## 5 Seismic Strengthening Mechanism Analysis of the Plastic Region
(**a**) Reinforcement within 0.15 m; (**b**) Reinforcement within 0.30 m.  
Figure 19 also presents the comparative results of the load-carrying capacity, energy dissipation capacity, elastic lateral stiffness, and residual displacement of the piers under the condition of bottom reinforcement within a range of 0.3 m. Based on the comparison between Piers 2 and 6, when thickened wall plates are applied within a range of 0.3 m, the maximum load-carrying capacity of the piers increases by 11.5%, energy dissipation value decreases by 0.1%, initial stiffness increases by 18.9%, and residual displacement decreases by 54.7%. Similarly, based on the comparison between Piers 2 and 9, when additional stiffeners are utilized within a range of 0.3 m, the maximum load-carrying capacity of the rock piers increases by 5.8%, energy dissipation value decreases by 2.6%, initial stiffness increases by 11.1%, and residual displacement decreases by 31.4%. From the comprehensive analysis, it can be concluded that regardless of the range, 0.15 m or 0.3 m, the reinforcement method of thickened wall plates is superior to additional stiffeners in improving the seismic performance. Further analysis will be conducted to explore the mechanism behind the enhancement in seismic performance via the thickened bottom wall plate reinforcement. Figure 20 compares the elastic lateral stiffness trends, residual displacement trends, and energy dissipation capacity of Piers 5, 6, and 7, which were reinforced with thickened wall plates, and the unreinforced Pier 2. Overall, the effect of thickened wall plates on the cyclic energy dissipation of the self-centering rocking steel bridge piers is not significant. However, after thickening the wall plates, the growth of residual displacement becomes slower and the lateral stiffness increases for each cycle, significantly improving the seismic capacity of the piers. Figure 20: Comparison of performance indicators of piers with thickened wall plates: (**a**) Elastic stiffness trends; (**b**) Residual displacement trends; (**c**) Energy dissipation capacity. Based on the comparison between Specimens 2 and 5, when the radius-to-thickness ratio of the wall plates within a range of 0.15 m decreases from 0.096 to the 0.048, the maximum load-carrying capacity of the rock piers increases by 5.5%, the maximum residual displacement decreases by 18.2%, and the initial stiffness increases by 8.9%. According to the comparison between Specimens 5 and 6, when the reinforced area with thickened wall plates is further increased to 0.3 m, the maximum load-carrying capacity increases by 5.7%, the residual displacement decreases by 45%, and the initial stiffness increases by 9.2%. On the other hand, based on the comparison between Specimens 2 and 7, when the radius-to-thickness ratio of the wall plates within a 0.3 m reinforcement range decreases to 0.063, the maximum load-carrying capacity of the piers increases by 7.7%, the maximum residual displacement decreases by 43.6%, and the initial stiffness increases by 11.4%. According to the comparison between Piers 6 and 7, when the diameter-to-thickness ratio of the wall plates decreases to 0.048, the maximum load-carrying capacity increases by 3.5%, the residual displacement decreases by 20%, and the initial stiffness increases by 6.7%. Therefore, when reinforcing self-centering steel bridge piers for seismic performance, attention should be paid to both the thickness of the reinforced steel plates and the height of the reinforcement. A larger reinforcement height is more effective in reducing the residual displacement of the piers compared to thickening the steel plates alone.