Tunnels for High-Speed Railways 1
CURRENT AND END SECTION DESIGN REQUIREMENTS FOR
HIGH-SPEED TUNNELS
PHILIPPE VAN BOGAERT
Professor of Civil Engineering
Ghent University
Gent - Belgium
ABSTRACT
A literature survey shows that a series of analytical expressions, mostly confirmed by
experimental data, allows making an accurate assessment of the effects of pressure waves in
tunnels during the crossing of high-speed trains. These pressure waves result both in
discomfort to passengers and crew, as well as in sonic boom at the tunnel ends as sudden
decompression of the air flow occurs. A parametric approach has enabled to determine the
necessary tunnel sections to satisfy both a health criterion and comfort conditions in the train.
The results demonstrate that for higher train speed unrealistic values of cross-section tunnel
areas should be provided. Consequently, an alternative method to reduce the effect of pressure
waves, through the use of tunnel extensions has been developed. The effect of tunnel
extensions can be determined by decrease factors compared to the original situation. The
extensions are efficient, both in reducing the maximum air pressure variation as well as the
pressure gradient, thus acting on both resulting parameters. Two examples of tunnels in
Belgium are commented for the reference situation. The application of tunnel extensions is
illustrated by the case of the Perthus tunnel between France and Spain.
1. INTRODUCTION
Requirements regarding the minimum cross section of railway tunnels for high-speed traffic
have constantly been revised. This is because the construction of high-speed railways has
preceded the development of knowledge on the effects caused by moving trains in confined
space. Initially, the requirements have been derived from the necessary distance between track
axes and air pressures initiated during the crossing of trains running in different directions. The
sudden variation of air pressures during the crossing is proportional to the square value of train
2 Tunnels for High-Speed Railways
speed. In addition, during the crossing transversal short term actions are initiated, causing
horizontal forces on the rails. These actions may rise up to 0.13 times g.
Already in 1988, in France minimum requirements for tunnel sections have been established,
based on the consideration of air pressures. Due to some less fortunate experiences and care to
improve passenger comfort, these quantities were adapted for the high-speed project in
Belgium to larger values. The values of required tunnel cross section are shown in Figure 1.
160
140
120
tunnel s ec tion (m ²)
100
80
60 S NC F S ingle trac k TG V
S NC F Double Trac k TG V
40
S NC B
20
spe e d (km /h)
0
200 250 300 350 400
Figure 1: Early requirements for tunnel sections (based on air pressure from crossing trains).
It may be noticed that the SNCB-line corresponds to a regression factor larger than the square
of train speed. Obviously, this approach does not consider the actual phenomena, occuring
during the crossing of a train in a confined space like a tunnel.
2. TRANSIENT PRESSURE FIELD OF TRAIN IN TUNNEL
2.1 Air pressures
2.1.1 Train crossing in single-track tunnel
When a train is entering a tunnel, the air inside the structure is being compressed. A
compression wave is created at the tunnel entrance and is travelling through the tunnel at sound
speed. An air flow is created into a single direction, towards the opposite tunnel end. The air is
being compressed at the tunnel entrance since the train nose occupies part of the free tunnel
cross section and is moving inside the confined tunnel space. In addition to the compression
wave generated at the train nose, another volume of the repulsed air is flowing through the
narrow space between the train circumference and the inside of the tunnel lining. As the train is
moving inside the tunnel, the area where the air flow is generated becomes longer and viscous
effects are increasing across the vehicle and tunnel lining surfaces. This increases the pressure
generated at the train nose. As soon as the train tail has entered the tunnel, a sudden
Tunnels for High-Speed Railways 3
decompression occurs, since the air flowing in the confined space can occupy the whole tunnel
section. An expansion wave is initiated and this wave is also travelling both in the direction of
the entrance and the opposite end of the tunnel at sound speed.
Tunnel
exit
el
nn
e nose
tu el
e tail
g nn
r in tu
te g
en in
n wav
n wa v
er
se nt
no il e
in ta
pressio
ressio
tra in
m tra
fro m
fro
Comp
ve
Decom
wa ve
n wa
sio n
es sio
pr res
m p
Co m
co
De
Tunnel Time
entrance
Figure 2: Diagram of pressure waves generated by a train entering a tunnel.
