## 4 Experimental Results and Discussions
This can be explained by the fact that some cracks get connected as their size increases during the LN\({}_{2}\) treatment, consequently reducing TNC. In freezing time experiments, ice behaves as a consolidating factor of the coal sample, which prevails over the frost forces that decrease the sample strength and create more cracks than in freezing-thawing cycle experiments. On the other hand, the last experiment for both processes is an exception where FTC5 relative change is higher than FT150 due to insufficient time for force frost to act and create small fissures inside the coal seams. These observations agree with the work of previous researchers [53; 54; 55]. For example, compression stress is minor when there are sufficient cycles, but in initial cycles, compression stress is higher than in freezing time experiments with the same time in LN\({}_{2}\) treatment. The crack density (CD) calculated by Equation (2) and its relative change (\(\delta_{\text{CD}}\)) are shown for various processes in Figure 8. The highest crack density is achieved for FT60 and FT150 before and after the LN\({}_{2}\) treatment. The highest values of CD were achieved for the FT60 (300 m\({}^{-1}\)) and FT150 (275 m\({}^{-1}\)), while the lowest value of CD was for FT90 (31.25 m\({}^{-1}\)) after LN\({}_{2}\) treatment. In the case of FTC processes, the highest CD was achieved for the FT5 (131.25 m\({}^{-1}\)), while the lowest was for FT3 (43.75 m\({}^{-1}\)) after LN\({}_{2}\) treatment. The highest CD is 9.6 or 3 times bigger than the lowest for FT or FTC processes. For all processes, \(\delta_{\text{CD}}\) stays positive from 0.5 to 1.0 for FT processes, whereas the range of \(\delta_{\text{CD}}\) is higher from 0.13 to 3.0. The relative changes in crack densities increase significantly for FTC2-FTC4 processes. The positive values of \(\delta_{\text{CD}}\) indicate that CD increases during the LN\({}_{2}\) treatment. The highest \(\delta_{\text{CD}}\) is achieved for FTC4 and FTC5, while the lowest for FTC2 and FTC3. Figure 8: **(a)** Crack density (CD) and **(b)** its relative change (\(\delta_{\text{CD}}\)) versus the process. Figure 7: **(a)** The total number of cracks (TNC) versus the type of process and **(b)** its relative change (\(\delta_{\text{TNC}}\)) versus the process. It can be noted that the average crack length and the quartiles decrease during the LN\({}_{2}\) treatment, as shown in Figure 9. There is no visible trend in results regarding crack length. The first and third quartiles for relative changes are the highest for the FTC4 process. For FT processes, the highest values of Q1, Q2, and Q3 after LN\({}_{2}\) treatment were achieved for FT150, while the lowest ones were for FT60. In the case of FTC, the highest values of Q1, Q2, and Q3 after LN\({}_{2}\) treatment were achieved for the FTC1, FTC1, and FTC5, while the lowest ones were for FTC2, FTC3, and FTC3, respectively. The negative trend of relative changes in the average crack length can be explained by the appearance of new cracks with small fracture lengths during the LN\({}_{2}\) treatment, as shown in Figures 5c and 10c for the FT60 process. Figure 9: (**a**) average length of cracks (Q2) and (**b**) its relative change (8_Q2), (**c**) 1 st quartile of crack lengths (Q1) and (**d**) its relative change (8_Q1), (**e**) 3 rd quartile of crack lengths (Q3) and (**f**) its relative change (8_Q3) versus the process. In each histogram presented in Figure 10, the kernel density estimator (KDE) that describes the randomness of the data for the sample are represented by the orange and blue lines, which stands for the data before and after the LN\({}_{2}\) treatment, respectively. In the case of process FT30 (Figure 10a), the number of cracks of length 0-7 mm doubled, whereas the  
Figure 10: The number of cracks versus their fracture lengths for coal samples before and after LN\({}_{2}\) for various processes: (**a**) FT30, (**b**) FT51, (**c**) FT60, (**d**) FT52, (**e**) FT90, (**f**) FT53, (**g**) FT120, (**h**) FT54, (i) FT150 and (**j**) FT5.