# Discrete Element Analysis of Grouting Reinforcement and Slurry Diffusion in Overburden Strata
## 4 Discrete Element Grouting Diffusion Results
### Grouting Reinforcement Mechanism Analysis  
(1) Variation of porosity and coordination number with time  
In this section, porosity and coordination number near the grout outlet are monitored throughout the grouting process to evaluate the consolidation behavior of the stratum at various locations during and after grouting. A circular monitoring zone with a diameter of 5 mm is employed, and its location is illustrated in Figure 7.  
Porosity monitoring reflects the extent of pore compression and filling by cement particles. The porosity results are shown in Figure 8a, with all monitoring zones exhibiting a decreasing trend. Specifically, the 1# monitoring zone is located at the slurry outlet. As cement particles enter the overburden, this region is first rapidly filled, causing the porosity to drop sharply from 21.4% to 7.1%. It then gradually increases to 11.5% before stabilizing. Monitoring zones 2# and 3# are positioned along the horizontal and vertical axes of the grouting hole. These zones are influenced by both pore compression and cement particle filling, resulting in a rapid decrease in porosity from 20.0% to approximately 4.0%. Monitoring zones 4# and 5# are located at the lower-left and upper-right of the grouting hole, respectively. These locations are relatively distant from the grouting hole, and grout particles do not reach them. These zones are influenced only by pore compression, leading to a relatively smaller reduction in porosity--from 20.3% to 15.6%. The coordination number refers to the number of neighboring particles that are in direct contact with a given particle. The coordination number results are shown in Figure 8b. Across all monitoring zones, the coordination number exhibits an overall increasing trend. The coordination number initially rises, then decreases, and finally stabilizes at 4.9. Specifically, it increases from 4.7 to 5.5 before decreasing to 4.9. This fluctuation results from the gradual expulsion of particles from the monitoring zone due to grouting pressure, as they are replaced by incoming cement particles. During the grouting process, the average coordination number at monitoring zones 4# and 5# increases slightly from 4.1 to 4.7, primarily due to pore compression in the overburden. Figure 6: Slurry diffusion pattern at different times. (2) Variation of porosity and coordination number with spatial position  
This section aims to monitor post-grouting changes in porosity and coordination number along the horizontal, vertical, and inclined directions. The grouting hole is defined as the coordinate origin, with the horizontal right direction as the positive \(X\)-axis and the vertical upward direction as the positive \(Y\)-axis. Measurement circles along the horizontal and vertical directions are spaced at 0.05 m intervals, with 13 measurement points arranged on each side of the origin. Along the inclined direction--set at 45\({}^{\circ}\) relative to the positive  
Figure 8: Monitoring results of particle contact law during grouting. (**a**) Distribution law of particle porosity during grouting. (**b**) Distribution law of particle coordination number during grouting. Figure 7: Layout of measuring circle. (**a**) Measure the circular monitoring position of grouting time characteristics. (**b**) Measure the circular monitoring position of grouting space characteristics. \(X\)-axis and centered at the origin--measurement circles are spaced at 0.07 m intervals. A total of nine measurement circles are arranged from the bottom left to the top right along this inclined direction. The overall layout of the measurement circles is illustrated in Figure 7b. The post-grouting porosity results are shown in Figure 9a. The porosity at all monitoring points first decreases and then increases with distance from the origin, ranging from 4.0% to 21.4%. The overall trend is approximately axisymmetric about the horizontal axis at the origin.