## 3 Results
### Three-Dimensional Progressive Cross-Scale Expansion Characteristics of Cracks  
Coal is formed through the transformation of ancient plant remains. During coalification, plant cellular structures are preserved, resulting in porous formations influenced by the original plant's cell structure and size. Over time, the pore structures are altered due to coalification and geological processes, with new pores and fissures forming. These struc \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**CT Test** & **Peak Stress** & **Height** & **Axial Strain** & **Diameter** & **Radial** & **Volume** & **Volume** & **Crack Volume to** \\
**No.** & **/MPa** & **/mm** & **/\%** & **/mm** & **Train** & **Train** & **Train** & **Total Volume** \\ \hline
1 & — & 101.493 & — & 49.659 & — & 196,569 & — & — \\
2 & 3.582 & 101.451 & \(-\)0.41 * & 49.661 & 0.04 & 196,499 & \(-\)0.36 * & — \\
3 & 7.043 & 101.396 & \(-\)0.96 * & 49.672 & 0.27 & 196,490 & \(-\)0.40 * & — \\
4 & 10.004 & 101.298 & \(-\)1.92 * & 49.713 & 1.10 & 196,583 & 0.07 & 2.17 \\
5 & 15.984 & 101.228 & \(-\)2.61 * & 49.847 & 3.79 & 197,574 & 5.11 & 58.20 \\ \hline \hline \end{tabular}  
* Negative strain values indicate a reduction in the corresponding physical quantity.  
\end{table} 
Table 2: Coal sample dimensions and strain values calculated from CT images. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loading** & **Loading Stage** & **Peak Stress** & **Ratio to** & **Peak Stress** & **Fracture Evolution Phenomena and Analysis** \\
**Number** & **Loading Stage** & **/MPa** & **Peak Stress** & **No new fractures observed; volume strain decreased, \\
1 & Compaction Stage & 3.582 & 22.4\% &
\begin{tabular}{c} No new fractures observed; volume strain slightly \\ decrease compared to the previous stage. \\ \end{tabular} \\ \hline
2 & Linear Elastic Stage & 7.044 & 44.0\% &
\begin{tabular}{c} No new fractures observed; volume strain decreased, \\ decreased compared to the previous stage. \\ \end{tabular} \\ \hline
3 & \
\begin{tabular}{c} Initial Fracture \\ Propagation Stage \\ \end{tabular} & 10.005 & 62.5\% &
\begin{tabular}{c} Clearly visible fractures appeared and converged; \\ volume strain increased compared to the previous stage. \\ \end{tabular} \\ \hline
4 & \
\begin{tabular}{c} Accelerated Fracture \\ Propagation Stage + \\ Post-peak Stage \\ \end{tabular} & 15.984 & 100\% &
\begin{tabular}{c} Significant increases in fracture quantity and density; \\ notable fracture length and width increases; main \\ fractures penetrating the sample were observed; volume \\ strain increased significantly. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental phenomena and analysis. Figure 7: Stress-strain curves after unloading of coal samples. (1) Compression stage; (2) Elastic stage; (3) Initial crack extension stage; (4) Accelerated crack extension stage. tures, predominantly at the micron scale and below, are randomly distributed throughout the coal, contributing to its heterogeneous nature. The microscopic structure of coal samples prior to loading was examined using SEM, as shown in Figure 8. The SEM images reveal the presence of matrix pores, plant cell wall residual pores, secondary pores, and microfissures. Matrix pores are characterized by small diameters, typically at the nanometer scale, and exhibit high abundance with diverse morphologies. Plant cell wall residual pores are remnants of plant cell walls, with diameters ranging from 10 to 40 \(\upmu\)m. Secondary pores include dissolution pores, exogenous pores, and thermogenic pores, with diameters ranging from hundreds of nanometers to tens of micrometers. Microfissures encompass endogenic (cleavage) and exogenic fissures, with tensile exogenic fissures being particularly well-developed. These fissures vary in length, typically not exceeding several hundred micrometers, and have widths at the micrometer scale or smaller.