field measurements of aerodynamic pressures in tunnels induced by high speed trains

J. Wind Eng. Ind. Aerodyn. 100 (2012) 19–29

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Journal of Wind Engineeringand Industrial Aerodynamics

0167-61

doi:10.1

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Field measurements of aerodynamic pressures in tunnels inducedby high speed trains

Yung-Yen Ko a,n, Cheng-Hsing Chen b, Ing-Tsang Hoe c, Shin-Tsyr Wang d

a National Center for Research on Earthquake Engineering, Taipei 10668, Taiwanb Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwanc Diagnostic Engineering Consultants Co. Ltd., Taipei 11492, Taiwand Taiwan High Speed Rail Corporation, Taipei 11568, Taiwan

a r t i c l e i n f o

Article history:

Received 14 May 2010

Received in revised form

19 October 2011

Accepted 20 October 2011Available online 22 November 2011

Keywords:

Tunnel aerodynamics

Pressure wave

High speed trains

Field measurement

05/$ - see front matter & 2011 Elsevier Ltd. A

016/j.jweia.2011.10.008

esponding author.

ail address: [email protected] (Y.-Y. Ko).

a b s t r a c t

The passage of high speed trains causes aerodynamic effects in tunnels, and considerable pressure

transients are generated because of the restricted airspace within the tunnel. This leads to passenger

discomfort, noise surrounding the tunnel, resistance to train movement, and possible damage to the

train body and tunnel facilities. For the real assessment of the aerodynamic pressures in the tunnel

induced by the passing trains of the high speed rail in Taiwan, a series of field measurements were

performed near the portal and the shaft or the adit of the tunnel during normal operation. The

measurements were conducted for several train speeds, including the maximum operation speed of the

high speed rail in Taiwan, which is 300 km/h. Pressure sensors were deployed along the tunnel to

investigate the propagation of pressure waves. The results show that the train nose entry/exit

generated a compression wave propagating throughout the tunnel, resulting in a sharp increase in

pressure. Conversely, the train tail entry/exit generated an expansion wave causing a pressure drop. The

successive reflections of these pressure waves between both ends of the tunnel were observed. The

pass-by of a train inside the tunnel also induced an immediate local pressure drop due to aerodynamic

drag. Based on the measurement results, the spatial variation of the train-induced pressure peaks inside

the tunnel is discussed. Furthermore, the relationship between the pressure peaks and the train speed

is established, and the influence of the cross-sectional area of the tunnel is also presented.

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1. Introduction

A forward-moving train displaces the air in front of the trainnose and induces a local rise in pressure, and the attenuation ofthis pressure transient is quick under free-field conditions. How-ever, when a train enters and travels through a tunnel, the air isforced to flow parallel to the tunnel axis and substantially aheadof the train, similar to a loose-fitting piston moving in a tube.Because of the restricted airspace, the aerodynamic effects areintensified and the pressure generated will dissipate very slowly(Gawthorpe, 2000).

Under a scenario where a high-speed train passes through atunnel, aerodynamic pressure is generated in the form of pressurewaves due to the confined airspace. These pressure wavespropagate throughout the tunnel at the speed of sound, andsteepen into weak shock waves in long tunnels. Scale-model testsand numerical analyses (Jiang et al., 2002; Ricco et al., 2007)

ll rights reserved.

showed that the nose entry of a high speed train generates asharp compression wave. It also showed that the entry of theuniform part of the train generates a gradual compression wave,and the tail entry generates an expansion wave, all propagatinginto the tunnel and inducing pressure transients as shown inFig. 1. This phenomenon was verified by field measurementscarried out at a Shinkansen (Japanese high-speed rail) tunnel inJapan (Iida et al., 2001). Similar to an entry scenario, themeasurements demonstrated that the exit of the train nose causesa compression wave, and the exit of the train tail causes anexpansion wave, both propagating backwards into the tunnel. Asthe compression wave travels, a positive pressure transient isexperienced, while the expansion wave induces a negative one.The pressure transient causes some adverse effects such aspassenger discomfort due to the sudden pressure change, thenoise surrounding the tunnel as an environmental problem, theresistance to train movement leading to energy efficiency losses,and possible structural damage to the train body and the tunnelfacilities that may increase maintenance costs.

When the pressure wave travelling in the tunnel encounter adiscontinuity of the medium, such as portals and junctions of

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Fig. 1. Pressure transient on tunnel wall induced by the entry of a scaled train

model (train length¼0.9 m; tunnel length¼6 m; blockage ratio¼14.75%; train

speed¼110 km/h) (modified from Ricco et al., 2007).

pi

pi

pt

pt

pr

pr

i: incidence, r; reflection, t: transmission

A1A2

A2A1

Fig. 2. Propagation and reflection of a compression wave at an abrupt

(a) enlargement and (b) reduction of the tunnel cross-section (modified from

Baron et al., 2001).

Fig. 3. Local pressure transient induced by high speed passing train in open-air

conditions (modified from MacNeill et al., 2001).

