## 5 Conclusions  
Relying on the No. 1 vertical auxiliary shaft project in the Gaoligongshan tunnel, this paper adopts on-site monitoring and numerical simulation methods to study the water pressure distribution characteristics and lining safety evaluation technology of deep vertical shafts in water-rich, fractured granite stratum. The main conclusions are as follows:  
1. For a deep shaft located in a water-rich, steep-dipping, large, fractured granite stratum, the water pressure on the outside of the lining on two horizontal planes of the shaft was monitored on-site, and the results showed that the water pressure distribution on the outside of the lining on the same horizontal plane was uneven.
2. For the uneven distribution of water pressure outside the shaft lining, a dual medium model, considering the existence of cracks, was established, and the reasons for the uneven distribution of water pressure were obtained by analyzing the two sections S1 ZK0 + 660 m and S1 ZK0 + 735 m. Due to the existence of large fissures in the surrounding rock, the hydraulic conductivity of the stone bodies formed after grouting of the surrounding rock in different regions was different. When the hydrostatic pressure outside the grouting ring reaches the outside of the lining through the grouting rings with different hydraulic conductivity in all directions, the osmotic pressure in different directions on the outside of the lining was different.
3. Based on the above water pressure distribution characteristics, in order to study the safety of the lining under the action of non-uniform pressure, the ratio of the lining's normal service limit state load to the actual load was defined as the lining safety factor. The normal service limit state load is the load when the lining has obvious cracks under the action of external load using RFPA software; the actual load is the monitoring load. Using this new method, the safety factors of the lining sections of the shafts S1 ZK0 + 660 m and S1 ZK0 + 735 m, under the action of non-uniform pressure, were 1.72 and 1.43, respectively. In addition, according to the \"Code for Design of Shafts and Chambers of Coal Mine Shafts\", the safety factors of lining sections of vertical shafts S1 ZK0 + 660 m and S1 ZK0 + 735 m, under the action of non-uniform pressure, were 1.9 and 1.6, respectively. The calculation results of the two methods were both less than the specified value of 1.1, thus indicating that the lining design meets the safety requirements.
4. Comparing the calculation results of the two methods, it can be seen that, under the same conditions, the judgment results of the two methods for the safety of the lining were consistent, thus indicating that the new method can effectively calculate the safety of the lining. In addition, the calculated values of the new method were all smaller than the calculated values of the mine code method, thus indicating that the design of the lining with the new method has a greater safety reserve.  
Conceptualization, M.H. and X.Y.; software, X.Y. and J.L.; validation, X.Y.; formal analysis, X.Y.; investigation, X.Y.; data curation, X.Y., J.L. and Z.T.; writing--original draft preparation, X.Y.; writing--review and editing, X.Y. and M.H.; supervision, M.H.; project administration, M.H. and Z.T.; funding acquisition, M.H. All authors have read and agreed to the published version of the manuscript.  
The authors acknowledge the financial support provided by the National Key R&D Program (P2019G055) and general program of the National Nature Science Foundation of China (No. 518783).  
Not applicable.  
Firstly, we thank the authors for their contributions to the article. Secondly, in addition to the authors of the article, [PERSON], who works for China Railway Construction Management Co., Ltd., also made important contributions to the conceptualization, project administration, and funding acquisition of the article. Thank you very much.