## 7 Conclusions  
1. The concept and connotation of roof self-stability were proposed by analyzing the roof structure types along the strike and dip of coal seams and under different backfill degrees. After that, the structural characteristics of self-stable rock beams were expounded from the perspectives of roof stress distribution, overburden subsidence, and energy transfer.
2. A mechanical model of roof self-stability along strike was established based on the elastic-foundation beam theory to analyze the effect laws of backfilling elastic-foundation coefficients, supporting-peak loads, and unsupported-roof and advancing distances on roof self-stability along strike. Roof stability was greatly impacted by backfilling elastic-foundation coefficient and slightly impacted by supporting-peak load and advancing distance. Unsupported-roof distance had no obvious effect on roof stability. A mechanical model of roof self-stability along dip was established to analyze the effect laws of the working face and coal-pillar lengths on roof stability. The working face and coal-pillar lengths significantly affected roof breakage. The reserved coal-pillar length was appropriately reduced within a certain range.
3. The control method of roof self-stability engineering was put forward at the engineering design and construction stages according to the analysis of the roof self-stability effect.
4. The control parameters for roof self-stability were calculated combined with the geological and mining conditions of the Xinjulong Coal Mine. Roof self-stability conditions were satisfied when the supporting intensity of backfilling hydraulic support was greater than 0.93 MPa; the backfill ratio was greater than 84.6%. Engineering practice showed that the maximum roof subsidence was 438 mm, and the backfill ratio was 86.3% when the supporting intensity of backfilling hydraulic support was 0.94 MPa; the advancing distance of the working face was greater than 638 m; the foundation coefficient of backfill material was 4.16 \(\times\) 10\({}^{8}\) N\(\cdot\)m\({}^{-3}\). The roof formed a self-stabile structure, which met the requirements of coal mining under buildings, water bodies, and railways.  
**Author Contributions:** Conceptualization, Q.Z. and K.Y.; methodology, J.Z.; software, K.Y.; validation, K.Y., Q.W. and L.Y.; formal analysis, K.Y.; investigation, X.X.; resources, Q.W.; data curation, Z.S.; writing--original draft preparation, Z.S.; writing--review and editing, L.Y.; visualization, X.X.; supervision, X.X.; project administration, J.Z.; funding acquisition, Q.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China number 52174134 and the Fundamental Research Funds for the Central Universities grant number 2021 GJZPY12.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The work was supported by the National Natural Science Foundation of China (52174134) and the Fundamental Research Funds for the Central Universities (2021 GJZPY12). The authors gratefully acknowledge the financial support from these organizations.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.