Y.-Y. Ko et al. / J. Wind Eng. Ind. Aerodyn. 100 (2012) 19–2920

airshafts or adits, a certain portion of the wave is reflectedbackwards, and travels over the tunnel several times aftersuccessive reflections between these discontinuities until it dis-sipates completely (Gawthorpe, 2000). When the pressure waveencounters a sudden expansion in its cross sectional area (such aswhen the wave travels from inside the tunnel to the portal), thereflected wave is out-of-phase with the incident one, while asudden contraction of the cross section causes an in-phasereflection, as shown in Fig. 2 (Baron et al., 2001).

The moving train also produces aerodynamic effects in theform of slipstreams and wakes around the train body, causingaerodynamic drag and generating local pressure transients wherethe train passes through. MacNeill et al. (2001) measured theaerodynamic pressure produced by a high-speed train (Bombar-dier HSNEL) on an adjacent stationary double-stack freight car inopen-air conditions. The pressure time history, as shown in Fig. 3,shows an initial positive gauge pressure corresponding to thetrain nose approaching the pressure sensor, followed by a suddennegative gauge pressure as the train nose passed the sensor.

Subsequently, the magnitude of the negative pressure decreasedand showed some trembles as the train body passed. Finally, apressure transient shift from negative to positive was observed asthe train tail passed. This pressure transient produced by thepass-by of high speed trains in an open-air condition can be wellpredicted by the computational fluid dynamics (CFD) simulations,e.g. Belloli et al. (2009). Their work of numerical analysis indi-cated that the pressure rise as the train nose approaching is fromthe overpressure positioned just in front of the train nose, and thesudden pressure drop as the train nose passing by is due to thesuction positioned aside the train nose. A similar phenomenoncan also be observed in the in-tunnel condition by the scale-model tests (Demmenie et al., 1998) and the field measurementsof the Shinkansen trains (Iida et al., 2001). The pressure changedue to aerodynamic drag also becomes more severe in the tunneldue to the confined airspace (Baron et al., 2001). However, unlikethe pressure waves, the effect of aerodynamic drag is restricted towithin the train surroundings.

Howe (1999) indicated that the pressure rise (exclusive of theatmosphere pressure, i.e., the gauge pressure) generated by thecompression wave, which is produced from the entry of a traininto the tunnel is proportional to the square of the train speed andproportional to the cross-sectional area ratio of the train to thetunnel (the blockage ratio) based on a simplified analytical model.Therefore, the train speed and the blockage ratio are the twoprimary factors influencing the magnitude of the train-inducedpressure transient in the tunnel. Other secondary factors includethe length of the tunnel (compared to the train), the configura-tions of the tunnel (existence of airshafts and adits, portal shapingetc.), and the presence of multiple trains in the tunnel (especiallythe crossing of trains). Mok and Yoo (2001) indicated that theentry of a TGV-A train at 220 km/h into the Villejust Tunnel with across-sectional area of 46 m2 produced a pressure rise of about1.3 kPa, which was measured on the tunnel wall 20 m from theportal.

The high speed rail in Taiwan began its operations in 2007 andprovides a convenient north–south transit system for the westerncorridor of Taiwan. The high speed rail uses the Shinkansenrolling stock built for Taiwan, which is composed of 12 cars.The rolling stock is 3.38 m in width, 3.65 m in height, and 304 min total length. The operation speed of the train can be up to300 km/h, linking Taipei to Kaohsiung with a 345 km total route

Y.-Y. Ko et al. / J. Wind Eng. Ind. Aerodyn. 100 (2012) 19–29 21

and offering a mere 90-min travel time, as opposed to 4.5 h byconventional rail. Since Taiwan is a mountainous island, there are48 tunnels along the high speed rail route, where each tunnel canbe up to several kilometres in length. Therefore, the aerodynamiceffects in tunnels induced by the high speed trains become animportant issue.

Although extensive research has been conducted, existingstudies rarely contain field measurement data, especially for themeasurements which were made at various train speeds and at ahigh train speed up to 300 km/h. For the real assessment of theaerodynamic pressure in the tunnels caused by the trains of thehigh speed rail in Taiwan so that its effects on the trains and otherfacilities inside the tunnel can be investigated, a series of fieldmeasurements were carried out during normal operating condi-tions (a train configuration of 12 cars) at several specified trainspeeds, from 120 km/h to 300 km/h, of which the latter is themaximum operation speed of the high speed rail in Taiwan.

This paper presents and discusses the results of these fieldmeasurements. Since in this measurement project the pressuresensors were deployed along the tunnel and several train speedswere specified, the following aerodynamic phenomena can beinvestigated:

�
propagation of pressure waves; � characteristics of the induced pressure transients; � extreme peak pressures that could potentially be generated
during the operation of high speed rail in Taiwan;
� the spatial variation of peak pressure values inside the tunnel; � the relationship between the pressure peak and the train
speed; and
�
Fig. 4. Profiles of target tunnels for aerodynamic pressure measurement and

measurement locations: (a) Linkou Tunnel and (b) Paghuashan Tunnel (modified

from BOHSR, 2005).

the influence of the cross-sectional area of the tunnel.

