Prediction of Railway-Induced Ground Vibrations in Tunnels

Carlo G. Lai1

European Centre for Training and Research inEarthquake Engineering (EUCENTRE) c/o

Università degli Studi di Pavia,Via Ferrata 1,

Pavia, 27100, Italye-mail: [email protected]

Alberto CallerioStudio Geotecnico Italiano SrL,

Via Ripamonti 89,Milano, 20139, Italy

e-mail: [email protected]

Ezio FaccioliDipartimento di Ingegneria Strutturale,

Politecnico di Milano,Piazza Leonardo da Vinci 32,

Milano, 20133, Italye-mail: [email protected]

Vittorio Morellie-mail: [email protected]

Pietro Romanie-mail: [email protected]

Italferr SpA,Via Marsala 53,

Roma, 00185, Italy

Prediction of Railway-InducedGround Vibrations in TunnelsThe authors of this paper present the results of a study concerned with the assessment ofthe vibrational impact induced by the passage of commuter trains running in a tunnelplaced underground the city of Rome. Since the railway line is not yet operational, it wasnot possible to make a direct measurement of the ground vibrations induced by therailway traffic and the only way to make predictions was by means of numerical simu-lations. The numerical model developed for the analyses was calibrated using the resultsof a vibration measurement campaign purposely performed at the site using as a vibra-tion source a sinusoidal vibration exciter operating in a frequency-controlled mode. Theproblem of modeling the vibrational impact induced by the passage of a train moving ina tunnel is rather complex because it requires the solution of a boundary value problemof three-dimensional elastodynamics in a generally heterogeneous, nonsimply connectedcontinuum with a moving source. The subject is further complicated by the difficulties ofmodeling the source mechanism, which constitutes itself a challenge even in the case ofrailway lines running at the surface. At last, the assessment of the vibrational impact ata receiver placed inside a building (e.g., a human individual or a sensitive instrument)requires an evaluation of the role played by the structure in modifying the computedfree-field ground motion. So far, few attempts have been made to model the whole vibra-tion chain (from the source to the receiver) of railway-induced ground vibrations, withresults that have been only moderately successful. The numerical simulations performedin this study were made by using a simplified numerical model aimed to capture theessence of the physical phenomena involved in the above vibration chain including theinfluence of the structural response as well as the dependence of the predicted vibrationspectra on the train speed. �DOI: 10.1115/1.2013300�

Keywords: Ground-Borne Vibrations, Railways, Trains, Tunnels, Vibration Modeling,Moving Train

1 IntroductionModeling the impact of railway-induced ground vibrations con-

stitutes a rather difficult problem whose solution requires, as aminimum, that the following subproblems be properly addressedand solved �see Fig. 1�:

1. The source problem connected to the definition of the physi-cal mechanisms responsible for the generation of therailway-induced ground vibrations.

2. The propagation problem connected to the transmission ofthe ground-borne vibrations from the source to the receiverunder free-field conditions.

3. The structural response problem connected to the evaluationof the role played by the structure in affecting the vibrationlevel at the receiver, e.g., a human individual or a sensitiveinstrument, located inside a building.

This decomposition of the vibration-modeling problem has only aformal significance since the solution of each of the above sub-problems is not independent from the others. However, mimickingan approach commonly used in engineering seismology, the abovesubdivision is instructive because it helps to enlighten the peculiaraspects in which can be decomposed the overall problem.

Unfortunately a numerical model that solves rigorously each ofthe above subproblems is still lacking. To date most of the studies

1Corresponding author. Formerly at Studio Geotecnico Italiano SrL, Via Ripam-onti 89, Milano, 20139 Italy.

Contributed by the Technical Committee on Vibration and Sound for publicationin the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 11, 2003.

Journal of Vibration and Acoustics Copyright © 20

conducted on this topic have focused on deepening a specific as-pect of the vibration chain like, for instance, the source problem,or at most the combination of the source and the propagationproblem. The attempts to predict the vibrational response at areceiver located inside a building have almost always been con-ducted using empirical or semiempirical approaches which bytheir intrinsic nature suffer for a lack of generality.

In case of underground railway lines the source problem isfurther complicated by the presence of the tunnel walls and of itsinteraction with the track system, the moving train, and the sur-rounding soil �see Fig. 1�. Empirical or semiempirical approachesfor solving the source and propagation problems of undergroundrailway lines have been proposed for instance by Refs. �1–3�.More rigorous formulations using the finite element method havealso been carried out, see, for example, Refs. �4–6�. In the evalu-ation of the vibrational response at the receiver Ref. �5� also ac-counted for the building dynamic response. More recently Ref. �7�developed an analytical approach for computing the surfaceground vibrations induced by a moving train in a tunnel based ona simplified two-dimensional model.

