# Finite Element Analysis of the Structural Behavior of a Corroded Pipe Culvert
## 4 Results and Discussion
### The Influence of Corrosion Depth and Stiffness Change on Pipe Culvert Deformation  
Based on an analysis of the information shown in Figures 11 and 12, this section examines the corrosion-induced reduction in thickness and stiffness of concrete pipe culverts, building upon the findings presented in the previous section. Each simulation is conducted based on the preceding section, with a 20 MPa reduction in pipe culvert stiffness. The corrosive effect leads to strength inversion and increased displacement. In terms of total displacement, overall corrosion exerts the most severe influence on pipe culvert displacement, while crown and middle corrosion effects are comparable, with invert corrosion having the least impact. Regarding horizontal displacement (\(u_{x}\)), middle corrosion exhibits the most significant influence, whereas for vertical displacement (\(u_{z}\)), crown corrosion has the predominant effect.  
It is worth noting that the stiffness and thickness of the examples in Figures 11 and 12 are weakened, while those of Figures 5 and 6 are only weakened in thickness; however, the displacement values simulated by the models in Figures 11 and 12 are smaller than those of the group with both weakened stiffness and thickness. This is the result of the soil arching effect [31]. That is, when the pipe culvert is buried underground, it interacts with the surrounding soil, resulting in the redistribution of soil pressure. This redistribution affects the stress transferred to the pipe culvert. The geometry of the underground structure and its stiffness relative to the surrounding soil have a significant effect on the size and distribution of the vertical stress. Because the stiffness of the buried structure is often higher than that of the surrounding soil, the settlement of the surrounding soil is larger than that of the  
Figure 10: Maximum stress–corrosion depth relationship of the elliptical pipe culvert (taking \(E=280\) MPa as an example).  
Figure 9: Culvert bending moment cloud diagram of the elliptical pipe culvert: (**a**) around the X axis, (**b**) around the \(Z\) axis (taking \(E=280\) MPa and the middle corrosion depth as 0.12 m as an example).  
central soil column above the pipe culvert structure [32]. The relative settlement produces shear stress between the surrounding soil and the central soil column [33; 34; 35], resulting in vertical stress concentration on the buried structure, as shown in Figure 13. Therefore, the vertical stress at the top of the rigid structure buried under the higher embankment is larger than the weight of the soil column above the structure, which is the result of the soil arching effect.  
Figure 11: The change in horizontal displacement (\(u_{x}\)) with corrosion depth and stiffness of the elliptical pipe culvert (the stiffness of each corrosion simulation is reduced by 20 MPa): (**a**) all species and (**b**) three-dimensional view of overall corrosion.  
Therefore, it can be inferred that the optimal stiffness of the pipe culvert should not be solely determined by its magnitude. The pipe culvert should be considered as an integral part of the entire culvert-soil structural system. Excessive stiffness may result in increased relative displacement between the soil and the culvert, leading to a tendency for soil uplift and downward movement of the pipe culvert. Consequently, this would cause an elevation in soil pressure above the pipe culvert and induce deformation within the structure.  
Figure 12: The change in vertical displacement (\(u_{z}\)) with corrosion depth and stiffness (the stiffness of each corrosion simulation is reduced by 20 MPa.): (**a**) all species and (**b**) three-dimensional view of overall corrosion.