## 3 Experimental Results
### Dynamic Mechanical Characteristics of Fine Sandstone under Different Axial Static Load  
Table 2 shows the initial design parameters of impact experiments of fine sandstone under different axial compression, including the preset air chamber pressure and axial static load. The sample density is between 2.34 and 2.41 g/cm\({}^{3}\), and the bullet incident velocity is between 1.86 and 2.05 m/s during dynamic load test.  
Figure 5 characterizes the fine sandstone's dynamic stress and strain response under various seismic and axial static load scenarios. From the figure, it can be seen that under the condition that other influencing factors remain unchanged, an increase in axial static load will lead to an increasing trend in the fine sandstone's dynamic stress. When the axial static load increases from 1.0 MPa to 9.0 MPa, the fine sandstone's dynamic peak stress increases from 57.25 MPa to 80.01 MPa, with an increase in dynamic peak stress ranging from 0.87 to 6.17. During the compaction stage, the fine sandstone's dynamic tangent elastic modulus is significantly higher than that of the linear elastic stage. From the dynamic stress and strain response of single sample, as the loading process progresses, the dynamic stress of fine sandstone exhibits two phenomena: (1) under low axial pressure conditions, the fine sandstone's dynamic stress of increases to its peak value, leading to stress rebound (Figure 5 (S7)); (2) under high axial pressure conditions, the fine sandstone's dynamic stress increases to its peak, then decreases, and then exhibits stress rebound (Figure 5 (S6, S8-S10)).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample No.** & \begin{tabular}{c} **Air Chamber** \\ **Pressure/MPa** \\ \end{tabular} & \begin{tabular}{c} **Axial Static** \\ **Load/MPa** \\ \end{tabular} & \begin{tabular}{c} **Temperature** \\ \(f^{\circ}\)**C** \\ \end{tabular} & \
\begin{tabular}{c} **Density** \\ **/g/cm\({}^{3}\)** \\ \end{tabular} &
\begin{tabular}{c} **Bullet** \\ **Incidence** \\ **Velocity/m/s** \\ \end{tabular} \\ \hline S6 & 0.07 & 1.0 & 40 & 2.36 & 1.98 \\ S7 & 0.07 & 3.0 & 40 & 2.41 & 1.86 \\ S8 & 0.07 & 5.0 & 40 & 2.40 & 2.02 \\ S9 & 0.07 & 7.0 & 40 & 2.39 & 2.02 \\ S10 & 0.07 & 9.0 & 40 & 2.34 & 2.05 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental parameter design of dynamic experiment of fine sandstone under different axial static load.  
Figure 4: Correlation between fine sandstone’s dynamic stress, dynamic strain, and temperature.  
The fitting relationship between the axial static load, dynamic maximal stress, and maximum strain of fine sandstone is shown in Figure 6. The fine sandstone's dynamic peak stress, peak strain, and axial static load are positively correlated, and the fitting relationship follows a cubic polynomial fitting relationship, as shown in Formulas (3) and (4). The dynamic peak stress increase gradient of fine sandstone ranges from 0.87 to 6.17, and the gradient of the stress rise increases in proportion to the axial static load. The bearing capacity of fine sandstone is significantly improved by axial pressure.  
\[\sigma=0.0986T^{3}-1.1166T^{2}+5.0365T+53.244\ \ R^{2}=0.99 \tag{3}\]  
\[\varepsilon=1E-05T^{3}-0.0002T^{2}+0.0011T+0.0022\ \ R^{2}=0.99 \tag{4}\]