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The Application and Effect of the Rayleigh Wave Speed Principle on High Speed Rail travel.

High Speed Rail

Written evidence from David Rayney (HSR 53)

The Application and Effect of the Rayleigh Wave Speed Principle on High Speed Rail travel.

Executive Summary

1)I wish to draw the attention of the committee to a phenomenon of physics that will impact uniquely upon the business and economic cases for the proposed High Speed Rail system HS2.

2)HS2 relies on the trains running at an intended speed of 400km/h (235mph), faster than any other High Speed Railway anywhere else in the world. That speed determines the capacity of the line – 18 trains per hour in each direction and must be sustained for the full journey.

3)We are all familiar with the concept of the sonic boom. When a military jet flying through the air reaches and passes the speed of sound in air a highly destructive high energy pressure wave is created.

4)The HS2 trains will not go through the same sound barrier (the speed of sound in air), But, the heavy train running on rails at speeds approaching the speed that the vibration waves travel through the track, infrastructure and ground, will set up pressure & vibration waves which are analogous to an sonic boom. The dynamics of such vibrations are such that the anticipated speed for HS2 compared to established high speed railways elsewhere can be expected to be disproportionately detrimental in this regard.

5)Concerns about these severe vibrations are not simply restricted to their effect on the local living environment. Rather these waves will have a substantial destructive and fatiguing effect on nearby buildings, on the infrastructure of the line – the rails, the bridges, the tunnel supports – and on the trains themselves.

6)At best the consequences of the pressure wave will substantially add to the requirements and costs of construction, and/or maintenance, and/or the associated disruption to service for repair. At worst, given the speed and number of passengers on each train the failure of a component of the system could lead to a potentially catastrophic failure of the system.

7)Whatever the strengths and weaknesses of the economic and business case put forward by HS2 Ltd, they are both founded upon an engineering design which because of the speed can, at best, only be described as experimental.


The Rayleigh Effect: The Physics

8)The particles within the structure of any given material can move. The theoretical maximum or ultimate speed at which the particles can move is dependent upon the mobility of those particles. This phenomenon is known as the "Rayleigh Wave Speed"[1]; and is an accepted principle that Sound travels through a material at a rate known as the Rayleigh wave velocity.

9)The speed of sound in a material is significant in the design and development, manufacture and construction of any and all engineering applications. It is of significant importance in design of HST track systems, as the increased speeds sought to make these trains viable, have raised new problems, in particular greater levels of train-track vibrations, and this is of particular relevance to HS2 with its ultra-high speed requirement.

10)A key research paper by Krylov et al describes the phenomenon thus:

11)"Unfortunately the increased speeds of modern trains are normally accompanied with increased transient movements of the rail and ground which may cause noticeable vibrations and structure born noise in nearby buildings. For modern high-speed trains those transient movements are especially high when train speeds approach certain critical wave velocities in the track-ground system. There are two main critical wave velocities in the track-ground system: The velocity of the Rayleigh surface wave in the ground and the minimum phase velocity of bending waves propagating in the track supported by ballast, the latter velocity being referred t as the track critical velocity. Both these velocities can easily be exceeded by modern high speed trains, especially in the case of very soft soil where both critical velocities become very low.

As has been theoretically predicted by one of the authors (6,7) if a train speed V exceeds a the Rayleigh wave velocity Cr in supporting soil, then a ground vibration boom occurs which is associated with a very large increase in generated ground vibrations, as compared with the case of conventional trains. This phenomenon is similar to a sonic boom for aircraft crossing the sound barrier and its existence has recently be confirmed experimentally (8). The measurements have been carried out on behalf of the Swedish Railway Authorities when there West coast main line from Gothenburg to Malmo was opened for the X2000 high speed train. The speed achievable by the X2000 train (up to 200 km/hour can be larger than Rayleigh wave velocities in this part of south western Sweden, which is characterized by very soft ground (see also reference (9)). In particular, at a location near Ledsgard, the Rayleigh wave velocity in the ground was as low as 45 m/s, so that the increase in train speed from 140 to 180km/hr, lead to an increase by a factor of about 10 in the generated ground vibration level (8). The above mentioned first observations of a ground vibration boom indicate that it is now possible to speak about "supersonic" or (more precisely) "trans-Rayleigh" trains (10-12). The increased attention of local authorities and railway companies to ground vibrations associated with high speed trains has stimulated a growing number of theoretical and experimental investigations in this area (see, e.g., references (13) to (16)).

