## 6 Conclusions and Discussion  
In this paper, non-pulse ground motion and pulse ground motion with varying characteristic periods (Tg = 0.45 s; Tg = 0.40 s; Tg = 0.30 s) were synthesized based on EQsignal software. A dynamic response analysis was conducted on the bridge pier at 0 m and 10 m water depths. This study investigated the influence of ground motion, pulse seismic motion, and the presence of water with different characteristic periods on the dynamic behavior of a bridge pier. The following conclusions were drawn:  
(1) A bridge pier is under ground motion actions with varying characteristic periods. This results in a distinct acceleration response, peak value, and stress peak value for the stress response. As the characteristic period Tg decreases, both the peak acceleration and the resulting peak stress in the pier structure increase progressively. (2) When subjected to identical characteristic periods, the acceleration and displacement response time histories of a bridge pier exhibit notable differences under non-pulse ground motion and pulse seismic motion actions. The peak acceleration and displacement under pulse seismic motion are notably higher than those under non-pulse motion, and the corresponding curves are more complex. (3) The existence of water around a bridge pier reduces its natural frequency, although whether this increases the acceleration and stress response primarily depends on the spectral characteristics of the ground motion in varying characteristic periods. While the pulse effect typically dominates the dynamic behavior of the pier, the hydrodynamic effect is less significant. The water surrounding the pier mitigates the intensity of the pulse effect. The interaction between water and the structure is complex, as the pulse effect tends to induce more significant acceleration and stress responses compared to the hydrodynamic forces. Nevertheless, the existence of water will mitigate the impact of the pulse effects. This study mainly investigates the dynamic behaviors subjected to pulse ground motion action with varying characteristic periods of action. Previous research has established that the significant and complex effects of pulse ground motion on bridge pier structures are both significant and complex, although this is based on a single dimension. Future research should investigate the determinants of pulse seismic motion, including the striking of the multi-dimensional pulse seismic motion input on the dynamic behaviors of a bridge pier, including multi-dimensional models. In comparison to non-pulse seismic motion, pulse ground seismic motion exerts a more pronounced destructive influence on a bridge pier. An examination of the mechanism of pulse ground motion will facilitate the identification of the destructive potential of pulse ground motion, which is a crucial consideration in the design of a bridge pier. Through the implementation of an appropriate design, timely maintenance, and continuous evaluation, the sustainability of bridge pier in the context of pulse ground motion can be enhanced, thereby ensuring the continued safe and stable utilization of the bridge following an earthquake. [PERSON] wrote the main manuscript text and prepared figures and tables. [PERSON] contributed to the supervision, project administration, and funding acquisition. All authors reviewed the manuscript. All authors have read and agreed to the published version of the manuscript. **Funding:** The authors express their gratitude for the National Natural Science Foundation of China (Grant No. 51678107) and Nankun Program for Young Scholars of ZJWEU (Grant No. RC2023021212) for taking charge of the finance work to assist with the project. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author. **Conflicts of Interest:** The authors declare no conflict of interest.