## 2 Experimental Materials and Methods
### Anisotropy in the Failure Pattern  
Shale failure is closely related to its matrix and bedding structures, confining pressure level, and loading and unloading stress paths. The failure patterns of shale under triaxial monotonic loading and triaxial incremental cyclic loading and unloading are shown in Figures 10 and 11, respectively. Figure 10: Shale failure under triaxial monotonic loading. Figure 9: Variation curve showing changes in the ratio between plastic strain and total strain as a result of the bedding inclination angle. Few fracture surfaces penetrated the shale under triaxial monotonic loading, and all show significant anisotropy. For 0\({}^{\circ}\) shale, failure occurs via tensile failure through the bedding planes, mixed tensile-shear failure through the bedding planes, and shear failure through the bedding planes resulting from two intersecting shear rupture surfaces at confining pressures of 10, 20, and 30 MPa, respectively. At 30\({}^{\circ}\), shale failure occurs via tensile failure, mixed tensile shear failure, and shear failure through the bedding planes at confining pressures of 10, 20, and 30 MPa, respectively. At 45\({}^{\circ}\), shale failure occurs via shear slip failure along the bedding planes, shear protrusion failure along the bedding planes, and shear failure through the bedding planes at confining pressures of 10, 20, and 30 MPa are, respectively. At 60\({}^{\circ}\), shale failure occurs via shear slip failure along the bedding plane, with a shear crack along the bedding plane and a secondary crack extending from the main crack at all confining pressures. At 90\({}^{\circ}\), failure occurs via tensile failure along the bedding plane, with the axial stress loading direction parallel to the direction of the bedding planes at 10 MPa and 20 MPa. In these cases, the increasing axial stress leads to an increase in the circumferential displacement, resulting in lateral expansion stress and the formation of tensile cracks along the bedding plane. However, at 30 MPa, failure occurs via mixed tensile-shear failure that is composed of tensile failure along the laminar surface and shear failure through the bedding plane. The results differed considerably under triaxial incremental cyclic loading and unloading, with large numbers of fracture surfaces penetrating the shale and strong anisotropy in the failure patterns. Failure was similar to that observed under triaxial monotonic loading at \(\theta\) = 0\({}^{\circ}\) and 90\({}^{\circ}\) for all confining pressures. However, these results differed for different \(\theta\), with 30\({}^{\circ}\) leading to tensile-shear mixed failure that penetrated the bedding  
Figure 11: Failure patterns of shale specimens under triaxial incremental cyclic loading and unloading. plane at all confining pressures; 45\({}^{\circ}\) resulting in Y-shaped shear failure through the bedding planes, two shear cracks through the bedding planes, and tensile-shear mixed failure composed of multiple tensile and shear cracks through the bedding planes at 10, 20, and 30 MPa, respectively; and 60\({}^{\circ}\) leading to shear failure through the bedding planes at all confining pressures, with the number of shear cracks increasing as the confining pressure increased. Comparing the two loading conditions, the failure patterns of shale are similar when \(\theta\) is 0\({}^{\circ}\), 30\({}^{\circ}\), and 90\({}^{\circ}\), while a significant difference is observed in the failure patterns of shale when \(\theta\) is 45\({}^{\circ}\) and 60\({}^{\circ}\), manifested by a lower degree of involvement of the bedding planes in shale crack evolution under incremental cyclic loading and unloading conditions. In addition, the number of macroscopic fracture surfaces and secondary cracks that were easily and partially connected along the bedding planes at the upper end of the shale increased significantly, and the degree of fragmentation was more severe under triaxial incremental cyclic loading and unloading conditions than it was under triaxial monotonic loading.