## 3 Methodology
### Simulation of Rock Blasting Fragmentation  
To investigate rock blasting fragmentation, the finite element software LS-DYNA was used to model the process. As group hole blasting is more commonly applied in engineering, a group hole blasting model was developed to simulate rock fragmentation.  
In practical engineering, the detonation of explosives generates both stress waves and detonation gases, which lead to the formation of macroscopic cracks in the rock. These cracks break the intact rock mass into fragments of varying sizes, resulting in rock fragmentation. To simulate this process, LS-DYNA was employed to model the rock fragments. The *MAT_ADD_EROSION keyword was used to remove mesh elements that exceed a damage threshold [16], which is widely used for simulating the macroscopic cracks in rock blasting.  
The plane strain model for group hole blasting, shown in Figure 9, was developed using the finite element software LS-DYNA. The model had dimensions of 4.9 m in length and 4.1 m in width, with a fine mesh grid size of 5 mm \(\times\) 5 mm. The explosive had a diameter of 70 mm, and a coupled charge structure was used. The RHT model was employed as the rock constitutive model. The relevant parameters are detailed in Table 2. The detonation process of the explosive was described using the JWL equation of state.  
The plane strain model for group hole blasting was established and solved to simulate the distribution of rock fragments induced by blasting. During the simulation, mesh  
Figure 8: Time–history curve of hole wall pressure under different charging structures.  
Figure 9: Plane strain model of group hole blasting.  
elements that reached the damage threshold were removed to represent the cracks in the rock caused by explosive detonation. Based on relevant data, when the damage variable \(D_{\text{c}}\) reaches 0.8 under slope blasting excavation conditions, the rock mass is considered to be fully fractured [41]. Therefore, the damage variable threshold for the rock mass in this numerical simulation was set at 0.8. The simulated rock fragmentation results in the simulation are shown in Figure 10.  
The image processing software WipFrag (version 3.3.14.0) was used to analyze the simulated rock fragmentation images. The blank regions in the image represent areas where the rock was completely fractured and were excluded from further analysis. WipFrag employs thresholding and fuzzy algorithms to identify the boundaries of the rock fragments. However, some of the recognition results deviated from the actual boundaries, requiring manual adjustments to align the results with the true conditions. The manually refined recognition results are shown in Figure 11, while the original recognition results from WipFrag for the rock fragments are displayed in Figure 12.  
As shown in Figure 12, the recognition results obtained from WipFrag software for the rock fragments are presented. The software uses color coding to indicate the size of the rock fragments, with red representing the larger fragments. Due to the explosive detonation effect, the rock near the blast hole is completely fractured, and this region is excluded from the analysis of rock fragments. In Figure 12, the black regions correspond to these excluded regions, which are not included in the statistical analysis of the rock fragmentation results.  
Figure 11: Boundary identification of rock fragments.  
Figure 10: Rock fragmentation results.  
Figure 13 shows the block grading curve generated by WipFrag after analyzing the rock blasting fragment image. Due to the directional effects of cylindrical explosive detonation, the explosion energy propagates primarily forward, resulting in a higher concentration of larger blocks at the base of the blast hole. The block grading curve indicates that larger fragments are more abundant, with rock pieces exceeding 1 m in diameter accounting for 21% of the total. By integrating numerical simulation and image processing, a novel method for simulating and analyzing rock fragments is proposed.