# 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  
Modulus and Poisson's ratio are the main parameters used to characterize the compressive deformation characteristics of rock, and the elastic modulus \(E_{\Theta}\), 50% strength deformation modulus \(E_{50}\), and Poisson's ratio \(v_{\Theta}\) of shale with different bedding angles are discussed, respectively. The average values of shale compressive deformation parameters measured by uniaxial and triaxial compression tests are shown in Table 5.  
According to Table 5, the values of elastic modulus \(E_{\Theta}\) and 50% strength deformation modulus \(E_{50}\) are close when the confining pressure \(\sigma_{3}\) is no less than 20 MPa, but there are some differences when the confining pressure is lower than 20 MPa. The reason for this phenomenon is that the compaction stage of shale stress-strain curve under low confining pressure conditions has different effects on the calculation process of these two moduli. The \(E_{\Theta}\) is calculated based on the straight section of the stress-strain curve, which reflects the deformation of rock in the linear elastic stage. However, the \(E_{50}\) reflects the average deformation of rock in the early compaction stage, and its value will be affected by the compaction stage, so is slightly lower than \(E_{\Theta}\). The ratio of elastic modulus \(E_{\Theta}\) to the 50% strength deformation modulus \(E_{50}\) of shale samples under different confining pressures are listed in Table 6, and it can be found that with the increase in the confining pressure applied synchronously in the first stage of the triaxial compression test, the value of \(E_{\Theta}/E_{50}\) rises and approaches 1, indicating that the compaction stage of the shale samples is gradually shortened. At the same time, when the confining pressure \(\sigma_{3}\) is greater than 20 MPa, the values of \(E_{\Theta}/E_{50}\) of shale samples at five bedding angles are all close to 1, showing that shale samples can be fully compacted under the action of confining pressure \(\sigma_{3}\). Figure 8: Variation of shale cohesion \(c\) and internal friction angle \(\varphi\) with bedding angle \(\theta\). \begin{table}
\begin{tabular}{c c c} \hline
**Bedding Angle \(\theta\) (\({}^{\circ}\))** & **Cohesion \(c\) (MPa)** & **Internal Friction Angle \(\varphi\) (\({}^{\circ}\))** \\ \hline
0 & 54.784 & 25.979 \\
30 & 38.064 & 24.874 \\
45 & 33.661 & 21.388 \\
60 & 23.796 & 15.382 \\
90 & 27.649 & 38.415 \\ \hline \end{tabular}
\end{table} 
Table 4: Parameters in Mohr–Coulomb strength criterion of shale samples. On the other hand, according to Table 5, it can be found that with the increase in confining pressure, the elastic modulus \(E_{\theta}\) and 50% strength deformation modulus \(E_{50}\) both increase, and the changes are similar. Therefore, only the variation of elastic modulus \(E_{\theta}\) with confining pressure \(\sigma_{3}\) is analyzed, and the change curve of elastic modulus \(E_{\theta}\) with respect to confining pressure \(\sigma_{3}\) is sorted out, as shown in Figure 9.  
It can be found from Figure 9 that the elastic modulus \(E_{\theta}\) with confining pressure \(\sigma_{3}\) show an approximate linear growth relationship, so the \(E_{\theta}\) and \(\sigma_{3}\) are linearly fitted, and the obtained linear fitting parameters and fitting index \(R\)-square are listed in Table 7, and the linear fitting equation is shown in Equation (3). \[E_{\theta}=C\sigma_{3}+D \tag{3}\]  
where \(C\) and \(D\) represent the sensitivity of shale elastic modulus \(E_{\theta}\) to confining pressure \(\sigma_{3}\) and the uniaxial compressive elastic modulus of shale at this bedding angle.