Estimation of elastic properties and failure strength of layered rocks with a multi-scale damage approach

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Layered rocks (LR) are composed of intact rock matrix (IRM) and various oriented rough weakness planes (e.g., fractures, bedding planes, and foliations). New microcracks can also be created and propagate in IRM during subsequent loading history. Effects of induced microcracks and pre-existing weakness planes on macroscopic mechanical behavior of LR are usually investigated separately. The novelty of the present work is to develop an original multi-scale damage approach to estimate the macroscopic anisotropic elastic properties and failure strength of LR. Two material scales are taken into consideration. At the macroscopic laboratory scale, a set of parallel rough weakness planes are embedded in the IRM, while at the microscopic scale, the IRM contains an elastic solid phase and randomly distributed microcracks. By means of a two-step homogenization technique, the effective elastic properties of LR is first determined. A multi-scale friction-damage model (MFDM) is further developed, by accounting for isotropic growth of closed microcracks and anisotropic evolution of rough weakness planes at two different scales. Subsequently, with the concept of critical damage, an analytical macroscopic strength criterion incorporating failure mechanisms of IRM and weakness planes is derived as an inherent result of the MFDM. Compared with experimental data, it shows that the macroscopic anisotropic elastic properties of LR are well estimated. However, the derived macroscopic strength criterion only provides a qualitative prediction of the anisotropic failure strength of LR for different orientations of weakness planes in conventional triaxial compression tests. By taking advantage of the fabric tensor approach, the strength criterion is further improved to take into account interaction between weakness planes and microcracks. The improved strength criterion is able to quantitatively capture the failure property of LR.