## 4 Numerical Simulation Analysis of Tunnel Stability
### Results of Simulation and Analysis
#### 4.2.3 Stress Analysis of Supports  
(1) Shotcrete stress. The corresponding nephogram of shotcrete and its variation curve can be seen in Figures 18 and 19. The minimum principal stress nephogram and its variation curve are presented in Figures 20 and 21. We can obtain from Figures 18 and 19 that maximum principal stress of shotcrete is tensile stress in the vault, spandrel, hance, and bottom, and the maximum is at the vault, followed by the spandrel and hance. It is compressive stress in the arch foot area. With the increase in the excavation step, the maximum principal stress of shotcrete increases gradually and tends to stabilize after the 10 th step. In the 5 th excavation step, the maximum stresses of the vault, spandrel, bottom, hance, and arch foot are 1.607 MPa, 1.122 MPa, 0.881 MPa, 0.077 MPa, and 0.025 MPa, respectively, whereas the convergence values are 1.443 MPa, 1.240 MPa, 0.911 MPa, 0.055 MPa, and 0.195 MPa, respectively. Convergence values of tensile stresses do not exceed the tensile strength of shotcrete structure, which indicates that the supporting structure is safe. Figures 20 and 21 show that stress of shotcrete at each key point is compressive, while and the stress at the hance is the largest, followed by the arch foot and bottom. With the increase in the excavation step, the minimum stress of shotcrete gradually increases and tends to stabilize after the 10 th excavation step. In the 5 th excavation step, the minimum principal stresses of the hance, arch foot, spandrel, vault, and bottom are 1.869 MPa, 1.350 MPa, 1.430 MPa, 1.158 MPa, and 0.199 MPa, respectively, and the convergence values of minimum principal stress are 2.672 MPa, 2.090 MPa, 1.635 MPa, 1.117 MPa, and 0.187 MPa, respectively. (2) Anchor axial force. The nephogram and variation curve of anchor axial force are presented in Figures 22 and 23. Calculation results show that the anchor axial force at the hance is the largest, followed by the spandrel, and the smallest is at the arch foot. The anchor axial force increases gradually with the excavation step and tends to stabilize after the 10 th excavation step. In the 5 th excavation step, the anchor axial forces of the hance, spandrel, vault, and arch foot are 7.651 MPa, 5.774 MPa, 6.036 MPa, and 0.011 MPa, respectively, and their convergence values are 10.682 MPa, 5.386 MPa, 5.201 MPa, and 0.267 MPa, respectively. (3) Secondary lining stress. The corresponding nephogram and its variation curve are presented in Figures 24 and 25. The  
As indicated in Figures 24 and 25, the maximum principal stress of the secondary lining is tensile stress, and the structure bears uniform force. With the advance of the working face, the maximum principal stress at each key point does not increase. The convergence values of stress at the arch foot, vault, spandrel, hance, and bottom are 4.660 MPa, 1.066 MPa, 0.914 MPa, 0.579 MPa, and 0.223 MPa, respectively. Figures 26 and 27 show that the minimum principal stress of the secondary lining is compressive stress, and the minimum principal stress at each point does not increase obviously with the advance of the working face. The convergence values of it at the arch foot, bottom, hance, vault, and spandrel are 10.382 MPa, 2.463 MPa  
lining construction, leading to the determination that the optimal construction time for the secondary lining is between days 26 and 27. (3) After the 10 th excavation, the main stresses in surrounding rock of the tunnel, as well as those in the shotcrete and anchor axial force, stabilize. This confirms that the chosen construction method and supporting scheme ensure project stability. The principal stress within the secondary lining remains relatively unchanged and at a low value. This observation aligns with the current tunnel design concept, where the secondary lining structure primarily serves as a safety reserve. [PERSON], [PERSON] and [PERSON]: methodology, simulation analysis, investigation, and writing of original manuscript. [PERSON] and Z.L. : reviewing the manuscript.