## 7 Conclusions  
1. Three structural models of the overlying rock were proposed when the MRFL is located above the gob-side entry. These models were classified as articulated, misaligned, and detached. Furthermore, a mechanical model was developed to simulate the shear subsidence of the top coal. By integrating this model with UDEC numerical simulations, we elucidated the mechanism of shear failure in the top coal when the MRFL is positioned above the roadway. The numerical results demonstrate that the roadway roof experienced tensile stresses of approximately 2 MPa, significantly exceeding the tensile strength 0.5 MPa for coal seams. The failure characteristics of the surrounding rock in the roadway obtained through similarity simulation experiments were generally consistent with those in the numerical simulation.
2. The prestress field of a five-hole tray combined with high-strength prestressed anchor cables was obtained by FLAC\({}^{\text{3D}}\) numerical simulation. It could be clearly seen that a continuous overlapping effective compressive stress zone covering the entire roof was formed between the anchor cables, which gave full play to the active support of the anchor cables. The coverage range of 0.01 MPa stress was significantly larger than that of 0.02 MPa. When comparing different angles, the stress coverage range at a deflection angle of 10\({}^{\circ}\) was markedly greater than that at 5\({}^{\circ}\).
3. After adopting the five-hole tray support system integrated with high-strength prestressed anchor cables, the deformations of the roof and both coal walls were effectively controlled within a limited range. The monitoring data indicated that the deformation stabilized approximately 30 days post-excavation, with a maximum roof subsidence of 159 mm. Additionally, maximum convergence values of 219 mm and 160 mm were recorded on the pillar side and solid coal side, respectively. These findings provide robust theoretical and technical support for roadway stabilization under similar geoengineering contexts.  
Conceptualization, D.C.; methodology, J.C., J.Z. and C.T.; software, J.C., F.G., X.Y. and Z.Z.; formal analysis, J.C. and J.N.; investigation, D.C.; resources, D.C.; data curation, S.X. (Shengrong Xie), J.Z., S.X. (Shikun Xing) and W.Z.; writing--original draft preparation, J.C.; writing--review and editing, D.C.; visualization, J.C.; supervision, D.C.; project administration, J.C.; funding acquisition, D.C. All authors have read and agreed to the published version of the manuscript.  
This research was supported with funding awarded from the National Natural Science Foundation of China (Grant Nos. 52374149, 52004286), the China Postdoctoral Science Foundation (Grant No. 2020T130701), and the Fundamental Research Funds for the Central Universities (Grant No. 2022 XJNY02).  
Not applicable.  
The original contributions presented in the study are included in the article, and further inquiries can be directed to the corresponding author.  
**Acknowledgments:** Heartfelt thanks to the following enterprises in the research process to provide support and assistance: Anhui Hengyuan Coal and Electricity Co., Ltd. for this study provides valuable on-site data and technical guidance; Jizhong Energy Co., Ltd. provides professional facilities and collaboration conditions for experimental analysis and results verification.  
**Conflicts of Interest:** Authors [PERSON] and [PERSON] ware employed by the company Anhui Hengyuan Coal & Electric Co., Ltd.; author [PERSON] was employed by the company Songxinzhuang Coal Mine; and author [PERSON] was employed by the company Jizhong Energy Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.