## 3 Dynamic Performance Analysis
### Dynamic Stress-Strain Curve  
The typical dynamic relationships of the SHPB test following the dry and wet cycling of sandstone ring samples with different inner diameters are shown in Figure 5.  
It can be seen in Figure 5 that the dynamic stress-dynamic strain curve of the sandstone ring specimen following the dry-wet cycle gradually became placid with the increase in the inner diameter, the peak point of the curve gradually moved to the lower right, and the slope of the pre-peak curve increased. With the increase in the inner diameter of the ring, the dynamic peak stress decreased and the dynamic peak strain increased.  
The relationship between the dynamic compressive strength of the sandstone ring specimen and its inner diameter following the dry-wet cycle is shown in Figure 5.  
It can be seen in Figure 5 that the dynamic compressive strength of the sandstone ring specimen decreased gradually with the increase in its inner diameter following the dry-wet cycle. The dynamic compressive strength of the complete specimen was 94.78 MPa, which decreased to 60.70 MPa when the inner diameter was 25 mm, and the decrease was measured at 35.96%. The dynamic compressive strength had an exponential negative correlation with the inner diameter change curve, and the correlation was obvious. The fitting relationship is shown in Equation (1).  
\[\sigma_{0}(\mathrm{d})=95.7770\mathrm{e}^{-0.0190\mathrm{d}}\ (\mathrm{R}^{2}=0.9887) \tag{1}\]  
where \(\sigma_{0}\) is the dynamic compressive strength.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Inside** \\ **Diameter** \\ **/mm** \\ \end{tabular} & \begin{tabular}{c} **Specimen** \\ **Number** \\ **/MPa** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **Pressing** \\ **/MPa** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **Peak Value** \\ _I\(\times\)10\({}^{-3}\)_ \\ **/MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Dynamic** \\ **Elastic** \\ **Modulus** \\ **/GPa** \\ \end{tabular} &
\begin{tabular}{c} **Average** \\ **Strain Rate** \\ **/s\({}^{-1}\)** \\ \end{tabular} \\ \hline \multirow{3}{*}{0} & PJ06-01 & 94.27 & 2.29 & 42.55 & 172 \\  & PJ06-02 & 96.34 & 2.27 & 44.49 & 174 \\  & PJ06-03 & 93.74 & 2.35 & 45.47 & 176 \\ \hline \multirow{3}{*}{5} & PJ06-04 & 89.62 & 2.57 & 41.55 & 178 \\  & PJ06-05 & 87.46 & 2.52 & 42.93 & 178 \\  & PJ06-06 & 90.97 & 2.38 & 42.68 & 182 \\ \hline \multirow{3}{*}{10} & PJ06-07 & 81.30 & 2.79 & 39.74 & 188 \\  & PJ06-08 & 79.93 & 2.73 & 38.20 & 185 \\  & PJ06-09 & 78.58 & 2.80 & 39.42 & 186 \\ \hline \multirow{3}{*}{15} & PJ06-10 & 71.30 & 3.34 & 36.45 & 195 \\  & PJ06-11 & 70.79 & 3.12 & 37.70 & 195 \\  & PJ06-12 & 69.12 & 3.19 & 37.75 & 198 \\ \hline \multirow{3}{*}{20} & PJ06-13 & 65.87 & 3.52 & 31.78 & 202 \\  & PJ06-14 & 67.53 & 3.87 & 32.84 & 204 \\  & PJ06-15 & 65.97 & 3.67 & 31.68 & 205 \\ \hline \multirow{3}{*}{25} & PJ06-16 & 60.23 & 4.18 & 26.80 & 211 \\  & PJ06-17 & 62.34 & 4.32 & 26.55 & 211 \\ \cline{1-1}  & PJ06-18 & 59.52 & 4.19 & 25.75 & 209 \\ \hline \hline \end{tabular}
\end{table}
Table 2: SHPB dynamic test data of the sandstone ring specimens.  
With the increase in the inner diameter of the sandstone ring specimen, the wall thickness decreased, and the effective bearing area of the specimen decreased, making this area more prone to being unstable and destroyed. At the same time, the increase in the inner diameter augments the contact surface between the specimen and the water and weakens its dynamic performance. The dry-wet cycle weakened the dynamic compressive performance of the sandstone ring, and the dynamic compressive strength decreased with the increase in the inner diameter of the specimen.