2. Measurement configurations

2.1. Measurement targets

The field measurements were conducted at the Linkou Tunneland the Paghuashan Tunnel. The Linkou Tunnel has a length of6482 m and a cross-sectional area of 74 m2. It passes through theLinkou Tableland in northern Taiwan. The field measurementswere made near its northern portal and shaft #A (2526 m fromthe northern portal), as shown in Fig. 5(a). The PaghuashanTunnel is 7364 m in length and 90 m2 in its cross-sectional area,which is the longest tunnel of the high speed rail in Taiwan. Thistunnel goes through the Paghuashan Hill in central Taiwan. Themeasurements were made near its northern portal and adit #A(1999 m from the northern portal), as shown in Fig. 5(b). It shouldbe noted that the portal at both tunnels have a tunnel hoodapproximately 20 m in length along the roof, with an increasedcross-sectional area to 1.5 times of a regular one. In addition, asshown in the left bottom corner of Fig. 4(b), two square holes,each with an area of 10 m2, are set up at the roof of the hood forthe purpose of reducing sonic boom, which is caused when thepressure wave is reflected at the portal.

2.2. Test equipment

Since the aerodynamic effects induced by high speed trains ina tunnel are quite unsteady, turbulent, and complicated, highsensitivity dynamic pressure sensors are essential for the accuratemeasurement of pressure transients. In this study, the piezo-electric pressure sensor, Model 106B50 of PCB Piezotronics, Inc.,was utilised, as shown in Fig. 5(a). It has a sensitivity of 72.5 mV/kPa, a measurement range up to 34.45 kPa, and a resolutionaround 0.5 Pa, providing a satisfactory level of precision for the

measurement of aerodynamic pressure within a tunnel. The16-bit multi-channel recording system CRONOS of IMC, Inc., asshown in Fig. 5(b), was used for data acquisition and storage. Thesampling frequency was chosen to be 100 Hz, which was con-sidered sufficient to capture the peak value and the variation ofthe aerodynamic pressure transient while maintaining a reason-able data size for efficient processing. It is noted that theaerodynamic pressures were measured in gauge pressure, whichis exclusive of the atmospheric pressure.

Although several trains with specific speeds were scheduled topass through the tunnel during the measurement period, theactual train speed would not always match the specified one.Additionally, it is impossible for a person to remain in the tunnelto observe the position and the direction of the trains for safetyreasons. Therefore, optical gate switching was introduced, and thevoltage signals of the switches were recorded synchronously withthe pressure sensors to monitor the position and the direction ofthe trains, as well as to provide an estimation of the actualtrain speed.

Fig. 5. Equipment for aerodynamic pressure measurement: (a) PCB-106B50

pressure sensor and (b) IMC-CR ONOS recording system.

Fig. 6. The installation of pressure sensors.


2.3. Measurement setup

The pressure sensors were installed on the tunnel wall at a heightof 2.5 m and 4.0 m, as shown in Fig. 6, and were deployed along thetunnel to investigate the propagation of pressure waves and thespatial variation of the peak pressure values. For the measurement atthe shaft or the adit, there were additional sensors installed at theemergency exit passageway. Two optical gate switches were installedat both end of the section for measurement of the tunnel. The layoutsof the sensors at the northern portal and shaft #A of the LinkouTunnel, and at the northern portal and adit #A of the PaghuashanTunnel are shown in Figs. 7(a) and (b), and 8(a) and (b), respectively.

During the measurements, the specified train speeds were270 km/h, 230 km/h, 170 km/h, and 120 km/h for the Linkou Tunnel,and 300 km/h, 230 km/h, 170 km/h, and 120 km/h at the PaghuashanTunnel. For each specified train speed, a total of 6 trains weremeasured, of which 3 were northbound and the remaining 3 weresouthbound. As mentioned, the sampling rate was 100 Hz, which issufficient to capture the variations in the pressure transient. In orderto observe the successive reflections of the pressure waves betweenboth ends of the tunnel, continuous measurements were carried outfor 5 additional minutes after the train had passed.

3. Overview of aerodynamic pressure in tunnels induced byhigh speed trains

3.1. Measurement at shaft #A of the Linkou Tunnel—southbound

train case

In order to obtain a clear and comprehensive view of the actualeffect of aerodynamic pressure in the tunnel caused by a high

speed train entry/exit as well as a pass-by event, the relative long-term variations induced by a southbound high speed train at shaft#A of the Linkou Tunnel have been identified in the pressure timehistory and presented, as shown in Fig. 9.

Fig. 9(a) gives one of the time histories of the pressuretransient recorded at sensor P1, which was located south of theemergency exit at a distance of 50 m (refer to Fig. 7(b), abbre-viated as ‘‘S-50 m’’ hereafter), and is firstly discussed since theoptical gate switch G2 was at the same location so that the trainmovements could be captured with precision. In addition, anotheroptical gate switch G1 was located 300 m north of the emergencyexit. The grey dashed lines with the tag ‘‘G1’’ in Fig. 9 indicate thearrival of the train nose and the departure of the train tail at G1 inaccordance with the signal of the optical gate switch G1, as issimilar for G2. Thus, the actual train speed as the train passedshaft #A is estimated to be 212.72 km/h.

