## 3 Analysis of Influencing Factors of Surface Settlement
### Influence of Arrangement Scheme on the Lubricant Controlling Effect  
Based on Case 1-2 in Scenario 1, a horseshoe-shaped system model was constructed as illustrated in Figure 9. To control for variables, the burial depth range of this system was maintained approximately identical to that of the gate-shaped system in Case 1-2. As a result, the horseshoe-shaped pipe roof was configured with a span of 13 m and a crown positioned 4 m below the ground surface, and the number of steel pipelines was accordingly adjusted to 25, while all other settings and parameters remained consistent with those in Case 1-2. Notably, to simplify the modeling process, no tunnel element was included in this section. The resulting simulation data were employed to analyze the impact of pipe-rod arrangement options on the control effectiveness of lubricant on surface settlement. Table 5 provides detailed information on Scenario 2, while Figure 10 presents the simulation results for this scenario. Figure 10a illustrates the surface displacement of the horseshoe-shaped system along monitoring Line 3 under different lubricant conditions. As the lubricant Young's modulus increases, the surface displacement progressively decreases, and the settlement curve becomes flatter and shallower. Figure 10b compares the transverse settlement troughs for the two arrangement schemes at a burial depth of 4 m and a Young's modulus of 400 kPa. By contrast, the settlement curve of the gate-shaped system  
Figure 9: Horseshoe-shaped system arrangement of pipe roof. adopts a V-shaped profile, appearing narrower and steeper, which results in a larger peak settlement. Conversely, the horseshoe-shaped system exhibits a U-shaped settlement curve that is broader and smoother, leading to slightly higher settlement values at the two sides of the crown. To further analyze the cause of this phenomenon, displacement contour maps for both systems are provided, as illustrated in Figure 11. Overall, the gate-shaped arrangement scheme is characterized by a larger disturbance range; however, the resulting soil deformation is predominantly concentrated on the upper side of the pipe roof. In contrast, the horseshoe-shaped arrangement scheme shows a smaller disturbance range, with soil deformation distributed evenly along both sides of the crown. The analysis implies that the horseshoe-shaped system yields a more rational force distribution on the pipe roof and facilitates the uniform transfer of disturbance loads to both sides. In comparison, the gate-shaped pipe roof, resembling a frame structure, subjects its cross-beam element to considerable bending moments, thereby heightening the risk of localized stress concentrations. The findings indicate that the horseshoe-shaped system is more conducive to the control effect of lubricant. Figure 10: Vertical displacement of the ground surface: (**a**) changes in ground settlement of horseshoe-shaped system considering different lubrications (Line 3): (**b**) comparison of surface settlement between the two systems when \(h=4\) m, \(E=400\) kPa, and tail void \(=20\) mm. On the other hand, a comparison of Figure 10a and 8b reveals that increasing the Young's modulus from 200 kPa to 500 kPa decreases the maximum surface settlement by approximately 3 mm for both schemes; however, the reduction amounts to only 16% for the gate-shaped arrangement, while it reaches 20% for the horseshoe-shaped system. Clearly, compared with the gate-shaped system, the pipelines in the horseshoe-shaped  
Figure 11: Ground displacement contour maps of different pipe-roof layout schemes: (**a**) simulation results of Case 1–2 in Scenario 1; (**b**) simulation results of Case 2–1 to Case 2–4 in Scenario 2.