## 3 Simulation on Rock Fracturing Characteristics
### Optimization Design of Drilling Parameters  
In this section, the fracturing effect of the static crushing agent with different hole spacings is simulated using Abaqus numerical software. Based on the background of the expansion project at a mine, the size of the numerical model is set to 2000 mm in height and length to match the site conditions. The boreholes are arranged with spacings of 300 mm, 400 mm, and 500 mm, totaling 25, 16, and 9 boreholes, respectively. The left boundary of the model is constrained, the right boundary is a free surface, and the distance from the right-side boreholes to the free surface is equal to their spacing. The confining pressure of the top boundary is set to 5 MPa, based on the overlying strata stress of the mining face. The mechanical parameters of simulation are selected based on the performance testing results of the rock sample from on-site engineering, as shown in Table 1. To facilitate the comparison and analysis of the evolution characteristics of the expansion force of the SCA, the total iteration steps of the expansion simulation under different working conditions are equivalently replaced by one hour.  
The fracturing effects under different hole spacings are shown in Figure 7. From Figure 7a, for the model with a 300 mm hole spacing, three to four large cracks and numerous microcracks are produced around the holes, resulting in a higher number of cracks. From Figure 7b, for the model with a 400 mm hole spacing, two to three large cracks and fewer microcracks are generated. While for the model with a 500 mm spacing, mostly two to three large cracks are formed, as shown in Figure 7c. Furtherly, the stress at the midpoint between two holes closest to the free surface was monitored, and the results are shown in Figure 7d. The maximum stresses at the midpoint stress monitoring points for the 300 mm, 400 mm, and 500 mm models are 5.12 MPa, 4.22 MPa, and 1.40 MPa, respectively. The greater the stress at the monitoring point between two expansion holes, the more significant the influence of the static cracking agent's expansion stress, indicating a better fracturing effect.  
Figure 7: Expansion fracturing results of rock mass. (**a**) 300 m hole spacing; (**b**) 400 m hole spacing; (**c**) 500 m hole spacing; and (**d**) middle stress between holes.  
Monitoring the stress around the model middle holes, stress changes at monitor points I, II, III, IV, and V are depicted in Figure 8. from analysis of Figure 8a-c, sharp drops in stress-time curves indicate the formation of cracks. By comparing the fluctuating number of stress curves, the stresses required for initial fracturing and complete breakage of the rock mass increase with larger hole spacing. Smaller hole spacing results in more cracks around the holes, leading to better fracturing effects. Concretely, from statistical analysis of the stress curves, as indicated in Figure 8d, the initial fracturing stresses of the rock mass under different hole spacings are 10.93 MPa, 14.52 MPa, and 21.81 MPa, while the complete breakage stresses of the rock mass are 21.58 MPa, 29.05 MPa, and 46.98 MPa, respectively.