## 4 Energy Evolution
### Kinetic Energy at the Failure Stage  
The important feature of the violent fracture of the rock material was the release of energy. It has been proposed by [PERSON] et al. (2019) that the kinetic energy could represent the energy released at the time of rock fracture.  
As shown in Table 4, as the rock/coal strength increases, the kinetic energy of the CRC specimen also increased. This result indicated that a higher strength CRC specimen contributes more to the problem of energy release and then leads to violent fracture because these specimens will accumulate large amounts of elastic strain energy prior to failure. This is the most fundamental reason why the violent fractures of coal pillars with hard roofs are much greater than those located in weak roofs.  
To further reveal the dependence of the kinetic energy on the rock/coal strength, the variation in the kinetic energy with the rock/coal strength is shown in Figure 13. The \(X\)-axis is the ratio of the rock strength to coal strength. In Figure 13, it can be observed that for the CRC specimens with the same coal section, the greater the difference in strength between the rock and coal is, the larger the kinetic energy is. Generally, the rock section with a higher strength has a greater ability to store elastic energy. When the CRC specimens with a higher strength rock section were loaded, the rock section accumulated more elastic energy than the coal section stored. Once the CRC specimens fail due to loading, some elastic energy stored in the rock section is released into the coal section, and the coal section is broken. Therefore, energy release was due to the difference in strength between the rock and coal.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \begin{tabular}{c} **Specimen** \\ **Label** \\ \end{tabular} & \begin{tabular}{c} \(\mathbf{U_{ec}}\) \\ **(kJ-m-3)** \\ \end{tabular} & **Average** & \
\begin{tabular}{c} \(\mathbf{U_{ed}}\) \\ **(kJ-m-3)** \\ \end{tabular} & **Average** &
\begin{tabular}{c} \(\mathbf{U_{r}}\) \\ **(kJ-m-3)** \\ \end{tabular} & **Average** \\ \hline \multirow{3}{*}{\(\text{NYM}_{1}\)} & \(\text{NYM}_{1}\)-3 & 21.54 & & 11.25 & & 10.29 & \\  & \(\text{NYM}_{1}\)-4 & 14.75 & 25.53 & 8.82 & 13.24 & 5.93 & 12.29 \\  & \(\text{NYM}_{1}\)-5 & 40.29 & & 19.65 & & 20.64 & \\ \hline \multirow{3}{*}{\(\text{NYM}_{2}\)} & \(\text{NYM}_{2}\)-6 & 32.29 & & 11.25 & & 21.04 & \\  & \(\text{NYM}_{2}\)-7 & 32.98 & 33.71 & 12.05 & 11.14 & 20.93 & 22.57 \\  & \(\text{NYM}_{2}\)-8 & 35.86 & & 10.12 & & 25.74 & \\ \hline \multirow{3}{*}{\(\text{XSM}_{1}\)} & \(\text{XSM}_{1}\)-3 & 50.07 & & 8.25 & & 41.82 & \\  & \(\text{XSM}_{1}\)-4 & 58.15 & 51.82 & 9.62 & 8.44 & 48.53 & 43.38 \\  & \(\text{XSM}_{1}\)-5 & 47.25 & & 7.45 & & 39.80 & \\ \hline \multirow{3}{*}{\(\text{XSM}_{2}\)} & \(\text{XSM}_{2}\)-6 & 45.67 & & 7.52 & & 38.15 & \\  & \(\text{XSM}_{2}\)-7 & 62.51 & 54.95 & 7.86 & 7.80 & 54.65 & 47.15 \\  & \(\text{XSM}_{2}\)-8 & 56.65 & & 8.02 & & 48.63 & \\ \hline \multirow{3}{*}{\(\text{ZSM}_{1}\)} & \(\text{ZSM}_{1}\)-3 & 58.57 & & 6.32 & & 52.25 & \\  & \(\text{ZSM}_{1}\)-4 & 61.08 & 60.69 & 6.55 & 6.62 & 54.53 & 54.07 \\  & \(\text{ZSM}_{1}\)-5 & 62.41 & & 6.98 & & 55.43 & \\ \hline \multirow{3}{*}{\(\text{ZSM}_{2}\)} & \(\text{ZSM}_{2}\)-6 & 54.13 & & 6.05 & & 48.08 & \\  & \(\text{ZSM}_{2}\)-7 & 79.56 & 68.05 & 5.02 & 5.52 & 74.54 & 62.52 \\  & \(\text{ZSM}_{2}\)-8 & 70.45 & & 5.5 & & 64.95 & \\ \hline \multirow{3}{*}{\(\text{FSM}_{1}\)} & \(\text{FSM}_{1}\)-3 & 58.17 & & 3.25 & & 54.92 & \\  & \(\text{FSM}_{1}\)-4 & 88.08 & 76.33 & 3.55 & 3.28 & 84.53 & 73.05 \\ \cline{1-1}  & \(\text{FSM}_{1}\)-5 & 82.74 & & 3.03 & & 79.71 & \\ \hline \multirow{3}{*}{\(\text{FSM}_{2}\)} & \(\text{FSM}_{2}\)-6 & 77.88 & & 3.11 & & 74.78 & \\ \cline{1-1}  & \(\text{FSM}_{2}\)-7 & 88.88 & 82.34 & 2.12 & 2.57 & 86.78 & 79.77 \\ \cline{1-1}  & \(\text{FSM}_{2}\)-8 & 80.26 & & 2.51 & & 77.76 & \\ \hline \hline \end{tabular}
\end{table}
Table 4: The kinetic energy of the CRC specimens.