# Finite Element Analysis of the Structural Behavior of a Corroded Pipe Culvert
## 4 Results and Discussion  
### The Influence of Corrosion Depth on the Deformation of Pipe Culvert (E = 320 MPa)  
The elliptical pipe culvert overall corrosion is taken as an example, as shown in Figures 5 and 6. It reveals that the horizontal displacement (\(u_{x}\)) gradually increases with the increase in corrosion depth, indicating a concave deformation of the pipe culvert that exhibits an approximately linear relationship. Similarly, the vertical displacement (\(u_{z}\)) also increases with the increase in corrosion depth, suggesting a gradual deflection of the pipe culvert. Through analysis of horizontal displacement (\(u_{x}\)), it can be observed that at a corrosion depth of 60 mm, there is a horizontal displacement (\(u_{x}\)) difference of approximately 3 mm compared to the uncorroded state, representing an increment of about 20%. Furthermore, at a corrosion depth of 120 mm compared to that at a corrosion depth of 60 mm, there is approximately a 5 mm horizontal displacement (\(u_{x}\)) difference, which represents an increment rate of about 30%. Regarding vertical displacement (\(u_{z}\)) analysis, it can be seen that at a corrosion depth of 60 mm, compared to the uncorroded state there is approximately a 6 mm horizontal displacement (\(u_{x}\)) difference, indicating an increment rate of about 30%. Moreover, when comparing vertical displacements (\(u_{z}\)) between depths of corrosion states (120 mm and initial stage), there is around an 8 mm difference, which corresponds to an increment rate of about 39%. Notably, the fact that the corrosion depth reaches 0.12 m, which accounts for 1/3 of the thickness of the pipe culvert plate, implies an increased deformation and increment with the increase in corrosion depth. After analyzing the information shown in Figure 7, it is observed that the maximum vertical displacement (\(u_{z}\)) of the pipe culvert consistently occurs at the position of its crown, which corresponds to the highest point on the curve's ordinate axis. Similarly, the maximum horizontal displacement (\(u_{x}\)) always manifests at the leftmost point of the pipe culvert cross section, representing its smallest abscissa value. In Figure 8, it can be seen that the numerical simulation model used in this experiment is a trench-type landfill pipe culvert, and the stress concentration does not occur on the top of the pipe culvert. In practical construction processes, the effect of load reduction on the top of the pipe culvert is also significant [30]. At the same time, the crown corrosion is analyzed. The decrease in stiffness and thickness of the culvert's crown due to corrosion leads to increased displacement of the soil column above it, resulting in reduced differential settlement between both sides of the culvert and its crown soil column. This phenomenon contributes to loading reduction on the top of the pipe culvert. In actual engineering design,  
Figure 4: The distribution of the vertical stress. reducing stiffness or thickness of the crown section can effectively reduce loads while ensuring safety. With the increase in the corrosion depth, the area experiencing the highest stress consistently lies within the corroded area, and the stress differential between this area and its surroundings becomes increasingly pronounced. The bending moment of the pipe culvert is illustrated in Figure 9.  
Pipe culvert stress can be expressed using the following formula:  
\[\sigma=(M\,^{*}\,y)/I \tag{1}\]  
where \(\sigma\) represents the stress, \(M\) represents the bending moment, \(y\) represents the distance from the central axis of the cross section, and \(I\) represents the moment of inertia of the cross section. Figure 5: The change in horizontal displacement (\(u_{x}\)) with corrosion depth of the elliptical pipe culvert. Figure 6: The change in vertical displacement (\(u_{z}\)) with corrosion depth of the elliptical pipe culvert.