## 3 Analysis of Influencing Factors of Surface Settlement
### Influence of Different Bural Depths on the Lubricant Controlling Effect  
Figure 7 depicts the model considering various burial depths. Drawing on the existing structure and its pipe-roof arrangement scheme described in the case study (Figure 2), the dimensions and relative positions of the tunnel and steel pipelines were determined. During the simulation, 28 steel pipelines were sequentially jacked following a center-to-sides procedure, while surface displacement induced by pipe-roof construction was monitored along lateral monitoring Line 3. Table 4 outlines the simulation scenario designed to assess the influence of burial depth on lubricant control effectiveness. In Cases 1-1 through 1-4, burial depths were set at 2 m, 4 m, 6 m, and 8 m, respectively. For each case, different lubricant Young's moduli (ranging from 200 kPa to 500 kPa) were considered, while the Poisson's ratio was assumed to be 0.4 to minimize the influence of additional variables. All other model settings remain unchanged.  
Figure 8 illustrates the transverse settlement trough generated by pipe-roof construction for each case in Scenario 1. Under identical lubricant conditions, as burial depth increases, surface settlement progressively rises, and the settlement curve transitions from a narrow, steep profile to a broad, gentle one. This trend demonstrates that increasing burial depth undermines the lubricant's capacity to control surface settlement.  
Figure 7: Schematic diagram of the model considering different burial depths.  
Conversely, as Young's modulus increases from 200 kPa to 500 kPa, the surface settlements in Cases 1-1 through 1-4 diminish; however, the extent of reduction differs among the cases. Specifically, at a burial depth of 2 m, the peak settlement is lowered from approximately 12.6 mm to 11 mm--a decrease of 14.5%. However, at a burial depth of 8 m, the maximum settlement declines from 25.4 mm to 20.7 mm, corresponding to a reduction of 22.7%. These suggest that, with the growth of burial depth, enhancing the lubricant elastic modulus can more significantly augment its control effect; conversely, the benefit of elevating the lubricant stiffness is attenuated. Furthermore, the results indicate that lower-stiffness lubricants consistently produce more pronounced surface displacements. Therefore, for greater burial depths, it is advisable to select a high-stiffness lubricant to reduce the impact of repeated pipe jacking on the ground surface, whereas, for shallower burial depths, a medium-stiffness lubricant is sufficient to inhibit the contraction of the soil layer surrounding the pipe.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{\begin{tabular}{c} **Modeling** \\ **Scenarios** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Modeling** \\ **Cases** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Burial** \\ **Depth** \(h\) **(m)** \\ \end{tabular} } & \multicolumn{3}{c}{**Lubricant Input Parameters**} & \multirow{3}{*}{\begin{tabular}{c} **Pipe Roof** \\ **Radius** \\ **(kPa)** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Pipe Roof** \\ **Arrangement** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Tail Void** \\ **(mm)** \\ \end{tabular} } \\ \cline{4-7}  & & Case 1–1 & 2 & & & & & \\ \cline{1-1} \cline{3-7}  & Case 1–2 & 4 & 200, 300, 400, & & & & & \\ \cline{1-1} \cline{3-7}  & Case 1–3 & 6 & 500 & & & & & \\ \cline{1-1} \cline{3-7}  & Case 1–4 & 8 & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Modeling scenario to study the effect of burial depth on lubricant control effectiveness.  
Figure 8: Influence of burial depths on the effectiveness of lubricants in controlling pipe-roof-induced settlement: (**a**) Case 1–1, \(h\) = 2 m; (**b**) Case 1–2, \(h\) = 4 m; (**c**) Case 1–3, \(h\) = 6 m; (**d**) Case 1–4, \(h\) = 8 m.