# Experimental Study on Anisotropic Mechanical Characteristics of Shale under Triaxial Loading
## 4 Analysis of Anisotropic Mechanical Characteristics of Shale
### Compressive Deformation Parameter Anisotropy of Shale
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Bedding Angle \(\theta\) (\({}^{\circ}\))**} & \multicolumn{5}{c}{**Confining Pressure \(\sigma_{3}\) (MPa)**} \\ \cline{2-6}  & **0** & **10** & **20** & **30** & **40** \\ \hline
0 & 0.940 & 0.974 & 0.985 & 0.994 & 0.975 \\
30 & 0.810 & 0.923 & 0.986 & 0.996 & 0.973 \\
45 & 0.895 & 0.977 & 0.984 & 0.989 & 0.985 \\
60 & 0.726 & 0.854 & 1.007 & 1.012 & 1.002 \\
90 & 0.919 & 0.872 & 1.003 & 0.996 & 0.999 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The ratio of \(E_{\theta}\) to \(E_{50}\) of shale samples under different confining pressures. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Bedding Angle \(\theta\) (\({}^{\circ}\))**} & \multicolumn{2}{c}{**Confining Pressure \(\sigma_{3}\) (MPa)**} & \multirow{2}{*}{**Elastic Modulus \(E_{\theta}\) (GPa)**} & \multicolumn{2}{c}{**Poisson’s Ratio**} & \multicolumn{1}{c}{**50\% Strength Deformation Modulus \(E_{\theta}\) (GPa)**} \\ \hline  & 0 & 27.59 & 0.124 & 25.94 \\  & 10 & 30.95 & 0.148 & 30.14 \\
0 & 20 & 33.53 & 0.153 & 33.03 \\  & 30 & 34.38 & 0.188 & 34.19 \\  & 40 & 34.48 & 0.172 & 33.62 \\ \hline  & 0 & 27.56 & 0.127 & 22.32 \\  &  
In addition to the elastic modulus \(E_{\theta}\), Poisson's ratio is also a very important elastic constant, and the variation curves of [PERSON]'s ratio \(v_{\theta}\) and confining pressure \(\sigma_{3}\) of shale samples obtained by uniaxial and triaxial tests are shown in Figure 11, and it can be found that the variation of [PERSON]'s ratio \(v_{\theta}\) of shale with confining pressure \(\sigma_{3}\) is disordered. According to the transverse isotropic properties and the experimental scheme, the Poisson's ratio \(v_{\theta}\) of shale samples with a bedding angle of \(0^{\circ}\) measured by the chain extensometer is a constant, while the \(v_{\theta}\) measured by the samples with other bedding angles are all mixed data of \(v_{\theta}\) in different directions. Therefore, only the relationship between \(v_{\theta}\) and confining pressure \(\sigma_{3}\) for samples with a bedding angle of \(0^{\circ}\) is discussed. As shown in Figure 11, \(v_{\theta}\) and \(\sigma_{3}\) for shale samples with a bedding angle of \(0^{\circ}\) are approximately positively correlated. On the other hand, according to the data in Table 5, the variation curves of elastic modulus \(E_{\theta}\) and 50% strength deformation modulus \(E_{50}\) of shale samples with bedding angle \(\theta\) under different confining pressures \(\sigma_{3}\) are drawn, as shown in Figure 12.  
It can be seen from Figure 12 that the \(E_{\theta}\) and \(E_{50}\) of shale have similar variation trends with the bedding angle, and the anisotropic characteristics are obvious. Both the \(E_{\theta}\) and \(E_{50}\) show a changing trend of first decreasing and then increasing with the increase in the  
Figure 11: Variation of [PERSON]’s ratio \(v_{\theta}\) with the confining pressure \(\sigma_{3}\). Figure 12: Variation of shale modulus with the bedding angle \(\theta\): (**a**) Elastic modulus \(E_{\theta}\); (**b**) 50% strength deformation modulus \(E_{50}\). bedding angle \(\theta\), and the variation is gentle when the bedding angle \(\theta\) is less than 45\({}^{\circ}\), while the change is drastic when the angle is greater than 45\({}^{\circ}\). Within the designed confining pressure range in the test, the maximum values of \(E_{\theta}\) and \(E_{50}\) of shale are obtained when the bedding angle is 90\({}^{\circ}\), while the bedding angle corresponding to the minimum value is basically 30\({}^{\circ}\). In addition, the relationship between the [PERSON]'s ratio \(v_{\theta}\) of shale and the bedding angle \(\theta\) in this experiment is unclear, so no further specific analysis is made.