These pressure waves are shown in the diagram of Figure 2. The bold lines correspond to the
train itself, whereas the thin lines show the air pressure waves, continuous lines being
compression- and dotted lines being depression waves.
The interaction of the various pressure waves generates complex fields in the tunnel. Since the
waves move at sound speed, sudden fluctuations of the air pressure, moving fastly are
generated. A superposition of some of the waves can also not be excluded. These pressure
fields are transmitted through the ventilation system to the inside of the train. This exposes
passengers to nauseating effects and discomfort.
Passenger discomfort is caused by the fact that the human ear can adapt to a change in
pressure, but needs sufficient time to equilibrate both sides of the eardrums. Hence, the
extreme values of pressure do not cause many harm, it are the sudden changes of pressure that
should either be slowed down or be eliminated. Reducing the pressure change can be achieved
either by removing the cause and increasing the tunnel cross-section, or by improving air
tightness of the trains. The last solution seems to be preferred at present. However air tightness
can also be the source of higher carbon dioxide concentration in the trains [1] and it can lower
with time, as the various components of the train are aging. Apparently, the TSI concerning
tunnels does not allow taking into account total air tightness.
4 Tunnels for High-Speed Railways
2.1.2 Micro-waves – Sonic Boom
The first compression wave of Figure 2 is travelling through the tunnel and as it reaches the
end, a sudden expansion occurs, since it exits into the free air. In a similar manner the tail
decompression wave, reaching the tunnel entrance implodes, reflects and travels back into the
tunnel. The reflection of pressure waves at both tunnel ends is accompanied by an impulse or
micro-pressure wave. This expansion produces sound and is also called the sonic boom.
The sonic boom causes nuisance to neighbouring locations and persons. It can be compared to
the nearby passing of a supersonic aircraft and cause noise as well as vibration of structures. As
an example, a train entering a 3 km long tunnel at 250 km/h may produce a micro-wave of
50 kPa pressure, corresponding to 128 dBA [2].
Various measures are possible to counteract the sonic boom. Obviously, trains are already
profiled and further reduction of the sonic boom seems unrealistic. Other measures consist of
providing air chimneys, interconnections between tunnels and sound absorbing panels.
However, an effective measure appears to be the construction of partially perforated tunnel
extensions. These devices allow reducing the pressure gradient, as a train is entering the tunnel.
They are discussed further.
2.1.3 Blocking ratio
For both aforementioned phenomena, the initial compression of the air inside the tunnel is an
important factor. Obviously, the latter is directly determined by the ratio of the train cross-
section to the free area of the tunnel section. This number is called the blocking ratio.
However, the cross-section varies only slightly, as all fabricators use similar characteristics to
manufacture rolling stock. At present it varies from 8.8 m² to a maximum of 12 m² for double-
stack trains.
The UIC-Code 779-11 [3] allows calculating pressure variations for several time laps, varying
from 1 to 10 s, as a function of the blocking ratio. This document also provides guidance
concerning acceptable pressure variations. The air tightness of trains is being discussed,
although the charts have been established for unsealed trains. An interesting fact is the health
criterion to which passengers may be exposed: the maximum variation may never exceed
10 kPa.
2.2 Microwave pressures
2.2.1 Pressure variation with time
For both aforementioned phenomena, the initial compression of the air inside the tunnel and
the pressure gradient, [4] provides analytical data, with reference to Figure 3. This shows that
the waves are characterised by the maximum amplitude Δpc as well as by the maximum value
of the gradient (d Δp / dt)max being the maximum slope of the diagram. The diagram can be
expressed by the formula:
Tunnels for High-Speed Railways 5
d Δp π t ⎞⎞
Δp(t) = Δpc ⎛ 2 + atan ⎛ ⎛ dt ⎞max
1 1
(1)
⎝ π ⎝ ⎝ ⎠ Δp c⎠ ⎠
(dΔ p/dt)max c
Δp f
b
Δ pc
a e
Δ tc
Patm t
Figure 3: Variation with time of the pressure wave.
For both quantities Δpc and (d Δp / dt)max various formulas have been proposed in literature.
