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Mathematical Problems in Engineering
Volume 2014, Article ID 126916, 12 pages
Research Article

Vertical Dynamic Response of Pile Embedded in Layered Transversely Isotropic Soil

1Engineering Faculty, China University of Geosciences, Wuhan, Hubei 430074, China
2School of Computing, Engineering and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith, Sydney, NSW 2751, Australia

Received 15 April 2014; Revised 24 June 2014; Accepted 24 June 2014; Published 17 July 2014

Academic Editor: Sarp Adali

Copyright © 2014 Wenbing Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The dynamic response of pile embedded in layered transversely isotropic soil and subjected to arbitrary vertical harmonic force is investigated. Based on the viscoelastic constitutive relations for a transversely isotropic medium, the dynamic governing equation of the transversely isotropic soil is obtained in cylindrical coordinates. By introducing the fictitious soil pile model and the distributed Voigt model, the governing equations of soil-pile system are also derived. Firstly, the vertical response of the soil layer is solved by using the Laplace transform technique and the separation of variables technique. Secondly, the analytical solution of velocity response in the frequency domain and its corresponding semianalytical solution of velocity response in the time domain are derived by means of inverse Fourier transform and convolution theorem. Finally, based on the obtained solutions, a parametric study has been conducted to investigate the influence of the soil anisotropy on the vertical dynamic response of pile. It can be seen that the influence of the shear modulus of soil in the vertical plane on the dynamic response of pile is more notable than the influence of the shear modulus of soil in the horizontal plane on the dynamic response of pile.