The assessment of pressure comfort on-board trains travelling through tunnels has been undertaken routinely in tunnel design since the 1960s. The assessment of pressures radiating from tunnel portals into the surrounding environment did not become important until much higher train speeds were adopted. In Japan, this was in the 1970s. Elsewhere, high speed trains in tunnels were unusual even in the 1990s and, importantly, so were aerodynamically sealed trains.
When trains are partially sealed to protect passengers from extremes of pressure fluctuations in tunnels, it becomes acceptable to allow larger pressure fluctuations in the tunnels and hence to have smaller cross-sectional areas. This leads to large savings in construction costs. It also leads, however, to increases in pressure fluctuations radiated from tunnel portals and in some cases, the resulting conditions have been found to be unacceptable. The radiated fluctuations are known as Micro-Pressure Waves (MPWs) and, in extreme cases, they have been experienced as sonic booms - although designers will surely prevent future occurrences of such severity.
Origins of MPWs
Pressure disturbances arriving at tunnel portals are reflected back along the tunnel. However, a small amount of energy escapes and, when the amplitudes of low frequency components are too large, doors and windows of adjacent buildings can be caused to vibrate. When the affected frequencies are sufficiently large, the disturbances can be audible. In practice, large amplitudes are experienced only when the pressure wavefront arriving at the portal is unusually steep and this is a relatively unusual occurrence. It is most unlikely to occur in tunnels with ballast-track construction, for instance, because these tend to restrict the steepness of pressure wavefronts propagating along tunnels.
In simple, slab-track tunnels, wavefronts tend to steepen as they propagate along a tunnel. In these cases, unacceptable radiation is possible provided that the tunnel is sufficiently long for a wavefront to become steep enough to cause nuisance. Any tunnel longer than this is a potential source of concern, but there is also an upper limit to the range of lengths that give trouble. This is because of the combined effects of (i) friction experienced by air flowing over the tunnel walls and (ii) dispersive influences of non-uniformities such as niches and cross-passages (even when these are nominally closed).
Three phases of MPWs
There are three key phases to the development of an MPW phenomenon, namely:
• generation of the causal pressure wavefront
• propagation of the wavefront towards a tunnel outlet
• radiation of the transmitted component of the incident wavefront
Alan Vardy’s research has embraced all three of these phases. His work in the 1970s on flared and ventilated tunnel entrance regions is directly relevant to the most common source of MPWs, namely the wavefront generated during the entry of a train nose to a tunnel. More recently, he has liaised with Michael Howe, University of Boston, who has developed powerful practical methods of allowing for three-dimensional effects during nose-entry.
Vardy has also devoted great attention to phenomena influencing the propagation of wavefronts. His work with Jim Brown on unsteady skin friction has been influential in a number of applications other than tunnels. Other work with Jim Brown has included the development of theoretical models of wave propagation in tunnels with ballast track. This is a subject that is not well understood and we do not regard our models as definitive. Nevertheless, they have helped us to identify some behaviour that was previously unrecognised, thereby shedding light for future workers on the topic. The most productive aspect of this work is likely to be assisting in the identification of methods of constraining steepening in slab-track tunnels without needing to consider fully ballasted track.
Vardy’s research on the third phase of MPW generation began more than 30 years ago with a study of the wave reflection process at tunnel extensions (e.g. flared). Later work with Jim Brown addressed reflections at abrupt portals and two projects with Japanese Universities have assessed passive and active methods of reducing MPWs by modifications to tunnel exit portals.
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| Tunnel portal | Shinkansen series N700 |
Selected references
Aoki T, Vardy AE & Brown JMB (1999) Passive alleviation of micro-pressure waves from tunnel portals. J Sound & Vibration, 220(5), 921-940
Brown JMB & Vardy AE (1994) Reflections of pressure waves at tunnel portals. J Sound & Vibration, 173(1), 95-111
Matsubayashi K, Brown JMB & Vardy AE (2000) Sonic booms - do I have a problem?, Proc 10th int symp on the Aerodynamics and Ventilation of Vehicle Tunnels, Boston, USA, BHR Group, 185-202
Matsubayashi K, Kosaka T, Kitamura T, Yamada S, Vardy AE & Brown JMB (2004) Reduction of micro-pressure wave by active control of propagating compression wave in high speed tunnel. Journal of low frequency noise, vibration and active control, 23(4), 259-270
Vardy AE (1975) Ventilated approach regions for railway tunnels. Transportation Engineering J, ASCE, 101(TE4), 609-619
Vardy AE (1978) Reflection of step-wavefronts from perforated and flared tube extensions. J Sound and Vibration, 59(4), 577-589
Vardy AE (2008) Generation and alleviation of sonic booms from railway tunnels, Engineering & Computational Mechanics, Proc ICE, 161 (EM3), 107-119 doi: 10.1680/eacm.2008.161.3.107
Vardy AE & Brown JMB (2000) Influence of ballast on wave steepening in tunnels, J Sound & Vibration, 238(4), 595-615
Vardy AE & Brown JMB (2000) The use of ballast to attenuate wavefronts, Proc 10th int symp on the Aerodynamics and Ventilation of Vehicle Tunnels, Boston, USA, BHR Group, 701-718
Vardy AE, Sturt R, Baker CJB & Soper D (2015) The behaviour of long entrance hoods for high speed rail tunnels, Proc 16th int symp on Aerodynamics, Ventilation and Fire in Tunnels, Seattle, USA, 15-17 Sep 2015, BHR Group, 449-466
Wang H, Vardy AE & Pokrajac ,D (2015) Perforated exit regions for the reduction of micro-pressure waves from tunnels, J of Wind Engineering & Industrial Aerodynamics, 146, 139–149 [doi: 10.1016/j.jweia.2015.07.015]
Wang H, Vardy AE & Pokrajac D (2016) Perforated tunnel exit regions and MPWs: geometrical influence, Engineering & Computational Mechanics, Proc ICE, [doi: 10.1680/jencm.15.00026]
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