# Prediction of Surface Deformation Induced by Ultra-Shallow-Buried Pilot Tunnel Construction
## 3 Case Validation of Deformation Predictions in Shallow-Buried Tunnels  
### Kunming Rail Transit Phase I Interval Tunnel  
The interval tunnel from East Passenger Station to Dabanqiao Station of the Kunming Rail Transit Line adopted the shallow-buried subsurface excavation method [31]. The overall total mechanical parameters of the main traversed strata are shown in Table 4, with tunnel design parameters visualized in Figure 5.  
The calculation parameter values are as follows: \(H\) = 14.5 m, \(A\) = 6.7 m, \(B\) = 3.5 m, \(C\) = 3.1 m, \(\Delta R\) = 30.26 mm, \(\tan\beta\) = 0.7 and \(\delta\) = 228.96 mm. Under these parameters, the posterior variance ratio of the proposed model is 0.02, indicating an \"excellent\" accuracy rating for the back-analysis. The reference literature converts the horseshoe-shaped section into an equivalent circle for calculations and assumes the circular section shrinkage occurs in two stages: a uniform inward shrinkage centered at the circle's origin followed by elliptical deformation. The overall deformation pattern is similar to the present model. A comparison of the calculation results between the two models is shown in Figure 6 (with the tunnel centerline at horizontal distance \(x\) = 0 m).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Stratum** & **Elastic Modulus (MPa)** & **Cohesion (kPa)** & **Internal Friction Angle (\({}^{\circ}\))** & **Poisson’s Ratio** \\ \hline Silty Clay & 7.24 & 12.8 & 15.6 & 0.28 \\ Argillaceous & 8.55 & 14.6 & 18.7 & 0.3 \\ Silstone & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Total mechanical parameters of traversed strata for Kunming Tunnel.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Grade** & **Excellent** & **Qualified** & **Marginal** & **Unqualified** \\ \hline \(C_{\mathrm{P}}\) & \textless{}0.35 & \textless{}0.5 & \textless{}0.65 & \textgreater{}0.65 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Back-analysis accuracy rating table.  
As shown in Figure 6, at the tunnel axis (horizontal distance = 0 m), the measured settlement is \(-\)38.3 mm and the calculated settlement by this model is \(-\)36.9 mm, with a relative error of 3.6% compared to the measurement. The calculated value from the reference literature is \(-\)30.8 mm, with a relative error of 19.6%--approximately 5 times larger than that of this model. At a horizontal distance of 7.5 m, the settlement curve exhibits an inflection point similar to that proposed by [PERSON], with a measured settlement of \(-\)16.9 mm, this model's calculation of \(-\)20.9 mm and a reference calculation of \(-\)19.2 mm. The overall settlement curve shows a bell shape, with larger settlement in the middle and smaller settlement on both sides--a trend observed in both measurements and the two calculation models.  
The error value is defined as the theoretical calculated value minus the measured value. As shown in Figure 7, the maximum deviation between the theoretical and measured values for this model is \(-\)3.06 mm, while the maximum error of the equivalent section method is 7.5 mm--twice as large as this model's error. The reference model exhibits smaller errors at the edges and the largest error at the tunnel center, whereas this model has smaller errors at both the edges and the tunnel center, with relatively larger errors at a horizontal distance of one tunnel diameter.  
Figure 5: Schematic diagram of calculation parameter values for Kunming Rail Transit Phase I Interval Tunnel.  
Figure 6: Comparison chart of measured and calculated surface settlement for Kunming Rail Transit Phase I Interval Tunnel.