## 4 Results and Analysis
### Simulation Results of Arch Culvert under Periodic Vehicle Load  
#### 4.2.1 Deformation of Steel Corrugated Pipe  
Figure 20 shows the vertical and horizontal deformations of the steel corrugated pipe after 700 times of wheel load has passed over. When the vehicle load moves in one direction (from the 4-hole side to the 6-hole side), the vertical and horizontal deformations of the 4-hole and 6-hole sides show notable differences. This indicates that the direction of the dynamic load affects the deformation of the culvert and must be fully considered in the design. The front end of the model is a sidewalk, which is far from the vehicle load. Therefore, the settlement of the front-end culvert vault is smaller than that of the back-end culvert vault. The vault of the culvert sinks, and at the same time, the arch shoulder rises. The maximum subsidence is 23 mm, and the maximum uplift is 6.8 mm. The maximum lateral movement of \(\pm\)15 mm occurred at the shoulder, not the waist. Because the C15 concrete protective masonry limited the horizontal displacement of the waist. Whereas the shoulder was constrained by backfill soil, and the constraint effect was visibly weakened. To further analyze the deformation of the steel corrugated pipe culvert, the 5-hole corrugated pipe culvert with the largest deformation was selected. Figure 21 shows a  
Figure 19: Post-construction contour of maximum principal stress of steel corrugated pipe. Figure 20: Displacement contour of steel corrugated pipe (unit: mm, PB represents the number of wheel load passing the arch culvert): (**a**) PB700 vertical deformation; (**b**) PB700 horizontal deformation. magnified view of the 5-hole steel corrugated pipe before and after deformation, revealing the initial state of the structure and the contours after deformation of PB700 (PB means the number of wheel load that passes bridge, and PB700 means the number of wheel load that passes bridge is 700). Two obvious transition points, ST1 and ST2, can be found in the deformation diagram. The deformation transition points ST1 and ST2 are symmetrically distributed, approximately 3.0 m from the vertical symmetry axis of the structure and 1.0 m from the vault. The structural deformation above the transition point is concave, and the structural deformation between the transition point and the arch waist C1 (C2) is convex. Several deformation curves of different vehicle load passing times are drawn in Figure 21. When the passing times of vehicle loads are small, the deformation of the structure is small. As the passing times increase, the deformation will continue to increase and eventually converge. Figure 21(a) shows the relationship between structural vault settlement and wheel load passing times. Because the vehicle load action point is biased towards CR1, the settlement at CR1 is the largest. The sedimentation from CR1 to CR5 decreased gradually. The settlement rate at each point from PB0 to PB300 is nearly linear. The settlement starts showing a slow trend after PB300, because the structure may quickly reach a cooperative deformation state with the surrounding soil after a certain degree of rapid and large deformation. At PB700, the settlements of CR1 and CR5 were \(-22\) mm and \(-14\) mm, respectively. The difference was 8 mm, and the ratio of settlement to structural vector height was 0.28% and 0.18%, respectively. To explore the settlement stability value of the vault, quadratic polynomial fitting was performed for CR1 and CR5. The fitting curves and their function are shown in Figure 21(b). The settlements of CR1 and CR5 were predicted to be stable in PB1500 and PB1950, respectively. The corresponding settlement stability values were \(-40\) mm and \(-20\) mm, respectively, and the ratio of CR1 and CR5 settlement to structural vector height was 0.51% and 0.26%, respectively. Figure 21: Profile of 5-hole steel corrugated pipe before and after deformation (magnification: 50 times). Figure 23 shows the settlement and lateral displacement of the arch's upper shoulder (the points of SP1 to SP5).