# Discrete Element Analysis of Grouting Reinforcement and Slurry Diffusion in Overburden Strata
## 5 Conclusions  
In this study, a slurry diffusion analysis model for overburden was developed using discrete element grouting simulation technology. The spatiotemporal distribution characteristics of slurry diffusion were investigated, and the regulatory mechanism of grouting pressure on slurry diffusion distance was examined. The main conclusions are as follows:  
(1) To address the invisibility of the grouting process and the inhomogeneity of the grouted medium, a visual numerical particle flow model was proposed to simulate slurry flow. The contact parameters of overburden and cement particles were calibrated through laboratory tests, and the computational load was significantly reduced by applying a coarse-graining method. The results indicate that the discrete element method can effectively simulate the diffusion of grout within the overburden, confirming the feasibility of this simulation approach. (2) A measurement circle was employed to monitor the grouting process and its effect on the overburden. The improvement in grouting effectiveness was characterized by the spatial and temporal distribution of porosity and coordination number before and after grouting. The numerical simulation demonstrates that under typical working conditions (grouting pressure of 2 MPa and formation pressure of 0.5 MPa), the porosity near the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Numerical**} & \multicolumn{5}{c}{**Theoretical Calculation Value/cm**} & \multicolumn{5}{c}{**The Calculated Value of**} \\
**Grouting** & \multicolumn{2}{c}{**Test**} & \multicolumn{2}{c}{**Value/cm**} & & & \multicolumn{2}{c}{**This Formula/cm**} \\
**Pressure/** & \multicolumn{2}{c}{**Diffusion**} & \multicolumn{2}{c}{**Mag**} & \multicolumn{2}{c}{**Formula**} & \multicolumn{2}{c}{**Diffusion**} & \multicolumn{2}{c}{**Error**} & \multicolumn{2}{c}{**Polynomial**} & \multicolumn{2}{c}{**Error**} & \multicolumn{2}{c}{**\(R_{\text{pin}}\)**} & \multicolumn{2}{c}{**Fitting**} \\
**MPa** & **Distance** & **Equation** & **Equation** & **Formula** & **Equation (\%)** & **Equation (\%)** & **Equation (\%)** & **Equation (\%)** & **Equation (\%)** & **Error** \\  & \multicolumn{2}{c}{**\(r_{\text{min}}\)**} & \multicolumn{2}{c}{**(5)**} & \multicolumn{2}{c}{**(5)**} & \multicolumn{2}{c}{**(5)**} & \multicolumn{2}{c}{**(5)**} & \multicolumn{2}{c}{**(5)**} & \multicolumn{2}{c}{**(5)**} \\ \hline
0.5 & 6.41 & 3.99 & \(-\)37.73\% & 4.95 & \(-\)22.75\% & 10.79 & 68.38\% & 6.21 & \(-\)3.09\% \\ \hline
0.75 & 6.55 & 4.56 & \(-\)30.38\% & 6.06 & \(-\)7.48\% & 13.11 & 100.15\% & 6.70 & 2.29\% \\ \hline
1 & 6.92 & 5.02 & \(-\)27.43\% & 7.01 & 1.34\% & 15.05 & 117.58\% & 7.06 & 2.07\% \\ \hline
1.25 & 7.28 & 5.41 & \(-\)25.69\% & 7.83 & 7.55\% & 16.76 & 130.22\% & 7.37 & 1.24\% \\ \hline
1.5 & 7.44 & 5.75 & \(-\)22.72\% & 8.58 & 15.32\% & 18.29 & 145.83\% & 7.62 & 2.42\% \\ \hline
2 & 7.74 & 6.32 & \(-\)18.37\% & 9.9 & 27.87\% & 21.01 & 171.38\% & 8.04 & 3.85\% \\ \hline
2.5 & 8.48 & 6.82 & \(-\)19.58\% & 11.08 & 30.66\% & 23.39 & 175.83\% & 8.38 & \(-\)1.18\% \\ \hline
3 & 8.77 & 7.24 & \(-\)17.45\% & 12.13 & 38.31\% & 25.53 & 191.11\% & 8.67 & \(-\)1.14\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison and error of results of classical slurry diffusion formula. grouting pipe decreases from 21% to 4%, while the coordination number increases from 3.8 to 6.5. The reinforcement range is clearly delineated in the horizontal, vertical, and inclined directions. The reinforcement effect in the overburden exhibits a synergistic mechanism involving pore structure compaction (porosity reduction) and cement-overburden bonding (coordination number increase). (3) Based on the discrete element simulation results, a correlation between grout diffusion radius and grouting pressure in the overburden was established. By integrating classical grout diffusion formulas, empirical correction equations for both maximum and minimum diffusion distances were derived.