## 6 Conclusions  
Based on the typical engineering case of gob-side roadway driving with a small coal pillar in the distant face mining, through theoretical analysis and numerical simulation, this paper studied the transferring pressure across the goaf effect and occurrence mechanism of a small-coal-pillar roadway in the distant face mining. This study provides actionable solutions for gob-side roadway stability in distant mining scenarios, directly supporting China's strategic priorities of'safe production' and 'green transition' in the coal sector. The following conclusions are obtained:  
1. Through theoretical analysis and numerical simulation, this study reveals the \"transferring pressure across goaf\" effect and its occurrence mechanism in gob-side roadways with small coal pillars under distant face mining. The results indicate that the island coal pillar collapses under the \"T\"-shaped strata stress after adjacent working face mining, leading to goaf interconnection, the subsequent breaking and rotation of key strata (KS), and severe disturbance to the roadway surrounding rock. These findings align with the research objectives stated in the Introduction, providing theoretical support for stability control in deep gob-side roadways;
2. Study Limitations: The numerical model is based on idealized geological conditions, ignoring the impact of complex faults or heterogeneous rock layers. Additionally, potential errors may arise from the laboratory-to-field conversion of coal-rock mechanical parameters, which could affect the accuracy of stress distribution predictions. Future studies should validate the model's universality by integrating field monitoring data and addressing multi-scale geological complexities;
3. Future Research Directions: Subsequent investigations should focus on the dynamic response of roadways under multi-working-face collaborative mining and coupled stress fields. Further optimization of active pressure relief techniques (e.g., directional hydraulic fracturing) and synergy control strategies (e.g., graded anchorage systems) is critical to enhance anti-disturbance capabilities in complex stress environments. Additionally, real-time monitoring technologies and multi-physics coupling models should be developed to quantify spatiotemporal correlations between mining-induced stress and roadway deformation.  
Conceptualization, H.Y.; methodology, C.H. and N.Z.; software, H.Y.; data curation, H.Y.; writing--original draft, H.Y.; writing--review and editing, H.Y.; supervision, H.Y.; J.W.; Q.C.; J.L. and S.H.; and funding acquisition, C.H. and N.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (52274101 and 52034007).  
Not applicable.  
Data Availability Statement: The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors are very grateful to the reviewers for carefully reading the manuscript and providing valuable suggestions.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript: