Numerical and experimental investigation of the anisotropic tensile behavior of layered rocks in 3D space under Brazilian test conditions

Brazilian disc (BD) testing is a typical method for measuring the indirect tensile strength of rock materials. Both experimental and theoretical studies involving BD testing of anisotropic rocks typically focus on the influence of the 2D bedding effect, where a specimen is parallel to the bedding planes, whereas the influence of the 3D bedding effect combining both the orientation and loading angle has rarely been investigated. Therefore, in this study, BD tests considering the 3D bedding effect were conducted on layered Longmaxi shale, and 3D BD models of layered shale were established using 3D globally embedded cohesive elements with zero thickness. The numerical results were compared to testing results. The 3D BD numerical model was then applied to simulate Asan gneiss and Silurian silty slate to verify the applicability. Finally, the influence of the 3D bedding effect on both the apparent tensile strength (ATS) and failure modes was analyzed. We also considered the influence of the spacing of bedding planes and bedding strength. The results indicated that the numerical results for both the ATS and failure modes were in good agreement with the test results with a maximum error of 17.8% for the ATS. The applicability of the developed 3D BD numerical model to different layered rocks was confirmed by the numerical results for both Asan gneiss and Silurian silty slate. Strong dependencies of the ATS and failure modes on both the orientation (α) and loading (β) angles were observed in the layered Longmaxi shale. The normalized ATS for various orientation and loading angles achieved high values of 3.15 and 2.90, respectively, indicating that the influence of the orientation angle is slightly stronger than that of the loading angle. The Longmaxi shale exhibited a distinct tensile failure mode at α = 0° @ β = 0–15°, α = 0° @ β = 75–90°, and α = 90°, but a more complicated mixed mode of both tensile and shear failure was observed under other conditions. The contribution of shear failure increased significantly at 0° < α < 90° compared to α = 0°. The spacing of the bedding planes had a limited influence on the ATS and failure modes, but the bedding strength had a significant influence. There may be a linear relationship between bedding strength and the spatial distribution parameter of the critical plane approach criterion.