Abstract
A numerical model is presented to predict vibrations in the free field from excitation due to metro trains in tunnels. The three-dimensional dynamic tunnel–soil interaction problem is solved with a subdomain formulation, using a finite element formulation for the tunnel and a boundary element method for the soil. The periodicity of the geometry in the longitudinal direction of the tunnel is exploited using the Floquet transform, limiting the discretization to a single-bounded reference cell. The responses of two different types of tunnel due to a harmonic load on the tunnel invert are compared, both in the frequency–wavenumber and spatial domains. The first tunnel is a shallow cut-and-cover masonry tunnel on the Paris metro network, embedded in layers of sand, while the second tunnel is a deep bored tunnel of London Underground, with a cast iron lining and embedded in the London clay.
Highlights
Underground trains create vibrations which are transmitted through the soil and interact with the foundations of adjacent buildings, resulting in disturbance from vibrations (1–80 Hz) and re-radiated noise (1–200 Hz).Numerical models with varying degrees of sophistication are under development to predict vibrations from trains running in tunnels
In order to analyse the performance of different track structures with respect to vibrations generated in the free field and in adjacent buildings, it is advantageous to differentiate between the degrees of freedom of the tunnel invert and the track
A periodic coupled finite element–boundary element formulation is used to study the dynamic interaction between a tunnel and a layered soil due to a harmonic excitation on the tunnel invert
Summary
Underground trains create vibrations which are transmitted through the soil and interact with the foundations of adjacent buildings, resulting in disturbance from vibrations (1–80 Hz) and re-radiated noise (1–200 Hz). After a brief review of the governing system of equations, details on the geometry and construction of both tunnels are presented in the present paper (the reader is referred to other papers [18,20,22] for a complete account of the formulation and solution of periodic dynamic soil–structure interaction problems) The response of both tunnels (and the surrounding soil) due to a harmonic load on the tunnel invert is considered, allowing to draw conclusions on the dynamic behaviour of both tunnel–soil systems. The application of this methodology to the response of periodic tunnel–soil systems due to moving loads will be discussed in a future publication
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