## 3 Results and Analysis
### Failure Characteristics of Lamellar Shale  
Figure 9 shows the failure characteristics of the lamellar shale samples after compression tests. It indicates that the failure of lamellar shale is controlled by the stress and the axial direction--lamina angle (\(\beta\)), showing a variety of failure modes. For example, under the confining pressure of 0 MPa, the sample with \(\beta\) = 0\({}^{\circ}\) mainly exhibits tension failure along the lamina (Figure 9a), while the sample with \(\beta\) = 90\({}^{\circ}\) exhibits shear failure with a certain angle to the lamina plane (Figure 9b). Under the confining pressure of 30 MPa, the sample with \(\beta\) = 0\({}^{\circ}\) has composite failures, constituted by tension failure (tension cracks) along the lamina (blue line in Figure 9c) and shear failure (shear cracks) at a certain angle relative to the lamina (red line in Figure 9c), while the sample with \(\beta\) = 90\({}^{\circ}\) exhibits shear failure at a certain angle relative to the lamina (Figure 9d).  
Previous studies indicate that the failure mode of bedding shale under high confining pressure is inclined shear failure [39]. In this paper, the reason for the composite failure of the lamellar shale sample with \(\beta\) = 0\({}^{\circ}\) under high confining pressure may be due to the sand-shale lamellar structure with weaker mechanical properties. In addition, the weak cementation between the lamina and the shale matrix has a large number of fractures near the lamellar structure [40], so there is also a tension failure along the lamellar structure. Thus, the lamellar shale sample with \(\beta\) = 0\({}^{\circ}\) after triaxial compression test under high confining pressure forms a complex composite failure mode. The failure mode of the lamellar shale sample with \(\beta\) = 30\({}^{\circ}\) is similar to that of bedding shale, both of which are shear slip failure along the lamina plane/bedding plane [39], as shown in Figure 9e. This is because of that the rock sample tends to fail at the angles of 30\({}^{\circ}\)-45\({}^{\circ}\) relative to axial stress under the compression test condition [32], especially for the lamellar shale after hydration, for which the clay minerals hydration can highly decrease the cohesive force and frictional force in clay minerals layers. This would be why the compressive strength of lamellar shale is lowest for the sample with \(\beta\) = 30\({}^{\circ}\), as mentioned in Sections 3.2 and 3.3.  
Figure 9: Shale samples after compression tests and schematic diagram of fractures: **(a)** the dry sample with an axial direction—lamina angle of 0\({}^{\circ}\) after uniaxial compression test; **(b)** the dry sample with an axial direction—lamina angle of 90\({}^{\circ}\) after uniaxial compression test; **(c)** the sample hydrated in distilled water at 80 \({}^{\circ}\)C for 48 h with an axial direction—lamina angle of 0\({}^{\circ}\) after triaxial compression test under confining pressure of 30 MPa; **(d)** the samples hydrated in distilled water at 80 \({}^{\circ}\)C for 48 h with an axial direction—lamina angle of 90\({}^{\circ}\) after triaxial compression test under confining pressure of 30 MPa; **(e)** the sample hydrated in distilled water at 80 \({}^{\circ}\)C for 48 h with an axial direction—lamina angle of 30\({}^{\circ}\) after triaxial compression test under confining pressure of 30 MPa. The blue line indicates the failure line along the lamina, the red line indicates the failure line intersected with the lamina.