# Finite Element Analysis of the Structural Behavior of a Corroded Pipe Culvert
## 4 Results and Discussion
### Cross-Sectional Shape  
The above simulation represents the typical shape of culverts commonly used in practical engineering applications. In pipe culvert engineering, elliptical pipe culverts are considered more practical than circular ones. However, based on the analysis from the simulation above, it can be observed that local corrosion of the invert section has a minimal impact on model deformation. This paper aims to further investigate whether the corrosion behavior of circular pipe culverts is similar to that of elliptical pipe culverts.  
In terms of model construction, compared with the original model, the soil and trench are unchanged, and the elliptical pipe culvert is replaced by the circular pipe culvert. Considering the influence of dimension on the experimental results, the cross section of the circular pipe culvert is set to a positive circle with a radius of 4 m, which is similar to the dimension of the elliptical pipe culvert in the experiment.  
The deformation patterns observed in both circular and elliptical culverts are comparable. Therefore, taking an elastic modulus value of 320 MPa and a corrosion depth of 0.12 m as examples, this study compares deformations between elliptical and circular culverts.  
The maximum displacement of circular culverts and elliptical culverts is analyzed in this section. The maximum horizontal displacement (\(u_{x}\)) of circular culverts and elliptical culverts is shown in Figure 14, and the maximum vertical displacement (\(u_{z}\)) is shown in Figure 15. It should be noted that, due to the size (the circumference of the circular culvert is slightly smaller than the elliptical culvert) and other factors, the horizontal displacement (\(u_{x}\)) of the circular culvert at different corrosion sites is less than that of the elliptical culvert model, and the maximum vertical displacement (\(u_{z}\)) is larger than that of the elliptical culvert. Therefore, to compare the maximum total displacement \(\mid u\mid\) of the two different sections and \(\mid u\mid\) under different corrosion conditions, refer to Figure 16.  
It can be seen that in the maximum total displacement of the uncorroded circular culvert \(\mid u\mid\) is less than that of the original model's maximum total displacement \(\mid u\mid\). However, the total displacement due to overall corrosion \(\mid u\mid\) is still larger than that of the elliptical culvert, which shows that the influence of overall corrosion on the circular culvert is greater than on the elliptical culvert. The corrosion and deformation behavior of other parts is similar. Comparing these observations allows us to draw two preliminary conclusions:  
1. The influence of corrosion on the deformation of circular and elliptical culverts is comparable. The corrosion behavior observed in circular culverts is similar to that observed in elliptical pipe culverts.  
Figure 13: Differential settlement diagram.  
2. Circular culverts are significantly affected by both overall and localized corrosion, resulting in a larger impact on their deformation compared to elliptical culverts.  
The cross-sectional curve of the circular culvert, as depicted in Figure 17 through finite element simulation, reveals that the crown position consistently exhibits the maximum vertical displacement (\(u_{z}\)). Furthermore, it is observed that the leftmost point of the culvert's cross-section consistently manifests the highest total displacement value, aligning with the corrosion pattern observed in elliptical culverts.  
Figure 14: Comparison of maximum horizontal displacement (\(u_{z}\)) (taking the elastic modulus of 320 Mpa and the corrosion depth of 0.12 m as an example).  
Figure 15: Comparison of maximum horizontal displacement (\(u_{z}\)) (taking the elastic modulus of 320 Mpa and the corrosion depth of 0.12 m as an example).