# Finite Element Analysis of the Structural Behavior of a Corroded Pipe Culvert
## 2 Modeling of Buried Pipe Culvert
### Parameter Setting  
The three-dimensional analysis of the pipe culvert in a homogeneous backfill trench was carried out using PLAXIS 3D software. The pipe culvert is considered to be buried below the earth's surface. Figure 1 presents a schematic diagram of the pipe culvert system embedded in the trench soil domain. The characteristics of soil medium in this numerical simulation are referenced from design specification [27]. The soil domain is considered as a three-dimensional prism cube with a size of 100 m (length) \(\times\) 50 m (width) \(\times\) 35 m (height), as shown in Figure 1a. A wedge element with fifteen nodes is utilized to create the soil domain, consisting of a six-node triangle horizontally and an eight-node quadrilateral vertically, as shown in Figure 1b. The soil domain is discretized using variable mesh density to enhance analysis accuracy and computational efficiency. Near the pipe culvert subsoil, local refinement coefficients of 0.5 for the pipe culvert, 0.7 for the backfill soil, and 1 for the foundation soil are employed to ensure analysis precision. Through a convergence study, a total of 13,915 nodes and 23,420 elements are obtained. The transverse boundary of the soil domain is set at seven times the width of the subsoil, while the vertical boundary is set at four times its width [28]. The horizontal constraint is used to constrain the boundary in the horizontal direction, and the horizontal constraint and vertical constraint are applied to the bottom boundary at the same time. The nonlinear, elastoplastic Mohr-Coulomb constitutive model is adopted for simulating the behavior of foundation soil. The HS-Small model is utilized to capture the stress-dependent characteristics of backfill soil. Considering that the pipe culvert is constructed using concrete material, the foundation soil consists of three layers: clay, which comprises fully weathered mudstone, at the bottom, semi-weathered mudstone in the middle, and natural soil as the backfill material. In the calculation model, the length is 100 m, the height is 35 m, and the width is 50 m. (Figure 1a). To mitigate boundary effects on the calculation results, a subsoil depth of 10 m at the bottom of the pipe culvert and a filling soil height of 16 m at the top are chosen (Figure 1c). The interface between soil and culvert is modeled using the face-to-face contact method, with the roughness coefficient represented by the strength reduction coefficient (Rinter). This coefficient signifies the ratio between interface strength and soil strength. For this study, Rinter = 0.7 is adopted based on previous research [29]. The front view of the pipe culvert is approximately circular in shape. In the PLAXIS 3D structure setting process, the pipe culvert is created by sequentially constructing three curved arcs, starting from the invert. The relative starting angles are set as 1:0.000\({}^{\circ}\), and the radii and line segment angles are defined as follows: 6 m with a segment angle of 30\({}^{\circ}\); 3 m with a segment angle of 70\({}^{\circ}\); and finally, a radius of 5 m with a segment angle of 45\({}^{\circ}\). Subsequently, it extends towards the symmetry axis to form the last curve on the right half before symmetrically closing to complete the entire curve. The front view design of the pipe culvert adheres to circular geometry with a radius of 4 m. The pipe culvert is modeled by the plate element and meshed by 6-node triangular elements. To simulate corrosion in pipe culverts under plane strain conditions, two-dimensional numerical analysis is conducted using PLAXIS 3D finite element software, incorporating contact elements at interfaces between different materials such as pipe culverts and fills.