## 4 Analysis of the Crushing Morphology and Energy of the Sample
### Energy Analysis  
According to the waveform signals collected in the SHPB dynamic-static combination tester, the incident energy, reflected energy, transmitted energy, and absorbed energy of the specimen under different axial pressures were calculated using Equation (6). The calculated energy data of the specimen are shown in Table 3:  
\[E_{\text{I}}(t) =E_{\text{0}}C_{\text{0}}A_{\text{0}}\int_{0}^{t}e_{\text{I}}^{2}(t )dt \tag{6}\] \[E_{\text{R}}(t) =E_{\text{0}}C_{\text{0}}A_{\text{0}}\int_{0}^{t}e_{\text{R}}^{2}(t )dt\] \[E_{\text{T}}(t) =E_{\text{0}}C_{\text{0}}A_{\text{0}}\int_{0}^{t}e_{\text{T}}^{2}(t )dt\] \[E_{\text{D}}(t) =E_{\text{I}}(t)-E_{\text{R}}(t)-E_{\text{T}}(t)\]  
where \(E_{\text{I}}(t)\), \(E_{\text{R}}(t)\), \(E_{\text{T}}(t)\), and \(E_{\text{D}}(t)\) are the incident, reflected, transmitted, and absorbed energy of the sample.  
Table 3 shows that the incident energy remains within a certain range when the loading rate is constant. The variation in the reflected, transmitted, and absorbed energy of the sample with axial pressure in the SHPB test is shown in Figure 13.  
Figure 13 shows that the absorbed energy of sandstone specimens increases with an increase in axial pressure. This result indicates that as axial pressure increases, the energy absorption in the sandstone specimens also increases, promoting the formation of more cracks and resulting in smaller fragments and greater fragmentation. The transmission energy of the sample decreases gradually with an increase in axial pressure, possibly because the increase in axial pressure makes the original cracks in the sample expand and extend, accompanied by the formation of new cracks, which reduces the effective area available for the transmission of the transmission wave. This phenomenon reduces the transmission wave through the specimen, decreasing the transmission energy.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Axial Pressure** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Specimen** \\ **Number** \\ \end{tabular} & \begin{tabular}{c} **Incident** \\ **Energy (J)** \\ \end{tabular} & \begin{tabular}{c} **Reflected** \\ **Energy (J)** \\ \end{tabular} & \
\begin{tabular}{c} **Transmission** \\ **Energy (J)** \\ \end{tabular} &
\begin{tabular}{c} **Absorbed** \\ **Energy (J)** \\ \end{tabular} \\ \hline \multirow{2}{*}{0} & PJ12-01 & 61.91 & 21.57 & 31.18 & 9.16 \\  & PJ12-02 & 62.15 & 23.64 & 27.21 & 11.30 \\ \hline \multirow{2}{*}{0.5} & PJ12-03 & 64.32 & 24.85 & 29.24 & 10.24 \\  & PJ12-04 & 62.41 & 22.43 & 27.88 & 12.09 \\ \hline \multirow{2}{*}{1.0} & PJ12-05 & 59.88 & 22.86 & 26.41 & 10.62 \\  & PJ12-06 & 64.60 & 24.99 & 26.30 & 13.31 \\ \hline \multirow{2}{*}{1.5} & PJ12-07 & 65.95 & 25.18 & 27.62 & 13.15 \\  & PJ12-08 & 60.93 & 25.73 & 22.67 & 12.52 \\ \hline \multirow{2}{*}{2.0} & PJ12-09 & 67.87 & 28.97 & 24.27 & 14.63 \\  & PJ12-10 & 61.73 & 26.45 & 23.17 & 12.10 \\ \hline \multirow{2}{*}{2.5} & PJ12-11 & 64.36 & 25.65 & 22.78 & 15.93 \\  & PJ12-12 & 70.81 & 30.50 & 25.11 & 15.20 \\ \hline \multirow{2}{*}{3.0} & PJ12-13 & 70.74 & 29.43 & 23.84 & 17.47 \\  & PJ12-14 & 65.54 & 27.28 & 21.13 & 17.13 \\ \hline \multirow{2}{*}{3.5} & PJ12-15 & 73.21 & 32.02 & 22.53 & 18.67 \\  & PJ12-16 & 65.09 & 27.29 & 20.51 & 17.29 \\ \hline \multirow{2}{*}{4.0} & PJ12-17 & 70.80 & 32.78 & 19.78 & 18.24 \\  & PJ12-18 & 69.06 & 31.05 & 18.66 & 19.35 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Energy data of sandstone specimens under different axial pressures.