For instance in [5] the relation
1 ⎛ (1-β)²⎞
2 γ p0 M² ⎝1 - 1+K ⎠
Δpc = (2)
1-β ⎛ (1-β)² ⎛ 1 (1-β)²⎞⎞
1+K + M ⎝1 - 1+K - M² ⎝1 - 2 1+K ⎠⎠
γ being the ratio of heat air mass, K the friction loss and p0 atmospheric pressure. The value of
K may be taken as 0.125. M is the Mach number of the train, U equals the train speed and β is
the blocking ratio. The pressure gradient may be derived from :
⎛dΔp⎞max = 1 ρ0 U³ 1 - (1-β)²
(3)
⎝ dt ⎠ 2 τ D (1-M) (M+ (1-β)²)
D being the hydraulic diameter of the tunnel and τ a dimensionless parameter which may be
taken as 1.1. Formulas (2) and (3) have been compared to values recorded at the Villejust and
Vouvray tunnels. Table 1 shows the characteristics of these tunnels :
Table 1: Characteristics of tunnels.
T u n n e l A re a b lo c k in g ra tio tra in sp e e d
V ille ju st 46 m ² 0 .2 2 2 0 k m /h
V o u v ra y 71 m ² 0 .1 2 5 2 7 3 k m /h
6 Tunnels for High-Speed Railways
Table 2: Measured and calculated pressure values.
max amplitude Δpc max gradient (dΔp/dt)max
measured calculated measured calculated
Villejust 1263 Pa 1243 Pa 8300 Pa/s 8023 Pa/s
Vouvray 1273 Pa 1248 Pa
Table 2 justifies the use of expressions (2) and (3) through comparison with measured values.
2.2.2 Propagation of compression waves through tunnels
Expressions (2) and (3) allow calculating the wave characteristics at the tunnel entrance.
Further propagation of the waves and especially the sonic boom at the tunnel end, depend on
the modification of the characteristics during its travelling through the tunnel. The compression
waves can be lowered partially by viscosity and friction between the moving train and the
tunnel lining. Both important quantities can be expressed at a distance x from the initial point
1. The variation of the pressure can be found from:
Δpc u1 x - x1⎞
= exp ⎛ -f c (4)
Δpc1 ⎝ 0 D ⎠
In (6) Δpc1 is the pressure variation at the origin, which mostly corresponds to the tunnel
entrance, whereas Δpc is the same quantity at the coordinate x. The value of the friction
coefficient f may be subject to discussion, since it may depend on the track composition.
Obviously, ballasted track will result in higher friction values, whereas a reliable value for slab
track equals 0.02. The speed introduced by the pressure wave u1 can be determined from
γ-1
2 c0 ⎛⎜ ⎛ Δpc1 2γ ⎞
u1 = 1+ p ⎞ - 1⎟ (5)
γ-1⎝⎝ 0 ⎠ ⎠
The evolution with coordinate x of the pressure gradient is also called the distortion of this
wave. The ratio of the maximum gradient to the value at the tunnel entrance can be derived
from:
(dΔp/dt)max
ξ = (6)
(dΔp/dt)max,1
The value of ξ has been determined experimentally. The distortion factor appears to be related
to the cube of the train speed. The experimental data can be summarised in a regression curve
according to
dΔp 1.22
ξ = 0.5 + 0.62 ⎛⎛ dt ⎞max,1 ⎞ (7)
⎝⎝ ⎠ ⎠
Finally, the sonic boom pressure can be related to the gradient at the tunnel end as:
2 S ⎛dΔp⎞
p’(r,t) = (8)
Ω c0 r ⎝ dt ⎠end
Tunnels for High-Speed Railways 7
In expression (8) Ω is the angle containing the micro-pressure wave. This angle may be taken
as 2.3 radians. S is the tunnel section and r is the distance between the observation point and
the tunnel end.
2.3 Minimum tunnel sections
The expressions (1) to (8) allow making a fair prediction of the pressure field in a tunnel and of
the sonic boom. More precise predictions can be made through the various types of software,
which have been developed in connection with air flow through tunnels. In [6] a parametric
study has been carried out.