This paper illustrates the results of a study concerned with theevaluation of the vibrational impact induced by underground rail-way traffic at the receivers located inside two buildings of the cityof Rome. Since the railway line is currently not yet operational,the prediction of the impact was made using a combination ofexperimental measurements and numerical simulations. The ex-perimental measurements were used to determine at two sectionsof the tunnel, the transfer functions of the transmission chain fromthe source to the receiver free field and inside the buildings �see

OCTOBER 2005, Vol. 127 / 50305 by ASME

ments was a sinusoidal vibration exciter �i.e., a electrodynamicshaker� operating in a frequency-controlled mode in the range10–50 Hz and at a constant frequency step of 0.5 Hz. The numeri-cal simulations were needed to extend the results of the experi-mental measurements, obtained using a fixed point source, to theconditions corresponding to the transit of a train.

Section 2 describes the numerical model and the methodologyused for the prediction of the vibration levels at the receivers.Section 3 presents the results obtained from the experimentalmeasurement campaign. Finally Sec. 4 illustrates the results of thenumerical simulations in terms of vibration levels predicted insidethe buildings and compares them with experimental data from theliterature.

2 Numerical ModelFollowing the scheme illustrated in Fig. 1, the prediction

through a numerical model of the vibrational impact induced by

Fig. 1 Schematic representation of the visystems

Fig. 2 Methodology used for the evaluation

504 / Vol. 127, OCTOBER 2005

the railway traffic at a receiver located inside a building requiresat least the definition of the following pieces of information:

�1� A train loading function giving the variation in space andtime of the system of forces generated at the basement ofthe track by a train traveling at a uniform velocity V. Pleasenote that defined in this way the train loading function takesinherently into account the dynamic response of the track.

�2� A dynamic influence function �also called dynamic Green’sfunction� defining the vibrational response at the receiverfree field as a function of space and time due to an impul-sive unit point source �i.e., a Dirac-��·� distribution� placedat the basement of the track.

�3� A dynamic influence function defining the vibrational re-sponse at the receiver placed at a specific position inside abuilding as a function of space and time due to a unit im-pulse of vibration acting at the receiver free-field.

tion-path involved in underground railway

vibrational impact from railway traffic „from

bra

of

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In case of an underground railway line the dynamic influencefunction of point �2� accounts also for the effects induced at thereceiver free field by the tunnel lining. Figure 2 shows schemati-cally in a form of a flow chart the elements composing the vibra-tion chain from the source to the receiver.

By invoking linearity and time translation invariance the abovelisted pieces of information are sufficient to solve the vibrationalproblem associated to the passage of a train via a convolutionintegral. This approach is in a sense natural and it has been pre-viously used also by other researchers, see for instance Refs. �8,9�.

It is well known from the theory of linear systems that theimplementation of the above procedure is greatly simplified bysetting the problem in the frequency domain in which case theconcept of dynamic influence function is replaced by that of trans-fer function �see Fig. 2�. The numerical model developed in thisstudy and whose details are presented next is developed in thefrequency domain.

2.1 Train Loading Function. Ground vibrations generated bymoving trains arise from the combination of different types ofmechanisms. The most significant are the quasistatic deformationof the track system caused by the successive axle loads, the dy-namic forces originated by the unevenness of rails and of car-riages’ wheels, the dynamic forces resulting from the imperfec-tions of joints’ rails, and the dynamic effects resulting from thedeformability of the wheel axle and carriage systems �6,8�. Someof these mechanisms are more important than others. At low fre-quencies it has been shown that the quasistatic pressure of wheelaxles onto the track is the dominant mechanism �8,10,11� ofground-borne vibrations. In this study the train loading functionhas been defined with reference to the following two excitationmechanisms: �a� the quasistatic deformation caused by the axleloads and �b� the dynamic forces arising from the unevenness ofthe rails. The loading function associated with the first mechanismwas computed using a numerical model developed by the ItalianRailway Company Italferr �12�. For a given train category andtrack characteristics, this model computes the average verticalpressure at the basement as a function of frequency and trainspeed. The loading spectra are computed by modeling the track asa dynamic vertical oscillator resting over a fixed basement andconstituted by the rails supported by the rubber pads, the sleepers,the ballast bed, and possibly a vibration mitigation device. Therails are modeled as Euler-Bernoulli elastic beams whereas theirsupports as a series of masses connected by spring and dashpotelements �see Fig. 3�. The oscillating system is subjected to aseries of point forces representing the wheel loads of a train trav-

Fig. 3 Dynamic vertical oscillator used to mfied from †12‡…

eling at a particular speed. Further details of the model used to

Journal of Vibration and Acoustics

compute the train loading spectra can be found by consulting theoriginal Ref. �12� which also considers the case of a track sup-ported by a floating slab system.

