The Effects of a Second Tunnel on the Propagation of Ground-Borne Vibration from an Underground Railway

  • K. A. Kuo
  • M. F. M. Hussein
  • H. E. M. Hunt
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 118)


Accurate predictions of ground-borne vibration levels in the vicinity of an underground railway are greatly sought in modern urban centers. Yet the complexity involved in simulating the underground environment means that it is necessary to make simplifying assumptions about this environment. One such commonly-made assumption is to model the railway as a single tunnel, despite many underground railway lines consisting of twin-bored tunnels.

A unique model for two tunnels embedded in a homogeneous, elastic full space is developed. The vibration response of this two-tunnel system is calculated using the superposition of two displacement fields: one resulting from the forces acting on the invert of a single tunnel, and the other resulting from the interaction between the tunnels. By partitioning of the stresses into symmetric and anti-symmetric mode number components using Fourier decomposition, these two displacement fields can by calculated with minimal computational requirements.

The significance of the interactions between twin-tunnels is quantified by calculating the insertion gains that result from the existence of a second tunnel. The insertion-gain results are shown to be localized and highly dependent on frequency, tunnel orientation and tunnel thickness. At some locations, the magnitude of these insertion gains is greater than 20dB. This demonstrates that a high degree of inaccuracy exists in any surface vibration-prediction model that includes only one of the two tunnels.


Displacement Field Vibration Response Traction Vector Fourier Decomposition Railway Tunnel 
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Copyright information

© Springer 2012

Authors and Affiliations

  • K. A. Kuo
    • 1
  • M. F. M. Hussein
    • 2
  • H. E. M. Hunt
    • 1
  1. 1.Engineering DepartmentUniversity of CambridgeCambridgeUnited Kingdom
  2. 2.University of NottinghamUnited Kingdom

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