## 3 Results and Analysis
### Analysis of Surface Subsidence during Different Treatment Methods of Goaf  
According to the stable state of the goat above, targeted treatment was implemented in the three goaves between 2018 and 2019. As depicted in Figure 6, distinct characteristics are exhibited by the surface settlement curves of the goaves with different treatment methods.  
1. As shown in Figure 6a, specifically, the settlement curve trend of the goat subjected to full-filling treatment is nearly identical to that prior to treatment. The settlement rates for A1, A2, A3, and A4 are recorded as 55 mm/year, 33.00 mm/year, 80.96 mm/year, and 108 mm/year, respectively. It can be observed from Figure 7a that these values represent decreases of approximately 51.2%, 61.3%, 40.52%, and 31.63% compared to their untreated counterparts. By comparing A1 and A2, it can be observed that mining depth plays a significant role, resulting in a limited degree of mitigation. Moreover,when comparing A3 and A4, it becomes evident that the presence of more unstable pillars leads to a decreased level of mitigation. Additionally, as depicted in the figure, the combination of shallow mining depth and challenges in roof filling contributes to a reduced degree of mitigation. This suggests that during complete goat filling and treatment, the pillars primarily bear the overburden load; consequently, at greater mining depths with unstable pillars present, there is accelerated movement within the overburden rock layer [59].
2. As shown in Figure 6c, the surface subsidence trend of the goat undergoes significant changes after local filling and reinforced pillar treatment, compared to before the treatment. The subsidence rates of B1, B2, B3, B4, and B5 are 51.53 mm/year, 28.18 mm/year, 68.81 mm/year, 84.02 mm/year, and 52.95 mm/year, respectively. As illustrated in Figure 7a, these values demonstrate reductions of 40.02%, 70.46%, 42.29%, 2.04%, and 63.43%, respectively, when compared to pre-treatment levels. Through comparison analysis, it can be observed that the degree of surface subsidence control is ranked as follows: locally filled areas (B2, B5) exhibit superior performance compared to reinforced pillars (B1, B3), while unfilled and reinforced areas (B4) show less effectiveness; this indicates that the unstable region in the filled part plays a significant role in controlling surface subsidence. In goat with smaller spans, the movement of the overlying rock layer tends to cease; however, larger subsidence continues in unfilled and reinforced areas. These findings suggest that during treatment involving locally filled and reinforced pillars in goat, the overlying rock layer behaves similarly to a cantilever beam, resulting in an \"inverted trapezoidal\" pattern of surface subsidence. Faster movement occurs within unfilled and reinforced areas.
3. As shown in Figure 6e, the surface subsidence of the closed goat still exhibits significant settlement, forming a concave curve with a subsidence trend similar to before. The subsidence rates of C1, C2, and C3 are 58.56 mm/year, 98.63 mm/year, and 81.76 mm/year, respectively. As illustrated in Figure 7a, compared to pre-treatment values, the subsidence rates of C1 and C3 decreased by 25.73% and 8.46%, respectively; however, the subsidence rate of C2 increased by 16.02%. This indicates that the center of the subsidence basin has shifted toward adjacent stable pillars due to their ability to bear the load of overlying rock layers [59]. In contrast, unstable pillars exhibit weaker support capacity, resulting in an increased load on neighboring pillars and, subsequently, higher subsidence rates.