An up to date literature survey on the dynamics of underground structures is presented briefly. The dynamic response of large three-dimensional underground structures to external or internal dynamic forces or to seismic waves is numerically determined by the frequency domain boundary element method. This method is used to model both the structure and the soil medium, which are assumed to behave as linear elastic or viscoelastic bodies. The full-space dynamic fundamental solution is employed in the formulation and this requires a free soil surface discretization, confined to a finite portion around the area of interest, in addition to soil—structure interface and free structural surface discretizations. The dynamic disturbances can have a harmonic or a transient time variation. The transient case is treated with the aid of numerical Laplace transforms with respect to time. Various numerical examples involving lined cavities and long lined tunnels buried in the full- or the half-space subjected to harmonic or transient external forces or seismic waves are presented to illustrate the method and demonstrate its advantages.

Dynamic analysis of large 3-D underground structures by the bem

http://users.ntua.gr/gbouck/downfiles/3-D_shell_analysis_of_cylindrical_underground_structures_under_seismic_shear_wave_action.pdf

3-D shell analysis of cylindrical underground structures under seismic shear (S) wave action

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

Dynamic response of a long, continuous pipeline buried at a depth, h, below the free surface of the ground is analyzed. It is assumed that the pipe is disturbed by plane seismic waves traveling at an arbitrary angle to its axis. Thus, the problem is three dimensional. The pipe has been modeled as a cylindrical shell. Both the pipe and the surrounding ground are assumed elastic, isotropic, and homogeneous. The solutions of equations of elastodynamics governing the motions of both are obtained in terms of cylindrical eigenfunctions modified to satisfy the boundary conditions on the free surface of the ground. Numerical results are presented in the accompanying paper.

Three‐Dimensional Motion of Buried Pipeline. I: Analysis

An exact analysis for three-dimensional dynamic interaction of monochromatic seismic plane waves with two lined circular parallel tunnels within a boundless fluid-saturated porous elastic medium is presented. The novel features of Biot dynamic theory of poroelasticity along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to obtain a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which two identical tunnels, lined with concrete and embedded within water-saturated soils of distinct frame properties (i.e., soft or stiff soils), are insonified by plane fast compressional or shear waves at end-on incidence. The basic dynamic field quantities such as the hoop and axial stress amplitudes are evaluated and discussed for representative values of the parameters characterizing the system. The effects of formation material type, angl...

P. M. O’Leary

Papers

Three-Dimensional Dynamic Response of Buried Pipelines to Incident Longitudinal and Shear Waves