Elastodynamic Analysis of Underground Structural Failures Induced by Seismic Body Waves

Abstract

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.