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Journal of Applied Mathematics
Volume 2014, Article ID 905194, 11 pages
Research Article

Soil-Pile Interaction in the Pile Vertical Vibration Based on Fictitious Soil-Pile Model

1School of Civil Engineering, Central South University, Changsha, Hunan 410075, China
2Engineering Faculty, China University of Geosciences, Wuhan, Hubei 430074, China

Received 15 November 2013; Revised 9 April 2014; Accepted 12 April 2014; Published 15 May 2014

Academic Editor: Hui-Shen Shen

Copyright © 2014 Guodong Deng 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.


By introducing the fictitious soil-pile model, the soil-pile interaction in the pile vertical vibration is investigated. Firstly, assuming the surrounding soil of pile to be viscoelastic material and considering its vertical wave effect, the governing equations of soil-pile system subjected to arbitrary harmonic dynamic force are founded based on the Euler-Bernoulli rod theory. Secondly, the analytical solution of velocity response in frequency domain and its corresponding semianalytical solution of velocity response in time domain are derived by means of Laplace transform technique and separation of variables technique. Based on the obtained solutions, the influence of parameters of pile end soil on the dynamic response is studied in detail for different designing parameters of pile. Lastly, the fictitious soil-pile model and other pile end soil supporting models are compared. It is shown that the dynamic response obtained by the fictitious soil-pile model is among the dynamic responses obtained by other existing models if there are appropriate material parameters and thickness of pile end soil for the fictitious soil-pile model.