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Article

An Efficient Hydrodynamic Force Calculation Method for Pile Caps with Arbitrary Cross-Sections Under Earthquake Based on Finite Element Method

by
Wen Zhang
1,
Shizhou Xiao
2,
Xiaokun Geng
1,
Wanli Yang
1 and
Yifei Xu
3,*
1
School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
2
China Road & Bridge Corporation, Beijing 100010, China
3
Sichuan Communication Surveying and Design Institute Co., Ltd., Chengdu 610017, China
*
Author to whom correspondence should be addressed.
Eng 2025, 6(7), 167; https://doi.org/10.3390/eng6070167
Submission received: 9 June 2025 / Revised: 13 July 2025 / Accepted: 14 July 2025 / Published: 21 July 2025
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Abstract

The pile group-pile cap structure is a key foundation form for deep-water bridges. However, current effective methods for calculating the earthquake-induced hydrodynamic forces on pile caps with arbitrary cross-sections remain insufficient. In this study, the hydrodynamic force is considered as the added mass, and the dynamic equilibrium equations of the isolated pile cap structure (IC model) and the pile group-pile cap structure (PC model) under earthquakes are established, respectively, based on the structural dynamics theory. Correspondingly, the relationships between the hydrodynamic added masses and the fundamental frequencies in the IC model and the PC model are derived, respectively. The fundamental frequencies of the IC model and the PC model are obtained by numerical models built with the ABAQUS (2019) finite element software, and then the added masses on the IC and PC models are calculated accurately. The calculation method proposed in this study avoids the complex fluid–structure interaction problem, which can be applied for the seismic design of deep-water bridge substructures in real practice.
Keywords: pile group-pile cap structure; earthquake; hydrodynamic force; dynamic equilibrium equations; finite element method pile group-pile cap structure; earthquake; hydrodynamic force; dynamic equilibrium equations; finite element method

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MDPI and ACS Style

Zhang, W.; Xiao, S.; Geng, X.; Yang, W.; Xu, Y. An Efficient Hydrodynamic Force Calculation Method for Pile Caps with Arbitrary Cross-Sections Under Earthquake Based on Finite Element Method. Eng 2025, 6, 167. https://doi.org/10.3390/eng6070167

AMA Style

Zhang W, Xiao S, Geng X, Yang W, Xu Y. An Efficient Hydrodynamic Force Calculation Method for Pile Caps with Arbitrary Cross-Sections Under Earthquake Based on Finite Element Method. Eng. 2025; 6(7):167. https://doi.org/10.3390/eng6070167

Chicago/Turabian Style

Zhang, Wen, Shizhou Xiao, Xiaokun Geng, Wanli Yang, and Yifei Xu. 2025. "An Efficient Hydrodynamic Force Calculation Method for Pile Caps with Arbitrary Cross-Sections Under Earthquake Based on Finite Element Method" Eng 6, no. 7: 167. https://doi.org/10.3390/eng6070167

APA Style

Zhang, W., Xiao, S., Geng, X., Yang, W., & Xu, Y. (2025). An Efficient Hydrodynamic Force Calculation Method for Pile Caps with Arbitrary Cross-Sections Under Earthquake Based on Finite Element Method. Eng, 6(7), 167. https://doi.org/10.3390/eng6070167

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