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Research Papers

Vibration Analysis of a Circular Tunnel With Jointed Liners Embedded in an Elastic Medium Subjected to Seismic Waves

[+] Author and Article Information
Dong-Sheng Jeng1

Division of Civil Engineering, University of Dundee, Dundee, Scotland DD1 4HN, United Kingdomd.jeng@dundee.ac.uk

Jian-Fei Lu

Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, 212013, P.R.C.ljfdoctor@yahoo.com

1

Corresponding author.

J. Vib. Acoust 131(2), 021005 (Feb 17, 2009) (8 pages) doi:10.1115/1.2827362 History: Received March 29, 2006; Revised August 16, 2007; Published February 17, 2009

This paper presents a frequency domain analysis of a circular tunnel with piecewise liners subjected to seismic waves. In our model, the surrounding medium of the tunnel is considered as a linear elastic medium and described by the dynamic elasticity theory, while piecewise liners and connecting joints are treated as curved beams and described by a curved beam theory. Scattered wave field in the surrounding elastic medium are obtained by the wave function expansion approach. The governing equations for vibrations of a curved beam are discretized by the general differential quadrature method. We use domain decomposition methods to establish the global discrete dynamic equations for piecewise liners. Boundary least squares collocation methods, based on the continuity conditions of stresses and displacements between surrounding soil and the piecewise liners, are used to determine the response of the liners and the surrounding medium. Numerical results conclude that the presence of the joints significantly changes the distributions of the tunnel internal force, and dramatically increase shear forces and moment of the tunnel liners around joints.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A circular tunnel with piecewise liner embedded in an elastic medium and subjected to seismic waves

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Figure 2

A curved beam segment with an attached curvilinear coordinate system

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Figure 3

Comparison of the dynamic response of an integral liner tunnel and a piecewise liner tunnel when subjected to a P wave with frequency f=10Hz: (a) nondimensional axial force N̂*=N̂(θ)∕λ(Ap(I)kp); (b) nondimensional shear force Q̂*=Q̂(θ)∕λ(Ap(I)kp); (c) nondimensional bending moment M̂*=M̂(θ)∕λ(Ap(I)kp)2

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Figure 4

Comparison of the dynamic response of an integral liner tunnel and a piecewise liner tunnel when subjected to a P wave with frequency f=50Hz: (a) nondimensional axial force N̂*=N̂(θ)∕λ(Ap(I)kp); (b) nondimensional shear force Q̂*=Q̂(θ)∕λ(Ap(I)kp); (c) nondimensional bending moment M̂*=M̂(θ)∕λ(Ap(I)kp)2

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Figure 5

Comparison of the dynamic response of an integral liner tunnel and a piecewise liner tunnel when subjected to a P wave with frequency f=150Hz: (a) nondimensional axial force N̂*=N̂(θ)∕λ(Ap(I)kp); (b) nondimensional shear force Q̂*=Q̂(θ)∕λ(Ap(I)kp); (c) nondimensional bending moment M̂*=M̂(θ)∕λ(Ap(I)kp)2

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