## 3 Results and Discussion
### Curvature Distribution at the Bottom of the Pier  
The curvature distribution along with the height of the bridge pier is a characteristic property to determine the length of the plastic hinge and the resistance to rotation under flexural loading. Figure 8 illustrates the variations between the cycle lateral loading versus vertical displacements of all transducers from the collected data. The testing results of PPECC-1 are chosen as a representative one, while other results with a similar relationship can be found in [35]. The identical vertical displacements (\(h_{1}\) and \(h_{2}\)) of each cable-extension transducer are extracted from Figure 8, and then the curvature is calculated at each cross-section through Equation (1). Figure 9 depicts the variations in curvature with respect to the height of the pier, where Figure 9a-f are for PP-ECC and Figure 9g,h for RC pairs, respectively. It can be obviously seen from Figure 9, the curvature at the plastic hinge region gradually increases with the increase in cyclic lateral loading/displacement level, regardless of the concrete type for the pier. When reaching the ultimate loading, the curvature also reaches the maximum values in the plastic hinge region. The maximum curvature is usually located at the bottom of the pier. The curvature distribution, along with the height, shows a linear trend within 300 mm from the pier bottom. Under the same displacement level, the rotation and curvature at the plastic hinge region gradually decrease with the height of the cross-section. It is indicated that the upper portion of the pier is still under the elastic stress stage, while the bottom presents plastic deformation. The curvature distribution is consistent with the failure pattern of the pier under seismic loadings. The axial loading ratio has a significant effect on the curvature distribution along with the height of the pier. Figure 9a,c is the scenario for PP-ECC with the same height of 250 mm but axial loading ratios of 0.1 and 0.3, respectively. The ultimate curvature values of the pier are 0.2852 and 0.2333 1/m. Similarly, Figure 9b,d is the scenarios for PP-ECC with the same height of 500 mm but axial loading ratios of 0.1 and 0.3, respectively. The ultimate curvature values of the pier are 0.3068 and 0.2720 1/m. The curvature increases significantly when a greater axial loading is applied on the top of the pier. It is indicated that a lower axial load tends to improve the resistance to plastic deformation. Alternatively, by comparing Figure 9a with Figure 9b, or Figure 9c with Figure 9d, where the height of the PP-ECC portion is the only difference, there is also some obvious influence. The curvature increases when the height increases from 250 mm to 500 mm, especially when the axial force ratio is 0.3. This indicates that increasing the height of PP-ECC portion would be beneficial to enhance the rotation capacity and plastic deformability. The influence of transverse reinforcement in the plastic hinge region can be determined by comparing the results in Figure 9b,e,f. The corresponding volume ratios of transverse reinforcement bars \(\rho_{\rm Si}\) are 0.79%, 0.46%, and 0%, respectively. The ultimate curvature values of the pier are determined as 0.3068, 0.2511, and 0.2476 1/m. The results indicate that the transverse reinforcement in the plastic hinge region had a positive influence on the curvature of the pier. With denser stirrups, the bridge pier generally exhibits greater curvature and better resistance to plastic deformation and rotation. The volume hoop ratio of the plastic hinge area at the bottom of the pier has a certain influence on the curvature of the pier: the larger the volume hoop ratio, the greater the final curvature of the pier, and the appropriate increase in PP-ECC in the volume hoop ratio of the plastic hinge area of the pier is beneficial to the plastic rotation of the pier, and then the displacement ductility of the pier is improved.