Dundee Tunnel Research

Applied Research - Pressure Waves in Tunnels

Alan Vardy’s research on pressure waves in railway tunnels began in 1971 and continues to this day.  From the outset, the primary motivation has been to minimise the consequences of the pressure waves for all users of the tunnels.

Vardy’s work began at the University of Leeds, where John Fox and David Henson had already developed a numerical model of pressure waves caused by a single train in a tunnel.  They were about to embark on a physical and numerical study of pressure waves and air flows in a proposed version of the Channel Tunnel that closely resembled the tunnel that subsequently opened in 1994.  Vardy’s target was different, namely assessing the potential of flared tunnel entrances to improve passenger comfort, and the understanding that he gained was one of the important inputs to the early development of the program ThermoTun.

Usually, the most important pressure waves in railway tunnels are generated when the nose and tail of a train enter the tunnel.  Further waves are generated when the train passes by air shafts and side passages, etc and when it leaves the tunnel.  The waves propagate back and forth along the tunnel, reflecting at its portals and shafts, etc.  Passengers are affected by the cumulative effect of all the waves.  If maintenance personnel are allowed in the tunnel, they too experience the waves and, in addition, they experience large changes in pressure and air speed when the trains pass by.

Pressure relief

The early study of flared entrances was followed by studies of other types of tunnel extension regions and then by an assessment of the potential of airshafts to improve passenger comfort.  It was found that extended entrances are most suitable for non-crossing trains in short tunnels and that airshafts are especially effective for crossing trains.  Cross-connections between adjacent running tunnels can also be effective and, in long tunnels, they have the special advantage of reducing train power requirements. However, they pose special problems in the event of fire.


In early years, validation of the theoretical predictions was restricted to relatively simple cases that were available from full-scale measurements and from limited model-scale measurements. In 1977, however, Vardy was extremely fortunate to be asked to provide theoretical predictions for use with model-scale measurements to be obtained by Bain Dayman at the Jet Propulsion Laboratory.  Dayman’s experience in experimental processes at full-scale and model-scale ranged from developing supersonic wind tunnels to playing a leading role in the control of systems on Voyager space craft exploring the solar system. His tunnel measurements enabled the broad validity of an early version of ThermoTun to be demonstrated with high confidence for a wide range of tunnel and train geometries, including designs more complex than those likely to be implemented in practice.

Real train data

Having developed prediction methods of high accuracy, it became clear that the ability of designers to make full use of them was limited by inadequate knowledge of train properties.  This difficulty persists to the present day.  The amplitudes of pressure disturbances in tunnels depend strongly on the cross-sectional blockage effects of trains and upon their resistance characteristics.  The software assumes that questions such as “What is the cross-sectional area of the train?” have already been answered satisfactorily.  This is straightforward for smooth cylindrical “trains” used in model tests, but it is far from straightforward for real trains. Likewise, how can the resistance characteristics of the trains be deduced reliably, given that they are not the same as for trains travelling overland and that they are not even the same in different tunnels.  The required information can be obtained from full-scale tests, but it would not be plausible to propose this method for every train. Vardy has shown how reliable data can be inferred from measurements during routine operation and has attempted to derive parameters that are indicative of general types of train.

Sonic booms

The prediction of pressure fluctuations in railway tunnels is a relatively mature subject.  Nevertheless, one particular aspect remains a source of considerable uncertainty.  This is the likelihood of unacceptably large pressure disturbances radiating from tunnel portals.   In extreme cases, these disturbances can be experienced as loud sonic booms.  Much of Vardy’s research over the past two decades has been relevant to this topic.  It is one of the justifications for his long-standing interest in <unsteady skin friction> and it led to separate collaborative work with two Japanese Universities on passive and active methods of countering the problem through modifications to tunnel exit portals.  Nevertheless, the most reliable and cost effective ways of  overcoming the problem are (i) elongating train noses and (ii) providing special entrance regions for tunnels.  The latter brings us back full circle to Vardy’s original work at the University of Leeds in the early 1970s- although the motivation for that work was very different.

Unusally large area airshaft

British Rail's Advanced Passenger Train (APT, 1980)

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

Dayman B & Vardy AE (1979) Alleviation of tunnel entry pressure transients. Proc 3rd int symp on the Aerodynamics and Ventilation of Vehicle Tunnels, Sheffield, UK, BHRA Group, 343-376 [2 papers]

Fox JA & Vardy AE (1973) The generation and alleviation of air pressure transients in tunnels. Tunnels and Tunnelling, 5(6), 575-585. [Warning: the train nose coefficient used in this early work is far too large]

Hagenah B, Reinke P & Vardy AE (2006) Effectiveness of pressure relief shafts - full-scale assessment, Proc 12th int symp on the Aerodynamics and Ventilation of Vehicle Tunnels, Portoroz, Slovenia, 11-13 Jul, Ed: AE Vardy, BHR Group, 379-391

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

Montenegro Palmero N & Vardy AE (2014) Tunnel gradients and aural health criteria for train passengers, J Rail & Rapid Transit, ImechE , 228(7), 821-832

Vardy AE (1975) Ventilated approach regions for railway tunnels. Transportation Engrg 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 & Brown JMB (2000) Influence of ballast on wave steepening in tunnels, J Sound & Vibration, 238(4), 595-615

Vardy AE & Howe MS (2009) Rapid prediction of train nose entry pressure gradients, Proc 13th int symp on the Aerodynamics and Ventilation of Vehicle Tunnels, New Brunswick, USA, 13-15 May, BHR Group, 429-443

Vardy AE & Reinke P (1999) Estimation of train resistance coefficients in tunnels from measurements during routine operation. J Rail & Rapid Transit, Proc IMechE Part F, 213(2), 71-87

Vardy AE, Rhodes N & Wang A (2009) Train-induced pressures and flows in large underground stations, Proc 13th int symp on the Aerodynamics and Ventilation of Vehicle Tunnels, New Brunswick, USA, 13-15 May, BHR Group, 445-456

Vardy AE, Rudolf A & Gloth O (2009) Thermal, Mach-number and inertial compressibility in railway tunnels, Proc 13th int symp on the Aerodynamics and Ventilation of Vehicle Tunnels, New Brunswick, USA, 13-15 May, BHR Group, 505-520