# Calculation Method for Settlement Deformation of Existing Tunnel Induced by Underpass Construction
## 4 Engineering Case Comparison
### Engineering Measurements and Numerical Simulations
It is evident that the theoretical conclusions, numerical simulation results, and on-site monitoring results of the existing tunnel's settlement value deviate only slightly. At \(x=10\) m, the maximum settlement value of the existing tunnel obtained from on-site monitoring is 1.82 mm, while the theoretically calculated value is 2.09 mm, with an error of only 14.8%. The outcomes of the numerical simulation and field monitoring are substantially similar. This is mainly because the theoretical derivation ignores factors such as construction progress and construction technology. The largest settlement is found at the vertical junction of two tunnels, but overall, the trends of the settlement curves produced by the three approaches are consistent. The theoretical calculation of this study is more accurate after taking into account the extra stress induced by the tunnel construction components. The maximum settlement of the existing tunnel, as determined by the theory in the literature [18], is 2.39 mm, with an error of 31.3%. Figure 10 investigates the correlation between the boring distance and the maximum settlement value of the existing tunnel. It also presents a comparison of the maximum settlement values obtained from theoretical calculations, numerical simulations, and on-site monitoring results. The settlement of the existing tunnel steadily grows as the shield moves \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Material Type**} & **Ontological** & \multirow{2}{*}{**Thicknesses/m**} & \multicolumn{2}{c}{**Modulus of Compress-**} & \multirow{2}{*}{**Capacity/(kN/m\({}^{2}\))**} & \multirow{2}{*}{**Cohesive**} & **Angle of** & \multirow{2}{*}{**Poisson’s Ratio**} \\  & & & & & & & & \\  & & & & & & & & \\ \hline landfill & Mohr-Coulomb & 1.38 & 9 & 19 & 10 & 28 & 0.25 \\ ooze & Mohr-Coulomb & 2.02 & 2 & 16.5 & 7.5 & 25 & 0.32 \\ silly clay & Mohr-Coulomb & 21.6 & 7.5 & 19.1 & 14 & 26 & 0.35 \\ grit & Mohr-Coulomb & 5 & 20 & 20 & 26 & 31.5 & 0.28 \\ shield & elastic & 0.09 & \(2.1\times 105\) & 78 & - & - & 0.3 \\ Lining Pipe-Sheets & elastic & 0.2 & \(2.88\times 104\) & 25 & - & - & 0.2 \\ Grouting (before hardening) & elastic & 0.1 & 1 & 22 & - & - & 0.28 \\ Grouting (after hardening) & elastic & 0.1 & 100 & 22 & - & - & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical and mechanical parameters of material. Figure 8: Three-dimensional numerical calculation model. toward it, and the settlement's rate of change also gradually rises. The settlement rate decreases as the shield machine travels beneath the existing tunnel; the settlement value essentially tends to stabilize when the cutter plate is located at the rear of the shield tail, around 12 m from the existing tunnel. Overall, there is a high degree of agreement in the distribution law of the maximum settlement value determined by the three techniques of theoretical analysis, numerical simulation, and on-site observation. Therefore, the theoretical method of this paper is effective and reliable in predicting the settlement and deformation of the existing tunnel.