Journal of Applied Mathematics
Volume 2013 (2013), Article ID 124782, 10 pages
http://dx.doi.org/10.1155/2013/124782
Research Article

Mixed Boundary-Value Analysis of Rocking Vibrations of an Elastic Strip Foundation on Elastic Soil with Saturated Substrata

Xiaohua Ma,1,2 Zhenyu Wang,3 Yuanqiang Cai,3 and Changjie Xu3

1Geotechnical Engineering Institute, Zhejiang University, Hangzhou 310058, China
2College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
3Zhejiang Geofore Geotechnical Engineering Co., Ltd., Hangzhou 310013, China

Received 23 October 2012; Accepted 24 February 2013

Academic Editor: Juan Torregrosa

Copyright © 2013 Xiaohua Ma 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

The dynamic response of an elastic strip foundation lying on elastic soil with saturated substrata is greatly affected by pore pressure induced by a rocking moment. In this paper, we explore the mixed boundary-value problem of the rocking vibration of an elastic strip foundation on elastic soil with saturated substrata via Biot dynamic equations. First, the wave equations concerning both the single-phase elastic layer and the saturated half-space are solved using a Fourier integral transform technique. The dual integral equations of the rocking vibration of an elastic strip foundation are established according to the mixed boundary conditions. Finally, the relationship of the dynamic compliance coefficient with the dimensionless frequency is obtained by applying Simpson’s rule to conduct numerical calculation. We also analyse the influences of the elastic layer’s thickness and elastic characteristic parameters of the foundation on the rocking vibration.