13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- 8. Conclusion On the basis of a limit analysis approach, we have proposed an extension of available models (devoted to the macroscopic strength of porous media). This extension concerns porous materials with a Drucker- Prager solid phase, reinforced by rigid particles. The proposed model concerns in particular, the Callovo Oxfordian clay as a composite material made up of rigid inclusions embedded in a porous clay matrix. The obtained results has been compared to the estimate of the strength recently derived by [4] on the basis of a variational non linear homogenization approach. A good accuracy of the estimate of the strength under isotropic loadings has been shown by a comparison with the results of a static (stress based) approach of the limit analysis problem. An interesting observation is that the estimates of the isotropic strength in traction or in compression do not depend on the homogenization method (limit analysis, variational method). Furthermore, the isotropic strength proves to be only slightly affected by the rigid core volume fraction. The practical implication is that the isotropic strength properties of the clay matrix and of the Callovo Oxfordian argillite are very close, irrespective of the quartz/calcite content. In contrast, a significant discrepancy between the failure envelopes is observed on the shear strength for large values of the rigid inclusions concentration. Acknowledgements The work presented in this paper was partly funded by ANDRA, the French national Agency for the management of radioactive wastes, which is gratefully acknowledged. References [1] A. Abou-Chakra Guery, F. Cormery, J.-F. Shao, D. Kondo, 2008. A micromechanical model of elasto-plastic and damage behavior of a cohesive geomaterial. Int. J. Solid. Struct., 45 (5), 1406–1429. [2] Andra, 2005. Referentiel du site meuse-haute marne. Report. [3] L. Dormieux, D. Kondo, 2010. An extension of gurson model incorporating interface stresses effects. International Journal of Engineering Science, 48(6), 575–581. [4] A.L. Gurson, 1977. Continuum theory of ductile rupture by void nucleation and growth: Part I–Yield criterion and flow rules for porous ductile media, J. Engrg. Mat. Technol. 99, 2–15. [5] J.-B. Leblond, G. Perrin, P. Suquet., 1994. Exact results and approximate models for porous viscoplastic solids. International Journal of Plasticity, 10(3):213–235. [6] S. Maghous, L. Dormieux, J. Barthelemy, 2009. Micromechanical approach to the strength properties of frictional geomaterials. European Journal of Mechanics A/Solids., 28, 179–188. [7] V. Monchiet, E. Charkaluk, D. Kondo, 2007. An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields. Comptes Rendus Mecanique., 335(1), Pages 32–41 [8] P.Ponte Castaneda, 1991. The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids, 39, 45–71. [9] J-C. Robinet, P. Sardini, D. Coelho, J-C. Parneix, D. Pret, S. Sammartino, E. Boller and S. Altmann., 2012. Effects of mineral distribution at mesoscopic scale on solute diffusion in a clay-rich rock: Example of the Callovo-Oxfordian mudstone (Bure, France). Water Resources Research, 48, W05554, doi:10.1029/2011WR011352. [10] J. Salencon, 1990. An introduction to the yield theory and its applications to soil mechanics. European Journal of Mechanics A/Solids, 9(5),477–500. [11] W.Q. Shen, L. Dormieux, D. Kondo, J.F. Shao, 2013. A closed-form three scale model for ductile rocks with a plastically compressible porous matrix, Mechanics of Materials, 59 73--86 [12] W.Q. Shen, J.F. Shao, D. Kondo, B. Gatmiri., 2012. A micro-macro model for clayey rocks with a plastic compressible porous matrix, International Journal of Plasticity, 36, 64–85
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