## 3 Simulation Results and Analysis
### Uniaxial Loading Conditions
#### 3.1.1 Mechanical Properties  
Figure 5 illustrates the effect of bedding characteristics on the uniaxial compressive strength of shale. The results show that the compressive strength is significantly lower when the bedding is inclined compared to the \(0^{\circ}\) and \(90^{\circ}\) bedding orientations. With an  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Homogeneity** & \begin{tabular}{c} **Elastic** \\ **Modulus/GPa** \\ \end{tabular} & \begin{tabular}{c} **Compressive** \\ **Strength/MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Poisson’s Ratio** \\ \end{tabular} &
\begin{tabular}{c} **Friction Angle/\({}^{\circ}\)** \\ \end{tabular} \\ \hline Matrix & 3 & 68.756 & 710.56 & 0.25 & 36 \\ bedding & 4 & 34.378 & 340.28 & 0.2 & 24 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mesoscopic parameters of shale numerical model.  
Figure 4: Uniaxial compression test and numerical simulation results. (**a**) Stress–strain curves; (**b**) Failure modes.  
an overall decrease of 8.62%. This is primarily because the deformation resistance of the bedding plane decreases less relative to the matrix, leading to a more minor reduction in the elastic modulus. Additionally, the variation in bedding distribution at the same bedding angle causes more minor fluctuations in the elastic modulus of shale. Overall, the presence of bedding planes results in noticeable anisotropy in the elastic modulus of shale.  
Figure 7 displays the changes in the peak strain for shale at different bedding angles and distributions. Like the compressive strength variation, the peak strain follows a concave trend: low in the middle and high at both ends. When the bedding angle is 0\({}^{\circ}\) or 90\({}^{\circ}\), the peak strain is nearly the same, while for inclined bedding, failure occurs more rapidly, and the peak strain is lower. Unlike isotropic rock masses, the failure mechanism in anisotropic rock masses is distinct. For shale, the presence of weak bedding planes means that changes in the bedding orientation alter the interaction of bedding planes, leading to different instability failure modes and significantly affecting the peak strain.  
Figure 8 shows the direct tensile test results for shale with three different bedding distributions. The results reveal that the tensile strength is negatively correlated with the bedding angle. The tensile strength is highest at a 0\({}^{\circ}\) bedding angle (approximately 22.84 MPa) and lowest at a 90\({}^{\circ}\) bedding angle (15.73 MPa). The anisotropy index for tensile strength is 1.452, with the tensile strength being significantly lower than the compressive strength. The variability in the tensile strength across different bedding distributions is  
Figure 6: Elastic modulus under different bedding angles and distribution.  
Figure 7: Peak strain under different bedding angles and distribution.  
notably smaller than that for compressive strength. The difference in the tensile strength primarily arises from the bonding between the bedding and matrix. When the bedding angle is 0\({}^{\circ}\), the tensile strength is closer to the matrix strength, while at 90\({}^{\circ}\), it is closer to the bedding strength. As the bedding angle increases, bedding gradually dominates the failure process. Due to the weak bonding between bedding layers, the tensile strength decreases somewhat.