If train speeds increase further and approach the track critical velocity, then rail deflections due to applied axle loads become especially large. Possible very large rail deflections at this speed may even result in train derailment, thus representing a serious problem of train and passenger safety (9.17-19).

12)This is corroborated by to research being carried out at the Heriot – Watt University[2] and the School of Engineering at Edinburgh University[3] This phenomenon is brought about by the fact that the characteristic wave speeds of the track components are dependant upon the Rayleigh Wave Velocities of the underlying track sub structures, [embankments and the subgrade] and the natural flexural wave velocity of the rail.

13)As previously stated, the ultimate speed of the material[its Rayleigh wave speed] is critical: When train speeds approach this critical speed the track structure and supporting ground undergo excessive dynamic changes, [motions] and therefore can become inherently unstable. These motions can cause rapid deterioration of the sub- rail components [ballast, sub-ballast] and the track itself which can ultimately lead to catastrophic failure. It is obvious therefore that to overcome any threat of derailment or to the safety of the train caused by the theoretical constraints placed on the system by Rayleigh’s wave speed principle, it would be necessary to significantly reduce the speed of the train.

14)The above paper by Krylov et al documented concerns in 2000 in respect of established trains with the speed of the French TGV and the Eurostar. Since then there has been little increase in maximum operating train speeds.

Existing High speed train speed statistic.


Max Rail speed limit

Fastest average speed for a timetabled journey.



















South Korea
























From Railway Gazette Speed Survey 2007.

15)Certainly there have been record breaking runs in the interim at which speeds substantially greater that that planned for HS2 were achieved. But these one off events were undertaken on specifically selected sections of straight track with significant adaptations of the infrastructure creating circumstances that have not been used in a sustained environment.

16)It is also necessary to determine the effect of the applied stabilization methods have on the dynamic response of the railway track.

17)The dynamic response of the track is a complex issue but the theoretical application is well documented in research carried out by Krylov et al, for the Institution of Mechanical Engineers.[4]

18)The dynamics involve the interaction between the train wheels, the rail itself, and the components of the rail supports [pad, sleeper, ballast, formation and subgrade], and in order to provide a safe, reliable high-speed system accurate predictions of the track response up to and including critical track velocities [CTRV], is of vital importance.

19)A further consequence of these issues is that CTRVs can lead to significantly increased ground vibration transmissions to adjacent structures with their attendant stress waves. This is significant in this instance due to the close proximity of this line to dwelling and industrial structures.

Further questions

20)The questions I wish to raise are

a)Given the research being done, and the already accepted research findings on this phenomenon which indicate that these transients can be extremely high when train speeds approach the Critical Wave Velocities of both the rails and the supporting ground and sub-structure and can therefore cause large rail deflections as well structural vibrations and noise in nearby dwellings, has the government taken the noise, vibration and safety issues raised by this research into account in its promulgated forecast of costings? [Bearing in mind that all costs were done using the Ministry formulae based on 2009 structures and costs and applicable to a system supporting trains moving at almost half the projected speed of HS2].

b)Secondly the research by Krylov is of particular importance where the rail is to be built over soft ground where wave velocities are much lower. HS2 is faster, heavier and longer than any other rail-guided vehicle in use: as such it is an unknown quantity, furthermore, its path from London to Birmingham crosses flood plains, soft alluvial ground etc: The research would indicate that extra measures are required to ensure the safe operation of this train in such areas particularly, and an enhanced Railtrack design to cope with the transients in all other areas. Have HS2 covered or even planned for such contingencies in their proposed planning and costing documents?

c)Thirdly, if and when the statutory blight conditions are enforced, have HS2 made allowance for the possible increased effects of ground wave transmission and the subsequent increase in vibrations etc brought about by the higher speeds required by HS2 on private dwellings etc, given that HS2 will be moving through a far more densely populated track than any of its other HS counterparts in Europe and beyond?

d)Lastly have HS2 made full account of the additional research and development costs and made allowances for overruns etc bearing in mind the extra costs that will almost certainly be incurred owing to inflation and other fiscal measures introduced since their original costings were promulgated?

21)There is certainly no evidence that these questions have been addressed in any of the HS2 ARUP documents available to the public. Certainly in the HS2 document of August 2010 HS2 Route Optimisation of Route 3 there appears to be no mention of special needs or particular issues arising from the above research, nor any allowance for cost overruns should any such issues arise.

