## 3 Results  
### Size Distribution of Fragments  
Fragment size not only reveals the fragmentation degree of coal subjected to water jets, but also directly affects the fragment removal efficiency in WJD. The larger the particle sizes of the coal fragments are, the lower the coal fragment removal efficiency is, resulting in the high-pressure hose becoming stuck and the occurrence of high drag [13; 51]. Therefore, it is worth investigating the fragment size distribution in WJD. There are too many coal fragments to obtain the geometric dimensions of each particle, so the sizes and shapes of a certain percentage of fragments in each grade were considered to be the size and shape distributions of the entire grade. Considering the proportion of chosen fragments among all fragments of each grade, the size and shape distributions of all coal fragments generated from each WJD hole can be obtained. As shown in Figure 7, the cumulative probability distributions based on the particle number (NUM-based cumulative probability) for the equivalent diameters were obtained [21]. The GEV distribution was chosen to fit the data. The fitting correlation coefficients of all the distribution curves were more than 0.98. This indicates that the cumulative distribution model of the GEV distribution is very suitable for characterizing the size distribution of coal fragments. It can be observed from Figure 7 that all the NUM-based cumulative probabilities of coal fragments follow the same change trend: on the one hand, as the particle sizes increase, the distribution curves first increase extremely slowly, then increase rapidly and finally stabilize. For instance, the proportions of fragments with sizes less than 0.6 mm and greater than 2.0 mm are less than 15% and 4%, respectively, whereas the particles with a size of 0.6\(\sim\)2.0 mm account for the vast majority of the total fragments. On the other hand, the distribution fitted curves of coal fragments are more intensive at the section for relatively small particle size. In addition, these curves become sparser with increasing particle sizes. Moreover, the change differences among curves are influenced by the coal properties and the hydraulic parameters of water jets. With the jet velocity increasing, there is an obvious shift of the distribution curves toward smaller sizes (Figure 7a), implying that the average fragment size decreases and most of the fragments decrease as the jet impact velocity increases. It is also observed that the number of coal fragments obtained with high impact velocity is more than that obtained with low velocity. This behavior may be caused by the increasing impact energy magnitude of water jets. Compared with the M8 coal seam, the coal fragment sizes of the M7 coal seam are larger at the same jet impact velocity (Figure 7b). This is because the M7 coal seam has a better ability to resist breakage because of the higher coal strength and fewer joints and fissures inside the coal. The size distributions of fragments are mainly determined by the dominant fragment size. Therefore, in order to obtain the dominant fragment size for various jet velocities and coal mass strength, the probability density function is obtained as shown in Equation (4). The peak values of curves correspond with the dominant fragment sizes. Figure 8 shows the distribution density for coal fragments of equivalent diameters under various jet velocities and coal strengths. The peak values for each experiment are given in these figures. It can be seen that the distribution density curves move toward the upper left with the increase in jet impact velocity (Figure 8a), whereas the curves move toward the bottom right as the coal mass strength increases (Figure 8b). This indicates that the dominant fragment size increases gradually as the jet impact velocity decreases; the curves become flat, and the particle size range is more scattered. Figure 9 is the relationship between the dominant fragment size and the jet impact velocity in the M8 coal seam.