## 3 Experimental Results
### Dynamic Mechanical Characteristics of Fine Sandstone under Different Strain Rates  
Table 3 shows the initial design parameters of impact experiments of fine sandstone at different temperatures and different bullet incident velocities, including the preset air chamber pressure and axial static load. The sample density was between 2.30 and 2.43 g/cm\({}^{3}\). The strain rate was between 49.1 s\({}^{-1}\) and 140.9 s\({}^{-1}\). And, when the dynamic load experiment was carried out, the bullet preset growth gradient was 0.5 m/s. The actual bullet incident velocity is shown in the column of Table 4 (bullet incidence velocity). Figure 5: The dynamic stress–strain behavior of fine sandstone. Figure 6: Correlation between fine sandstone’s dynamic stress, dynamic strain and axial static load. Figure 7 shows the characteristics of fine sandstone's dynamic stress and strain response at different temperatures and different strain rate. When the temperature were 18 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, 60 \({}^{\circ}\)C, 80 \({}^{\circ}\)C, and 100 \({}^{\circ}\)C, the increase in strain rate led to an increase in the fine sandstone's dynamic stress and strain. For example, when the temperature was 18 \({}^{\circ}\)C, the fine sandstone's peak dynamic stress increased from 35.14 MPa to 110.91 MPa. When the temperature was 40 \({}^{\circ}\)C, the peak dynamic stress increased from 54.86 MPa to 87.93 MPa. When the temperature was 60 \({}^{\circ}\)C, the peak dynamic stress increased from 54.57 MPa to 118.72 MPa. When the temperature was 80 \({}^{\circ}\)C, the peak dynamic stress increased from 34.47 MPa to 50.42 MPa. When the temperature was 100 \({}^{\circ}\)C, the peak dynamic stress increased from 87.53 MPa to 136.24 MPa. According to the macro change response of the stress-strain curve, under the different strain rates, fine sandstone quickly enters the elastic deformation period, and the stress increases rapidly. Once the stress peak has been reached, the stress changes in two states: (1) the stress decreases rapidly and rebounds directly; (2) the stress slowly drops to a low value (Figure 7b (107.5 s\({}^{-1}\)), Figure 7c (140.9 s\({}^{-1}\)), Figure 7d (87.9 s\({}^{-1}\)) and Figure 7e (114.4 s\({}^{-1}\))), the phenomenon of stress rebound occurs, and the ratio of the stress inflection point value to its peak value is 60.7%, 88.7%, 78.6%, and 65.1%, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temperature/\({}^{\circ}\)C** & **E\({}_{\text{1}}\)/GPa** & **E\({}_{\text{2}}\)/GPa** & **F\({}_{\text{0}}\)** & **m** \\ \hline
18 & 9.12 & 17.43 & 85.33 & 1.0 \\
40 & 9.57 & 15.95 & 74.25 & 2.0 \\
60 & 9.86 & 19.87 & 67.89 & 1.0 \\
80 & 9.41 & 26.77 & 82.46 & 1.2 \\
100 & 9.24 & 24.12 & 143.60 & 1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of dynamic stress–strain one-dimensional constitutive model of fine sandstone at different temperatures. \begin{table}
\begin{tabular}{c 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** \\ \({}^{F}\)**C** \\ \end{tabular}  & \begin{tabular}{c} **Density** \\ **/g/cm\({}^{3}\)** \\ \end{tabular}  & \ \begin{tabular}{c} **Bullet Incidence** \\ **Velocity/m/s** \\ \end{tabular}  & \begin{tabular}{c} **Srain Rate/s\({}^{-1}\)** \\ \end{tabular}  \\ \hline S11 & 0.06 & & & 2.31 & 1.31 & 53.1 \\ S12 & 0.07 & & 18 & 2.40 & 2.79 & 101.5 \\ S13 & 0.07 & & & 2.42 & 3.28 & 118.1 \\ S14 & 0.07 & & & 2.37 & 4.97 & 137.7 \\ \hline S15 & 0.06 & & & 2.38 & 1.02 & 47.1 \\ S16 & 0.07 & 3. We statistically analyzed the relationship between fine sandstone's peak stress, peak strain, and bullet incident velocity at the same temperature and different bullet incident velocities, as shown in Figure 8. The fine sandstone's peak stress and strain were positively correlated with the bullet incident velocity under different temperatures.