# Experimental Study on Anisotropic Mechanical Characteristics of Shale under Triaxial Loading
## 4 Analysis of Anisotropic Mechanical Characteristics of Shale
### Compressive Strength Anisotropy of Shale  
The compressive strength of all the shale samples with different bedding structures obtained from uniaxial and triaxial compression tests are sorted out, and the average values of the compressive strength of shale samples under the same loading condition are used as the compressive strength \(\sigma_{\rm cs}\) to carry out anisotropic analysis; meanwhile, the relationship curves of compressive strength \(\sigma_{\rm cs}\) and bedding angle \(\theta\) with confining pressure \(\sigma_{3}\) are drawn, as shown in Table 2 and Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Bedding Angle \(\theta\) (\({}^{\circ}\))**} & \multirow{2}{*}{\begin{tabular}{c} **Confining Pressure \(\sigma_{3}\)** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **IDs of Shale** \\ **Samples** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Compressive Strength** \\ **of Each Shale Samples** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Average Values of** \\ **Compressive Strength** \\ **(MPa)** \\ \end{tabular} } \\ \hline \multirow{6}{*}{0} & 0 & A\({}_{1}\), A\({}_{2}\), A\({}_{3}\) & 180.0, 165.7, 168.5 & 171.4 \\  & 10 & A\({}_{4}\), A\({}_{5}\), A\({}_{6}\) & 203.1, 219.4, 196.4 & 206.3 \\  & 20 & A\({}_{7}\), A\({}_{8}\), A\({}_{9}\) & 227.4, 237.3, 221.1 & 228.6 \\  & 30 & A\({}_{10}\), A\({}_{11}\), A\({}_{12}\) & 244.7, 255.5, 240.2 & 246.8 \\  & 40 & A\({}_{13}\), A\({}_{14}\), A\({}_{15}\) & 281.4, 270.8, 285.1 & 279.1 \\ \hline \multirow{6}{*}{30} & 0 & B\({}_{1}\), B\({}_{2}\), B\({}_{3}\) & 112.8, 106.3, 119.9 & 113.0 \\  & 10 & B\({}_{7}\), B\({}_{8}\), B\({}_{9}\) & 142.5, 146.3, 157.9 & 148.9 \\  & 20 & B\({}_{7}\), B\({}_{8}\), B\({}_{9}\) & 170.4, 177.5, 170.2 & 172.7 \\  & 30 & B\({}_{10}\), B\({}_{11}\), B\({}_{12}\) & 191.4, 200.8, 187.7 & 193.3 \\  & 40 & B\({}_{13}\), B\({}_{14}\), B\({}_{15}\) & 199.4, 241.5, 199.3 & 213.4 \\ \hline \multirow{6}{*}{45} & 0 & C\({}_{1}\), C\({}_{2}\), C\({}_{3}\) & 93.7, 102.9, 99.2 & 98.6 \\  & 10 & C\({}_{4}\), C\({}_{5}\), C\({}_{6}\) & 153.0, 150.1, 155.3 & 152.8 \\  & 20 & C\({}_{7}\), C\({}_{8}\), C\({}_{9}\) & 143.2, 140.8, 139.9 & 141.3 \\  & 30 & C\({}_{10}\), C\({}_{11}\), C\({}_{12}\) & 163.8, 161.7, 166.2 & 163.9 \\  & 40 & C\({}_{13}\), C\({}_{14}\), C\({}_{15}\) & 184.2, 190.3, 177.8 & 184.1 \\ \hline \multirow{6}{*}{60} & 0 & D\({}_{1}\), D\({}_{2}\), D\({}_{3}\) & 65.0, 59.4, 58.6 & 61.0 \\  & 10 & D\({}_{4}\), D\({}_{5}\), D\({}_{6}\) & 74.8, 79.1, 77.1 & 77.0 \\  & 20 & D\({}_{7}\), D\({}_{8}\), D\({}_{9}\) & 104.0, 107.1, 106.6 & 105.9 \\  & 30 & D\({}_{10}\), D\({}_{11}\), D\({}_{12}\) & 110.1, 105.4, 114.8 & 110.1 \\  & 40 & D\({}_{13}\), D\({}_{14}\), D\({}_{15}\) & 130.5, 130.8, 130.2 & 130.5 \\ \hline \multirow{6}{*}{90} & 0 & E\({}_{1}\), E\({}_{2}\), E\({}_{3}\) & 117.4, 115.8, 119.9 & 117.7 \\  & 10 & E\({}_{4}\), E\({}_{5}\), E\({}_{6}\) & 234.3, 216.6, 225.3 & 225.4 \\ \cline{1-1}  & 20 & E\({}_{7}\), E\({}_{8}\), E\({}_{9}\) & 200.9, 203.8, 210.0 & 204.9 \\ \cline{1-1}  & 30 & E\({}_{10}\), E\({}_{11}\), E\({}_{12}\) & 221.6, 228.0, 210.4 & 220.0 \\ \cline{1-1}  & 40 & E\({}_{13}\), E\({}_{14}\), E\({}_{15}\) & 291.6, 307.4, 302.5 & 300.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Compressive strength of shale under different confining pressures. As shown in Table 2 and Figure 6a, the compressive strength \(\sigma_{\text{cs}}\) of the shale samples exhibits significant anisotropy, and \(\sigma_{\text{cs}}\) under the same confining pressure \(\sigma_{3}\) shows a \"U-shaped\" trend of first decreasing and then increasing with the increase in the bedding angle \(\theta\). Secondly, the minimum value of \(\sigma_{\text{cs}}\) of shale samples with or without confining pressure \(\sigma_{3}\) is achieved at the bedding angle of \(60^{\circ}\), which is consistent with the experimental results of other researchers [9,17,19].