13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- XFEM modelling of degradation-permeability coupling in complex geomaterials B. Sonon1, B. François1, A.P.S. Selvadurai2, T.J. Massart1,* 1 Building, Architecture and Town Planning CP 194/2, Université Libre de Bruxelles (ULB), Avenue F.D. Roosevelt 50, 1050 Brussels, Belgium 2 Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, Canada, H3A 2K6 * Corresponding author: thmassar@ulb.ac.be Abstract The theory of poromechanics is widely used to examine problems in the environmental geosciences. In classical poromechanics, the material parameters such as the elastic stiffness or the permeability are assumed to remain constant. The porous fabric can, however, experience micromechanical processes that can lead to alterations in the stiffness and fluid transport characteristics. Experiments on rocks indicate permeability increases even at deviatoric stress states well below peak stress levels, which can contribute to errors in predicting the progress of transient phenomena. This paper presents a multi-scale approach for investigating permeability evolution in a heterogeneous geomaterial. The complex microstructure of geomaterials is modelled using a level set-based extended finite element description (XFEM) that allows uncoupling the meshing operations from the presence of the fine scale material interfaces. A dedicated tool for the generation of representative volume elements based on similar concepts is exploited. Fine scale plastic constitutive laws are used to model the progressive mechanical degradation under stress. The local (fine-scale) permeability evolution can then be coupled to the local plastic dissipation quantities. These fine-scale developments are combined with a versatile computational homogenization technique to upscale mechanical and transport properties corresponding to heterogeneous microstructures. Using this procedure, the effect of progressive degradation on the averaged permeability properties of geomaterials is investigated. These procedures are illustrated by estimating the variation of permeability with the confining pressures and deviatoric stresses applied in triaxial testing. Keywords Mechanical Degradation, Degradation-induced permeability, Level Set functions, XFEM modelling 1. Introduction Heterogeneous geomaterials possess complex microstructures. The computational homogenisation of such microstructures requires specific tools to take this complexity into account, both from the point of view of the availability of representative volume elements, and from the point of view of the discretisation technique. This paper presents a level set-based extended finite element description (XFEM), that allows uncoupling the meshing operations from the modelling of the fine scale material interfaces. A dedicated tool for the generation of representative volume elements based on similar concepts is also exploited. Fine-scale plastic constitutive laws are used to model the progressive mechanical degradation under stress. The local (fine-scale) permeability evolution is assumed to be coupled to the local plastic dissipation. Using this procedure, the effect of progressive degradation on the averaged permeability properties of geomaterials is investigated. These procedures are illustrated by estimating the alteration of permeability with the confining pressures and deviatoric stresses applied in triaxial testing. 2. Computational homogenisation of mechanical and transport properties The upscaling framework described in detail in [1] can be used to extract the homogenised behaviour of a heterogeneous material, starting from its microstructure. The essential features of this approach are summarized below. For completeness, a detailed derivation of the averaging relationships can be found in [1] and references therein.
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