A numerical model for ground-borne vibrations from underground railway traffic based on a periodic finite element–boundary element formulation

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.

Fully three-dimensional analysis of high-speed train–track–soil-structure dynamic interaction

“…In addition, the floating slab tracks can be used to control ground-borne vibrations generated by railway traffic [40,41,42,43]. The growing interest in this relatively new track technology in recent years, calls for additional studies to be conducted.…”

Band Structures Analysis Method of Two-Dimensional Phononic Crystals Using Wavelet-Based Elements

“…In the search for complete band-gaps, many mathematical models are constructed to calculate band-gaps (BGs) of two-dimensional phononic crystals (2DPCs), such as the plane-wave expansion method (PWE) [6][7][8], multiple scattering theory (MST) [9], finite difference time-domain method (FDTD) [10,11], lumped mass method (LM) [12], wavelet method [13,14], boundary element method (BEM) [15][16][17], etc. However, when materials are anisotropic, nonlinear, or have large acoustic mismatch, PWE requires a large number of plane waves to obtain a reliable band structure and results are non-convergent for PCs composed of different media.…”

Using Periodicity to Mitigate Ground Vibration

“…Such models have been used, for example, by Manconi and Mace [4] to study curved panels, and by Domadiya et al [5] to study wave propagation in beams with periodically placed masses or changes to the cross section. The combination of Floquet theory and finite-elements has also be used for analysis of railways [6], mainly to allow studying long structures with low computational cost. For a similar reason, Bian et al [7] used a so-called 2.5D model to study ground vibrations from a train running on a track with irregular surface.…”