## 5 Conclusions  
This paper introduces a calculation model for the deflection of key strata and a prediction model for ground surface subsidence under conditions of grouting into overburden separation. These models are suitable for conditions such as horizontal or nearly horizontal coal seams, longwall mining with natural roof-caving management, thick and uniformly hard rock layers as key strata, and grouting in the void space beneath the key layer for subsidence reduction. Also, these models incorporate analytical methods such as elastic foundation beam theory and the principle of equivalent mining height. Additionally, a numerical simulation approach using the discrete element method is proposed for grouting into overburden separation. This method facilitates a thorough investigation of the subsidence and tilting characteristics of key strata and ground surfaces under different injection-extraction ratios. The accuracy and reliability of the ground subsidence prediction model were substantiated by comparing it with on-site measured data. The main findings from this study are summarized as follows:  
1. The coal-rock mass beneath the key strata is treated as an elastic foundation, segmented into a solid coal area, an insufficiently compacted area, and a compacted area, all symmetrically distributed across the region. We proposed a method to calculate the elastic foundation coefficients for these distinct sections, along with a deflection calculation model for the key strata. Theoretically, the maximum subsidence of the key strata, in the absence of grouting, is determined to be 4961 mm. However, an increase in the injection-extraction ratio consistently results in a reduction in this maximum subsidence, emphasizing its crucial role in controlling subsidence within the key strata. 2. Using a discrete element numerical simulation method for grouting into overburden separation, the subsidence behavior of the overburden on the working face under varying injection-extraction ratios was studied. It was observed that as the injection-extraction ratio increases, the subsidence of both the key strata and the ground surface progressively decreases. The alignment of the subsidence curves for key strata from the numerical simulations with those from the proposed calculation model  
Figure 17: The surface tilt along the observation station. underscores the reliability of the latter. The use of fly ash as a filling material plays a crucial role in impeding the ongoing displacement of rock layers at both the upper and lower interfaces of the separation. This effectively reduces the subsidence of key strata and their overlying rock layers. Notably, when the injection-extraction ratio is set at 40%, the maximum surface subsidence observed in numerical simulations is only 76 mm, compared to a substantial 3485 mm in scenarios without grouting. * A predictive model for surface subsidence, incorporating the equivalent mining height theory and the probability integral method, was developed to assess conditions under grouting into overburden separation. This model's reliability was validated through on-site measurement data from the 8006 working face at the Wuyang Coal Mine. The maximum observed surface subsidence at the grouted working face was recorded at 546 mm, closely aligning with the theoretical prediction of 557 mm. This results in a relative error of merely 2%, demonstrating the model's high accuracy. Following the implementation of a grouting into overburden separation project with an injection-extraction ratio of 33% at the working face, the maximum surface tilt recorded was less than 3 mm/m. This performance meets the specified stability requirements for surface structures, confirming the effectiveness of the grouting intervention in managing subsidence and maintaining structural integrity. Conceptualization, F.M. ; Methodology, W.L. ; Software, W.L. ; Resources, W.L. ; Data curation, W.L. ; Writing--original draft, F.M. ; Writing--review & editing, S.J. ; Supervision, H.N.