## 4 Discussion  
In this paper, we describe the particle size distribution, morphology and fractal characteristics of coal fragments generated from WJD. These features are determined by the coal failure patterns subjected to water jets in WJD, which are mainly related to the hydraulic parameters of water jets and the coal strength and its structure. The various failure patterns inside the rock under water jet impact are shown in Figure 14 [52; 53; 54; 55]. When the water jet impacts the rock, the \"water-hammer\" pressure will initially be generated owing to the compression of the liquid jet. This pressure is extremely high, as given by Equation (8), and is responsible for most of the rock damage. As shown in Figure 14b, the disturbance induced by the \"water-hammer\" pressure will transmit throughout the rock in the manner of stress waves, such as longitudinal waves, transverse waves and Rayleigh surface waves. In the process of propagation, the longitudinal wave will generate the radial tensile stress, the transverse wave will cause the circumferential tensile stress and shear stress, and the Rayleigh wave will cause tensile stress and shear stress. \begin{table}
\begin{tabular}{c c c} \hline
**Impact Velocity (m/s)** & **Fractal Dimension** & **Dominant Fragment Size** \\ \hline
219 & 2.6684 & 0.7129 \\
237 & 2.6878 & 0.6632 \\
253 & 2.7248 & 0.6422 \\
268 & 2.7536 & 0.6381 \\ \hline \end{tabular}
\end{table} 
Table 4: Relationship between the fractal dimension and dominant fragment size. Figure 12: Diagrams of the relative mass versus the relative fragment size for coal fragments generated from WJD holes in coal seams: (**a**) M8 coal seam and (**b**) M7 and M8 coal seams for an impact velocity of 268 m/s. Figure 13: Relationship of the fractal dimension and jet impact velocity. stress, respectively [52]. Once the tensile stress and shear stress reach the tensile strength and shear strength of rock, respectively, cracks will initiate and expand in the rock (Figure 14a). Moreover, in the case of coal, it has a typical porosity-cracks structure, and coal is rich in cleats and fractures, as shown in Figure 15. When stress waves are transmitted to the inherent cracks in coal, these waves will be reflected. The interference and reflection among these waves will reinforce the destructive effect of the stress wave, which is conducive to the generation of cracks. \[P_{wh}=\frac{v\rho_{w}c_{w}\rho_{s}c_{s}}{\rho_{w}c_{w}+\rho_{s}c_{s}} \tag{8}\]  
where \(P_{wh}\) is the \"water-hammer\" pressure; \(v\) is the jet impact velocity; and \(\rho_{w}\), \(\rho_{s}\) and \(c_{w}\), \(c_{s}\) are the densities and the shock velocities of the water and the rock, respectively. The duration of the \"water-hammer\" pressure is very short, usually a few microseconds. Once the impact of the water jet becomes steady, the pressure will fall to a much lower value, namely, Bernoulli stagnation pressure as calculated in Equation (9). On the one hand, the pressurized water will act on both sides of the crack caused by the \"water-hammer\" pressure (Figure 14c). This will cause stress concentration at the tip of the crack, resulting in the propagation of cracks, which is called the pressured water wedge effect. On the other hand, the high-velocity water flow will scour the rock surface, leading to rock breakage and the formation of rock chips (Figure 14d). Because coal has a relatively low strength compared with other rock, such as sandstone and granite, the breakage degree will be more severe. \[P_{s}=\frac{\rho_{w}v^{2}}{2} \tag{9}\]  
where \(P_{s}\) is the Bernoulli stagnation pressure. The formation of coal fragments in WJD is the result of the expansion of internal fractures inside coal induced by multiple water jets. When the water jet impact the coal surface, a shear fracture zone will be created immediately beneath the impacted surface (Figure 14a).