# Safety Evaluation of a Water-Immersed Bridge Against Multiple Hazards via Machine Learning
## 2 Bridge Modeling  
In this research, nonlinear behaviors of steel bars were established according to the theory proposed by [PERSON] et al. (1993). As the steel bars selected were 36 mm in diameter (#11), its limit strain value \(\varepsilon_{su}\) was set at 0.09, and the stress-strain hardening initial value \(\varepsilon_{sh}\) was set at 0.0115. The corresponding stress-strain curve was drafted as shown in Figure 3. In this research, the bridge pier was configured as a tapered cylindrical column where the top and bottom diameters were 1.8 and 2.4 m, respectively. Because different steel bars were used, the mechanical behaviors of the sectional profile will vary. For this reason, the variable section was divided into 5 sectional profiles in order to calculate the nonlinear mechanics behaviors. Accordingly, 4 tapered cylindrical columns were generated in SAP2000. For example, the topmost portion used the sectional properties of the 1.8 and 1.95 m in diameter, as shown in Figure 4. The interpolated sectional diameters of different height levels were 1.8, 1.95, 2.1, 2.25, and 2.4 m.  
The strength of the concrete will be affected by the confining force of stirrups. For this reason, they will be divided into two portions for calculation. One of which is the protection layer, which is the unconfined concrete; and the other is the core concrete, which is a confined layer. For the calculation of confining concrete, the method proposed by [PERSON] et al. (2000) was adopted here. Because the steel bars used for this research were 36 mm (#11) in diameter, the limit strains (\(\varepsilon_{su}\)) of the steel bar and concrete were 0.09 and 0.004, respectively. Note that the limit strain for concrete is 0.003 if American Concrete Institute (ACI) is adopted. After being calculated, the stress-strain curves of the desired sectional profile were obtained (Figures 5 and 6) for confined and unconfined concretes. Figure 4: Diameter schematic layout of the selected sectional profile. Figure 3: Stress–strain curve of a steel bar used in this study. Depending on the damage mode, the plastic hinge used for the finite element model had the following properties: flexural damage (corresponding to the bending moment of plastic hinge M\({}_{2}\) or M\({}_{3}\) in SAP2000), shear damage (corresponding to shear plastic hinge V\({}_{2}\) or V\({}_{3}\) in SAP2000), and flexural-shear damage (corresponding to the axial force interacting with the bending moment of plastic hinge P-M\({}_{2}\).M\({}_{3}\) in SAP2000). In SAP2000, the aforementioned three types of plastic hinges can be simulated in three different ways--link, sectional hinge, and fiber--which will vary in accuracy and analysis time. [PERSON] et al. [14] suggested that the fiber hinge possesses the best accuracy; therefore, it was selected in this article. The fiber hinge resembles the bending moment of the plastic hinge featuring an axial force interaction (P-M\({}_{2}\).M\({}_{3}\)). During analysis, the profile of a target section will affect the analysis time according to the mesh size. For the sake of balancing accuracy and time, the trial-and-error method was used for deciding the mesh size. The finalized meshes for pier and caisson are described in Figures 7 and 8. Figure 5: Stress–strain curve for confined concrete. Figure 6: Stress–strain curve for unconfined concrete. This article used the formula defined by [PERSON] and [PERSON] [15] to calculate the length (\(L_{p}\)) of plastic hinge as below:  
\[L_{p}=0.08h+0.022d_{bl}\sigma_{y}\ (\mathrm{mm}), \tag{1}\]  
where \(h\) means pier length (mm), \(d_{bl}\) means diameter of the longitudinal steel bar (mm), and \(\sigma_{y}\) means steel bar yielding stress (MPa). Soil resistance around the foundation was simulated by a spring element, in which the front and bottom sides of the foundation were separately considered. During simulation, the soil spring was assumed as a bilinear spring, in which the maximum value did not exceed the passive soil pressure.