Poroelasticity and damage theory for saturated cracked media

  • Luc Dormieux
  • Djimedo Kondo
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 480)


First, basic results of linear homogenization applied to porous media are presented and applied in order to derive a linear poroelasticity theory for saturated cracked materials. The emphasis is put on the geometrical modelling of the cracks as well as on the cracks-induced anisotropy. The effect of interactions between cracks and the role of the spatial distribution of cracks on the poroelastic properties are also analyzed. The non linear poroelastic behavior of cracked media due to the progressive cracks closure is also investigated. The last section is devoted to damage induced by crack propagation.


Crack Closure Crack Density Stiffness Tensor Damage Criterion Macroscopic Stress 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. S. Andrieux, Y. Bamberger, and J.-J. Marigo. Un modèle de matériau microfissuré pour les roches et les bétons. J. Mech. Théor. Appl., 5(3):471–513, 1986.zbMATHGoogle Scholar
  2. M. Bouteca, D. Bary, J.-M. Piau, N. Kessler, M. Boisson, and D. Fourmaintraux. Contribution of poroelasticity to reservoir engineering: lab experiments, application to core decompression and implication in hp-ht reservoirs depletion. In Proceedings of Eurock’94, Delft, 1994. Balkema, Rotterdam.Google Scholar
  3. B. Budiansky and R. O’Connell. Elastic moduli of a cracked solid. Int. J. Solids Struct., 12:81–97, 1976.CrossRefzbMATHGoogle Scholar
  4. J.-L. Chaboche. Damage induced anisotropy: on the difficulties associated with the active/passive unilateral conditions. Int. J. Damage Mech., 2:311–329, 1992.Google Scholar
  5. V. Deudé, L. Dormieux, D. Kondo, and S. Maghous. Micromechanical approach to nonlinear poroelasticity: application to cracked rocks. J. Eng. Mech., 128:848–855, 2002a.CrossRefGoogle Scholar
  6. V. Deudé, L. Dormieux, D. Kondo, and V. Pensée. Non linear elastic properties of a mesocracked medium. C. R. Acad. Sci. Paris, série IIb, t. 330:587–592, 2002b.Google Scholar
  7. L. Dormieux, E. Lemarchand, D. Kondo, and E. Fairbairn. Elements of poromicromechanics applied to concrete. Concrete Sc. Eng. Mater. Struct., 265:31–42, 2004.Google Scholar
  8. L. Dormieux, A. Molinari, and D. Kondo. Micromechanical approach to the behavior of poroelastic materials. J. Mech. Phys. Solids, 50:2203–2231, 2002.zbMATHCrossRefGoogle Scholar
  9. J.D. Eshelby. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A, 241:376–396, 1957.zbMATHMathSciNetGoogle Scholar
  10. H. Horii and S. Nemat-Nasser. Overall moduli of solids with microcracks: load-induced anisotropy. J. Mech. Phys. Solids, 31(2):155–171, 1983.zbMATHCrossRefGoogle Scholar
  11. D. Krajcinowic. Damage mechanics. North Holland, 1996.Google Scholar
  12. M. Lion, F. Skoczylas, and B. Ledésert. Determination of the main hydraulic and poroelastic properties of a limestone from bourgogne, france. Int. J. Rock Mech. Mining Sci., to appear, 2005.Google Scholar
  13. V.A. Lubarda and D. Krajcinovic. Damage tensors and the crack density distribution. Int. J. Solids Structures, 30(20):2859–2877, 1993.zbMATHCrossRefGoogle Scholar
  14. T. Mura. Micromechanics of defects in solids, 2nd edition. Martinus Nijhoff Publ., 1987.Google Scholar
  15. S. Murakami and K. Kamiya. Constitutive and damage evolution equations in elastic-brittle materials based on irreversible thermodynamics. Int. J. Mech. Sci., 39(4), 1997.Google Scholar
  16. S. Nemat-Nasser and M. Horii. Micromechanics: overall properties of heterogeneous materials. North Holland, 1993.Google Scholar
  17. V. Pensée, D. Kondo, and L. Dormieux. Micromechanical analysis of anisotropic damage in brittle materials. J. Engng. Mech., ASCE, 128(8):889–897, 2002.CrossRefGoogle Scholar
  18. P. Ponte-Castaneda and J.R. Willis. The effect of spatial distribution on the effective behavior of composite materials and cracked media. J. Mech. Phys. Solids, 43(12):1919–1951, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  19. M. Thompson and J.R. Willis. A reformulation of the equations of anisotropic poroelasticity. J. Appl. Mech., 58:612–616, 1991.zbMATHGoogle Scholar
  20. L.J. Walpole. Elastic behavior of composite materials: theoretical foundations. Advances in Applied Mechanics, 21:169–242, 1981.zbMATHCrossRefGoogle Scholar
  21. J.R. Willis. Bounds and self consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Solids, 25:185–202, 1977.zbMATHCrossRefGoogle Scholar
  22. A. Zaoui. In P. Suquet, editor, Continuum micromechanics. Springer, 1997.Google Scholar
  23. A. Zaoui. Continuum micromechanics: survey. J. Eng. Mech., 128:808–816, 2002.CrossRefGoogle Scholar
  24. R.W. Zimmermann. Compressibility of sandstones. Elsevier, 1991.Google Scholar

Copyright information

© CISM, Udine 2005

Authors and Affiliations

  • Luc Dormieux
    • 1
  • Djimedo Kondo
    • 2
  1. 1.Ecole Nationale des Ponts et ChausséesFrance
  2. 2.Laboratoire de Mécanique de LilleLille University of TechnologyFrance

Personalised recommendations