## 3 Results and Discussion
### Results of Calculations of Grouting Subsidence Reduction in Goaf Areas with Different Spacing
Figure 5: The subsidence reduction rate of subgrade center grouting treatment for different OB/IB conditions. In summary, due to the large spacing between coal seams, the OB/IB is relatively small. At this time, the compaction amount of the lower coal seam caving zone is relatively large, and the upper coal seam caving zone and crack zone undergo compaction and closure under the disturbance, resulting in poor grouting treatment and a subsidence reduction effect. When the spacing between coal seams is small and OB/IB is larger, the load on the overlying rock mass is smaller, and the long-term deformation of the reinforcement after grouting is reduced, making the grouting subsidence reduction effect better. Calculation Results of Subsidence Reduction in Goaf Areas of Multi-Coal Seam Goafs with Different Grouting Ranges  
To analyze the impact of different grouting treatment ranges on the subsidence reduction effect of grouting in multi-coal seam goafs, this study considered four grouting treatment ranges: half-width range of subgrade, width range of subgrade, trapezoidal range, and full-range grouting. Figure 6 shows the residual subsidence cloud map of the goaf under different grouting treatment conditions. From the residual subsidence cloud maps of grouting, it can be concluded that under different grouting range conditions, the residual subsidence near the goaf opening and stopping line is relatively more significant than that in the mining center area. When grouting is carried out in the goaf of multi-coal seam according to the half-width of the subgrade, the width of the subgrade, and the trapezoidal range, the residual subsidence at the subgrade is controlled, and the overall residual subsidence control effect of the model after full-range grouting is the most obvious. This is because when grouting is carried out according to the width of the subgrade, half-width of the subgrade, and the trapezoidal range, the broken rock masses near the stop mining line are not treated, resulting in damage to the cantilever beam structure near the stop mining line when residual subsidence occurs, and large-scale subsidence occurs at the stop mining line. According to the full range of grouting, the damage of the cantilever beam structure near the stop mining line is controlled, forming a relatively stable structure, and the most obvious effect of reducing subsidence control is achieved [30]. Figure 7 shows the surface residual subsidence curve for different grouting treatment scopes. The results show that when using full-range grouting treatment, the residual subsidence on the surface presents a symmetrical \"W\"-shape on both sides. The overall trend of the fluctuations of the residual subsidence curve in the \"W\"-shape is relatively stable, and the best subsidence reduction effect is achieved. When grouting treatment is performed according to the entire width of the subgrade, half-width of the subgrade, and trapezoidal range, this results in damage to the cantilever beam structure near the stopping line during residual subsidence. The residual subsidence shows a tilted \"W\"-shape inclined toward the opening. Figure 8 shows the amount of subsidence reduction \(\Delta\)L and the ratio of R at the center of the subgrade for the range of grouting treatments. From the figure, it can be concluded that when using the full-range grouting treatment, the grouting has the best effect on reducing subsidence. At this time, the subsidence reduction amount and ratio at the center of the subgrade are 0.158 m and 81.1%, respectively. When the grouting treatment range is trapezoidal, the width of the subgrade, or half-width of the subgrade, the subsidence reduction rate at the center of the subgrade gradually decreases. Therefore, during the same period after the completion of mining, the maximum controlled residual subsidence value of the surface can be achieved when the treatment width is the full-range of the caving zone, followed by the trapezoidal range > the width of the subgrade > the half-width of the subgrade.