## 3 Numerical Model
### Influencing Factors and Parameter Values  
The deformation of underground pipelines around the tunnel was affected by its factors, design factors, construction factors and other factors. Therefore, according to the parameter analysis method, the main influencing factors were divided into the relative position relationship between underground pipeline and tunnel, pipeline parameters and tunnel construction parameters. The relative position relationship between the underground pipeline and the tunnel included the horizontal distance of the pipeline and the buried depth of the pipeline. Pipeline parameters included pipeline diameter, pipeline wall thickness, pipeline shape and pipeline material. The tunnel construction parameters were the excavation method. Among them, the horizontal distance of the pipeline was considered in the modelling. Nine pipelines were set in the same horizontal plane with a spacing of 6.25 m, as shown in Figure 5. For the convenience of subsequent analysis, the pipeline directly above the central axis of the central pilot tunnel was set as No. 1, the pipeline in the negative direction of the X-axis on the left side of the central axis was set as No. 2, No. 3, No. 4 and No. 5 from left to right, and the pipeline in the positive direction of the X-axis on the right side of the central axis was set as No. 6, No. 7, No. 8 and No. 9 from left to right. Except for the horizontal distance of the pipeline, three values were set for the other five factors on the basis of reasonably considering the parameter value range according to the actual situation. For example, the buried depth parameter of pipelines was taken into account that the buried depth of pipelines around the tunnel was  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{\begin{tabular}{c} **Density** \\ **(kg/m3)** \\ \end{tabular} } & \begin{tabular}{c} **Elastic** \\ **Modulus** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Frictional** \\ **Angle (°)** \\ \end{tabular} & \begin{tabular}{c} **Cohesive** \\ **Force (kPa)** \\ \end{tabular} & \
\begin{tabular}{c} **of** \\ **Permeability** \\ **(10\({}^{-6}\) m\(\cdot\)s)** \\ \end{tabular} &
\begin{tabular}{c} **Thickness** \\ **(m)** \\ \end{tabular} \\ \hline Miscellaneous fill & 1900 & 10.76 & 0.32 & 19.4 & 26.8 & 52.52 & 4 \\ Completely weathered granite & 1950 & 13.00 & 0.35 & 20.0 & 108.0 & 63.00 & 22 \\ Fragmentary strongly & 2300 & 10.72 & 0.3 & 30.5 & 56.5 & 82.00 & 24 \\ weathered granite & 1400 & 2000 & 0.34 & — & — & — & 0.01 \\ Pipeline & 2500 & 10,500.00 & 0.25 & — & — & — & 0.3 \\ The pilot tunnel lining & 2500 & 34,000.00 & 0.15 & — & — & — & 0.3 \\ Inverted arch primary & 2600 & 34,000.00 & 0.15 & — & — & — & 0.3 \\ support & Middle partition wall and & 2500 & 30,000.00 & 0.20 & — & — & — \\  & & & & & & & \\ Primary support of the first & 2600 & 34,000.00 & 0.15 & — & — & — & 0.3 \\  & & & & & & & \\ Primary support of the second & 2550 & 32,000.00 & 0.15 & — & — & — & 0.22 \\  & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model material parameters.  
Figure 4: Numerical model (unit: m).  
within 2.5 m below the road surface as indicated in the survey documents. The diameter of pipelines around the tunnel was between 400 mm and 1000 mm. The construction method in the construction was considered when taking the value of tunnel construction parameters. The influencing factors and parameter values of pipeline deformation are shown in Table 2. When studying the influence of the change of one influencing parameter on the deformation and stress of the underground pipeline, the other five parameters were set according to working condition 2.