3.1.1. Pressure waves induced by the entry of trains

According to Fig. 9(a), a positive pressure peak followed by anegative one is initially observed, approximately between 200 and210 s. The time history of S-50 m is further compared with thatrecorded at pressure sensor P17, which is 50 m north of theemergency exit (abbreviated as ‘‘N-50 m’’ hereafter), with a smallertime scale, as shown in Fig. 9(b). It can be concluded that thepressure transient around 200–210 s was caused by the southboundpressure waves when considering the slight time lag between thepressure peaks of N-50 m and S-50 m. Thus, these pressure wavesare presumed to be the compression and expansion waves gener-ated by the nose and tail entry into the northern portal.

From Fig. 9(a) we know that the time difference from thepresence of the positive peak to the arrival of the train nose at S-50 m is about 37 s. The distance from S-50 m to the northernportal is 2576 m. Theoretically, pressure waves propagate at thesound of speed, which is 346 m/s at a air temperature of 25 1C.This implies that the propagation time of the nose-entry com-pression wave from the northern portal to S-50 m is 2576/346¼7.4 s. Thus, the time interval between nose entry into thenorthern portal to the nose arrival at S-50 m is 37þ7.4¼44.4 s,

Fig. 7. Measurement setup at Linkou Tunnel: (a) at the northern portal and (b) at shaft #A.


and therefore the average train speed is estimated to be 2576/44.4¼58.0 m/s¼208.8 km/h, which is relatively consistent withthe actual train speed measured at shaft #A. Consequently, thisvalidates the above postulate.

3.1.2. Reflection of pressure waves

According to Fig. 9(a), a negative pressure peak followed by apositive one is observed around 225–230 s. This was induced bythe northbound pressure waves derived from Fig. 9(b) consideringthat this peak arrived at S-50 m earlier than at N-50 m. It ispresumed that the southward train-entry-induced waves werereflected by the discontinuity at the southern portal and propa-gated northward. Since the distance from S-50 m to the southernportal is 3906 m, the time interval between the southward train-entry induced waves passing S-50 m and the northward reflectedwaves passing S-50 m (again) is 22.55 s. This implies that thepressure waves should have propagated 3906�2¼7812 m if thispostulate is valid. Thus, the speed of the pressure waves is 7812/22.55¼346.4 m/s, which is close to the speed of sound at 25 1C,thereby validating the postulate. Additionally, the phenomenonthat the reflected wave is out-of-phase with the incident wave canbe confirmed. This is based on the findings that a compressionwave followed by an expansion wave was changed into an

expansion wave followed by a compression wave after reflectionat the southern portal.

3.1.3. Pressure transient induced by the pass-by of trains

From Fig. 9(a) and (b), the train nose arrived at S-50 m at 240 sand the pressure dropped suddenly and substantially. As the trainbody was passing by S-50 m, the pressure decreased yet sometremble were observed. When the train tail departed fromS-50 m, a noticeable positive peak was noted. At N-50 m, a similarevent was observed but the time of occurrence was slightlyearlier since the southbound train arrived at N-50 m prior toS-50 m. Because this pressure transient was directly related to themovement of the train and was observed merely within the trainsurroundings, it is known to be induced by the aerodynamic dragof the passing train. It is noted that the tendency observed here issimilar to that in Fig. 3, the open-air case, and this pressuretransient as the train passing by is due to the overpressurepositioned just in front of the train nose and the suctionpositioned aside the train nose according to the CFD simulationof Belloli et al. (2009). However, the pressure rise prior to thearrival of the train nose is not as significant as in Fig. 3 in this in-tunnel case. It is possible that the air compressed by the trainnose tends to propagate forward in the form of a pressure wave

Fig. 8. Measurement setup at Paghuashan Tunnel: (a) at the northern portal and (b) at adit #A.


and therefore the local pressure rise in front of the train nose isrelatively minor compared to the local pressure drop adjacent tothe nose.

3.1.4. Pressure waves induced by train exiting

According to Fig. 9(a), a relatively large positive pressure peakfollowed by a negative one is again noted at 315–320 s. Based onthe time of occurrence and the train speed, this pressure transientwas deemed to be due to the northward compression andexpansion waves generated by the train nose and tail exitingfrom the southern portal.

A negative pressure peak followed by a positive pressure peakshortly after the above-mentioned pressure transient is observedat 330–335 s in Fig. 9(a). This may be caused by the out-of-phasesouthward pressure waves reflected from the northern portalcorresponding to the above-mentioned northward train-exitinduced pressure waves, which can be also verified against theobserved time interval between the incident and reflected waves(14.86 s) as well as the propagation distance, similar to thatpresented in Section 3.1.2.

3.1.5. Successive reflections of pressure waves between tunnel ends

Continued from Section 3.1.4, a northward pressure wave pairshows again at 350–355 s in Fig. 9(a), which are out-of-phasewith the southward reflected waves observed at 330–335 s, aftera time interval of 22.47 s. This should represent the reflection of

the above-mentioned southward reflected waves from the south-ern portal, that is, the double reflection of the northward train-exit induced pressure waves observed at 315–320 s. Anotherout-of-phase pressure wave pair corresponding to the doublereflection is noted after a time interval of approximately 15 s.These multi-reflected pressure waves prevailed repeatedly withsimilar recurrence intervals until they decayed gradually, andeach of them was out-of-phase with the preceding wave. It shouldalso be mentioned that the recurrence interval of the successivereflections is only related to the sound speed and the observationlocation, and is unrelated to the train speed. This phenomenoncan also be observed at 260–310 s in Fig. 9(a), representing thesuccessive reflections of the train-entry induced pressure wavesbetween both ends of the tunnel. In addition, the pressure wavesthat have been reflected an even number of times are in-phasewith the original incident wave, while those that have undergonean odd number of reflections are out-of-phase.

