## 6 Conclusions and Summary  
In this paper, the structural characteristics and instability process of the first weighting in large mining height working face were analyzed through a physical experiment and a numerical simulation, performed in order to study roof sliding and instability along the coal wall during the first weighting in the working face with large mining height in shallow coal seam. An analysis model based on catastrophe theory was developed to study roof sliding and instability along the coal wall. The necessary and sufficient conditions of system instability were obtained, and the main factors affecting the system stability were analyzed. The influence of each parameter on the stiffness ratio \(K\) was discussed and compared. The calculation equations of support resistance and roof step sinking were obtained, and the mechanical mechanism and main influence factors of the main roof step sinking were analyzed. Combined with the monitoring example, the rationality of judging roof instability by catastrophe theory was verified, and the rationality of the support resistance selected in the working face was checked. The following conclusions can be drawn through analysis of the theoretical results. The formation and weighting characteristics of composite cantilever beam structure of the first weighting in large mining height working face were analyzed through a physical test and a numerical simulation. The premise of working face stability was to ensure that the direct roof was not destroyed. 2. The sufficient and necessary conditions for system instability were obtained by analyzing the system model consisting of main roof, immediate roof, and support through catastrophe theory. The system instability was related not only to the stiffness ratio \(K\) and material parameters of the support and immediate roof, but also to the load \(Q\) and the first weighting interval of the main roof. 3. The influence degree of each parameter on the stiffness ratio \(K\) was as follows: elastic modulus \(E>\) support stiffness \(k_{1}>\) sectional area \(A>\) immediate roof thickness \(H\). Increasing the support stiffness within a certain range had a positive effect on reducing the roof step sinking. 4. The main roof step sinking \(\Delta h\) increased linearly with the external load \(q\), and was inversely proportional to the thickness of immediate roof \(h\) and support stiffness \(k_{1}\). By comparing the three parameters, we found that the influence degree on step sinking was overburden load \(q>\) immediate roof thickness \(H>\) support stiffness \(k_{1}\). 5. The stability of no. 12401 working face was calculated and analyzed by the catastrophe theory, with the calculation results showing that the working face met the instability condition of the system, which was consistent with the monitoring results, and the support resistance should be greater than 19,232 kN to ensure the stability of the main roof. In this article, [PERSON] and [PERSON] put forward the study ideas, [PERSON] designed the article structure and wrote the paper, [PERSON] conducted the theoretical derivation and analyzed the data, [PERSON] and [PERSON] collected and analyzed the data from mine site, and [PERSON] and [PERSON] revised the English writing. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (grant no. 51704173 and 51674151), and the Key R&D projects of Shandong Province (grant no. 2019 GSF111029), the Science and Technology program of colleges and universities in Shandong Province (grant no. J17 KA203), the National Program on Key Basic Research Project (2018 YFC1505300), and the Qingdao postdoctoral researcher application research project. The authors declare no conflict of interest.