## 4 Study of the Fracture Development Mechanism of the Coal Samples
### Simulation Results and Analysis
When the model was loaded to Steps 76, the stress concentration at the fracture's tip led to the expansion of the fracture, and the damaged units passed through each other and eventually aggregated to form macroscopic fractures; thus, the coal sample was unstable and damaged. As shown in Figure 10b2, when the model was loaded to Steps 76-27, the lower-left corner of the model produced evident acoustic emission, and the lower-left corner presented micro-fractures. Due to the stress concentration at the end of the fractures, the fractures expanded upward along the lower-left corner as the load continued to increase. When the model was loaded to Steps 76-31, the acoustic emission penetrated the entire model at 45 degrees substantially along the lower-left corner of the fractures. When the model was loaded to Steps 76-35, the model was damaged, and the acoustic emission was concentrated at the fractures, thus forming a visible shear-damage acoustic emission band. Similarly, in this process, the gas permeability also changed with the changes in the porosity of the coal sample. When the model was loaded to Steps 76-27, the damaged units in the coal sample converged to form tiny fractures at the lower-left corner. With the continuous increase of the load, the damaged units in the coal matrix continued to unite and connect, and the porosity of the coal sample continued to increase; thus, the gas permeability gradually increased. When the model was loaded to Steps 76-35, the gas permeability reached the peak due to the formation of the through fractures. As shown in Figure 10c1, when the confining pressure of the coal sample was 4 MPa, the axial stress was still loaded from 10 MPa, 0.1 MPa was loaded per step, and a total of 104 steps were loaded. The damaged process is described as follows: When the model was loaded to Steps 35, the coal matrix produced distinct damaged units. When the model was loaded to Steps 60, the damaged units were distributed in the coal matrix. When the model was loaded to Steps 104, significant fractures occurred at the lower end of the coal sample. The coal sample underwent damage at Steps 104-20, producing an \"X\"-type fracture. As shown in Figure 10c2, the fractures first occurred in the lower part of the coal sample. When the model was loaded to Steps 62, this part began to produce a red acoustic emission circle. When the model was loaded to Steps 104, the acoustic emission was concentrated in this part, and the model was unstable and damaged; the acoustic emission finally formed an acoustic emission band along the fracture surface. In this process, the gas permeability changed with the changes in the porosity of the coal sample. When the model was loaded to Steps 104-12, the damaged units in the coal sample converged in the middle and lower part of the coal matrix, and the gas permeability began to increase. When the model was loaded to Steps 104-16, the damaged area was enlarged, and the gas permeability continued to grow. When the model was loaded to Steps 104-20, the coal sample was unstable and damaged. At this time, the corresponding gas permeability reached a peak value. The AE (acoustic emission) energy of coal samples during loading is shown in Figure 11, and the AE (acoustic emission) counts are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{\(\sigma\) = 2 MPa} & \multicolumn{2}{c}{\(\sigma\) = 3 MPa} & \multicolumn{2}{c}{\(\sigma\) = 4 MPa} \\ \hline
**Step** & **AE Counts** & **Step** & **AE Counts** & **Step** & **AE Counts** \\ \hline
34 & 105 & 73 & 78 & 101 & 5 \\
35 & 55 & 74 & 92 & 102 & 9 \\
36 & 160 & 75 & 142 & 103 & 26 \\
37 & 12,071 & 76 & 17,225 & 104 & 18,401 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Counts of acoustic emission. Figure 11: Acoustic emission (AE) energy diagram of coal samples. (**a**) Acoustic emission energy change at \(\sigma\) = 2 MPa; (**b**) acoustic emission energy change at \(\sigma\) = 3 MPa; (**c**) acoustic emission energy change at \(\sigma\) = 4 MPa.