## 4 Safety Evaluation of Shaft Lining
### Calculation Method of Safety Factor of Shaft Lining  
(1) Calculate the lining safety factor according to the mine code.  
The MIDAS-GTS software was used to establish a two-dimensional load-structure model and calculate the axial force and bending moment of the lining. The safety factor of the shaft lining was calculated according to the safety factor calculation formula of \"Code for design of coal mine shaft and chamber\".  
Shaft linings may occur in two forms of failure: compressive and tensile. The \"Code for design of coal mine shaft and chamber\" (GB 50384-2016) stipulates that the bearing capacity of the circular ring section of the concrete shaft wall should be calculated separately under the actions of both uniform and uneven pressure.  
Figure 16: Description of the principle of water pressure characteristics.  
Figure 15: Comparison of simulation results with monitoring results. (**a**) S1 ZX0 + 660 m; (**b**) S1 ZX0 + 735 m.  
Under the action of uniform pressure, the calculation of the safety factor of the bearing capacity of the ring section of the plain concrete shaft wall is shown in Equation (1).  
\[KN\leq 0.85\varphi_{1}tf_{c} \tag{1}\]  
Under the action of uneven pressure, the calculation of the safety factor of the bearing capacity of the ring section of the plain concrete shaft wall is shown in Equation (2).  
When the eccentric distance is \(\epsilon_{0}<0.225t\), it should be calculated according to the following equation:  
\[KN\leq 0.85\varphi_{1}f_{c}b_{n}(t-2\epsilon_{0}) \tag{2}\] \[\epsilon_{0}=\frac{M_{A}}{N_{A}}\sigma\frac{M_{B}}{N_{B}}\]  
When the eccentric distance \(\epsilon_{0}\geq 0.225t\), it should be calculated according to the following equation:  
\[KN\leq\varphi_{1}\frac{0.8525f_{1}b_{n}t}{\frac{6\epsilon_{0}}{T}-1} \tag{3}\]  
where \(K\) represents the safety factor; \(N\) represents the calculated value of axial force on the annular section of shaft wall per meter height, MN/m; \(\varphi_{1}\) represents the stability coefficient of plain concrete members; \(t\) represents the shaft wall thickness, m; \(b_{n}\) represents the calculated width of shaft wall section, taken as 1.0 m; \(f_{c}\) represents the design value of axial compressive strength, N/mm\({}^{2}\); \(f_{i}\) represents the design value of concrete tensile strength, N/mm\({}^{2}\); \(N_{A},\ N_{B}\) represent the calculated value of axial force of sections A and B, MN; \(M_{A},\ M_{B}\) represent the calculated value of bending moment of sections A and B, MN:m; and \(\epsilon_{0}\) represents the distance from the point of application of axial force to the point of resultant force, mm.  
The specification stipulates that the safety factor of wellbore lining is not less than 1.35 under uniform water and soil pressure, and the safety factor of wellbore lining is not less than 1.1 under uneven water and soil pressure.  
(2) Calculate the lining safety factor based on the ratio of the normal service limit state load to the actual load.  
The lining analysis model was established using RFPA software, and the field monitoring load around the lining was used as the actual and initial loads; the single-step increment was set to 0.1 MPa for simulation analysis. When the lining has obvious cracks, the load at this time is defined as the normal service limit state load.  
When defining the safety factor \(K\) to equal the ratio of the normal service limit state load to the actual load, the formula is as follows:  
\[K=\frac{P_{f}}{P_{a}} \tag{4}\]  
where \(K\) represents the safety factor, MPa; \(P_{f}\) represents the normal service limit state load, MPa; and \(P_{a}\) represents the actual load, MPa.