Modelling ground vibration from tunnels using wavenumber finite and boundary element methods

Sheng, X., Jones, C.J.C. and Thompson, D.J. (2005) Modelling ground vibration from tunnels using wavenumber finite and boundary element methods. Proceedings of the Royal Society A, 461 (2059), 2043-2070. (doi:10.1098/rspa.2005.1450).

Abstract

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.

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Contributors

Author: D.J. Thompson

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