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Vibration from Underground Trains * Pipe-in-Pipe Software

Vibration from Underground Trains * Pipe-in-Pipe Software. Hugh Hunt Cambridge University Engineering Department www.hughhunt.co.uk. “Common sense will carry one a long way but no ordinary mortal is endowed with an inborn instinct for vibrations” .

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Vibration from Underground Trains * Pipe-in-Pipe Software

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  1. Vibration fromUnderground Trains* Pipe-in-Pipe Software Hugh Hunt Cambridge University Engineering Department www.hughhunt.co.uk

  2. “Common sense will carry one a long way but no ordinary mortal is endowed with an inborn instinct for vibrations”. “Vibrations are too rapid for our sense of sight … common sense applied to these phenomena is too common to be other than a source of danger”. Professor C E Inglis, FRS, James Forrest Lecture, 1944

  3. The basis for “common sense” • Stiffness Frequency = • Mass • Damping ? • Continuous media ? The mkc model

  4. Vibration from Railways … where is the “mass-on-spring”? … how do I use my “intuition”? Source: Talbot

  5. Vibration isolation of rail track in tunnels Floating Slab Track Source: Tiflex Ltd

  6. Undersleeper pads Source: Edilon

  7. Novel designs for vibration control Source: Pandrol Ltd

  8. Insertion Gain for Floating Slab Track Isolation frequency 6.3Hz Insertion gain (dB) 20100-10-20-30-40-50 Floating Slab Track 2 4 5 10 12.5 25 50 100 125 200 Source: GERB

  9. m T2 k kadditional Insertion Gain after “insertion” T2 T1 0 dB Amplification atnew resonancetypically 10dB Benefit, typically 10 to 20 dB frequency What is Insertion Gain? response m T1 k before “insertion” frequency

  10. The Pipe-in-Pipe model e q e r e z R 2 R 1 (a) (b) z y x z r q h q a q Soil:thick-walled cylinder• inner radius R• outer radius • infinite length Tunnel: thin-walled cylinder• radius R• wall thickness t• infinite length CouplingDiscrete Fourier transform around Continuous Fourier transform along z

  11. isolation vertical vibration dB ref mm (rms) virtual free surface

  12. rms insertion gain (dB) Insertion Gain isolation Acknowledgements: Dr James Forrest Dr Mohammed Hussein

  13. When downloading the software you will need to enter a username and password. These are available on request. This is a requirement of Mathworks (ie MATLAB) to permit use of the MCR-installer which is a suite of DLLs needed to run PiP as a pre-compiled MATLAB executable. Please be patient when installing and running PiP for the first time – it may take a few minutes to get started. Subsequent uses are quick. This is a demonstration of the Pipe-in-Pipe software. It is freeware and can be obtained by following the PiP link at www.hughhunt.co.uk I am hugely indebted to Dr Mohammed Hussein from the University of Nottingham for his enormous contribution to the development of PiP software.

  14. This shows how different – by as much as 5dB - the vibration levels can be when the material properties are changed by only 15%. This begins to put into question the possibility of prediction accuracy any better than ± 10dB. -75 -80 -85 -90

  15. This shows how an increase in the bending stiffness of the slab leads, in this case, to an increase in vibration. -75 -80 -85 -90

  16. This shows how an increase in the mass and bending stiffness of the slab plus a reduction in the natural frequency of the slab from 40Hz to 25Hz leads to a reduction in vibration. -70 -75 -80 -85 -90 -95

  17. It is convenient to plot Case2, Case 3 and Case 4 as “Insertion Gains” measured relative to Case 1. These show clearly where the changes made lead to reduction in vibration (ie IG < 0dB) 5 0 - 5 - 10 0dB

  18. Here the measurement point is shifted from being 20m directly above the tunnel to being 20m above and 5m to one side. Note that the response is as much as 5dB different at certain frequencies. This again puts into question the possibility of obtaining prediction of vibration within an accuracy of better than ±10dB. -70 -75 -80 -85 -90 -95

  19. The PiP software also allows the user to plot contour plots such as these which illustrate where the vibration is greatest at different frequencies. This can help guide the location and distribution of piled foundations. The PiP software can also include the effect of rigid bedrock and the latest version of PiP (soon to be released) includes a free surface and layered soil. -40 -50 -60 -70 -80 5 - 0 - 5 -10

  20. Validation – PiP vs. coupled FEM-BEM The PiP software is in excellent agreement with other models Source: Mohammed Hussein / Shashank Gupta / Lars Rikse

  21. Conclusions • The mass-on-spring model is not good for predicting Insertion Gain • The PiP model is a very fast and convenient tool for computing vibration from railway tunnels • The use of PiP puts into question the possibility of obtaining better than ±10dB prediction accuracy from any model – no matter how detailed. • PiP is freeware and is easy to use.

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