X. Sheng

A comparison of a theoretical model for quasi-statically and dynamically induced environmental vibration from trains with measurements

This paper presents comparisons between a theoretical ground vibration model and measured data at three sites. The model, which is briefly outlined here, encompasses both the quasi-static and dynamic mechanisms of excitation. The vertical dynamics of a number of vehicles travelling at a constant speed on an infinite track are coupled to a semi-analytical model for a three-dimensional layered ground. This model is also used to demonstrate the roles of the two components of vibration at different frequencies and for train speeds below and above the lowest ground wave speed. It is found that, in most practical cases, the dynamic component gives rise to the higher level of vibration.

Modelling ground vibration from railways using wavenumber finite- and boundary-element methods

A mathematical model is presented for ground vibration induced by trains, which uses wavenumber finite- and boundary-element methods. The track, tunnel and ground are assumed homogeneous and infinitely long in the track direction (x-direction). The models are formulated in terms of the wavenumber in the x-direction and discretization in the yz-plane. The effect of load motion in the x-direction is included. Compared with a conventional, three-dimensional finite- or boundary-element model, this is computationally faster and requires far less memory, even though calculations must be performed for a series of discrete wavenumbers. Thus it becomes practicable to carry out investigative study of train-induced ground vibration. The boundary-element implementation uses a variable transformation to solve the well-known problem of strongly singular integrals in the formulation. A ‘boundary truncation element’ greatly improves accuracy where the infinite surface of the ground is truncated in the boundary-element discretization. Predictions of vibration response on the ground surface due to a unit force applied at the track are performed for two railway tunnels. The results show a substantial difference in the environmental vibration that could be expected from the alternative designs. The effect of a moving load is demonstrated in a surface vibration example in which vibration propagates from an embankment into layered ground.

Ground vibration generated by a harmonic load moving in a circular tunnel in a layered ground

All modes of transport impact on e environment. Although railways are seen as environmentally advantageous in many ways, the issues of noise and vibration are often seen as their weakness. For trains running in tunnels where direct airborne noise is effectively screened, structure-borne or ‘ground-borne’ noise caused by vibration propagated through the ground is the most important concern. The vibration of interest in this case has frequency components from about 15 Hz to 200 Hz. To understand the mechanisms of vibration propagation from tunnels, a predictive model has been developed for ground vibration generated by a stationary or moving harmonic load applied in a circular lined or unlined tunnel in a layered ground. This study is the first step towards the use of discrete wavenumber methods to model ground vibration from underground trains. Discrete wavenumber methods fall into three categories: the discrete wavenumber fictitious force method, the discrete wavenumber finite element method and the discrete wavenumber boundary element method. This study uses the discrete wavenumber fictitious force method. Based on the moving Greens functions for a layered half-space and those for a cylinder of infinite length, boundary integral equations over the tunnel-soil interface are established. Unlike the conventional boundary integral equation in elastodynamics, the method used here only requires the displacement Greens function. This is achieved by introducing the excavated part of the ground as an extra substructure. The boundary integral equations are further transformed into a set of algebraic equations by expressing each quantity involved in the boundary integral equations in terms of a Fourier series. Results presented in this paper illustrate the effect of a tunnel on vibration propagation at the ground surface and the difference between a lined tunnel and an unlined tunnel.