## 5 Seismic Performance Analysis
### Seismic Responses under the DBEs  
Under the DBEs, damage is found in the prototype tall piers due to the exceedance of the yield curvature. In this study, the modified Park-Ang index is used to analyze the damage states of the bridge models. The modified Park-Ang index is defined as follow according to [PERSON] et al. (2018):  
\[D=\frac{\phi_{m}-\phi_{y}}{\phi_{u}-\phi_{y}}+\beta\frac{E_{h}}{\phi_{u}M_{y}} \tag{5}\]  
where \(\phi_{m}\), \(\phi_{u}\), \(\phi_{y}\), \(M_{y}\) indicate the maximum sectional curvature, the ultimate curvature, the yield curvature, yield flexural capacity of the component, respectively; \(\beta\) is the energy dissipation coefficient. For the component subject to compression and bending simultaneously, the accumulated hysteretic energy \(E_{h}\) can be obtained by integrating the bending moment over the curvature within the plastic hinge zones. Based on the Park-Ang index, the damage states of the bridge models can be classified as no damage (D \(<\) 0.10), slight damage (0.10 \(\leq\) D \(<\) 0.25), medium damage (0.25 \(\leq\) D \(<\) 0.40), and significant damage (0.40 \(\leq\) D \(<\) 1.0). Accordingly, the maximum modified Park-Ang indices and corresponding damage levels of the conventional RC tall-pier bridge under above-mentioned ground motions, are listed in Table 6. The result indicates that both the P2 and P3 tall piers suffer moderate or significant damage under the DBEs. Figure 7: Relative displacements at the pier tops under the SLEs. For the new composite tall-pier bridge, under the DBEs, the maximum curvatures at the top and bottom of the CFST column in the tall piers are 0.00196 and 0.00170, respectively, which are less than the yield curvature of 0.00240. Therefore, the four-limb CFST columns remain elastic. The maximum Mises stress of the steel beams is 263 MPa, which is less than the yield stress of 345 MPa. Thus, the steel beams also remain elastic. Furthermore, as shown Table 7, the average maximum displacements of the new composite tall-pier bridge is significantly less than the conventional one under the DBEs. The average values of maximum pier-top displacements in the longitudinal and transverse directions are reduced by 37.4% and 28.6%, respectively. And the average values of maximum relative displacement between the superstructure and the side pier is reduced by 21.9%. Figure 8 compares the maximum displacement responses of the bridge under the different ground motions. The results indicate that the lateral displacements of the new composite tall-pier bridge are apparently less than the conventional one under all the selected ground motions considering DBEs, indicating that the new bridge performs much better than the prototype under near-fault ground motions. Meanwhile, it should be noted that the CFST columns of the new bridge remain elastic with sufficient stiffness. The red parts and gray parts represent the yield parts and elastic parts of the EDMSPs, respectively. It is evident that the EDMSPs have yielded to a large extent and serve as the energy-dissipating components and sacrificial components. With similar static performances, the new composite tall-pier bridge shows better seismic performance under different strong near-fault ground motions. With the help of the hysteretic energy dissipation of the mild steel components, the displacement at the pier top under near-fault ground motion is greatly reduced. Meanwhile, no damage is found in the four-limb CFST columns of the new tall pier during the ground motion inputs. After the DBEs, the CFST columns remain elastic. The load-carrying capacities of the new composite tall piers do not decrease, which helps maintain the necessary function of the lifelines in the facilities.