## 2 Conventional Triaxial Compression Test of Sandstone
### Analysis of Test Results  
The stress-strain curves of the sandstone samples obtained from the uniaxial and triaxial compression tests are shown in Figure 2.  
The basic mechanical parameters of the sandstone obtained from the experimental results are listed in Table 1, and the cohesion (\(c\)) and internal friction angle (\(\varphi\)) are obtained according to the Mohr-Coulomb criterion. The relationships between the confining pressure and the sandstone peak strength, peak axial strain, peak circumferential strain, peak volumetric strain, elastic modulus, and [PERSON]'s ratio are shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\sigma_{3}\)/MPa & \(\sigma_{c}\)/MPa & **Peak Axial Strain/\%** & **Peak Circumferential Strain/\%** & **Peak Volumetric Strain/\%** & _E_/GPa & \(\mu\) & _c_/MPa & \(\varphi\)/(\({}^{\circ}\)) \\ \hline
0 & 52.32 & 0.56 & \(-\)0.22 & 0.12 & 9.33 & 0.18 & & \\
5 & 78.53 & 0.57 & \(-\)0.18 & 0.21 & 14.94 & 0.20 & & \\
10 & 92.70 & 0.65 & \(-\)0.22 & 0.21 & 15.02 & 0.21 & & \\
15 & 106.88 & 0.74 & \(-\)0.19 & 0.36 & 16.19 & 0.19 & & \\
20 & 130.68 & 0.79 & \(-\)0.21 & 0.37 & 18.06 & 0.19 & & \\
25 & 147.81 & 0.91 & \(-\)0.51 & \(-\)0.11 & 18.62 & 0.21 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical parameters of sandstone.  
Figure 1: Sandstone specimens and test system.  
Figure 2: Stress–strain curve.  
Table 1 and Figure 3 show that the peak strength, peak axial strain, and elastic modulus of sandstone increase significantly with an increase in the confining pressure. When the confining pressure increases from 0 to 25 MPa, the peak strength, peak axial strain, and elastic modulus increase by 182.5%, 62.5%, and 99.6%, respectively, indicating that confining pressure can effectively improve the strength and deformation resistance of sandstone. When the confining pressure is between 0-20 MPa, the peak circumferential and volumetric strains of the sandstone change slightly, whereas when the confining pressure is 25 MPa, both significantly decrease. This is because, under high confining pressure, the side of the sandstone sample is greatly restricted, resulting in a smaller circumferential and volumetric deformation during its failure. As the confining pressure increases, the Poisson's ratio fluctuates between 0.18 and 0.21, indicating a small correlation between the two.  
The failure modes of the sandstone under different confining pressures are shown in Figure 4. As shown in the figure, the failure mode of the sandstone varied under different confining pressures. When the confining pressures are 0 and 5 MPa, the failure mode is vertical compression failure, and the failure surface is parallel to the axial direction of the sandstone; when the confining pressures are 10, 15, 20, and 25 MPa, the failure mode is an oblique shear failure. This is because a higher confining pressure suppresses the expansion of vertical cracks, and the shear stress on the inclined section of sandstone under a triaxial high-stress state is greater than its shear strength, ultimately leading to oblique shear failure along the weak plane.  
Figure 4 also shows that when the confining pressures are 0 and 5 MPa, the fracture angle of the sandstone is approximately 90\({}^{\circ}\), and under other confining conditions, it is approximately 45\({}^{\circ}\). This indicates that the fracture angle of sandstone under high confining pressure was smaller than that under low confining pressure. This is because when the confining pressure is high, sandstone failure requires a greater load, and the internal friction effect of sandstone is more evident, which suppresses the fracture of sandstone and reduces the fracture angle.  
Figure 4: Failure modes of sandstone.  
Figure 3: Relationship between mechanical parameters and confining pressure: (**a**) axial stress and strain, (**b**) elastic modulus and Poisson’s ratio.