3.2. Measurement at the northern portal of the Linkou

Tunnel—southbound train scenario

For the measurement of the aerodynamic pressure at thenorthern portal of the Linkou Tunnel, one of the pressure timehistories recorded at sensor P18 is discussed, as shown inFig. 10(a). This sensor was installed at a location 300 m south ofthe roof of the northern portal (refer to Fig. 7(a), abbreviated as

200 205 210 215 220 225 230 235 240 245 250 255-0.8

-0.4

0

0.4

0.8

Time (sec)

Pre

ssur

e (k

Pa)

G2 G2

G1 G1S-212.72 kph

S50m-TN50m-TN50m-B

180 200 220 240 260 280 300 320 340 360 380 400 420-0.8

-0.4

0

0.4

0.8

Time (sec)

Pre

ssur

e (k

Pa)

G2 G2

G1G1S-212.72 kph

S50m-T

Fig. 9. Pressure time history during the measurement at shaft #A of Linkou

Tunnel (train speed¼212.72 km/h): (a) at S-50 m (180–420 s); (b) at S-50 m and

N-50 m (200–255 s), where T (top) denotes a sensor height of 4 m and B (bottom)

of 2.5 m.

190 195 200 205 210 215 220 225 230 235 240 245-1

-0.5

0

0.5

1

Time (sec)

Pre

ssur

e (k

Pa)

G2 G2

G1 G1S-209.25 kph

300m-B100m-T100m-B

180 200 220 240 260 280 300 320 340 360 380 400 420-1

-0.5

0

0.5

1

Time (sec)

Pre

ssur

e (k

Pa)

G2G2

G1G1S-209.25 kph

300m-B

Fig. 10. Pressure time history during the measurement at the northern portal of

Linkou Tunnel (train speed¼209.25 km/h): (a) at 300 m (180–420s); (b) at 300 m

and 100 m (190–245 s), where B (bottom) denotes a sensor height of 2.5 m.


‘‘300 m’’ hereafter). Thus, the pressure transients due to the entryand the pass-by of trains can be clearly distinguished.

The optical gate switch G2 was installed at the same locationas sensor P18, while the optical gate switch G1 was locatedexactly at the northern portal, as shown in Fig. 8(a). This enabledthe train movements and the time of the nose and tail entry to beprecisely captured. Based on the optical gate switches, the actualtrain speed upon entering the northern portal was 209.25 km/h.

According to Fig. 10(a), the train nose entered the portal (or,passed optical gate switch G1) at 195 s, and a positive pressurepeak was measured at 300 m about 1 s later, which was caused bythe southward compression wave induced by nose entry. Asshown in Fig. 10(b), this peak arrived at the 100 m locationearlier than it arrived at 300 m. Shortly after, the train nosepassed the 300 m location (or, passes optical gate switch G2), andalmost simultaneously, the tail entered the portal. At this exactinstance, a negative pressure peak was observed at 300 m, whichwas caused by the train-nose-passing aerodynamic drag togetherwith the train-tail-entry expansion wave. When the train bodywas passing by 300 m, the negative pressure gradually decreaseduntil at 204 s when the train tail passed by 300 m. At this stage, apositive peak prevailed which was caused by the drag of the tail.

At about 230 s, 270 s, and 310 s, a negative pressure peakfollowed by a positive one was observed at 300 m, with a gradualdecay in magnitude. Since they were out-of-phase with the train-entry waves, they were deemed to be the northward pressurewaves (when referring to Fig. 12(b)) that had been reflected anodd number of times. This could be verified by their recurrencetime interval (37.44 s) and propagation distance. As for thesouthward pressure waves that had been reflected an evennumber of times, they were not easily distinguishable since their

passage at the 300 m location closely coincided with the corre-sponding incident northward waves, only allowing a lag time ofless than 2 s.

Another apparent positive pressure peak followed by a nega-tive one was measured at 300 m at 320–325 s, which was due tothe northward compression and expansion waves generated bythe exiting of the train nose and tail from the southern portal. Thein-phase northward pressure wave pairs, which had beenreflected an even number of times, can be observed with arecurrence time interval of around 37 s. Similarly, the southwardpressure waves, which were reflected an odd number of timescould not be isolated.

4. Discussions on peak values of aerodynamic pressure intunnels

It can be concluded from the previous section that themeasured maximum positive pressure is generally due to thecompression pressure wave generated by the entry of the trainnose, while the maximum negative pressure is mainly caused bythe aerodynamic drag from the pass-by of a train. Based on thecollective train-induced extreme pressure values, further discus-sions are provided in this section.