The criteria used for this simulation are on one hand the health requirement not to exceed a
maximum pressure rise of 10 kPa and on the other hand the limitation of a pressure increase to
2 kPa during 4 seconds. This has resulted in the diagram of Figure 4, allowing a preliminary
design of single track tunnel sections.
120
100
80
tunnel area (m²)
60
40
20 v = 250 km/h v = 300 km/h v = 350 km/h
Tunnel length (m)
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Figure 4: Required tunnel area, based on health and comfort criteria.
The diagram shows that for train speed up to 250 km/h, pressure effects are of no consequence,
since the required tunnel section is lower than the pratical values, to allow for necessary
clearance. For a train speed reaching 300 km/h the necessary area becomes important, whereas
the values corresponding to 350 km/h are unrealistic. This demonstrates that at higher train
speed, efficient countermeasures must be taken, either to lower the maximum pressure
variation or, more effectively, the pressure gradient.
8 Tunnels for High-Speed Railways
Such measures have been implemented for the Perthus tunnel on the international section
between Perignan (F) and Figueras (E), which are discussed further.
3. RECENT TUNNELS ON HET BELGIAN HIGH-SPEED NETWORK
This paragraph provides two examples of tunnels on different sections of the Belgian high-
speed network. The principles of the former paragraphs are tested to these cases, although train
speed is insufficient to introduce serious aerodynamic problems.
3.1 Peerdsbos tunnel
This tunnel is located on the high-speed section between Brussels and Amsterdam, at some 15
km to the North of Antwerp. In this section, the line is close to the E 19 motorway and travels
through the forest ‘Peerdsbos’, which was originally cut by the motorway. A view from the air
is shown in Figure 5. The tunnel has a total length of 3250 m and was built in open air. The
actual
Figure 5: Overview of Peerdsbos tunnel.
purpose of the structure is twofold. It provides mechanical shelter to the railway line from
falling trees and constitutes an efficient sound barrier for one side of the wood. The tunnel wall
directed towards the motorway has large openings, which certainly prevent the initiation of
pressure waves. In addition, the openings are effective in smoke evacuation in case of fire.
Hence, forced ventilation is unnecessary, although fire detection by optical fibres has been
installed. The tunnel has 12 emergency exits, 7 giving access towards the wood and 5 towards
the motorway. The latter exits can also be reached by road vehicles, coming from the
motorway and provide efficient access for emergency services.
Tunnels for High-Speed Railways 9
Figure 6: Cross-section of Peerdsbos tunnel.
Figure 6 shows the cross-section of the double-track tunnel. The tunnel area equals 118 m² and
the design speed is 300 km/h. Although the openings are sufficient to prevent any pressure
effect, applying the curves of UIC-Code 779-11 shows a blocking ratio of 0.085 and a pressure
variation of 3.6 kPa for a time lap of 4 s during the simultaneous crossing of 2 high-speed
vehicles at 300 km/h. If a high-speed train is travelling at 300 km/h and crosses a conventional
train at 220 km/h, the pressure variation becomes 2.8 kPa. These values are well below the
comfort thresholds, since they concern rare situations of simultaneously crossing trains.
3.2 Soumagne tunnel
Figure 7: Entrance of Soumagne tunnel.
Other recent and future tunnels in Belgium are reported in [7]. Among them is the 5940 m long
tunnel from Vaux-sous-Chevremont to Ayeneux, located on the high-speed section from Liège
to Aachen. The tunnel was built by drill and blast method, the southern entrance being shown
in Figure 7. This double-track tunnel was designed for train speed of 220 km/h. The cross-
10 Tunnels for High-Speed Railways
section is shown in Figure 8. If 2 high-speed trains are simultaneously crossing tunnel at
220 km/h, a pressure variation of 6.1 kPa per 4 s may be expected. This is lowered to 4.4 kPa if
the speed is reduced to 200 km/h. For mixed traffic the pressure becomes 3.3 kPa. The first
case does not correspond to acceptable comfort. However, no account has been taken of the
two ventilation shafts in the tunnel, which have sufficient area to allow pressure and gradient
reduction. As can be seen in Figure 7 the tunnel entrance has somewhat been adapted, which
also contributes to improving the aerodynamic phenomena.
