## 3 Results
### Characteristics of Crack Disturbance Range under Different Splitting Angles
The main crack propagation stage is concentrated at 0.2-0.65 s, and the crack propagation length at this stage accounts for 95% of the total. In engineering applications, the crack propagation at this stage can be completed. The crack propagation is mainly concentrated in the second stage because the coal damage belongs to the disturbed deformation. The whole process needs to go through the following processes: stress accumulation-breakthrough limit-stress release [31; 32]. Therefore, at 0\(\sim\)0.2 s, it is in a state of stress accumulation, and the crack propagation length is very short at this time. When the stress exceeds the limit, the coal is broken, the crack rapidly propagates along the principal stress direction, and the stress is released. For the next stage of the crack propagation, the stress needs to accumulate again, but as the accumulated stress is still not enough to initiate the next stage of the coal after the splitting pistons travel to the maximum, the length of the crack in the coal stops increasing. As the splitting angle increases, the overall length of the crack increases. The main reason for this phenomenon is that with the development of cracks, the stress of coal and rock on both sides of the cracks changes. The distance between the damaged area on both sides of the cracks is close, and the damaged areas are connected; thus, the damage to the surrounding coal is greatly reduced. The cracks propagate into the damage in the coal. Deformation, which occurs when the damage to the coal is reduced, will lead to a reduction in the length of crack propagation. Therefore, when the crack-splitting angle increases, the distance between the damaged area of the two cracks increases, and the superposition effect weakens. The influence on the coal around the borehole becomes smaller. Therefore, the damage to the coal is less affected, and the crack propagation length is longer. The data in Figure 8 indicate that when the included angle is 70\({}^{\circ}\), the crack length is about 392 mm, and the crack area is about 441 mm\({}^{2}\). When the included angle is 80\({}^{\circ}\), the crack length is about 400 mm, and the crack area is about 458 mm\({}^{2}\). When the included  
Figure 8: Variation in crack length (**a**) and crack area (**b**) for different splitting angles. angle is 90\({}^{\circ}\), the crack length is about 560 mm, and the crack area is about 480 mm\({}^{2}\). When the included angle is 100\({}^{\circ}\), the crack length is about 481 mm, and the crack area is about 507 mm\({}^{2}\). When the included angle is 110\({}^{\circ}\), the crack length is about 460 mm, and the crack area is about 530 mm\({}^{2}\). In comparison, when the splitting angle is 90\({}^{\circ}\), the crack length and area are in the middle. Combined with the qualitative analysis, the damage effect on the coal around the borehole is the best when the included angle of splitting is 90\({}^{\circ}\). Whether the combined effect is optimal can be judged according to the range change in the crack-damaged area. The data of the width R of the damaged area of the crack was extracted, and the joint damage effect of the crack was analyzed. The extraction path and fitting results are shown in Figure 9.  
An analysis of Figure 9 indicates that the overall change trend is consistent, and the two results are roughly the same, as shown by a comparison of the simulation results with the numerical substitution results. However, the width of the damaged area obtained by the simulation is slightly larger than that obtained by the calculation. This is mainly because the interaction between the damaged areas is not considered when calculating through the formula. The damaged areas interact with each other because of the close distance between the two cracks. This situation intensifies the degree of damage to the coal, and eventually, a larger area of damage is formed.