## 3 Comparison and Verification
Figure 4a demonstrates the logarithmic strain of the rock and soil mass around the tunnel when the tunnel burial depth is 30 m and the plastic strain zone in the figure has gone through to the Earth's surface. It is evident that at this point, considering only the effect of the geotechnical weight forces in the loose circle of the tunnel surrounding rock, this does not completely reveal the mechanical characteristics of tunnel construction. Figure 4b demonstrates the logarithmic strain of the rock and soil mass around the tunnel when the tunnel burial depth is 60 m, the plastic strain zone in the figure is concentrated with respect to the tunnel face and adjacent to the cavern, and it is also more widely distributed above the tunnel excavation faces. Therefore, the validity and applicability of the PH\(-\)1 damage mode and the PH\(-\)2 damage mode should be further determined after comparative analyses of the calculation results obtained through inputting the physical property parameters of the rock-soil mass. As shown in Figure 4c, when \(\varphi=45^{\circ}\), the safety factor for the M\(-\)1 area in the PH\(-\)1 failure model is 12.59% smaller than that for the P\(-\)1 area and the P\(-\)2 area in the PH\(-\)2 failure model. And the safety factor in the P\(-\)1 region and the P\(-\)2 region in the PH\(-\)2 failure mode is 7.13% smaller than that in the non-intrusive stochastic finite element  
Figure 4: Contrast verification: (**a**) the diagram of the logarithmic strain (i.e., LE, \(H_{3}=30\) m); (**b**) the diagram of the logarithmic strain (i.e., LE, \(H_{3}=60\) m); (**c**) the internal friction angle; and (**d**) the buried depth of the tunnel. method. The safety factor obtained by the finite element strength discounting method is 31.62% greater than that obtained for the M\(-\)1 zone in the PH\(-\)1 failure model and 21.76% greater than that obtained for the P\(-\)1 zone and the P\(-\)2 zone in the PH\(-\)2 failure model. In conclusion, the largest factor of safety could be obtained by applying the finite element strength reduction method, while the result calculated on the basis of the PH\(-\)1 failure model could be the smallest. As shown in Figure 4d, when the tunnel depth is 50 m, the safety factor achieved by the finite element strength reduction method is 0.30% larger than that of the PH\(-\)2 failure model. The safety factor obtained in the PH\(-\)1 failure model is 3.10% greater than that calculated in the PH\(-\)2 failure model. At a tunnel depth of 100 m, the safety factor obtained in the PH\(-\)1 failure model is 8.38% greater than in the PH\(-\)2 failure model. The safety factor obtained in the PH\(-\)2 failure mode is 5.84% greater than that calculated by the finite element strength reduction method. This study has revealed that the safety factor obtained by the finite element strength reduction method and the safety factor [27] based on the PH\(-\)2 failure model decreases significantly with an increasing tunnel depth. The curve of the safety factor in the PH\(-\)1 failure model fluctuates only slightly with an increasing tunnel depth. However, this is attributed to the consideration of the full self-weight of the overburden above the tunnel excavation face by the finite element strength reduction method and the calculation method for the analytical solution of instability probability based on the PH\(-\)2 failure model, whereas the analytical solution for the instability probability based on the PH\(-\)1 failure model only takes into account the gravitational force of the structural block \(A_{t,0}B_{t,1}B_{t,0}\) within the range of the disturbance area.