# Finite Element Analysis of the Structural Behavior of a Corroded Pipe Culvert
## 5 Conclusions  
Returning to the original perspective of research and analysis in this paper, it is important to note that the culvert should be considered an integral part of the structure-soil system. Corresponding to previous research results, the outer wall of the culvert is susceptible to corrosion from ions and microorganisms present in the soil, leading to a reduction in overall or local stiffness. Additionally, it is influenced by soil forces from all directions, which are constrained by soil deformation [36; 37].  
1. The corrosion effect leads to a reduction in both the thickness and stiffness of the culvert, resulting in an overall decrease in stiffness. For the total displacement \(\left|u\right|\)  
Figure 16: Comparison of maximum total displacement (taking the elastic modulus of 320 MPa and the corrosion depth of 0.12 m as an example).  
Figure 17: Corrosion cross-section curves of different parts (taking \(E=280\) MPa, \(d=0.28\) m as an example, magnified by 100 times).  
overall corrosion has the most severe influence on culvert deformation, with similar effects observed for the crown and middle sections, while the invert part exhibits minimal influence. In terms of the horizontal displacement component \(u_{x}\), central corrosion exerts the most severe influence. As for vertical displacement component \(u_{z}\), crown corrosion has the most pronounced effect.
2. The impact of culvert corrosion on structural deformation is negligible. For elliptical culverts, this can be attributed to two factors: firstly, its closer resemblance to a straight line curve at the invert section; secondly, it experiences higher earth pressure from backfill soil and undergoes larger compaction compared to the crown part.
3. Excessive rigidity of the culvert induces soil arching and exacerbates structural deformation. This phenomenon should be duly considered in finite element analysis. Appropriately reducing the stiffness at the top also contributes to loading reduction at that location by minimizing settlement discrepancies between the culvert's upper part and surrounding soil columns.
4. In practical engineering scenarios, a comprehensive consideration of various aspects is imperative. During the design stage, it is crucial to identify optimal material properties for engineering components and implement measures, such as incorporating protective layers or increasing thicknesses, to appropriately enhance stiffness. Subsequently, during the construction and maintenance stages, potential requirements may arise for rust removal or additional lining/protective layer installation even after culvert placement.  
This work is the result of collaboration among all authors. Q.M.: Supervision, Resources, Funding acquisition, Conceptualization, Writing--review and editing. C.X.: Writing--review and editing, Validation, Software, Methodology, Investigation, Data curation. J.L.: Writing-review and editing, Supervision, Methodology. X.L.: Conceptualization and Supervision, Validation, Methodology, Formal Analysis. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (Nos. 52478338, 52078194), the Outstanding Young and Middle-aged Science and Technology Innovation Team of Colleges and Universities in Hubei Province (T2022010), the Innovation Demonstration Base of Ecological Environment Geotechnical and Ecological Restoration of Rivers and Lakes (2020 EJB004), the Science Fund for Distinguished Young Scholars of Hubei Province (2022 CFA043), and the National Young Top-notch Talent of \"Ten Thousand Talents Program\", and the Young Top-notch Talent Cultivation Program of Hubei Province.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.