# Finite Element Analysis of the Structural Behavior of a Corroded Pipe Culvert
## 3 Parametric Cases  
In order to investigate the impact of corrosion on the structural response of pipe culvert foundation systems, a parametric study was conducted considering various influential factors in the soil-culvert system. The parameters examined include relative stiffness, thickness, and position of corrosion within an acceptable range. Therefore, the thickness of  
Figure 1: Test configuration of the experiment: (**a**) mesh layout and overall geometry, (**b**) element node (**c**) elevation view showing overall dimensions.  
the pipe culvert is reduced by 0.02 m in each phase, based on an initial thickness of 0.34 m, to account for deformation behavior resulting from corrosion. Considering the stiffness change caused by corrosion, the elastic modulus E of the pipe culvert is utilized to represent its stiffness and is decreased by 20 MPa in each phase, starting from an initial modulus of 320 MPa. Furthermore, this study aims to investigate the impact of two different shapes of pipe culverts--circular and elliptical--on corrosion, as shown in Figure 2. A comprehensive summary detailing all parameter cases considered in this research can be found in Table 2.  
This study investigates the variation of corrosion in different sections of the pipe culvert, including the overall culvert and the crown, middle, and invert parts, considering factors such as cross-section shape, corrosion location, and culvert stiffness reduction caused by corrosion. Four relative positions of corrosion were considered: crown corrosion, middle corrosion, invert corrosion, and overall corrosion. Figure 3 illustrates the division between overall and localized corrosion.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\bullet\) & Shape & \(\bullet\) & \(E\) (MPa) & \(\bullet\) & \(d\) (m) & \(\bullet\) & Corrosion location \\ \hline \multirow{5}{*}{\(\bullet\)} & & \(\bullet\) & 320 & \(\bullet\) & 0.34 & & \\  & & \(\bullet\) & 300 & \(\bullet\) & 0.32 & & \\  & & \(\bullet\) & 280 & \(\bullet\) & 0.30 & & \\  & & \(\bullet\) & 260 & \(\bullet\) & 0.28 & & \\  & & \(\bullet\) & 240 & \(\bullet\) & 0.26 & & \\  & & \(\bullet\) & 220 & \(\bullet\) & 0.24 & & \\  & & \(\bullet\) & 200 & \(\bullet\) & 0.22 & & \\ \hline \multirow{5}{*}{\(\bullet\)} & & \(\bullet\) & 320 & \(\bullet\) & 0.34 & & \\  & & \(\bullet\) & 200 & \(\bullet\) & 0.32 & & \\ \cline{1-1}  & & \(\bullet\) & 200 & \(\bullet\) & 0.22 & & \\ \cline{1-1}  & & & & & & & \\ \end{tabular}
\end{table}
Table 2: Corrosion parameters design.  
Figure 3: Overall corrosion and localized corrosion division: (**a**) overall corrosion, (**b**) crown corrosion, (**c**) middle corrosion, and (**d**) invert corrosion.  
Figure 2: Pipe culvert shapes: (**a**) elliptical and (**b**) circular.  
The construction phase of the numerical model commences from the initial stage, encompassing the entire soil continuous medium and incorporating plate elements to represent the pipe culvert. The second stage involves simulating excavation in the test area by deactivating the existing soil, thereby assessing anticipated changes in stress and strain resulting from excavation activities. In the third stage, installation elements pertaining to surrounding interfaces and bedding materials are simulated through activation of the pipe sheet. Figure 4 illustrates a vertical stress cloud subsequent to pipe culvert installation.