## 2 PMGIM Induction Mechanism
### Numerical Simulation Analysis of PMGIM  
#### 2.2.1 Numerical Methods and Modeling  
Microseismic monitoring of the mine working face spans kilometers, covering a vast range. Attempting to simulate the entire floor numerically is impractical and could lead to significant errors or experimental failure due to overlooking small joints. Therefore, in this study, we selected a unit size of 160 cm \(\times\) 160 cm after conducting several numerical simulation experiments, considering the actual grout diffusion radius and factors induced by micro-earthquakes during grouting. This size selection enhances the clarity of grouting engineering's fragmentation effects and rationalizes microseismic-intensive areas. The numerical simulation employs the parallel cementation model as its constitutive model, complemented by the smooth joint model for handling discontinuous structures like faults and folds. Initially, a collection of rock particles is generated, and for scenarios involving discontinuous structures, smooth joints with a specified inclination azimuth are strategically inserted. Fluid exchange between domains is facilitated by pipe flow interacting with particles. Contact under the effective stress of particles results in compression or expansion, altering the permeability of the flow conduit. Fluid flow induces changes in pore pressure, thereby altering the effective stress on the particles and achieving fluid-structure coupling. Initial confined water pressure (pore pressure) is incorporated into the model through boundary condition application. This is achieved using the servo control principle, where the sum of stiffness between the wall and the particle is computed and then applied to the wall. Throughout the grouting process, servo control is consistently maintained, ensuring the stress boundary conditions remain unchanged. Initially, the water pressure transitions to free flow during the grouting process, followed by modification of the grouting hole boundary conditions and application of a fixed grouting pressure of 24.24 MPa. Model parameters are selected through a trial-and-error method [24], with specific details provided in Tables 1 and 2. The grouting hole, located centrally, has a diameter of 152.4 mm and contains a total of 17,405 particles, as depicted in Figure 2.  
The fluid domain was established. Subsequently, the initial confined water pressure (pore pressure) was applied to the model via boundary conditions. The implementation was based on servo-control principles. Specifically, the stiffness summation between the wall and particles was computed, and a velocity boundary condition was imposed on the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Density** & **Diameter** & **Linear** & **Parallel** & **Parallel** & **Friction** & **Parallel Bond** & **Parallel Bond** & **Bond** \\
**(kg/m3)** & **(mm)** & **Modulus** & **Stiffness** & **Modulus** & **Stiffness** & **Coeffi-** & **Coeffi-** & **Cohesion** & **Strength** & **Angle** \\
2300 & 0.5–0.8 & 2 & 0.8 & 2 & 0.8 & 0.5 & 6.5 & 9 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mesoscopic parameters of parallel cement model of rock mass. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**SJ Normal** & **SJ Tangential** & **SJ Friction** & **SJ Normal** & **SJ** \\
**Stiffness** & **Stiffness** & **Stiffness** & **Coefficient** & **SJ Strength** (MPa)** & **Cohesion** (MPa)** & **SJ Friction Angle (\({}^{\circ}\))** \\ \hline
100,000 & 50,000 & 0.5 & 1 & 6 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mesoscopic parameters of smooth joint (SJ) model of rock mass. Figure 2: Model diagram. wall. After a predefined time step, the resultant wall reaction stress could be derived. By dynamically adjusting the servo-control gain to regulate wall velocity, the discrepancy between the reaction stress and the target confining pressure was iteratively minimized.