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Journal of Engineering
Volume 2017, Article ID 6145375, 12 pages
Research Article

Dynamic Response of a Circular Tunnel in an Elastic Half Space

Faculty of Civil Engineering, Yıldız Technical University, Davutpaşa Campus, Esenler, 34210 İstanbul, Turkey

Correspondence should be addressed to İrfan Coşkun; rt.ude.zidliy@nuksoc

Received 17 November 2016; Revised 1 March 2017; Accepted 9 March 2017; Published 26 April 2017

Academic Editor: Mohamed Ichchou

Copyright © 2017 İrfan Coşkun and Demirhan Dolmaseven. 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 vibration of a circular tunnel in an elastic half space subjected to uniformly distributed dynamic pressure at the inner boundary is studied in this paper. For comparison purposes, two different ground materials (soft and hard soil) are considered for the half space. Under the assumption of plane strain, the equations of motion for the tunnel and the surrounding medium are reduced to two wave equations in polar coordinates using Helmholtz potentials. The method of wave expansion is used to construct the displacement fields in terms of displacement potentials. The boundary conditions associated with the problem are satisfied exactly at the inner surface of the tunnel and at the interface between the tunnel and surrounding medium, and they are satisfied approximately at the free surface of the half space. A least-squares technique is used for satisfying the stress-free boundary conditions at the half space. It is shown by comparison that the stresses and displacements are significantly influenced by the properties of the surrounding soil, wave number (i.e., the frequency), depth of embedment, and thickness of the tunnel wall.