## 4 Analysis of the Numerical Calculation Results
### Stress Analysis of the Support  
Figure 9 illustrates the maximum principal stress distribution in the initial lining under three different excavation methods. The figure highlights that peak stress variations within the tunnel are primarily located at the arch waist and arch foot positions. According to the model's calculations, both the double-side drift method and the three-benching seven-step method register the highest principal stress at the left arch footing, with values of 2.9 MPa and 3.1 MPa, respectively. Conversely, the CRD method shows the highest principal stress at the right arch footing, measuring 3.6 MPa. From these observations, several insights can be drawn (Figure 9). Firstly, the areas experiencing peak stresses, specifically the tunnel girdle and foot of the arch, should be carefully monitored, as these are likely sites of significant stress concentration within the tunnel structure. Secondly, the variability in stress distribution across the different excavation methods suggests that each method impacts the structural stresses differently. This variability must be thoroughly considered in the engineering design and the planning of construction sequences. For instance, when choosing an excavation method, its effects on the tunnel stresses should be evaluated individually, and appropriate strategies should be implemented to mitigate the effects of stress concentrations, thereby enhancing the overall safety and stability of the structure. Figure 8: Variation curves of the perimeter rock displacement for the three working methods. (**a**) Settlement of the top of the perimeter rock arch by the three methods; (**b**) rise of the bottom of the perimeter rock arch by the three methods. Figure 10 depicts the minimum principal stress distribution in the primary lining under three excavation methods. It reveals that all three methods exhibit the lowest principal stresses at the right arch waist position. Specifically, the minimum principal stress recorded for the double-side drift method is \(-9.8\) MPa, for the three-benching seven-step method, it is \(-11.3\) MPa, and for the CRD method, it reaches \(-13\) MPa. From this analysis, several important observations can be made. First, the minimum principal stress at the right arch girdle warrants particular attention due to its potential complexity in terms of structural stresses. Second, the variation in stress distribution across different excavation methods underscores the need for a tailored approach in both design and construction phases. By understanding these differences, engineers and construction managers can implement targeted measures to enhance the stability and safety of the tunnel structure. Figure 9: Maximum principal stress contour map of the support under the three working methods. (**a**) Double-sided drift method; (**b**) CRD method; (**c**) three-benching seven-step method (unit: Pa). During the excavation process of the three excavation schemes, the minimum stress in the initial lining reaches its peak value as excavation progresses, with the rate of change gradually slowing down. For the three-benching seven-step method, the development phase of the minimum principal stress in the initial lining is concentrated during the first step of excavation, reaching its maximum after the excavation of the second set of steps, then decreasing and finally stabilizing at around \(-11.3\) MPa. In the CRD method, the minimum principal stress changes by about \(60\%\) during the first stage of excavation. As excavation and support proceed, the rate of decrease gradually slows, finally stabilizing at \(-13\) MPa. The double-side drift method shows a more even and gentle rate of change in the minimum principal stress of the initial lining compared to the CRD method and the three-benching seven-step method, without experiencing a concentrated release process, ultimately stabilizing at \(-9.8\) MPa.