## 3 SHPB Test Results of the Prefabricated Fractured Sandstone Specimens
### Dynamic Stress-Strain Curve of Prefabricated Fractured Sandstone Specimens  
Compression tests were conducted on sandstone specimens, including intact specimens and five groups with varying prefabricated crack thicknesses; the physical and dynamic parameters of the fractured sandstone specimens are shown in Table 1.  
From Table 1, it is clear that the discrete dynamic parameters of the specimen were relatively good. The average strain rate of the fractured sandstone specimens fluctuated slightly, but the overall change was not significant; the reason for this fluctuation in strain rate may be due to errors that occurred during the operation of the equipment. Typical dynamic stress-strain curves were drawn, as shown in Figure 5.  
It can be seen from Figure 5 that the dynamic stress-strain curve of the intact sandstone specimen is located above those of the prefabricated fractured sandstone specimens, and the changes are similar, which can be divided into three stages. The first is the elastic stage. In this stage, the dynamic stress-strain curve rises linearly and obeys Hooke's law. The \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Crack** \\ **Thickness** \\ **/mm** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Test Piece** \\ **Number** \\ **\end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Volume** \\ _/\(\times\)10-3 \\ **cm** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Physical Parameters** \\ **Quality** \\ **/\(\times\)**10-3 \\ **cm** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Effective** \\ **Volume** \\ **/g** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Dynamic** \\ **Density** \\ **/cm** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Dynamic** \\ **Compressive** \\ **Strain** **/\(\times\)**10-3 \\ **Strength/MPa** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Dynamic** \\ **Modulus of** \\ **Elasticity/GPa** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Average** \\ **Strain Rate** \\ \end{tabular} } \\ \hline \multirow{4}{*}{0} & PJ23-16 & 98.20 & 273.67 & 2.8 & 98.20 & 103.23 & 5.78 & 46.05 & 89.8 \\  & PJ23-17 & 98.65 & 275.77 & 2.8 & 98.65 & 97.72 & 5.47 & 47.50 & 84.5 \\  & PJ23-18 & 98.36 & 273.62 & 2.8 & 98.36 & 96.56 & 5.27 & 50.28 & 89.3 \\ \hline \multirow{4}{*}{1.5} & PJ23-01 & 98.99 & 272.56 & 2.8 & 97.69 & 84.57 & 4.25 & 38.33 & 86.7 \\  & PJ23-02 & 98.70 & 270.59 & 2.7 & 97.39 & 91.20 & 3.81 & 30.62 & 91.7 \\  & PJ23-03 & 99.23 & 268.72 & 2.7 & 97.92 & 87.72 & 4.52 & 36.08 & 86.6 \\ \hline \multirow{4}{*}{2.0} & PJ23-04 & 98.31 & 270.30 & 2.7 & 96.35 & 73.46 & 3.21 & 30.50 & 88.7 \\  & PJ23-05 & 98.59 & 266.92 & 2.7 & 96.63 & 78.48 & 3.76 & 30.96 & 85.9 \\  & PJ23-06 & 98.55 & 261.90 & 2.7 & 96.59 & 77.24 & 3.54 & 34.33 & 92.9 \\ \hline \multirow{4}{*}{2.5} & PJ23-07 & 98.78 & 269.84 & 2.7 & 96.33 & 73.96 & 3.28 & 23.51 & 85.1 \\  & PJ23-08 & 98.88 & 262.79 & 2.7 & 96.43 & 71.58 & 3.48 & 25.43 & 84.7 \\ \cline{1-1}  & PJ23-09 & 98.69 & 257.02 & 2.6 & 96.24 & 78.14 & 3.58 & 20.19 & 87.3 \\ \hline \multirow{4}{*}{3.0} & PJ23-10 & 98.26 & 258.98 & 2.6 & 95.65 & 64.45 & 3.30 & 18.12 & 91.2 \\ \cline{1-1}  & PJ23-11 & 98.86 & 265.23 & 2.7 & 96.24 & 67.53 & 3.27 & 19.95 & 90.1 \\ \cline{1-1}  & PJ23-12 & 98.07 & 246.60 & 2.7 & 95.46 & 60.86 & 3.16 & 16.55 & 88.0 \\ \hline \multirow{4}{*}{3.5} & PJ23-13 & 98.11 & 264.47 & 2.7 & 95.06 & 58.68 & 2.81 & 13.93 & 93.7 \\ \cline{1-1}  & PJ23-14 & 98.14 & 259.78 & 2.6 & 95.09 & 50.49 & 2.18 & 12.35 & 86.0 \\ \cline{1-1}  & PJ23-15 & 98.54 & 264.44 & 2.7 & 95.50 & 61.46 & 2.97 & 11.56 & 93.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dynamic parameters of fractured sandstone specimens. stress concentration zone at the tip of the prefabricated crack begins to crack and gradually expands. The second is the plastic stage, in which the dynamic stress-strain curve is convex. As the stress increases, the slope of the curve gradually decreases to 0.