## 3 Results and Discussion  
### Results of Calculations of Grouting Subsidence Reduction in Goaf Areas with Different Spacing  
Based on the method described earlier, the residual subsidence of the surface after grouting was simulated under different coal seam spacing conditions. The calculation results are shown in Figure 3, which are the residual subsidence cloud maps of grouting with coal seam spacings of 10 m, 30 m, 50 m, 70 m, and 90 m. From the residual subsidence cloud maps of grouting, it can be concluded that under different coal seam spacing conditions, after grouting treatment, the residual subsidence value of the surface near the stop mining line and the opening hole is relatively large. In contrast, the residual subsidence value of the surface near the center of the roadbed is relatively small, and as the burial depth of goaf in multi-coal seam increases, the residual subsidence after surface grouting treatment gradually increases. When the distance between coal seams reaches 70 m, there is little difference in the residual subsidence cloud maps of multi-coal seam goat, and the influence of coal seam distance on the grouting treatment effect of multi-coal seam goat is weakened. The cantilever beam structure of the roof near the opening and stopping lines in the goaf of the multi-coal seam is relatively long, resulting in under-compaction in this area. Therefore, there will still be some subsidence after grouting treatment compared to the compacted area below the surface subsidence basin. The greater the burial depth of the goal in the multi-coal seam, the greater the pressure on the goaf from the overburden, resulting in more significant residual subsidence after treatment [22]. According to the calculation results in Figure 3, the subsidence of the subgrade center under grouted and non-grouted conditions for the spacing conditions of each coal seam are calculated and recorded as \(L_{1}\) and \(L_{2}\), respectively. Then, the grouting subsidence reduction for different coal seam spacing conditions is calculated according to Equation (1) for \(\Delta L\). According to Equation (2), the grouting subsidence reduction rate \(R\) is obtained for different coal seam spacing conditions. \[\Delta L=L_{1}-L_{2} \tag{1}\]  
\[R=\Delta L/L_{1} \tag{2}\]  
The relationship between the center subsidence reduction ratio \(R\) of the subgrade and the distance between coal seams is shown in Figure 4. From the figure, it can be concluded that when the spacing between coal seams is 10 m, the grouting has the best effect on reducing subsidence, and the ratio of subsidence reduction at the center of the subgrade can reach 81.1%. As the spacing between coal seams continues to increase, the ratio of subsidence reduction at the center of the subgrade gradually decreases after grouting treatment. When the spacing between coal seams is greater than 80 m, the rate of decrease in the center subsidence rate of the subgrade gradually decreases with the increase in the spacing between coal seams, and the curve tends to be flat. During the process of increasing the spacing between coal seams from 10 m to 80 m, the reduction ratio significantly decreases from 81.1% to 50.1%. Afterwards, the reduction ratio at the center of the subgrade is approximately 46%, and there is no significant change with the increase in the spacing between coal seams. Figure 3: Grouting residual subsidence nephogram of different coal seam spacings. Figure 5 shows the relationship between the center subsidence reduction rate of the subgrade and OB/IB after grouting treatment with different coal seam spacing. From the graph, it can be concluded that when the burial depth (OB) of the upper coal seam is constant, the ratio of subgrade center subsidence reduction after grouting treatment first increases linearly (1 \(\leq\) OB/IB \(\leq\) 2), then increases exponentially (2 \(<\) OB/IB), and finally tends to be flat. Figure 4: The subsidence reduction rate for subgrade center grouting treatment under different spacing conditions.