## 4 Experimental Results and Discussions  
The coal samples were investigated under different LN\({}_{2}\) treatment conditions, comparing freezing time and freezing-thawing processes. Figure 5 presents the high-resolution photos of coal samples before and after different LN\({}_{2}\) treatment processes. The red dots were located on the samples as regions of interest to conduct SEM analysis. The digital images of coal samples were post-processed using our Python program, see Appendix A. It can be observed that the number of black pixels corresponding to cracks increased after the LN\({}_{2}\) treatment. In particular cases, the parameters for the image processing function _process_image_ were adjusted manually to reduce noise due to non-constant light conditions. The total crack area (TCA) by Equation (1) and its relative change (\(\delta_{\rm TCA}\)) by Equation (3) are presented for each process in Figure 6a,b, respectively. In the following, we investigate \(\delta_{\rm TCA}\) for FT and FTC processes of different durations. The highest \(\delta_{\rm TCA}\) is achieved for the processes FTC4 and FTC5, while the maximal TCA is observed in FT150. The \(\delta_{\rm TCA}\) for FT30-FT150 and FTC1-FTC5 processes show an increasing tendency. Additionally, it can be noted that \(\delta_{\rm TCA}\) for FT30 and FT60 remains the same, but it increases by 430% and 390% from FT60 to FT90 and from FT90 to FT150, respectively. For the FTC process, we can see a similar trend, namely \(\delta_{\rm TCA}\) for FTC1 and FTC2 is almost identical; however, there is an increase of 600% and 690% from FTC2 to FTC3 and from FTC3 to FTC5. The relative changes for FT30 and FTC1 are the same, as shown in Figure 4b. The relative change of TCA for FTC2 is more by 66% compared to FT60, while for the FTC3 process, it is more by 130% compared to FT90. The trend remains for FT120 compared to FTC4 and FT150 compared to  
Figure 4: Steps of image processing: (**a**) image of the original sample, (**b**) resizing and converting to grayscale, (**c**) bilateral filtering, (**d**) adjusting brightness, (**e**) adaptive thresholding, (**f**) cropping, (**g**) removing noise, (**h**) manual cleaning, (**i**) erosion and dilation. FTC5: \(\delta_{\text{TCA}}\) of FTC4 is six times larger than for FT120, and \(\delta_{\text{TCA}}\) of FTC5 is four times larger than for FT150. Figure 5: _Cont._  
LN\({}_{2}\) treatment weakens coal at the pore level with dependency on grain sorting, pressure, and temperature, but it is ambiguous if one or more mechanisms dominate over others. Pore water can induce damage to coal specimens through three distinct mechanisms: frost force, formation of ice lenses or wedges, and hydraulic pressure. Among these, frost force emerges as the primary factor responsible for pore structure damage, ultimately leading to increased permeability. The total number of cracks (TNC) and its relative change (\(\delta_{\text{TNC}}\)) are presented for each process in Figure 7a,b, respectively. FT processes achieved the highest TNC after LN\({}_{2}\) treatment for FT60 (173 cracks), while the lowest was for FT90 (7 cracks). In the case of FTC processes, the highest TNC was achieved for FTC2 (61 cracks), while the lowest was for FTC4 (17 cracks). Hence, the highest TNC is 25 or 3.5 times more significant than the lowest  
Figure 5: Coal samples and their processed images. Figure 6: (**a**) Total cracks area (TCA) and (**b**) its relative change (\(\delta_{\text{TCA}}\)) versus the process. TNC for FT or FTC processes, respectively. The \(\delta_{\text{TNC}}\) increases for FTC1-FTC5 processes, whereas there is no similar trend for FT30-FT150 processes. In the case of FT90, the TNC slightly decreases. Comparing FT and FTC processes with the exact duration of treatment, we observe that \(\delta_{\text{TNC}}\) of FT30, FT60, and FT120 are more significant than for corresponding FTC processes, namely FTC1, FTC2, and FTC4.