## 3 Results and Discussion
### Moment-Curvature Behavior  
To better understand the relationship between the moment and curvature and classify the advantage of PP-ECC to RC, the moment at the measured cross-section is calculated from the loading and displacement history using Equation. (2) [36]. The moment-curvature relationships are calculated at the location of 15, 30, and 60 cm. Figure 10 illustrates the constructed moment-curvature hysteretic curves for eight bridge piers. The skeleton curve reflects the relationship between the maximum moment and the corresponding curvature of specimens at each loading level. The moment-curvature envelop curves of all specimens obtained from the hysteretic curves are plotted in Figure 11.  
\[M=P\cdot L+N\cdot\Delta \tag{2}\]  
in which \(M\) is the moment, \(P\) is the lateral loading, \(L\) is the distance between the measured cross-section and the bottom of the pier, \(N\) is the axial loading, and \(\Delta\) is the lateral displacement at the top. It can be seen from Figure 10 that the shapes of the moment--curvature hysteretic curves are very similar for all bridge pier specimens, regardless of the concrete type. At the early stage in the loading period, the moment increases linearly with the increase in curvature. Then, it is followed by a strong moment-hardening behavior when the curvature continues increasing. However, the moment exhibits a nonlinear decreasing trend during the unloading period. The maximum moment slightly increases at each loading level and a small residual moment presents after unloading. The shape of hysteresis curves of all specimens is very similar for all loading levels, while the hysteresis loop enlarges with a continuous increase in curvature, especially in the horizontal direction. When comparing the maximum moment at a different measured cross-section, it is observed that it is generally located at the 15 cm one, which is the closest to the bottom of the pier. This explains why pier pier most likely fail near the bottom under seismic activities. It can be seen that PP-ECC is beneficial to the seismic resistance of bridges piers. PP-ECC-1-PP-ECC-6 specimens have relatively higher peak moments and larger areas of hysteretic curve, when compared to RC-7 and RC-8 specimens. The reductions in moment attenuation are also relatively slower after the peak loading, indicating that the seismic resistance of the PP-ECC piers is better than those of RC piers. It can be contributed to the excellent ductility and energy absorption characteristics associated with PP-ECC piers. The test variables in the study have different influences on the moment-curvature hysteretic curves of PP-ECC piers. By comparing the hysteretic curves of PP-ECC-2, PP-ECC-5, and PP-ECC-6, it can be seen that the area becomes larger, and the moment capacity increases when more stirrups are used in the plastic hinge region. Apparently, PP-ECC piers exhibit better seismic resistance when the stirrup ratio increases. This is consistent with the effect of stirrup ratio on the seismic behavior of ordinary reinforced concrete pier [18]. Figure 9: Curvature distributions along with the height of the pier. (**a**) PP-ECC-1; (**b**) PP-ECC-2; (**c**) PP-ECC-3; (**d**) PP-ECC-4; (**e**) PP-ECC-5; (**f**) PP-ECC-6; (**g**) RC-7; (**h**) RC-8. Figure 10: \(Cont\). Figure 11: _Cont_. Figure 10: Moment-curvature hysteretic curves of piers at different cross section. The influence of axial loading on the moment-curvature hysteretic curves of PP-ECC pixels sheds another light. The area of the hysteretic curves of PP-ECC-1 and PP-ECC-2 are respectively wider than those of PP-ECC-3 and PP-ECC-4 in the horizontal direction (i.e., curvature), but narrower in the vertical direction (i.e., moment). This indicates that piers under lower axial loading exhibit relatively greater curvature but lower moment capacity. The PP-ECC pixels with high axial loading ratio have better resistance to plastic deformation but worse resistance to moment under cyclic loadings.