4.1. Effects of observation location

4.1.1. Pressure transients at different heights

According to Fig. 9(b), it can be noted that at N-50 m, thepressure time history recorded at a height of 4 m (the curveN-50 m-T) is quite close to the one recorded at a height of 2.5 m

-1.20-1.00-0.80-0.60-0.40-0.200.000.200.400.600.80

-60Position (m)

Pres

sure

(kP

a)

Maximum Positive Pressure Maximum Negative Pressure

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

Pres

sure

(kP

a)


-50 -40 -30 -20 -10 0 10 20 30 40 50 60

-60Position (m)

-50 -40 -30 -20 -10 0 10 20 30 40 50 60

Fig. 12. Pressure peak distribution with respect to the longitudinal position of

sensors for the measurement at adit #A of Paghuashan Tunnel: (a) for the

southbound train at a speed of 235.61 km/h and (b) for the northbound train at

a speed of 303.58 km/h.


(the curve N-50 m-B). A similar phenomenon is observed inFig. 10(b). This is somewhat different from the open-air condition(refer to Fig. 3) and may be due to the confined airspace in thetunnel, especially in the radial direction, causing little to noattenuation in the pressure peaks with respect to the height.

4.1.2. Pressure peak values at different longitudinal positions near

the portal

As for the distribution of pressure peak values with respect tothe longitudinal position of the sensors, the measurements nearthe Paghuashan Tunnel are discussed here since the sensors werebetter deployed for the investigation of spatial variation.

Fig. 11(a) and (b) depict the pressure peak distribution withrespect to the longitudinal position of the sensors near the northernportal of the Paghuashan Tunnel induced by the southbound train(train speed¼226.61 km/h when passing the optical gate switches)and the northbound train (train speed¼281.03 km/h when passingthe optical gate switches), respectively. Fig. 11(a) depicts the south-bound train scenario, where the positive pressure peaks induced bythe compression wave generated by nose entry remained almostconstant at the positions where the distance to the roof of the portalwas larger than 50 m, and decayed as the distance to the portaldecreased below 50 m. The negative pressure peaks induced by thepass-by of the train showed a similar trend, where it decayed for adistance of less than 50 m and was constant for distances between50 m and 200 m. However, the peaks increased to a certain extent at300 m and 400 m. As mentioned in Section 3.2, when the train nosepassed 300 m, the train tail entered the portal almost simulta-neously. Therefore, it can be said that the negative pressure peaksobserved at 300 m and 400 m were caused by the aerodynamic dragduring a pass-by event together with the expansion wave generatedfrom tail entry, and thus were larger than those at 50–200 m.

-1.50

-1.00

-0.50

0.00

0.50

1.00

-50Position (m)

Pres

sure

(kP

a)


-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

-50

Position (m)

Pres

sure

(kP

a)


0 50 100 150 200 250 300 350 400

0 50 100 150 200 250 300 350 400

Fig. 11. Pressure peak distribution with respect to the longitudinal position of

sensors for the measurement at the northern portal of Paghuashan Tunnel: (a) for

the southbound train at a speed of 226.61 km/h and (b) for the northbound train

at a speed of 281.03 km/h.

As for the northbound train scenario, shown in Fig. 11(b), thepositive peaks remain approximately constant where the distanceto the roof of the portal is larger than 100 m, while the negativepeaks remain unchanged where the distance is larger than 25 m.

4.1.3. Pressure peak values at different positions near the adit

Fig. 12(a) and (b) shows the pressure peak distribution withrespect to the longitudinal position of the sensors near adit #A ofthe Paghuashan Tunnel induced by the southbound train (trainspeed¼235.61 km/h when passing the optical gate switches) andthe northbound train (train speed¼303.58 km/h when passingthe optical gate switches), respectively. In both cases, both thepositive and negative pressure peaks remained almost constantalong the tunnel, except that the pressure measured at theemergency exit passageway (P10, refer to Fig. 8(b)) was appar-ently smaller because the passageway provided airspace for thepressure to be relieved. The slightly lower pressure at S-50 m inboth cases may be due to local tunnel configurations.

4.1.4. Spatial variation of pressure peak values inside the tunnel

According to the results described in Sections 4.1.2 and 4.1.3, itcan be concluded that the pressure peaks measured inside thetunnel, both the positive (induced by the nose entry compressionwave) and the negative (induced by the train pass-by drag), areapproximately constant if the distance to the portal is sufficientlylarge. This may be due to the restricted airspace in the tunnel.However, the pressure peaks measured near the portal attenuateas the distance to the portal decreases, and this is possibly due tothe pressure relief provided by approaching to the externalenvironment as well as the enlargement of the cross-sectionalarea at the hood.

Paghuashan: y = 3.759E-05x1.826

Linkou: y = 1.377E-06x2.454

0.00

0.20

0.40

0.60

0.80

1.00

1.20

100Train Speed (km/hr)

|Pre

ssur

e| (

kPa)

Shaft #A of Linkou Tunnel Adit #A of Paghuashan Tunnel

150 200 250

Fig. 14. Negative pressure peaks induced by the pass-by of southbound trains

versus train speed for the measurement at shaft #A of Linkou Tunnel and at adit

#A of Paghuashan Tunnel.


Linkou: y = 5.690E-07x2.575

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60


|Pre

ssur

e| (

kPa)

Shaft #A of Linkou Tunnel Adit #A of Paghuashan Tunnel

150 200 250 300

Fig. 15. Negative pressure peaks induced by the pass-by of northbound trains

versus train speed for the measurement at shaft #A of Linkou Tunnel and at adit

#A of Paghuashan Tunnel.


