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`Mathematical Problems in EngineeringVolume 2017, Article ID 1794950, 11 pageshttps://doi.org/10.1155/2017/1794950`
Research Article

## Vertical Vibration Characteristics of a Variable Impedance Pile Embedded in Layered Soil

1Engineering Research Centre of Rock-Soil Drilling & Excavation and Protection, Ministry of Education, China University of Geosciences, Wuhan, Hubei 430074, China
2College of Civil Engineering and Architecture, Guangxi University, Nanning, Guangxi 530004, China
3Institute of Drilling Engineering and Fluid Mining, TU Bergakademie Freiberg, Freiberg, Germany

Correspondence should be addressed to Changliang Fang; ed.grebierf-ut.tbt@gnaf.gnailgnahc and Bin Dou; moc.361@uodnairb

Received 30 September 2016; Accepted 21 February 2017; Published 3 April 2017

Academic Editor: Dane Quinn

Copyright © 2017 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.

#### Abstract

In engineering applications, various defects such as bulging, necking, slurry crappy, and weak concrete are always observed during pile integrity testing. To provide more reasonable basis for assessing the above defects, this paper proposed simple and computationally efficient solutions to investigate the vertical vibration characteristics of a variable impedance pile embedded in layered soil. The governing equations of pile-soil system undergoing a vertical dynamic loading are built based on the plane strain model and fictitious soil pile model. By employing the Laplace transform method and impedance function transfer method, the analytical solution of the velocity response at the pile head is derived in the frequency domain. Then, the corresponding semianalytical solution in the time domain for the velocity response of a pile subjected to a semisinusoidal force applied at the pile head is obtained by adopting inverse Fourier transform and convolution theorem. Based on the presented solutions, a parametric study is conducted to study the vertical vibration characteristics of variable cross-section pile and variable modulus pile. The study gives an important insight into the evaluation of the construction quality of pile.