## 3 Simulation Results and Analysis
### Triaxial Loading Conditions  
#### 3.2.1 Mechanical Properties  
Figure 11a illustrates the influence of different confining pressures and bedding angles on the compressive strength of shale. Across varying confining pressures, the trend in compressive strength is consistent with that observed in uniaxial compression tests. Regardless of the confining pressure, the compressive strength is highest when the bedding is parallel to the loading axis and lowest when the bedding is inclined. As the bedding angle increases, the compressive strength exhibits a \"U\"-shaped trend, first decreasing and then increasing, demonstrating significant bedding effects and anisotropy. Furthermore, as the confining pressure increases, the compressive strength shows a noticeable increase. At a confining pressure of 22.5  
significant at a bedding angle of 0\({}^{\circ}\) and gradually diminishes as the bedding angle increases. At a bedding angle of 90\({}^{\circ}\), the peak strain changes minimally across different confining pressures. This behavior arises because the bedding has a greater capacity for deformation, and high confining pressures can somewhat suppress bedding deformation. When the bedding angle is 90\({}^{\circ}\), the confining pressure acts perpendicular to the bedding plane, resulting in a higher peak strain. As the bedding angle increases, the suppressive effect of the confining pressure diminishes. When the bedding is vertical (0\({}^{\circ}\)), the confining pressure's impact on the bedding plane is minimal, leading to a more pronounced anisotropy in the peak strain.  
The relationship between the maximum principal stress \(\sigma_{1}\) and the minimum principal stress \(\sigma_{3}\) can be expressed using the Mohr-Coulomb criterion as follows:  
\[\sigma_{1}=\frac{1+\sin\varphi}{1-\sin\varphi}\sigma_{3}+\frac{2c\cos\varphi}{ 1-\sin\varphi} \tag{10}\]  
where \(\varphi\) represents the angle of internal friction, and \(c\) denotes the cohesion.  
The cohesion \(c\) and internal friction angle \(\varphi\) of shale can be calculated using the linear fitting curve of compressive strength based on Equation (10) to evaluate the material's shear performance. Figure 11(a) depicts the linear fitting curves of compressive strength for different bedding angles under triaxial conditions. The correlation coefficients exceed 0.98 for all cases, indicating a strong linear fit. The shear strength parameters of shale at various bedding angles are obtained by substituting the slope and intercept of the linear expressions into Equation (10). Figure 11(b) presents the cohesion and internal friction angle calculated using the Mohr-Coulomb criterion. The results reveal significant differences  
Figure 11: Mechanical parameters under different bedding angles and confining pressure. (**a**) Compressive strength; (**b**) Elastic modulus; (**c**) Peak strain.  
in the shear strength parameters across bedding angles, primarily due to variations in the orientation of the weak bedding plane relative to the axial force. These differences result in anisotropic mechanical properties and distinct failure mechanisms. Notably, at a bedding angle of 30\({}^{\circ}\), the cohesion is only 50.94 MPa, significantly lower than at other angles. This behavior is attributed to the weak bonding within the bedding plane, which has a reduced capacity to resist shear stress and is prone to shear slip failure during loading.