4.2. Influences of train speed and cross-sectional area of tunnels

In order to investigate the relationship among the peak valuesof aerodynamic pressure in tunnels, the train speed, the cross-sectional area of tunnels, and the exact train speed when the trainpasses the sensors must be known. Additionally, the positivepressure peak is generally caused by the compression pressurewaves from nose entry and the negative pressure peak by thetrain pass-by drag. Therefore, the positive peak induced by thenose entry of southbound trains in the measurements at thenorthern portal, and the negative peak induced by the pass-by ofsouthbound and northbound trains in the measurements at theshaft/adit, are discussed. Regarding the negative peaks induced bytrains passing the northern portal, they may be influenced by thepass-by drag and the pressure waves generated by the entry orexit of the trains simultaneously. Hence, this case is morecomplicated and is not considered here. According to the resultsin Section 4.1, those pressure peaks which remained near-con-stant with respect to the position of the sensor are investigatedhere to establish the relationship between the pressure inside thetunnel and the train speed.

4.2.1. Positive pressure peaks induced by the nose entry of trains

versus train speed

Fig. 13 shows the peak value of the positive pressure inducedby the nose entry of the southbound trains versus the train speedduring the measurements at the northern portal of both tunnels,and also gives the corresponding trend curves in the form of apower function (f(x)¼xa) derived by regression. For the LinkouTunnel, the positive peaks are approximately proportional to thetrain speed to the power of 2.242. When the train speed is around205–210 km/h, the measured peaks are about 0.5–0.6 kPa. For thePaghuashan Tunnel, the positive peaks are approximately propor-tional to the train speed to the power of 2.114. When the trainspeed is around 220–230 km/h, the pressure peaks are about0.45–0.65 kPa.

As a result, the relationship between the positive peak and thetrain speed in both tunnels is quite close to the simplifiedanalytical model (Howe, 1999), which indicates that the pressurerise generated by nose entry is proportional to the square of thetrain speed.

4.2.2. Negative pressure peaks induced by the pass-by of trains

versus train speed

Fig. 14 shows the peak value of the negative pressure inducedby the pass-by of the southbound trains versus the train speedduring the measurements at shaft #A of the Linkou Tunnel, at adit#A of the Paghuashan Tunnel, and the corresponding trend lines


Linkou: y = 3.494E-06x2.242

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70


|Pre

ssur

e| (

kPa)

Northern Portal of Linkou Tunnel Northern Portal of Paghuashan Tunnel

150 200 250

Fig. 13. Positive pressure peaks induced by the nose entry of southbound trains

versus train speed for the measurement at the northern portal of Linkou Tunnel

and of Paghuashan Tunnel.

as well. The negative peaks fluctuate at a higher level than thepositive ones. For the Linkou Tunnel, the negative peaks areapproximately proportional to the train speed to the power of2.454. When the train speed is about 210 km/h, the pressurepeaks are around 0.7–0.8 kPa. As for the Paghuashan Tunnel, thenegative peaks are approximately proportional to the train speedto the power of 1.826. When the train speed is around225–235 km/h, the pressure peaks are around 0.6–1.0 kPa.

Fig. 15 depicts the negative pressure peak induced by the pass-by of northbound trains versus the train speed during themeasurements at shaft #A of the Linkou Tunnel, at adit #A ofthe Paghuashan Tunnel, and also the corresponding trend lines.For the Linkou Tunnel, the negative peaks are approximatelyproportional to the train speed to the power of 2.575. When thetrain speed is up to 270 km/h, the pressure peaks are around0.8–1.4 kPa. As for the Paghuashan Tunnel, the negative peaks areapproximately proportional to the train speed to the power of2.202. When the train speed is up to 300 km/h, the pressure peaksare about 1.0–1.1 kPa.

Accordingly, the relationship between the negative peak andthe train speed in both tunnels is proportional to the train speedto the power ranging between 1.83 and 2.58, still close to 2 butwith a higher level of fluctuation than the scenario depicting thepositive pressure peaks.

4.2.3. Comparison of positive and negative pressure peak values

Although the negative pressure peaks induced by the train-passing drag fluctuate with a higher level than the positive ones,the trend lines help to make comparison between them. It showsthat even with different generation mechanism, the positive

50%55%60%65%70%75%80%85%90%95%

100%

100

Train Speed (km/hr)

Pres

sure

Rat

io

From Trend LinesTheoretical

150 200 250 300

Fig. 17. The ratios of the negative pressure peaks induced by the pass-by of

northbound trains at the Paghuashan Tunnel to those at the Linkou Tunnel.


pressure peaks induced by the nose-entry compression wave andthe negative pressure peaks induced by the train-passing drag at aspecific train speed are proximate in magnitude.

4.2.4. Pressure peaks versus cross-sectional area of tunnels

The influence of the cross-sectional area of tunnels on the peakvalues of aerodynamic pressure could be better investigated atthe same train speed, yet the train speeds obtained during themeasurements at different tunnels were not exactly the same.Therefore, the trend lines obtained in Sections 4.1.1 and 4.1.2 arereferenced for further investigation.

