## 6 Case Study  
Based on the actual blasting parameters, a rock fragmentation calculation model is established, as shown in Figure 26. The charging structure consists of a 90 mm diameter charge and a 115 mm diameter blast hole. In the three-dimensional numerical model simulating explosive cracks in the rock, the element size is set to 6 cm to manage computational costs. However, this coarse mesh resolution prevents the simulation of smaller rock fragments, resulting in noticeable discrepancies between numerical and actual blasting outcomes. To improve accuracy and efficiency, a two-dimensional plane strain model is adopted. In this model, the maximum element size is refined to 1.3 cm, while the stemming and explosive column lengths are set to 2.5 m and 12.5 m, respectively. In Figure 26, the variable \(L\) represents the distance between adjacent blast holes, which significantly influences stress wave interactions. Non-reflective boundaries are applied to the left, right, and bottom surfaces to prevent reflected stress waves, while the top surface remains a free boundary.  
The RHT model is employed as the constitutive model for the rock, with the specific material parameters provided in Table 5. To simulate explosion-induced cracks in the rock, the *MAT_ADD_EROSION keyword is used to delete elements that exceed the damage threshold.  
For the explosive material, the *MAT_HIGH_EXPLOSIVE_BURN keyword is applied. The relationship between pressure, volume, and energy of detonation products is modeled using the JWL equation of state. The detailed parameters for the explosives are listed in Table 2.  
The simulated rock blasting fragments results are shown in Figure 27. Due to the non-reflective boundaries on the sides and bottom of the model, damage at the edges of the blast hole is minimal. In practical engineering, the primary focus is on the rock fragments between adjacent blast holes. Therefore, this simulation specifically examines the rock fragments in the central region between the blast holes. As shown in Figure 27, when the distance between adjacent blast holes is 3.0 m, the shock waves from the explosive detonation cause the rock between the two blast holes to collide, enhancing fragmentation in the middle. However, large rock fragments are still present in the model. As the distance (\(L\)) between the blast holes decreases, the size of the larger rock fragments gradually reduces. The WipFrag software is used to process the simulated rock blasting fragments images, calculate the size and distribution for various distances (\(L\)), and generate the fragment gradation curve, as illustrated in Figure 28.  
Figure 26: Two-dimensional rock blasting fragment calculation model.  
In Figure 28, the black curve represents the grading curve envelope for rockfill dam materials stipulated by state regulations, while the red curve indicates the lower envelope line. The grading curve of rock blasting fragments obtained directly through blasting must fall between these two curves.  
As shown in Figure 28, when the distance between adjacent blast holes is 3.0 m, there are more rock blocks, and the grading curve does not meet the required standards. As the distance (\(L\)) decreases, the size of the rock fragments gradually becomes smaller. At a distance of \(L=2.0\) m, the grading curve lies between the upper and lower envelope lines,  
Figure 27: Rock fragmentation distribution under different blast hole spacings.  
meeting the standard requirements. However, when the distance \(L\) is further reduced to 1.75 m, the maximum rock size becomes smaller than the standard, and excessive crushing occurs. Based on this analysis of the distance \(L\) in terms of blasting damage, the optimal distance between adjacent blast holes is found to be 2.0 m.