## 6 Discussion and Conclusions  
In the process of physical similarity simulation tests, human factors prevent the complete simulation of the natural physical and mechanical properties of rock strata. Additionally, considering the time effects at the actual mine site, there are inherent limitations in the physical similarity simulation test. As a result, the test outcomes may differ slightly from the actual site phenomena. However, monitoring field data from the coal mine shows that the test results are largely consistent with real-world conditions. Therefore, despite its limitations, the physical similarity simulation experiment can effectively reflect the mine's actual conditions and serve as a valuable tool for addressing mining challenges. 1. Based on the physical similarity model at a scale of 1:100, the experimental results demonstrate that during the reduction of the coal pillar, the overlying bearing layer fractures and forms a \"hinged\" structure. Consequently, the coal pillar bears an increased load from the overlying strata. As the coal pillar continues to narrow, the upper key stratum also fractures under the influence of mining, resulting in a \"hinged-hinged\" combination composed of the upper and lower key strata. This combined structure impacts the coal pillar. According to stress data from the floor stress meter, reducing the coal pillar width from 25 m to 14 m significantly increases the stress to 19.4 MPa. Given that the No. 5 coal seam at Anyang Coal Mine is a soft coal seam, an insufficient coal pillar width leads to concentrated stress on the side of the roadway coal pillar, potentially causing significant deformation and the risk of partial collapse. Therefore, the coal pillar width is ultimately determined to be 15 m.  
Figure 10: Roadway deformation. Based on the results of the physical similarity simulation test and the geological conditions of Anyang Coal Mine, a mechanical model of the coal pillar-bearing structure was established. The forces acting on the coal pillar were analyzed using a high and low \"hinged\" structure model, leading to the development of a \"hinged-hinged\" combination to calculate the load on the overlying strata. Using the load calculation results of the double \"hinged\" bearing layer structure and applying [PERSON]'s coal pillar strength calculation formula, the optimal coal pillar width was determined to be 20 m.
3. Field monitoring data indicate that reducing the coal pillar width from 25 m to 20 m, resulting in significant deformation on the side of the coal pillar in the 1513 return airway. With support strength unchanged, the displacement on both sides increases by 41-42% compared to the original coal pillar width. However, the maximum displacement is observed 40 m to 60 m ahead of the working face, with relatively minor deformation at other locations. Thus, with stable coal pillars, safe production in the mine can be ensured. Additionally, these findings can provide guidance and reference for mines with similar geological conditions. Conduct field research on Y.Z., R.B., Y.H., Y.Y., P.L., H.W., J.S. and H.P. ; Y.Z. manuscript writing; similar simulation experiments include Y.Z., H.W., J.S. and H.P. ; writing review and correction of T.Y., J.Z. and H.L. All authors have read and agreed to the published version of the manuscript. This study was supported by the National Natural Science Foundation of China, which was chaired by Associate Professor [PERSON] and Professor [PERSON], (no. 52004200 and no. 51774229). Thank you very much for the support of the National Natural Science Foundation project. Not Applicable. The relevant data of this manuscript are obtained from field measurements and tests, which are real and effective. Thanks to [PERSON], [PERSON], [PERSON], and [PERSON] for their technical help in collaborating on the experimental work. I would also like to thank [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] for providing helpful inspiration, suggestions, guidance, review, and supporting work.