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Mathematical Problems in Engineering
Volume 2015, Article ID 495253, 13 pages
Research Article

Dynamic Response of an Inhomogeneous Viscoelastic Pile in a Multilayered Soil to Transient Axial Loading

1Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China
2College of Urban Construction, Zhejiang Shuren University, Hangzhou 310015, China
3Key Laboratory of Soft Soils and Geoenvironmental Engineering, Ministry of Education, Zhejiang University, Hangzhou 310027, China
4Department of Civil Engineering, Zhejiang Ocean University, Zhoushan 316004, China
5School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received 15 October 2014; Accepted 15 April 2015

Academic Editor: Igor Andrianov

Copyright © 2015 Zhiqing Zhang 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.


A quasi-analytical solution is developed in this paper to investigate the mechanism of one-dimensional longitudinal wave propagating in inhomogeneous viscoelastic pile embedded in layered soil and subjected to a transient axial loading. At first, the pile-soil system is subdivided into several layers along the depth direction in consideration of the variation of cross-sectional acoustic impedance of the pile or differences in soil properties. Then, the dynamic governing equation of arbitrary soil layer is established in cylindrical coordinates and arbitrary viscoelastic pile segment is modeled using a single Voigt model. By using the Laplace transform and boundary conditions of the pile-soil system, the vertical impedance at the top of arbitrary pile segment is defined in a closed form in the frequency domain. Then by utilizing the method of recursion typically used in the Transfer Function technique, the vertical impedance at the pile top can be derived in the frequency domain and the velocity response of an inhomogeneous viscoelastic pile subjected to a semi-sine wave exciting force is obtained in a semi-analytical form in the time domain. Selected numerical results are obtained to study the mechanism of longitudinal wave propagating in a pile with a single defect or double defects.