# Prediction of Surface Deformation Induced by Ultra-Shallow-Buried Pilot Tunnel Construction
## 3 Case Validation of Deformation Predictions in Shallow-Buried Tunnels
### Xi'an Metro Line 8 Mining Method Tunnel  
Xi'an's first circular metro line, Metro Line 8, features a horseshoe-shaped cross-section constructed by the mining method [23]. The overall mechanical parameters of the main traversed strata are shown in Table 5, with tunnel design parameters visualized in Figure 8.  
The parameter values used in the calculation of this model are as follows: \(H\) = 13.8, \(A\) = 6.4 m, \(B\) = 3.6 m, \(C\) = 2.0 m, \(\Delta R\) = 44.5 mm, tan\(\beta\) = 0.35 and \(\delta\) = 200 mm. Under these parameters, the posterior variance ratio of the proposed model is 0.05, indicating an \"excellent\" accuracy rating for the back-analysis. The reference literature uses a modified double-gap non-uniform convergence model for horseshoe-shaped tunnels. In contrast, this model employs a single-gap, two-stage non-uniform convergence method while maintaining the horseshoe-shaped cross-section. A comparison of the calculation results between the two models is shown in Figure 9 (with the tunnel centerline at horizontal distance \(x\) = 0 m).  
Figure 8: Schematic diagram of calculation parameter values for Xi’an Metro Line 8 Mining Method Tunnel.  
\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 Medium Sand & 33 & 2 & 33 & 0.29 \\ Layer & & ground surface & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Total mechanical parameters of traversed strata for Xi’an Tunnel.  
Figure 7: Comparison chart of settlement calculation errors for Kunming Rail Transit Phase I Interval Tunnel.  
As shown in Figure 9, the measured settlement at the tunnel axis is \(-26.4\) mm, with the calculated value by this model being \(-24.5\) mm--slightly smaller than the measurement, yielding a relative error of \(6.8\%\). The reference model's calculated settlement is \(-28.4\) mm--slightly larger than the measurement--with a relative error of \(7.7\%\). At a horizontal distance of \(10\) m, the measured settlement is \(-18.7\) mm, this model's calculation is \(-19.2\) mm (relative error \(0.8\%\)) and the reference calculation is \(-20.3\) mm (relative error \(8.3\%\)). The overall settlement curve shows larger values at the center and smaller values on both sides, with the settlement change rate decreasing as the horizontal distance from the axis increases--a trend observed in both measurements and the two calculation models.  
Figure 10 shows that the maximum deviation between the theoretical and measured values for this model is \(1.9\) mm, while the reference model has a maximum error of \(3.7\) mm--twice as large as this model's error. The reference model exhibits the largest error at a distance of twice the tunnel diameter from the axis, with smaller errors at the edges and axis, contrary to the error characteristics of this model, which has the smallest error at twice the tunnel diameter and larger errors at the edges and axis.  
Figure 10: Comparison chart of settlement calculation errors for Xi’an Metro Line 8 Mining Method Tunnel.  
Figure 9: Comparison chart of measured and calculated surface settlement for Xi’an Metro Line 8 Mining Method Tunnel.  
Analysis of Surface Deformation Induced by Ultra-Shallow-Buried Pilot Tunnel of Beijing Metro Line 13 Based on Non-Uniform Convergence Model