## 3 Simulation Results and Sensitivity Analysis
### Influence of Backfill Compaction on the Pipe During Installation  
In the process of simulating the backfill of the pipe, it was assumed that the compaction of the backfill met the requirements of the specification, and the deformation of the pipe was only affected by the compaction of the backfill. The pipe was 600 mm and 4 kPa, and the buried depth was 1.5 m. The deformation and von-Mises stress distribution of the pipes are shown in Figures 7 and 8. In Figure 7, \"Initial\" represents the shape of the pipe before deformation due to soil compaction, \"0.15 m\" represents the deformed shape of the pipe when the backfill thickness (from the invert to the surface of the backfill) was 0.15 m, and \"Stable\" represents the deformed shape of the pipe when it reached a stable state after installation was completed.  
During the installation of the pipe, the compaction of the backfill on the pipe side caused horizontal compression of the pipe, and the deformation of the pipe was a \"vertical elliptical deformation\" (Figure 7). Similar conclusions have been reached by previous authors [55; 56]. The vertical deflection of the pipe first increased and then decreased. When the backfill was compacted to 3/4 of the diameter of the pipe, the vertical deflection of the pipe reached its maximum value, and the deformation of the pipe was still a vertical ellipsis after the assembly was completed. This might be because when the soil was not backfilled to the springline, the pipe was only affected by the lateral earth pressure; with the increase in backfill thickness, the lateral earth pressure acting on the pipe increased. After backfilling to the springline, the pipe was subjected to the combined effect of vertical earth pressure and lateral earth pressure, and the vertical deflection of the pipe gradually decreased. As the burial time increased, the pipe changed from a vertical elliptical deformation to a horizontal elliptical deformation. The vertical elliptical deformation that occurs during the installation of a flexible pipe will reduce the deflection deformation under the action of soil covering the top of the pipe, thus prolonging the service time of the pipes [12].  
Similar to the vertical deflection of the pipe, with the increase in the thickness of compacted backfill, the Von-Mises stresses of the crown, springline, and invert first increased and then decreased (Figure 8). When the vertical deflection of the pipe was at its maximum, the Von-Mises stresses also reached the maximum. When the pipe assembly was completed, the Von-Mises stress of the invert was the largest, and the Von-Mises stress of the springline was the smallest. After the pipe was buried for some time, the stress of the crown decreased slightly, the stress of the springline increased, and the stress of the invert decreased. This proved that the soil and pipe reached a new equilibrium. In the process of backfilling, the maximum Von-Mises stress of the pipe was several times that of the stable state (2.5 times at the crown, 3.2 times at the springline, and 3.4 times at the invert). However, this high-stress state of the pipe had a very short duration: in general, the pipe would not be damaged during the backfilling. Thus, although the pipe experienced great strain during installation, the long-term load (such as the earth pressure, surface load, and traffic load) that the pipe bears was considered to have a greater impact on its deformation during its service period.