## 2 Numerical Model Establishment and Validation
### Validation Result and Influence Mechanism of Lubricant Young's Modulus  
The L-shaped arrangement was implemented on-site for the sequential jacking of steel pipelines, with ground displacement monitored as a reference indicator for analysis. Although the main tunnel construction has been finalized, the validation results are confined to a comparison of surface settlement values recorded during the construction phase of the new pipe roof, in accordance with the objective of this study. In shallow-buried soft foundations, significant discrepancies are often observed between numerical results and monitoring data. Consequently, the measured data were applied to calibrate the model, aiming to achieve a numerical representation that closely replicates the actual deformation. The calibrated model is then utilized to simulate the effect of the lubricant Young's modulus and its interaction with construction conditions on surface settlement. Figure 4 compares the simulation results with actual monitoring data after completing the new pipe roof. The black curves correspond to the simulation results for the lubricant used on-site. Figure 4a displays the transverse settlement trough (Line 1), where a notable error appears at the leftmost monitoring point. At this location, the measured settlement is approximately 5 mm, whereas the numerical simulation result is around 2.5 mm--m merely half of the measured value. However, the actual settlement peak reaches 8 mm, which is slightly lower than the peak value from the simulation (9.5 mm). Despite these variations, discrepancies elsewhere persist at minimal levels, and, overall, the simulation and monitoring data exhibit comparable transverse settlement troughs. Figure 4b depicts the surface settlement curve located directly above the pipe-roof centerline (Line 2). The simulation results stabilize at approximately 8.9 mm, whereas the actual surface displacement fluctuates along the entire monitoring line, likely due to the assumption in the simulation that the lubricant is uniformly distributed in the tail void. The maximum difference occurs at the midpoint of the jacking direction (Point O), where the field monitoring value is around 7 mm, resulting in an error of approximately 20%. Nevertheless, both curves show a similar trend. This result is deemed reasonable, as similar findings have been reported in previous studies [31]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variables** & **Consolidation** & **Young’s** & **Poisson’s** & **Density** & **Thickness** & **Components** \\  & **Time** & **Modulus (MPa)** & **Ratio** & **(kg/m\({}^{3}\))** & **(mm)** & **Components** \\ \hline  & After injection & 0.1 & 0.49 & & & \\  & 7 days & 0.23 & 0.4 & & & \\  & 14 days & 0.32 & 0.4 & 2100 & 20 & Silicate minerals + Polymers + Fibers \\  & 21 days & 0.37 & 0.4 & & & \\  & 28 days & 0.40 & 0.4 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Lubricant mechanical parameters considering consolidation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Young’s Modulus (MPa)** & **Poisson’s Ratio** & **Density (kg/m\({}^{3}\))** & **Thickness (mm)** \\ \hline Concrete & 22,000 & 0.2 & 2400 & - \\ Steel pipe & 210,000 & 0.25 & 210,000 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mechanical parameters of concrete and steel pipe. To examine the impact of lubricant Young's modulus on surface settlement induced by pipe-roof construction, an additional simulation was conducted for a control group with a lower Young's modulus, as presented in Figures 4b and 5. In the figure, the blue and black curves represent the simulation results for the control group and the lubricant used on-site, respectively. The results indicate that the vertical displacement caused by the lubricant with a lower Young's modulus is substantially higher than that produced by the lubricant with a higher Young's modulus (Figure 4b).