Dynamics of underground tunnels

Abstract

Underground tunnels are important infrastructures due to diverse applications in civil engineering. The dynamic behavior of the underground tunnels when exposed to seismic waves or the passage of high-speedmoving trains is of particular interest. Amplifications of displacements and stress concentrations may occur due to wave scattering and wave interference. Engineers concern about the vibration stability of moving trains as so-called anomalous Doppler waves may be generated when trains move at high speeds; the corresponding energy is fed into the vibration of the vehicle. Therefore, the traintrack- soil interaction should be properly considered to predict when the vehicle vibration becomes unstable. This thesis aims to present a semi-analytical solution for the response of a half-space with an embedded tunnel subject to seismic waves and to analyse the vibration stability of high-speed trainsmoving through that underground tunnel. Previous studies indicate that the method of conformal mapping is a promising analytical method to solve the two-dimensional (2D) wave scattering problem due to its computational efficiency and accuracy. Thus, the first objective of this thesis is to extend the method of conformal mapping to three-dimensional (3D) case and systematically evaluate its performance. Results reveal that inaccurate results maybe obtained, particularly at high frequencies. This observation motivates the second objective of this thesis, which focuses on verifying the accuracy of the specific application of the method of conformal mapping in which thewaves scattered fromthe half-space surface are represented by cylindricalwaves that originate from an image source of a priori unknown intensity. To this end, a simpler 2D model is considered, involving a cylindrical cavity embedded in an elastic half-space subject to a harmonic anti-plane shear wave. The performance of the indirect Boundary Element Method (indirect BEM) is evaluated too for this model in view of the choice of the appropriate solution method for the second type of dynamic problem considered in this thesis. For this second type of dynamic problem, due to the identified inaccuracies at high frequencies for the 3D problem, the indirect BEM is utilised to investigate the stability of vibrations of an oscillator moving at high speeds through a tunnel embedded in soft soil, which is the third objective of this thesis…