Reference �12� also provided the basis to account for the dy-namic forces caused by the unevenness of the rails. Their effect onthe loading spectra was computed using the following empiricalrelation:

GD��� =A · a

���

v�2

+ b2���

v+ a� �1�

where GD is the pressure power spectral density, � is the angularfrequency, � is the train speed, A is a coefficient of quality of thetrack �A=1.558·10−7 m rad for track in good conditions, A=8.974·10−7 m rad for track in poor conditions�, and a and b areempirical constants whose values are a=0.8246 rad/m and b=0.0206 rad/m.

Figures 4 and 5 show the loading emission spectra of verticalpressure that have been adopted in this study for Freight and TAFtrain categories �13�. The acronym “TAF” stands for “Treno adAlta Frequentazione” that in Italian denotes a special type of com-muter train composed by two-floor carriages. In the figure’s cap-tion, standard track means a track without a mitigation device.The figures show that for both train categories most of the energyassociated to the loading emission spectrum is concentrated in thefrequency range between 0 and 120 Hz. For the train categoryTAF �see Fig. 4� the maximum value of pressure occurs at about33 Hz and is approximately equal to 1500 N/m2. For the traincategory Freight the shape of the loading spectrum is similar tothat of TAF category, although the pressure values associated tothe Freight train are consistently higher �see Fig. 5�. The maxi-mum pressure is about 7500 N/m2 and occurs at a frequency ofapproximately 27 Hz.

The spectral values predicted by the numerical model of Fig. 3were found in good agreement with experimental loading spectrafrom the literature �5�.

2.2 Transmission of Ground Vibrations at the Free-Surface.In the numerical model used in this study each sleeper acts as asingle excitation point source and the overall motion caused at theground surface by the moving train is built from the superpositionof the wave fields generated by the activation of all sleepers. Asmentioned previously this approach to model the train sourcemechanism is rather natural and it has been used previously by

el the multicomponent track system „modi-

other researchers �8,9�. Sometimes the method is called the Kry-

OCTOBER 2005, Vol. 127 / 505

lov’s model from the researcher that in recent times has system-atically used it to simulate the vibration generation mechanism oftrains running at the ground surface �8�.

The procedure is formalized mathematically by a convolutionintegral between the forces distributed along the track �i.e., thetrain loading function� and the corresponding dynamic influencefunction. In the frequency domain the convolution integral can bewritten as follows:

a�FF�x,y,�� =

−�

� −�

�

P�x�,y�,�,v�G�FF��,��dx�dy� �2�

where a�FF�x ,y ,�� is the acceleration induced at the receiver free

field by the moving train along the directions �=x, y, z that are,respectively, transversal, longitudinal, and vertical to the track,G�

FF�� ,�� is the dynamic influence function �or transfer function�representing the acceleration generated at the ground surface at

Fig. 4 Loading emission spectrum adopted in the nustandard ballasted track—Train category TAF—Transi

Fig. 5 Loading emission spectrum adopted in the nu

506 / Vol. 127, OCTOBER 2005

the position �x ,y ,0� by a unit vertical force oscillating at theangular frequency � and placed at the basement of the track, �

=�x−x��2+ �y−y��2+z2 is the distance between the point of ap-plication of the force along the track at the position �x� ,y� ,z� andthe receiver at the ground surface having coordinates �x ,y ,0�.Last, P�x� ,y� ,� ,v� represents the train loading spectra and it isgiven by the following relation:

P�x�,y�,�,v� = �m=−�

m=+�

�PB��,v�ei·�·y�/v · ��y� − md���x�� �3�

where m denotes the dummy index for the current sleeper numberalong the direction of the track, d is the distance between sleepers,i=−1, ��¯� represents the Dirac’s delta distribution, and

PB�� ,v� is the average vertical pressure at the basement of the

erical model—Vertical pressure at the basement of alocity: 100 Km/h „from †13,12‡…

erical model—Vertical pressure at the basement of a

mt ve

m

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track computed by the numerical model defined in the previoussection. Figure 6 shows schematically the various terms appearingin Eq. �2�.