Figure 8: Cross-section of Soumagne tunnel.
4. TUNNEL EXTENSIONS
Figure 4 has clearly demonstrated that for train speed beyond 300 km/h increasing the tunnel
area is no option to solve the problems related to pressure waves. Other structural measures
must be adopted, mainly to decrease the pressure gradient. An effective provision is the use of
tunnel extensions.
4.1 Effect of tunnel extension
The purpose of a tunnel extension is to decrease the slope of the diagram of Figure 3, by
obtaining a more smooth transition from the open air to the confined space of the tunnel. There
should be a double effect, namely to decrease the initial pressure variation, because of the
transition and also a larger time lap Δtc. If the value of Δpc is identical for the actual tunnel and
the tunnel extension – which obviously is not true – and the length of the extension equals l, Δtc
increases from D/U to (D + l)/U. A relative decrease of the pressure gradient α is obtained
from :
(dΔp/dt)T τD
α= = (9)
(dΔp/dt)HT τD+1
Tunnels for High-Speed Railways 11
In addition, a tunnel extension should not have a vertical end section. A sloping edge is
preferred, since this also contributes to lower the pressure gradient. It is believed that an edge
slope between 30° to 40° with respect to a horizontal plane further reduces the maximum
gradient by about 10%.
Another question concerns the area of the tunnel extension, or the ratio of areas SHT/ST. As the
train will first pass through the extension and initiate a first pressure wave and subsequently
enter the actual tunnel, thus originating a second wave, an optimum value can exist to
equilibrate these effects. Previous research [8] shows that the shape of the tunnel extension
section has virtually no influence on the pressure wave. Hence, the shape may depend entirely
on constructional requirements. In addition, the transition between the extension and actual
tunnel section may be sudden, without smoothening. The value of SHT/ST = 1.4 certainly seems
effective. Should a larger value be adopted, the fractioning of the pressure waves drops below
the optimum.
Tunnel extensions are intended to reduce the pressure gradient and thus the first pressure wave
should be less aggressive. This can be achieved by providing openings in the extension wall.
An adequate distribution of openings, both for the location as well as the required area, has to
be determined. The largest openings should be located near the edge of the extension. The
location of the openings along the perimeter has little importance. Numerical simulation, as in
[9] might be the better way to determine adequate openings.
4.2 Application to Perthus Tunnel
The Perthus Tunnel is located on the 44 km long international high-speed section between
Perpignan (F) and Figueras (E). The state border is located across this tunnel. Total length of
the tunnel equals 8300 m and it should allow operating with trains at 350 km/h. The tunnel
consists of two single track tubes, bored through the Pyrenees Mountains. The infrastructure
must also allow freight traffic at 180 km/h. The boring of the tunnels required evacuating about
1.3 million m³ of soil.
Figure 9 shows the cross-section of a single tube. To minimize cost, the inner diameter has
been limited to 8.50 m resulting in a tunnel area of 49 m². This means that the blocking factor
varies from 0.18 for normal train to 0.24 for double stack. Obviously this tunnel requires
special measures for aerodynamic effects. Expressions (1) through (8) have enabled to predict
the pressure variation and gradient, if no special provisions would be made. These are
summarized in table 3 and clearly demonstrate the unacceptable character of the pressure
fields. According to expression (3) gradient values up to 30000 Pa/s are found. Practically, the
maximum pressure variation should be a factor 2 lower, whereas the gradient should be limited
to about one third of the value from Table 3.
12 Tunnels for High-Speed Railways
Figure 9: Cross-section of Perthus Tunnel.
Table 3: Estimate of pressure fields Perthus Tunnel.
TGV Δpc (dΔp/dt)max
single stack 2947 Pa 29326 Pa/s
double stack 4206 Pa 42728 Pa/s
Hence, tunnel extensions of about 50 m length have been built. The overview of the extensions,
as well as the sloping edge can be seen in Figure 10. The openings are also clearly visible, as
well as the gradually decreasing of each individual opening. The relative area of the openings
to the cross-section area of the extension equals 10%.
