## 3 Tunnel Stability Based of In-Site Monitoring
### Monitoring and Analysis of Subsidence of Vaults and Horizontal Convergence  
The variation curves of displacement and tunnel vault subsidence and horizontal convergence rates are shown in Figure 6.  
After observing Figure 6, the following can be noted: (1) Vault subsidence [23; 24] increased sharply in the first 11 days after tunnel excavation, during which the subsidence accounted for 86% of the total subsidence. After that, the vault subsidence entered a slow growth stage, lasting about 14 days, and the subsidence amount accounted for 9% of the total subsidence amount. After 26 days of tunnel excavation, vault subsidence converges,  
Figure 4: Vertical displacement vs. time curves of the monitoring points. Figure 5: Surface settlement. and the measured convergence value of vault settlement is 51.77 mm. (2) After excavation, the subsidence rate of the vault varies significantly within 11 days, whereas the daily average subsidence rate is about 4.22 mm/d, showing that the surrounding rock is in rapid deformation. After that, it gradually decreases and tends to be stable. Figure 6 also shows the following: (1) Within 11 days of tunnel face excavation, horizontal convergence of the upper step reaches a sharp growth stage, during which the convergence value accounts for 72% of the total. After that, it enters a slow growth stage, lasting about 12 days, while the convergence value accounts for 25% of the total. After 25 days of excavation, the horizontal convergence is stable, and the final convergence is 24.77 mm. (2) During the first 11 days, the horizontal convergence rate changed significantly, and the daily average convergence rate was about 1.80 mm/d and then gradually decreased and tended to zero. While excavating the tunnel, the convergence value of the lower step is smaller than the upper step, and this is due to the initial support immediately after the excavation of the upper-step arch, which has an inhibition effect on the surrounding rock deformation. The construction time for secondary lining plays a crucial role in ensuring the self-supporting capacity of the surrounding rock and long-term stability. While technical specifications for tunnel engineering in China determine optimal supporting times for the secondary lining, these guidelines primarily apply to general tunnels. However, for shallow soft-rock tunnels, a clear and unified conclusion regarding optimal timing remains elusive. Field monitoring results have been instrumental in determining the effective and critical time for the secondary lining [25]. To address this, the study employs nonlinear fitting analysis using exponential, logarithmic, and hyperbolic functions to assess vault subsidence and horizontal convergence [22] and to determine the optimal time for secondary lining. The fitting results are shown in Figures 7 and 8. Observations from Figures 7 and 8 reveal that the predicted results from the exponential function closely align with the field-measured results, regardless of whether we consider vault subsidence or horizontal convergence. Specifically, the calculated subsidence and convergence using the exponential function are 53.20 mm and 26.38 mm, respectively. According to the \"Technical Specification for Construction of Highway Tunnel\" [26], the allowable relative displacement of Grade V rock with a buried depth less than 50 m ranges from 0.20% to 0.80%. Given that the final displacement value for vault subsidence in the monitored section is 51.77 mm, and the tunnel excavation height is approximately 9.62 m, the relative displacement of vault subsidence (0.53%) meets the allowable requirements. Figure 6: Displacement vs. rate of vault subsidence and horizontal convergence.