The dynamic influence function G�FF�� ,�� was computed using

the following relationship:

G�FF��,�� = JEXP��*,��

C · e−�P·�

�n �4�

where JEXP��* ,�� is the experimental transfer function betweenthe point in the tunnel where the harmonic vibration exciter wasplaced and the corresponding point aligned at the ground surface��* is the vertical distance between these two particular points�.JEXP��* ,�� is the acceleration measured at the ground surface andinduced by the oscillations of a unit vertical load generated by theelectrodynamic shaker placed inside the tunnel at a point imme-diately below the ground surface �at the angular frequency ��.The term C ·e−�P·� /�n is a scale factor used for computing thetransfer functions G�

FF�� ,�� at the points along the basement ofthe track where no measurements are available. This factor ac-counts, even if in a simplified way, of the attenuation of a vibra-tion field occurring in a dissipative medium because of materialand geometric damping. More specifically the term e−�P·� simu-lates the effect of material damping through the viscous attenua-tion coefficient �P=� ·DP /VP where VP is the velocity of propa-gation of P waves and DP is the dilatational damping ratio. Thelatter is usually measured in geotechnical laboratory tests. In un-consolidated sediments at low-strain levels DP ranges typicallyfrom 0.5%–2% �14�. Geometric attenuation is accounted for inG�

FF�� ,�� by the term C /�n where C and n are parameters cali-brated using the experimental data measured at the ground surfaceat the points immediately above the electrodynamic shaker and 20m from it along the axis of the tunnel �see Sec. 3 for more details�.For a source placed within a homogeneous medium, the exponentn depends on its geometry and on its position in relation to theground surface. Here the source is a vertically oscillating forcepositioned inside a cased tunnel surrounded by an heterogeneousmedium. Thus, the geometric attenuation law chosen in this studyrepresents inevitably a simplification of the real, certainly morecomplex, attenuation law.

For the simplified attenuation law the calibration procedureyielded a value of n equal to 0.4. Figure 7 shows a comparisonbetween the experimental transfer function measured at the

Fig. 6 Computation scheme adopted for det„from †13‡…

ground surface at an horizontal distance of 20 m along the tunnel

Journal of Vibration and Acoustics

axis from the electrodynamic shaker, and that computed using Eq.�4�. Despite the simplicity of the model used for the attenuation ofthe dynamic influence function the results of the comparison areconsidered satisfactory.

As a final remark of this section, it is noted that the infinite sumappearing in Eq. �3� is formal and only a finite number of termsneed to be considered. A parametric study indicated that since thecontributions of the active sleepers in the sum decrease with m, asuitable value for convergence is m�300.

2.3 Propagation of Ground Vibrations in the Far Field. Thevibration measurement campaign conducted in this study hasshown clear evidence that the attenuation of the vibration fieldinduced at the ground surface by the electrodynamic shaker isvirtually negligible up to a distance of about 20 m from the tunnelaxis for the vertical component and it is low to moderate for thetwo other components. This experimental result is thought to becaused by a geometrical effect due to the relatively low depth ofembedding of the tunnel �at one measurement site of the tunnel,the top of the tunnel cap is located about 10 m below the groundsurface� if compared with the tunnel diameter.

The vertical oscillations of the electrodynamic shaker are trans-formed into an excitation of the tunnel cap that thus becomesitself a large source of vibrations. The weak attenuation of thevibration field observed experimentally at the ground surfacewithin a certain distance from the tunnel axis is then caused by thepropagation of vibrations radiating away from the tunnel capalong cylindrical wave fronts. Although this phenomenon was de-tected using a point source, it is expected to be even more pro-nounced for the case of a moving train since the latter acts geo-metrically like a finite line source �for horizontal distances that aresmall when compared with the train length�.

In light of these considerations, in the numerical model used forthe prediction of the vibrational impact induced at the groundsurface by the underground railway traffic, it was postulated theexistence of a near-field band across the tunnel axis where all thethree component of the wave field do not undergo any type ofspatial attenuation. The size of the near-field band was assumed tobe 20 m at each side of the tunnel axis. Outside this band, here-inafter named far field, the wave field was computed according tothe following assumptions:

�1� The medium where the propagation of ground-borne vibra-

ining the free-field response at the receiver

tions takes place is weakly dissipative;

OCTOBER 2005, Vol. 127 / 507

an

�2� The vibration field is composed exclusively by surfaceRayleigh waves;

�3� The moving train acts as a line source for horizontal dis-tances from the tunnel axis greater than 20 m and less than1/� times the length of the train �15�.