22)In the ARUP Document of February 2011 "HS2 Route Engineering Report", the section on Geotechnical Assumptions makes no allowance, or contingencies for, nor recognises any specific problems or issues with rail design, ground wave transmissions, critical wave speeds or any of the problems being researched.

23)There is a complete lack of research regarding the effect of these vibrations in respect of the exacerbation of mining subsidence, and, vice versa, of the effect on the pressure waves of additional track bed reinforcement that might be needed in areas that are vulnerable to mining subsidence. This is not a factor for the London to Birmingham sector but is a key attribute of the terrain for both branches to the north

24)HS2 Ltd has not yet undertaken the soil and geological analysis that they acknowledge is needed. Such analysis is not planned until after the government has made a commitment to undertaking the HS2 project through the introduction of the hybrid bill.

25)An equivalent analysis of the possible routes to the north of Birmingham will not be undertaken until after the Government is bound in to contracts for the London to Birmingham section. This is putting the cart before the horse.

26)In conclusion, I can do no better than draw the attention of the committee to a successful research funding bid submitted to the Engineering and Physical Sciences Research Council by Professor PK Woodward of the Heriot Watt University School of the Built Environment in Edinburgh[1]. Professor Woodward recently hosted an engineering study day attended by the Chief Engineer for HS2 Ltd and colleagues. The application for a project entitled states :

27)"Apart from the 186mph Channel Tunnel Railway Line (CTRL) the maximum speed of trains in the UK is generally 125mph. In France the TGV now operates at 200mph, but a land speed record of 356mph was recently set on the Paris to Strasbourg line. An increasing demand for higher train speeds is therefore clearly evident. Introduction of high-speed systems to the railway network across the world has however brought new problems in terms of railway geotechnics, namely the significant amplification of train-track vibrations at high train speeds. This phenomenon has been attributed to the characteristic wave speeds of the track, which mainly depend on the Rayleigh wave velocity of the subgrade, underlying embankments, and the natural flexural wave velocity of the rail. When train speeds approach this critical speed the track structure and supporting ground experiences excessive dynamic motions. These motions cause rapid deterioration of the track, ballast and sub ballast, including possible derailment and ground failure. These may threaten the stability and safety of the train and hence lead to significant line speed restrictions, causing significant delays to the network. It is therefore evident that in order to increase line speeds in the UK (and overseas) it is necessary to not only be able to model and predict critical velocity affects, but also how to stabilize them. However research needs to be targeted to determine what affects stabilization technologies have on the dynamic response of the railway track. The dynamic behaviour of railway track is a very complex 3-dimensional problem with instantaneous interactions occurring between the wheel, rail, pad, sleeper, ballast, formation and subgrade. In order to provide a safe and reliable high-speed railway it is necessary to be able to correctly model and predict the track response, including speeds leading up to and including critical track velocities. In addition critical track velocity issues lead to significant ground vibration transmission to adjacent structures. The principal objective of the proposed work is to investigate the 3-dimensional dynamic behaviour of railway track up to and including critical track velocities using the advanced 3-dimenional finite element railway track model D.A.R.T.3D (Dynamic Analysis of Railway Track, 3-dimensional) and by looking at the stress wave patterns using a purpose built test track bed. The secondary objective of the research is to look at the available methods for track stabilization in order to access the affect of localized stiffness increases on the Rayleigh stress wave, the critical track velocity and hence the overall improvement in the dynamic track behaviour. The work is highly relevant to the future strategic development of both the UK rail industry and the rail industry world wide."

28)I congratulate Professor Woodward on the success of his research funding bid. Unfortunately, the research project is not scheduled to report until 2013 by which time construction is already scheduled to have commenced.

15 May 2011

[1] John William Strutt 3 rd Baron of Rayleigh - Theory of Sound 1877

[2] Woodward Dr P, Lagrouche Dr O, Medero Dr G: Development of Design Guidelines for High-Speed Railway Track Including Critical Track Velocities and Track Mitigation Strategies: School of the Built Environment, Heriot-Watt University [ongoing 2010-2013]

[3] Forde Professor M, Giannopoulos Dr. A: Development of Design Guidelines etc.

[4] Krylov V, Dawson A.R, Heelis M.E, Collop A.C.- Rail Movement and Ground Waves caused by High-Speed Trains approaching Track-Soil Critical Velocities: Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 214 pp107 -116: Published Professional Engineering Publishing 2000



Prepared 31st May 2011