# Seismic Performance Evaluation of Highway Bridges under Scour and Chloride Ion Corrosion
## 3 Effect of Cl\({}^{-}\) Corrosion on the Seismic Performance of Bridge Column
### Two-Parameter Seismic Damage Index  
The damage model with a single parameter that either considers displacement or energy dissipation level cannot provide an accurate assessment of the seismic performance of a structure. Therefore, a damage model with two seismic parameters which simultaneously considers the influence of the maximum deformation and the corresponding energy dissipation level on structural failure is put forward. Based on the Park-Ang model [55; 56], which is a damage model considering a linear combination of displacement deformation and hysteretic energy dissipation, the damage indicators of specimens with different column heights and different reinforcement ratios were calculated as Equations (18) and (19). \[\mathrm{D}=\frac{\delta_{\mathrm{m}}}{\delta_{\mathrm{u}}}+\beta\frac{\int d \varepsilon}{Q_{\mathrm{y}}\delta_{\mathrm{u}}} \tag{18}\]  
\[\beta=(-0.447+0.073\lambda+0.24n_{\mathrm{o}}+0.314p_{\mathrm{t}})\times 0.7^{ \mathrm{pw}} \tag{19}\]  
where \(\delta_{\mathrm{m}}\) is the maximum deformation of the structure or component under seismic action; \(\delta_{\mathrm{u}}\) is the ultimate deformation of the structure under monotonic loading; \(Q_{\mathrm{y}}\) is the yield strength of the structure or component; \(\int d\varepsilon\) is the cumulative demurrage energy dissipation; \(\beta\) is the combination parameter with a value between 0 and 0.85; \(\lambda\) is the shear span ratio, when \(\lambda<1.7\) take 1.7; \(n_{\mathrm{o}}\) is the ratio of axial compression stress to strength, when \(n_{\mathrm{o}}<0.2\) take 0.2; \(p_{\mathrm{t}}\) is the ratio of longitudinal rebar, when \(p_{\mathrm{t}}<0.75\%\) take 0.75%; and \(\rho_{\mathrm{w}}\) is the ratio of volume stirrup. In addition, The Park-Ang model is more accurate for larger ductility coefficients, while the damage model is prone to errors due to underestimation of the ultimate energy dissipation level of the component in quasi-static tests at small and medium displacements. Therefore, to improve the reliability of calculated results, Park-Ang model and the improved Park-Ang model (M-Park model) at small and medium displacements were considered comprehensively. The M-Park model is as follows [57]. \[\mathrm{D}=(1.0-\beta)\frac{\delta_{\mathrm{m}}-\delta_{\mathrm{y}}}{\delta_{ \mathrm{u}}-\delta_{\mathrm{y}}}+\beta\frac{\sum\beta_{\mathrm{i}}E_{\mathrm{ i}}}{Q_{\mathrm{y}}\big{(}\delta_{\mathrm{u}}-\delta_{\mathrm{y}}\big{)}} \tag{20}\]  
\[\beta_{\mathrm{i}}=\left\{ \begin{matrix}\gamma_{\mathrm{E}}&\mu_{\mathrm{i}} \leq\mu_{\mathrm{o}}\\ \gamma_{\mathrm{E}}+\frac{\mu_{\mathrm{i}}-\mu_{\mathrm{o}}}{\mu_{\mathrm{p}}- \mu_{\mathrm{o}}}(1.0-\gamma_{\mathrm{E}})&\mu_{\mathrm{i}}>\mu_{\mathrm{o}} \end{matrix} \right. \tag{21}\]  
where \(\delta_{\mathrm{y}}\) is the yield displacement of the structure or component; \(E_{\mathrm{i}}\) is the area enclosed by the i-th hysteresis circle; \(\beta_{\mathrm{i}}\) is the weighting factor for energy term related to the loading path; and \(\gamma_{\mathrm{E}}\) is the energy equivalent coefficient. Combined with the results obtained from simulation, including the level of energy consumption as well as the capacity of displacement and bearing of components in the yield  
Figure 34: Comparison of hysteresis curves between FEA and test for specimen MHE. state and ultimate state, a comparison of seismic performance was carried out. Based on the two damage models of Park-Ang and M-Park, the damage degree of columns under seismic action was evaluated, from which the damage indexes of specimens LL, LLE, MM, MME, MH, and MHE before and after corrosion could be obtained, as shown in Figures 35-37. The analysis and summarization of the Park-Ang damage model and modified M-Park damage model revealed the fitting accuracy between the variation in damage degree of columns derived from the test and the results of the two-parameter seismic damage model were satisfactory.