. J. Numer. Anal. Methods Geomech. 31, 1007–1032 (2007)CrossRefMATHGoogle Scholar
  26. F. Nicot, L. Sibille, F. Darve, Bifurcation in granular materials: an attempt at a unified framework. Int. J. Solids Struct. 46, 3938–3947 (2009)CrossRefMATHGoogle Scholar
  27. F. Nicot, N. Challamel, J. Lerbet, F. Prunier, F. Darve, Bifurcation and generalized mixed loading conditions in geomaterials. Int. J. Numer. Anal. Methods Geomech. 35(13), 1409–1431 (2011)Google Scholar
  28. F. Nicot, L. Sibille, F. Darve, Failure in rate-independent granular materials as a bifurcation toward a dynamic regime. Int. J. Plast. 29, 136–154 (2012a)CrossRefGoogle Scholar
  29. F. Nicot, N. Challamel, J. Lerbet, F. Prunier, F. Darve, Some insights into structure instability and the second-order work criterion. Int. J. Solids Struct. 49(1), 132–142 (2012b)CrossRefGoogle Scholar
  30. F. Nicot, N. Hadda, F. Bourrier, L. Sibille, R. Wan, F. Darve, Inertia effects as a possible missing link between micro and macro second-order work in granular media. Int. J. Solids Struct. 49(10), 1252–1258 (2012c)CrossRefGoogle Scholar
  31. F. Prunier, F. Nicot, F. Darve, F. Laouafa, S. Lignon, 3D multi scale bifurcation analysis of granular media. J. Eng. Mech. ASCE 135(6), 493–509 (2009a)CrossRefGoogle Scholar
  32. F. Prunier, F. Laouafa, S. Lignon, F. Darve, Bifurcation modeling in geomaterials: from the second-order work criterion to spectral analyses. Int. J. Numer. Anal. Methods Geomech. 33, 1169–1202 (2009b)CrossRefMATHGoogle Scholar
  33. F. Prunier, F. Laouafa, F. Darve, 3D bifurcation analysis in geomaterials, investigation of the second order work criterion. Eur. J. Env. Civ. Eng. 13(2), 135–147 (2009c)CrossRefGoogle Scholar
  34. L.A. Richards, Capillary conduction of liquids through porous mediums. Physics 1(5), 318–333 (1931)CrossRefMATHGoogle Scholar
  35. SGI (Studio Geotechnico Italiano), The Petacciato landslide: geological and geotechnical data. LESSLOSS report, 2004Google Scholar
  36. L. Sibille, F.V. Donzé, F. Nicot, B. Chareyre, F. Darve, From bifurcation to failure in a granular material, a DEM analysis. Acta Geotechnica 3(1), 15–24 (2008)CrossRefGoogle Scholar
  37. H.A.M. Van-Eekelen, Isotropic yield surfaces in three dimensions for use in soil mechanics. Int. J. Numer. Anal. Methods Geomech. 4, 89–101 (1980)CrossRefMATHGoogle Scholar
  38. M.T. Van-Genuchten, A closed form for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 4, 892–898 (1980)CrossRefGoogle Scholar
  39. R.G. Wan, P.J. Guo, Stress dilatancy and fabric dependencies on sand behavior. J. Eng. Mech. ASCE 130(6), 635–645 (2004)CrossRefGoogle Scholar
  40. R.G. Wan, M. Pinheiro, A. Daouadji, M. Jrad, F. Darve, Diffuse instabilities with transition to localization in loose granular materials. Int. J. Numer. Anal. Methods Geomech. (2012). doi:10.1002/nag.2085Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Florent Prunier
    • 1
  • François Nicot
    • 2
  • Richard Wan
    • 3
  • Jérôme Duriez
    • 4
  • Félix Darve
    • 4
  1. 1.INSA de Lyon, LGCIEVilleurbanneFrance
  2. 2.IRSTEA, Geomechanics group, ETNAGrenobleFrance
  3. 3.Department of Civil EngineeringUniversity of CalgaryCalgaryCanada
  4. 4.Grenoble INP, UJFCNRSGrenobleFrance

Personalised recommendations