A Coupled BEM Model for the Dynamic Analysis of a Pile Embedded in a Half-space Soil Covered by a Water Layer

Xu Zhang, Jian-Fei Lu*
Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, 212013, P.R. China.

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© 2013 Zhang and Lu;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, 212013, P.R. China; Tel: 0086-15951284152; Fax: 0086-88780030; E-mail:


Dynamic analysis of a pile embedded in a half-space soil covered by a water layer is crucial for the designs of the pile foundations for bridges, docks and offshore platforms etc. In this paper, a coupled boundary element method (BEM) model is developed to evaluate the dynamic response of the pile. In the proposed model, the pile and half-space soil are treated as elastic media, while the water layer is considered as an acoustic medium. Three BEM formulations are established for the pile, half-space soil and water layer by means of the boundary element method (BEM), respectively. Using the three BEM formulations as well as the continuity conditions at the interfaces between three regions, a coupled BEM model for the pile-soil-water system is established. To validate the proposed model, results due to our model are compared with existing results. With the coupled BEM model for the pile-soil-water system, dynamic response of the pile is investigated. Presented numerical results show that when the pile is subjected to an axial load and torque, resonance phenomena is not obvious. However, when the pile is subjected to a horizontal load and moment, resonance phenomena is pronounced and the pile-soil modulus and density ratios have a considerable influences on resonant frequencies.

Keywords: Pile, the half-space soil, the water layer, the boundary element method (BEM), compliance.