The transverse response of underground cylindrical cavities to incident SV waves is investigated. Analytical solutions are derived for unlined cavities embedded within an elastic half‐space using Fourier–Bessel series and a convex approximation of the half‐space free surface. The computed displacements at the half‐space free surface and the tangential stresses on the cavity are compared with the results of previous investigations. The analytical solutions are extended to formulate approximate solutions for assessing hoop stresses within cavity liners impinged by low‐frequency waves having wavelengths much longer than the cavity diameter. The approximate solutions are compared to existing numerical solutions, and used to evaluate the dynamic response of a flexible buried pipe shaken by the 1994 Northridge earthquake. The proposed approximate model for cavity liners is useful for the seismic analysis of underground pipes and small‐diameter tunnels. Copyright © 2001 John Wiley & Sons, Ltd.

No abstract

S U M M A R YThe 2-D scattering and diffraction of plane SH-waves by a semi-parabolic cylindrical canyon in an elastic half-space is analysed for the cases of SH-waves coming from the side of the half-space towards the front of the canyon. The exact analytic series solution of the problem is presented. It shows that the surface topography can have significant effects on the incident waves, which become prominent at high frequencies, or when the wavelengths of the incident waves are short compared with the focal length of the canyon. Higher frequencies will also lead to greater complexity of the pattern of surface displacement amplitudes involving abrupt changes of amplification or deamplification from one point to another.

No abstract

No abstract