## 2 PMGIM Induction Mechanism
### Numerical Simulation Analysis of PMGIM
#### 2.2.2 Influence Analysis of Primary Fractures and Structures on PMGIM  
1. Influence by primary fractures Natural fractures are widely distributed in strata and are typically characterized using statistical methods. Fracture density serves as one of the key indicators used to describe these fractures. In two-dimensional models, fracture density (represented by \(\rho\)) denotes the number of intersecting joints per unit length. This section examines the impact of fracture development on grouting effectiveness. The physical and mechanical properties of the rock mass and ground stress levels remain consistent with those previously discussed. Crack size follows a power law distribution, and crack positions follow a uniform distribution. \(\rho\) is categorized into 3 levels: 6, 8, and 10, respectively.  
Analysis of fluid injection simulation results reveals a strong correlation between grouting-induced crack distribution and primary crack density. Figure 3 illustrates a significant increase in induced cracks with increasing joint density. At lower primary crack densities, induced cracks exhibit directional morphology, forming three main cracks surrounded by numerous smaller cracks, resulting in a 109.6% increase in total crack count. Increasing primary crack density alters crack morphology, increasing main cracks from 3 to 6 with significantly longer lengths, resulting in a 139.7% increase in total crack count. At a primary crack density of 10, crack numbers increase exponentially, with higher tensile stress concentrations at crack tips. Furthermore, many cracks merge with existing natural cracks, forming a complex crack network totaling 1878 cracks.  
2. Influence by geological structures Grouting near geological structures results in distinct crack propagation patterns and varying microseismic events compared to more homogeneous areas. To address this issue, three experimental groups were devised to investigate how faults influence the grouting process at distances of 0.5, 0.6, and 0.7 m from the grouting holes, all under a consistent grouting pressure of 24.24 MPa. Figure 4 presents the numerical simulation results.  
Analysis of fluid injection simulation results reveals that the distribution of cracks induced by grouting correlates closely with the distance from the fault. As the distance from the fault decreases, the number of induced cracks significantly increases. At larger distances from the fault, induced cracks exhibit clear directional characteristics similar to the background scenario. Three main cracks are present, with their direction deflecting towards the fault. At a distance of 0.5 m from the fault, the number of cracks increases dramatically to 1111, with concentration near the fault. The force chain diagram exhibits a pattern similar to the previous simulation model, with tensile stress concentration observed at the crack tips. However, the force chain on the fault appears nearly blank. The relatively weak surface of the fault hinders force transmission, causing grouting pressure to concentrate in the space between the fault and the grouting hole, resulting in thicker force chains and greater tension stress areas.  
Figure 3: Crack distribution characteristics under different crack density levels.