Howe (1999) indicated that the pressure rise in the tunnel dueto the compression wave generated by the entry of train-nose isproportional to the blockage ratio. That is, if the cross-sectionalarea of the train is constant, then the pressure rise is inverselyproportional to the cross-sectional area of the tunnel. Since thecross-sectional area is 74 m2 for the Linkou Tunnel and is 90 m2

for the Paghuashan Tunnel, theoretically the pressure rise due tothe nose-entry compression wave at the Paghuashan Tunnelshould be 82.2% of that at the Linkou Tunnel for a specifictrain speed.

Based on the trend curves in Fig. 13, the ratios of the positivepressure peaks induced by the nose entry of southbound trains atthe Paghuashan Tunnel to those at the Linkou Tunnel can beobtained at different train speeds, as shown in Fig. 16. It is notedthat the ratio is not constant and ranges between 96.4% and 85.7%as the train speed ranges from 120 km/h to 300 km/h, which isgenerally larger than the theoretical ratio of 82.2%. However, thevariance is limited, especially at a higher train speed. The reasonfor this higher ratio when the train speed gets lower is possiblybecause the power values in the regression formulae are notexactly the same for the two tunnels. In addition, the effect ofambient pressure disturbances may be more significant at lowertrain speeds.

According to the trend curves in Fig. 14, the influence of thecross-sectional area is not noticeable for the negative pressurepeaks induced by the pass-by of southbound trains. In fact, thesouthbound trains were closer to the tunnel wall wherethe sensors were installed than the northbound ones since thetrains of the high speed rail in Taiwan are left-sided (as shown inFigs. 7(b) and 8(b)) so that the aerodynamic drag was moreintensive and not yet attenuated. Thus, the influence of the tunnelcross-sectional area was not significant in this case. As for thenegative pressure peaks induced by the pass-by of northboundtrains, the ratios of those at the Paghuashan Tunnel to those at theLinkou Tunnel are shown in Fig. 17. The ratio ranges from 92.1% to65.4% as the train speed ranges from 120 km/h to 300 km/h, witha much lower ratio at higher speeds compared to the scenario ofpositive pressure peaks due to nose entry.

50%55%60%65%70%75%80%85%90%95%

100%


Pres

sure

Rat

io

From Trend LinesTheoretical

150 200 250 300

Fig. 16. The ratios of the positive pressure peaks induced by the nose entry of

southbound trains at the Paghuashan Tunnel to those at the Linkou Tunnel.

The influences of the cross-sectional area in the two cases ofthe negative pressure peaks induced by the pass-by of trains aresubstantially different from each other, and neither is similar tothe case of the positive pressure peaks induced by nose entry.Since the generation mechanism of the negative pressure due tothe pass-by of trains is the aerodynamic drag, the distribution ofthe induced pressure transient is more complicated and moreregional than the compression wave caused by the train-noseentry. Therefore, the theoretical relationship indicated by Howe(1999), which is aimed at the compression wave generated bynose entry, may not be appropriate for the negative pressurescenario. However, the larger cross-sectional area still leads to asmaller pressure transient if the distance to the train body issufficiently large or the train speed is sufficiently high.

5. Conclusions

Based on the results presented herein, some general conclu-sions can be deduced as follows:

1.
The field measurements showed that the entry/exit of the trainnose generates a compression wave travelling along the tunnelwith a significant pressure increase, and the entry/exit of thetrain tail generates an expansion wave with a pressure drop.
2.
The successive reflections of the train-induced pressure wavesbetween both ends of the tunnel were observed, and thepropagation speed was estimated to be close to the speedof sound.
3.
An immediate local pressure drop was noted due to theaerodynamic drag caused by the pass-by of a train inside thetunnel, and the pressure drop is proximate in magnitude to thepressure rise induced by the nose-entry compression waves atthe same train speed.
4.
For locations inside the tunnel, when the distance to thetunnel exit is far enough (generally with a distance largerthan 50 m for the investigated tunnels), the peak pressurevalues remained constant for a specific passing train.
5.
The maximum positive pressure peaks measured in the tunnelwere generally due to the compression wave generated bynose entry, and were approximately proportional to the trainspeed to the power of 2.1–2.2, close to the simplified analyticalmodel in which the pressure is proportional to the square ofthe train speed. While the maximum negative pressure peakswere usually induced by the pass-by of trains, and showed arelationship with the train speed that had a similar tendencyyet exhibited higher levels of fluctuation.
6.
Both the positive pressure peak generated by nose entry andthe negative pressure peaks from train pass-by reached


a magnitude of around 1 kPa at train speeds of 230–300 km/h,which correspond to the typical operation speed of the high-speed rail in Taiwan.

7.
When the cross-sectional area of the tunnel is increased, themeasured train-induced pressure will generally be less inten-sive, especially for the positive pressure due to nose entry.When considering negative pressure due to the pass-by oftrains, the tendency is more complicated, depending on thedistance from the sensor to the train body.
Declaration

The opinions, findings, and conclusions presented in this paperare only those of the authors, and do not represent the views ofany organisation.

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field measurements of aerodynamic pressures in tunnels induced by high speed trains

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