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Research Papers

Elastodynamic Analysis of Underground Structural Failures Induced by Seismic Body Waves

[+] Author and Article Information
Koji Uenishi1

Research Center for Urban Safety and Security, Kobe University 1-1 Rokko-dai, Nada, Kobe 657-8501, Japanuenishi@kobe-u.ac.jp

1

Present address: Department of Aeronautics and Astronautics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan, e-mail: uenishi@mat.t.u-tokyo.ac.jp

J. Appl. Mech 79(3), 031014 (Apr 05, 2012) (10 pages) doi:10.1115/1.4005888 History: Received July 14, 2011; Revised January 20, 2012; Posted February 06, 2012; Published April 04, 2012; Online April 05, 2012

Scattering of elastic waves by structural inhomogeneities such as cylindrical cavities has been a subject of intensive study for decades. The time-harmonic elastodynamic analysis making use of the wave function expansions is one of the typical approaches for such problems, and since it gives semianalytical solutions that may show the effect of parameters of the problem rather explicitly, it is still repeatedly used in the study of dynamic response of elastic structures including inhomogeneities. Here, motivated by the observation of the unique underground structural failure patterns caused by the 1995 Hyogo-ken Nanbu (Kobe), Japan, earthquake, we analyze scattering of a plane harmonic body wave by a uniformly lined circular tunnel (cylinder), and from the structural failure patterns we evaluate possible mechanical characteristics of the associated incident seismic waves. In the two-dimensional, in-plane time-harmonic elastodynamic model employed, the lined circular tunnel may be located at a finite depth from an approximate flat free surface of a homogeneous isotropic linear elastic medium (half-space), and the plane wave impinges upon the tunnel at an arbitrary incident angle. We compare the effect of P and SV wave incidences by calculating the dynamic amplification of stresses and displacements around this simplified tunnel, and also show the influence of the wavelength and the incident angle of the plane wave, the overburden thickness, and the relative compliance of the linear elastic lining with respect to the surrounding medium. The results suggest that the observed underground structural failures, the exfoliation of the lining concrete and buckling of the reinforcing steel bars on the sidewall as well as the detachment of the subgrade from the invert, might have been induced by the incidence of P waves in a relatively high frequency range.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

The structural failures in the Bantaki Tunnel caused by the 1995 Hyogo-ken Nanbu (Kobe), Japan, earthquake: (a) exfoliation of the lining concrete and buckling of the reinforcing steel bars due to compression on the sidewall and (b) detachment of the subgrade from the invert (photographs courtesy of Professor Emeritus Shunsuke Sakurai of Kobe University)

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Figure 2

Geometry of the problem. (a) Scattering of a plane harmonic body wave by two circular tunnels (cylinders) running in parallel, one lined and the other unlined, is considered. (b) If the radius of tunnel 2, c, vanishes, tunnel 1 is located in an infinite medium (in the new coordinates (r, θ)). (c) If the radius c is sufficiently large, interaction of a plane body wave with a uniformly lined circular tunnel at some depths from an approximate flat free surface (of a half-space) may be investigated (θ12  = 0, θ21  = π).

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Figure 3

Amplification and reduction of the maximum dynamic circumferential stress |(σθθ )I | on the sidewall (at r = a, |θ| = π/2) of an unlined circular tunnel located in an infinite medium (b/a = 1, c = 0, Poisson’s ratio νI  = 0.25, δ = 0). The variations of the stress concentration factors are plotted against the nondimensionalized wavelength (λP )I /a and (λS )I /a for P and SV plane wave incidences.

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Figure 4

The effect of the shear moduli ratio of the lining to the surrounding medium μIII on the dynamic stress concentration factor |(σθθ )II /σ0 | on the free surface (at r = a) of a uniformly lined circular tunnel located in an infinite medium (b/a = 1.075, c = 0, νI  = 0.25, νII  = 0.15, ρIII  = 1, δ = 0). The nondimensionalized wavelength of the incident plane harmonic P wave (λP )I /a is (a) 10 and (b) 50.

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Figure 5

Variations of the maximum dynamic circumferential stress |(σθθ )II | (= |(σθθ )I |) on the outer boundary of the lining (at r = b) for the shear moduli ratio μIII  = 0.5, 1, and 2. The nondimensionalized incident wavelength (λP )I /a = (a) 10 and (b) 50, with the same material and geometrical conditions as those used in Fig. 4.

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Figure 6

The relation between the angle |θ| and the maximum dynamic radial displacement |(ur )II | on the free surface (at r = a) of a uniformly lined circular tunnel in an infinite medium for μIII  = 0.5, 1, and 2. The wavelength of the incident P wave (λP )I /a is (a) 10 and (b) 50, respectively. The material properties and the geometrical configurations remain unchanged (b/a = 1.075, c = 0, νI  = 0.25, νII  = 0.15, ρIII  = 1, δ = 0). For a reference purpose, in (c), the change of the radial displacement |(ur )I /u0 | with (λP )I /a is shown for an unlined circular tunnel located in an infinite medium (b/a = 1, c = 0, νI  = 0.25, δ = 0) at fixed r = a, |θ| = 0, π/2, and π.

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Figure 7

(a) The effect of overburden thickness h/a on the dynamic displacement amplification at r = a, |θ| = 0, and π on the free surface of a uniformly lined tunnel (b/a = 1.075, c/a = 100, νI  = 0.25, νII  = 0.15, ρIII  = μIII  = 1). The plane harmonic P wave ((λP )I /a = 10) propagates vertically from bottom with the incident angle δ = 0 to an approximate flat free surface. (b) With the same conditions but for fixed h/a = 2, the influence of the incident angle δ on the dynamic amplification and reduction of displacements around a lined tunnel is shown against θ on the tunnel free surface (at r = a). We assume only body waves exist.

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