# Chloride Resistance of Assembled Bridge Piers Reinforced with Epoxy-Coated Steel Bars
## 4 Service Life Prediction
### Modeling Methods  
This chapter employs the Nernst-Planck Equation for chemical substance transport within COMSOL Multiphysics software (v. 6.0) to simulate the natural diffusion process of chloride ions in seawater for assembled bridge pier joints, which are modeled at twice the size of the test specimens. The concrete surface layer with a thickness of 1 mm is defined on the erosion side of the model, and its chloride ion content is set to \(C_{\text{s}}\) as the boundary condition. The non-steady-state diffusion coefficients for chloride ions at various locations \((D_{\text{NSSD}})\) can be calculated from Equation (11) combined with \(D_{\text{nssm}}\) in Table 3. The specific value of each parameter is presented in Table 4: \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(C_{\text{s}}\) (mol/m\({}^{3}\)) & \(c\) (mm) & \(W\) (mm) & \(D_{\text{C50}}\) & \(D_{\text{C60}}\) & \(D_{\text{M}}\) & \(D_{\text{CC}}\) & \(D_{\text{CM}}\) & \(D_{\text{0}}\) \\ \hline
400.587 & 70 & 5 & 0.395 & 0.331 & 0.229 & 1.668 & 0.879 & 2032 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the model. Figure 19: Fabrication of the grouting interface specimen. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(C_{\text{s}}\) (mol/m\({}^{3}\)) & \(c\) (mm) & \(W\) (mm) & \(D_{\text{C50}}\) & \(D_{\text{C60}}\) & \(D_{\text{M}}\) & \(D_{\text{CC}}\) & \(D_{\text{CM}}\) & \(D_{\text{0}}\) \\ \hline
400.587 & 70 & 5 & 0.395 & 0.331 & 0.229 & 1.668 & 0.879 & 2032 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the model. Where \(C_{\rm s}\) represents the chloride ion concentration in the concrete surface of the bridge pier; \(c\) is the thickness of the protective layer for the steel bars; \(W\) refers to the thickness of the interface; \(D_{\rm C50}\), \(D_{\rm C60}\), \(D_{\rm M}\), \(D_{\rm CC}\), \(D_{\rm CM}\) and \(D_{\rm 0}\) respectively denote the non-steady-state diffusion coefficients of C50 concrete, C60 post-cast concrete, high-strength non-shrink mortar, the interface of the post-cast strip, grouting interface, and in aqueous solutions. The tidal and splash zones display significantly higher chloride ion concentrations than those submerged in seawater due to the cyclic wetting and drying processes, making them critical for service life prediction. Therefore, \(C_{\rm s}\) is determined as the chloride ion concentration in the surface concrete of the tidal or splash zones. Due to the considerable variability in the chloride ion concentration (\(C_{\rm s}\)) in tidal and splash zones, as found in studies [34; 35; 36], this chapter employs the empirical formula provided by DuraCrete [37] for calculations, as illustrated in Equation (13). \[C_{\rm s}=\frac{0.0776R_{\rm w/b}\rho_{\rm b}}{M_{\rm C1^{-}}} \tag{13}\]  
where \(R_{\rm w/b}\) is the water-cement ratio of the concrete (\(R_{\rm w/b}=0.366\)); \(\rho_{\rm b}\) is the density of the cementitious material, indicating the mass of cementitious material per cubic meter of concrete (\(500\) kg/m\({}^{3}\)); \(M_{\rm C1^{-}}\) is the molar mass of chloride ions (\(35.45\times 10^{-3}\) kg/mol). Substituting them into Equation (13) yields \(C_{\rm s}=400.587\) mol/m\({}^{3}\). Utilizing symmetry, the simulation was conducted for chloride ion erosion on only one side. The following presents chloride ion concentration contour maps and time-varying curves of chloride ion concentrations on the surface of the steel bars for two types of joints. The service life of each joint, when employing different types of steel bars, was determined based on the chloride ion concentration at the surface of the pier body's steel bars reaching the critical chloride ion concentration.