Microstructural approach in damage modeling

A microstructural approach is proposed for the modeling of brittle rock damage. The basic idea of this approach is to model, not directly the mechanical response of the rock but the changes in crack geometry. The term `crack geometry' is used in the sense of Oda et al. (cf. Oda, M., Yamabe, T., Kamemura, 1986. A crack tensor and its relation to wave velocity anisotropy in jointed rock masses. Int. J. Rock. Mech. Min. Sci. 23 (6), 387–397). It therefore implies both a crack density and a spatial crack organization. As Kanatani, K. (1984. Stereological determination of structural anisotropy. Int. J. of Eng. Sci. 22, 531–546.) has shown, if the PL stereological parameter is known, the accumulated crack length may be calculated in any direction, which in turn makes it possible to calculate the crack induced deformation for any given stress. Hence, our approach consists in formulating some laboratory-based laws for the evolution of PL as a function of applied stress as well as the criterion for crack initiation and for macroscopic failure. Some of the laboratory tests used to elaborate and validate this approach are described in detail in the accompanying paper. The parameters of the proposed model are calculated for a granite and the results of the running simulations are in good agreement with laboratory tests.

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