## 2 Experimental
### Subsection  
All the specimens presented increasing damage levels with displacement loads regardless of the specimen configurations. As expected, the damage (i.e., cracks) initiated at the pier base and propagated slowly prior to reinforcement yielding, but after reinforcement yielding, the damage developed relatively rapidly until the specimen failed. The cyclic crack open-closure phenomenon was observed under cyclic horizontal loading and constant compression loading. This was expected and  
Figure 6: Setup for testing bridge piers in \(X\) Direction and \(Y\) Direction. consistent with other studies [26]. The cumulative dissipated energy also consistently increased with the displacement load. To explore the similar damage characteristics of all the fourteen specimens during the bilateral cyclic loading, Figure 7 qualitatively shows the typical consecutive damage propagation stages at the critical position of B2 pier sample (as an example), that is, the interface between the top surface of footing and its above hollow pier:  
* Stage 1 (Figure 7a): Cracking on the concrete surface in the horizontal direction at the 4 mm displacement load after the formation of a plastic region. More cracks at higher position initiated with the increasing displacement loading;
* Stage 2 (Figure 7b): Yielding of longitudinal reinforcements at the 12 mm displacement load; the occurrence of yielding was indicated by the strain gauge values on longitudinal steels;
* Stage 3 (Figure 7c): Spalling of concrete at the footing interface after the yielding of longitudinal reinforcement at the 31 mm displacement load;
* Stage 4 (Figure 7d): Pier collapsing with the longitudinal reinforcement buckling or break in the testing end. Note that the above general observations are consistent with experimental findings from others such as [27]. The results indicate that the damage propagation is highly dependent on the tensile and compressive strain of concrete materials and tensile strain of steel bars. Figure 8 shows a typical horizontal and parallel crack pattern on the external surface of B2 concrete pier at Faces A and B (Figure 8a) and Faces C and D (Figure 8b) at the end of loading (after 2.5-h loading). The first crack with the width of 0.06 mm initiated at the interface (C and D surfaces, Figure 9) between the top surface of footing and its above hollow pier at the displacement loading of 4 mm. At the same pier height, another crack appeared on the A and B surfaces at the next displacement loading of 6 mm. With the increase of displacement loading until the maximum displacement loading of 70 mm, the cracks propagated with more than 2 mm wide, and more cracks appeared at the higher position of the concrete surface until they reached 1.8 m in height, as shown in Figure 8c. The cracks is represented as horizontal lines. The concrete crushing area is represented by the area of black zones; these areas are used to indicate the concrete crushing severity and damage level. Note that all the specimens present similar damage evolution characteristics as a consequence of flexure failure starting from concrete cracking to the yielding of longitudinal reinforcements, concrete spalling, and pier collapsing. Figure 7: Damage propagation of pier end at under bilateral cyclic loading: (**a**) Cracking on concrete surface; (**b**) Yielding of longitudinal reinforcements; (**c**) Spalling of concrete; (**d**) Pier collapsing. As this study focuses on the development of seismic damage model of bridge piers, the critical damage characteristics in terms of structural deformation and hysteretic energy were analyzed, as they mainly contribute to seismic damage of concrete structures. The other results regarding the influence of axial load ratio, slenderness ratio, and stirrup spacing on the damage characteristics were thus not analyzed in this study.