## 4 Key Parameters of Tunnelling Method for the FT
### Impact of Different Layer Thicknesses on the Stress of the Surrounding Rock  
According to the solution process in the previous section, an analytical solution for the stress of the cross-sectional surrounding rock can be obtained by writing a computational program using MATLAB R2023b software. To determine a reasonable width between the cross-sections of AT and FT-I, calculations are performed for various values of \(d_{2}\), such as 0.6, 1.2, 1.8, \(\ldots\), 5.4 m. Stress monitoring points are set on the contours of the two cross-sections, as shown in Figure 12. The monitoring points are located within the contour range near the interlaid rock. For the AT section, the monitoring points are analyzed within the range of \(\theta_{1}\) from \(-90^{\circ}\) to \(+90^{\circ}\), while for the FT-I section, monitoring points are selected within the range of \(\theta_{2}\) from \(90^{\circ}\) to \(270^{\circ}\). Twenty monitoring points were taken from each section, with an angular difference of \(9^{\circ}\) between the two points. Figure 13 illustrates the radial stress variation curves of the monitoring points on the cross-sectional contours under different values of \(d_{2}\). Due to the relatively small difference in radii between the two concentric circles, the calculated results show a minor discrepancy in the radial stress experienced by the two cross-sectional contours, and their variation patterns are similar. The peak stresses on the surrounding rock occur in the crown and invert regions. In the crown shoulder region, the stress on the surrounding rock increases with the thickness of the interlaid rock. However, in the crown waist region, the stress on the surrounding rock decreases with an increase in the thickness of the interlaid rock. For the cross-section of AT, this variation occurs within the crown waist range of \(-30^{\circ}\) to \(30^{\circ}\), while for the cross-section of FT-I, it occurs within the crown waist range of \(140^{\circ}\) to \(220^{\circ}\). Figure 12: Diagram of the stress monitoring point on the section contour. Analyzing the data from the feature points, the curve depicting the variation in radial stress with the thickness of the interlaid rock is plotted within the crown waist range, as shown in Figure 14. From the graph, it can be observed that when \(d_{2}\) is less than or equal to 3 m, the influence on radial stress is significant, and as the width decreases, the rate of stress increase becomes higher. Conversely, when \(d_{2}\) is greater than 3 m, the stress variation around the tunnel becomes gradual and tends to reach equilibrium as the width decreases. Figure 15 illustrates the results of hoop stress at different values of \(d_{2}\). The results indicate that the peak hoop stress occurs at monitoring points with \(\theta_{1}=0^{\circ}\) and \(\theta_{2}=180^{\circ}\), which correspond to the closest points on the profiles of the two tunnels. The hoop stress around the AT decreases with an increase in \(d_{2}\), especially in the arch waist region where the influence of \(d_{2}\) is more pronounced. Around the FT-I, in the arch shoulder region with \(\theta_{2}=90\)-\(150^{\circ}\) and \(\theta_{2}=210\)-\(270^{\circ}\), the hoop stress decreases with an increase in \(d_{2}\). However, in the range of \(\theta_{2}=150\)-\(210^{\circ}\), the hoop stress increases with an increase in \(d_{2}\). Analyzing the monitoring points within this range, the curves depicting the influence of different \(d_{2}\) values on hoop stress are shown in Figure 16. From the graph, it can be observed that with an increase in \(d_{2}\), the impact on hoop stress is minimal, and the curve changes gradually. When \(d_{2}\) is less than or equal to 3 m, the curve tends to reach equilibrium. Moreover, when \(d_{2}\) is greater than 3 m, hoop stress shows a slow increasing trend. Figure 14: Variation curves of radial stress with different values of \(d_{2}\) in the arch waist range. (**a**) AT section; (**b**) FT-I section.