|Abstract: ||Shales are highly anisotropic in their mechanical behaviour. The strength of anisotropic shales depends not only on the magnitude of the principal stresses, but also on the bedding plane orientations relative to the principal stresses. In this study, the failure of shales are investigated using triaxial compression and extension tests, while the role of intermediate stress (sigma2) on the strength of anisotropic shale is evaluated using data from new triaxial extension tests, as well as data from the literature.
Triaxial compression and extension experiments were made on two organic-rich shales, at different confining stresses and bedding angles (Beta). Examination of post-failure computed tomography (CT) and thin section images for high strength anisotropy shale show that, for large and small values of Beta, the fracture plane follows the angle that is predicted by the Coulomb’s failure criterion for an isotropic material. In the range of angles of roughly 35deg.<Beta<75deg, failure occurs along the bedding plane. Both of these results are consistent with the assumptions of Jaeger’s plane of weakness (JPW) model. However, there exists a transition regime of loading angles lying between about 10deg. and 35deg., wherein the failure surface follows an irregular path that may jump between the bedding plane and the plane defined by the Coulomb criterion. In this regime, the strength of the rock is lower than the strength predicted by JPW model. For the shale with low strength anisotropy, the failure plane angles agree with the predictions of JPW model.
The triaxial compression experimental data on shales and several data sets from the literature were fit with both Pariseau’s continuum model for the failure of transversely isotropic materials and JPW model. Comparison of both models show that the Pariseau model provided a better fit for ten of the twelve rocks, whereas the JPW model provided a better fit only for two low strength anisotropy shales. It was noted that all the rocks with a strength anisotropy ratio (SAR) > 2 were fit more closely by the Pariseau model, whereas both shales that were a better fit with the JPW model had SAR < 2. Pariseau’s model is also more robust and accurate than Jaeger’s model when using a reduced numbers of data (i.e., data collected at fewer confining stresses and/or fewer angles).
Finally, both the JPW model and Pariseau’s model was applied in the true-triaxial stress regime, in which sigma1 > sigma2 > sigma3. When analysed with Mogi’s experimental data on Chichibu Schist, both models could predict failure under true-triaxial stress conditions. Mogi’s data and the triaxial extension experiments for the two shales shows that an increase in the intermediate stress sigma2 increases the intact rock strength, whereas weak plane failure depends not only on intermediate stress sigma2, but also on bedding plane angle Beta and foliation direction (omega).|