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.

Transverse response of underground cavities and pipes to incident SV waves

A method to obtain the three-dimensional harmonic response of a infinitely long cylindrical shell of circular cross-section embedded in a layered viscoelastic half-space and subjected to harmonic plane waves impinging at an oblique angle with respect to the axis of the shell is presented. The procedure combines an indirect integral representation for the field in the exterior half-space with a model of the pipeline or tunnel based on Donnell shell theory. The integral representation for the soil is based on the use of moving Green's functions for the layered viscoelastic half-space. The accuracy of the formulation is tested by comparison of results obtained by using different discretizations. Extensive comparisons with previous two- and three-dimensional results for the case of a shell embedded in a uniform half-space and some new numerical results for a shell embedded in a multilayered half-space are presented in a companion paper.

Seismic response of a cylindrical shell embedded in a layered viscoelastic half-space; I, Formulation

Three dimensional dynamics of pipelines buried in backfilled trenches due to oblique incidence of body waves

A direct half-plane time-domain boundary element method (BEM) was developed and successfully applied to analyze the transient response of ground surface in the presence of arbitrarily shaped lined tunnels, embedded in a linear elastic half-space, subjected to propagating obliquely incident plane SH-waves. To prepare the model, only the interface and inner boundary of the lining need to be discretized. The problem was decomposed into a pitted half-plane and a closed ring-shaped domain, corresponding to the substructure procedure. After computing the matrices and satisfying the compatibility as well as boundary conditions, the coupled equations were solved to obtain the boundary values. To validate the responses, a practical example was analyzed and compared with those of the published works. The results showed that the model was very simple and the accuracy was favorable. Advanced numerical results were also illustrated for single/twin circular lined tunnels as synthetic seismograms and three-dimensional frequency-domain responses. The method used in this paper is recommended to obtain the transient response of underground structures in combination with other numerical methods.

Transient SH-wave scattering by the lined tunnels embedded in an elastic half-plane

Numerical analysis of surface-wave scattering by the boundary element method

: At present ultrasonic techniques for characterizing defects are being explored vigorously at various research centers around the world. Currently, the ultrasonic approach to defect sizing and characterization is beginning to find great favor for in- or out-of-service use. A recent review of practical ultrasonic nondestructive evaluation is referred. Because of recent advances in experimental ultrasonic technology, increasing demands are being put on quantitative theoretical modeling of scattering of ultrasonic (elastic) waves by cracks, cavities and other material inhomogeneities in an elastic medium. With a view to obtain detailed information about signals scattered from complex defects various analytical and numerical techniques have emerged. In this article we present a combined finite elements and eigenfunction expansion technique for solving scattering problems involving multiple scattering as well as complex geometries. Numerical results obtained by this method are compared with recent experimental results. In the following we first summarize the theoretical treatment. Then we present the finite elements and eigenfunction expansion technique (FEEET). Numerical and experimental results are presented next. Although the results presented here are for homogeneous materials, the method can readily be extended to composite materials.

Y. F. Chin

Papers

Elastic Wave Scattering by Surface-Breaking Planar and Nonplanar Cracks

Dynamics of buried pipes in back-filled trench