More details of the tunnel extensions are seen in Figure 11. For construction reasons the
openings are in the upper part of the section, thus reducing the effect of the dead weight. Since
the tunnel lining consists of regular segments, the extensions have a similar shape. The
extensions and openings allow lowering the maximum Δpc to 2136 Pa and (dΔp/dt)max to
14293 Pa/s. Combined with connections between both tubes every 200 m and additional
ventilation shafts, these values assure acceptable passenger comfort during the crossing of the
tunnel by trains at 350 km/h. The transition between the tunnel extensions and the current
tunnel section has a sudden character. This is in accordance with experimental results and does
not affect the efficiency of the provisions.
Tunnels for High-Speed Railways 13
Figure 10: Overview of tunnel extensions Perthus.
Figure 11: Detailed view of tunnel extension with openings.
14 Tunnels for High-Speed Railways
5. CONCLUSION
Analytical expressions of the maximum pressure variation and gradient allow accurate
prediction of the aerodynamic effects and comfort values during the crossing of high-speed
trains through tunnels. A parametric research has shown that below train speed of 250 km/h
minimum tunnel sections are sufficient to avoid air pressure problems. However, as soon as the
train speed approaches 300 km/h and higher, the tunnel section necessary to create acceptable
comfort and health conditions, both for passengers as for personnel, becomes unrealistic.
A cut-and-cover tunnel as well as a drill-and-blast double track tunnel have been verified in
this manner. In both cases, the overpressure chimneys or outlets allow reaching acceptable
comfort values.
As the aerodynamic improvement of trains is already at high level, additional structural
measures have to be implemented in the case of higher train speed. An effective manner to deal
with the effects of pressure waves, consists of building tunnel extensions. The length, as well
as the area of these extensions can be determined accurately by the assessment of reduction
factors with respect to the original situation. This has been applied to the case of the Perthus
tunnel, located on the international line between Perpignan and Figueras.
However, the tunnel extensions need to be equipped with openings of variable section. The
design of these openings requires the use of more sophisticated simulations, although it can be
established that the total area of the openings is about 10% of the extension cross-section area
and that the largest openings should be located near the end. In the aforementioned case an
effective reduction of the pressure effects has been implemented.
REFERENCES
[1] Kwon, S.B.; Cho, Y; Park, D.S. – “Relationships between carbon dioxide concentration
and presence of tunnel section of the high-speed train passenger cabin in Korea”, Korea
Railroad Research Institute 4 p.
[2] Howe, M.S. – “On the compression wave generated when a highspeed train enters a
tunnel with a flared portal”, Journal of fluids and structures, 1999, Vol 13, pp 481-498
[3] Code 779-11 UIC – Determination of railway tunnel cross-sectional areas on the basis of
aerodynamical considerations. 2005, UIC 2nd edition.
[4] Ozawa, S.; Maeda, T.; Matsumura, T.; Uchida, K.; Kajiyama, H.; Tanemoto, K. –
“Countermeasures to reduce micro-pressure waves radiating from exits of Shinkansen
tunnels”, Aerodynamics and ventilation of vehicle tunnels, 1991, pp 253-266
[5] Pope, C.W. – “Transient pressures in tunnels – a formula for predicting the strength of the
entry wave produced by trains with streamlined and unstreamlined noses”, British
Railways Research & Development Division Techn. Memo, 1975 AERO 12
[6] de Waeghe, B. – Etude paramétrique des phénomènes aérodynamiques lies à la
circulation des trains à grande vitesse dans les tunnels à voie unique. Master thesis
Université Libre de Bruxelles. 2006
Tunnels for High-Speed Railways 15
[7] Van Bogaert, Ph.; – “Recent and future railway tunnels in Belgium”, Proc. ITA World
Tunnel Congress 2009 Safe Tunnelling for the City and for the Environment. 2009, ITA
Budapest pp 689-690 + CD-Rom
[8] Réty, J.M.; Grégoire, R. – “Numerical investigation of tunnel extensions attenuating the
pressure gradient generated by a train entering a tunnel”, Transaero – a European
initiative on transient aerodynamics for railway system optimisation, Notes on numerical
fluid mechanics and multidisciplinary design, 2002, Vol 79, pp 235-244
[9] Anthoine, J.; Rambaud, P.; – “Reduction of the sonic boom from a high-speed train
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