# Energy Evolution Analysis of Coal Fracture Damage Process Based on Digital Image Processing
## 3 Analysis of Results
### Analysis of Energy Evolution during Coal Fracture Damage
#### 3.3.2 Analysis of Acoustic Emission Characteristics during Coal Fracture Damage  
In the numerical model, a fracture element represents an acoustic emission event, and the energy released by the fracture of the element is the acoustic emission energy. During the loading process, the accumulation of damage of the unit causes the overall damage of the macroscopic rock [47]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\alpha\)(\({}^{\circ}\)) & **Elastic Energy** & **Impact Energy** & **Effective Impact** & **Residual Energy** \\  & **Index** & **Index** & **Energy Index** & **Index** \\ \hline
0 & 5.95 & 36.27 & 15.80 & 14.80 \\
15 & 11.21 & 16.30 & 10.11 & 9.11 \\
30 & 9.06 & 20.36 & 10.77 & 9.77 \\
45 & 27.14 & 3.11 & 2.32 & 1.32 \\
60 & 23.13 & 2.10 & 1.81 & 0.81 \\
75 & 20.19 & 3.84 & 3.41 & 2.41 \\
90 & 7.03 & 12.66 & 7.33 & 6.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Energy characteristic index of coal at different azimuth angles. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\alpha\)(\({}^{\circ}\)) & **\(E_{1}\)/KJ\({}^{\bullet}\)m\({}^{-3}\)** & **\(E_{2}\)/KJ\({}^{\bullet}\)m\({}^{-3}\)** & **\(E_{3}\)/KJ\({}^{\bullet}\)m\({}^{-3}\)** & **\(E_{4}\)/KJ\({}^{\bullet}\)m\({}^{-3}\)** \\ \hline
0 & 67.26 & 29.31 & 44.69 & 38.26 \\
15 & 58.47 & 36.28 & 38.71 & 35.54 \\
30 & 64.29 & 34.00 & 42.40 & 38.19 \\
45 & 26.74 & 19.95 & 17.62 & 17.39 \\
60 & 19.76 & 17.09 & 13.19 & 12.72 \\
75 & 34.25 & 30.41 & 22.85 & 21.77 \\
90 & 44.33 & 25.67 & 29.65 & 25.96 \\ \hline \hline \end{tabular} \({}^{\star}E_{1}\) is the input energy density before the peak; \(E_{2}\) is the performance density of accumulation projectile before peak; \(E_{3}\) is the input energy density at 80% strength; \(E_{4}\) is the accumulated elastic performance density at 80% strength.  
\end{table} 
Table 3: Characteristic energy parameters of coal at different azimuth angles. Figure 9: Characteristic energy fitting curves of coal rocks with different azimuths. The relationship between coal stress, acoustic emission energy, cumulative acoustic emission and acoustic emission count and loading steps under diverse azimuth is shown in Figures 11 and 12. Calcite veins have a substantial effect on the energy evolution in the process of coal damage. With the increase of azimuth, the energy evolution law changes, which can be roughly divided into two categories: the energy evolution law under low dip angle (0\({}^{\circ}\), 15\({}^{\circ}\) and 30\({}^{\circ}\)) and the energy evolution law under high dip angle (45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\) and 90\({}^{\circ}\)). The specific analysis of energy evolution in the coal failure process under different azimuth angles is as follows:  
* At low dip angles (0\({}^{\circ}\), 15\({}^{\circ}\) and 30\({}^{\circ}\)), the compressive strength of coal is large, the stress required for fracture damage is large, the number of loading steps is large and more energy is released during coal and rock failure. When \(\alpha=0^{\circ}\), the maximum acoustic emission energy release is 149.9 J. From the AE counts, cumulative AE and acoustic emission energy curves, it is clear that the energy accumulation during coal rock destruction is slow when the calcite veins are at low angles. When the energy accumulation reaches its maximum, a large amount of accumulated energy is suddenly released and complete destruction of the coal rock occurs. * At high dip angles (45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\) and 90\({}^{\circ}\)), the compressive strength of coal is small, the stress required for fracture damage is small, the number of loading steps is small and the energy released by coal failure is less. When \(\alpha=60^{\circ}\), the acoustic emission energy release is the smallest, which is 22.9 J. Compared with the 0\({}^{\circ}\) sample, the release energy decreases by 84.7%. The AE counts, cumulative AE and acoustic emission energy curves exhibited significant jumps.