As a motivation for assumption �2� it is recalled that bulkwaves induced at the free surface of a homogeneous half space bya line load attenuate geometrically with a factor proportional to1/r1.5 �with r being the distance from the source�, whereas Ray-leigh waves do not suffer any geometrical attenuation �16�. Theassumption �2� is well substantiated also by other studies onrailway-induced ground vibrations �17�.

Based on these assumptions, the spatial attenuation of groundvibrations in the far field induced by underground railway trafficwas computed for all three components, via a term proportional toe−�R·r where r is the distance measured at the ground surface fromthe tunnel axis, and �R=�R��� is the Rayleigh attenuation coeffi-cient. In a stratified medium, �R is given by the following rela-tionship �16�:

�R =�

VR2��

i

N

VPi� �VR

�VP�

i

DPi+ �

i

N

VSi� �VR

�VS�

i

DSi� �5�

where VR=VR��� is the velocity of propagation of Rayleighwaves, VSi

VPiare, respectively, the transversal and longitudinal

Fig. 7 Comparison between experimental

wave velocity of each of the N layers of the soil deposit, and DSi,

508 / Vol. 127, OCTOBER 2005

DPiare the corresponding damping ratios. It is important to recall

that since VR and the partial derivatives appearing in Eq. �5� aremodal quantities, in this study they were computed with referenceto the fundamental mode of propagation. Accounting for highermodes of propagation may be required at sites where the variationof soil mechanical impedance with depth is strongly irregular.

2.4 Effects of Buildings Dynamic Response. In studying thepropagation of ground-borne vibrations in the interior of a build-ing it is possible to distinguish the following vibration-paths:

1. FROM �free-field ground motion in the proximity of thebuilding� TO �vibration field at the basement of the building��i.e., dynamic effect of ground-foundation coupling�;

2. FROM �vibration field at the basement of the building� TO�vibration field at a specific floor of the building and at aposition close to the perimeter wall� �i.e., dynamic effect ofvertical-resisting structure�;

3. FROM �vibration field at a specific floor of the building andat a position close to the perimeter wall� TO �vibration fieldat the center of a specific floor of the building� �i.e., dynamiceffect of floor diaphragms�.

Each of these components of the vibration chain can be charac-terized �in the frequency domain� by its own transfer functionH�

j ��� �j=1,3 ;�=x ,y ,z�. Computation of these transfer func-tions via numerical modeling constitutes a rather difficult task

d computed transfer functions „from †13‡…

mainly due to

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• The variability of structural resisting frame systems;• Difficulties in assessing the effects of cladding and in gen-

eral of not structural components;• Difficulties in retrieving data on structure geometry and ma-

terial properties;• The variability of building conditions with regard to conser-

vation and aging;• The wide frequency range of interest for which the transfer

functions must be defined.

In light of these difficulties and of the problems associated to theevaluation of the dynamic response of different categories ofbuildings, a more practical approach to determine the transferfunctions H�

j ��� is by way of a suitable number of experimentalmeasurements. This was the approach used in this study where themeasurements were made in the interior of two buildings, herein-after denoted by buildings A and B, using as a vibration source anelectrodynamic shaker. The main characteristics of the two build-ings are as follows:

• Building A: residential, not recent �1956–1960�, with con-crete resisting structure �moment-resisting frame�, four-stories, piled-foundations;

• Building B: Residential and commercial, relatively recent�1965–1970�, with concrete resisting structure �moment-resisting frame�, four-stories, shallow foundations.

The next two sections will describe the position where the mea-surements were made inside the two buildings and will illustratethe modulus of the measured transfer functions H

j ���.

Fig. 8 Measured transfer functions of groExperimental „thin line… and piece-wise strai

�

Journal of Vibration and Acoustics

2.4.1 Building A. The measurement devices were placed atthe following locations:

• Seismometer S3 was set to measure the free-field groundmotion and thereby positioned in the courtyard in proximityof the building;

• Seismometer S4 was positioned inside the building, at thebasement near a column;

• Seismometer S5 was positioned inside the building, at thecenter of the second floor diaphragm.

With the seismometers placed in these positions it was possible tomeasure the following transfer functions:

�H�1����A = � a�

S3���a�

S4����A

�6�

�H�2+3����A = � a�

S4���a�

S5����A

�7�

where a�S�K���� is the acceleration spectrum measured at the seis-

mometer K �K=3,4 ,5� along the directions �=x, y, z in buildingA. The modulus of the transfer function �H�

1����A is plotted in itsthree components in Fig. 8. The frequency range of these plots isbetween 10 and 50 Hz which coincides with the working range ofthe electrodynamic shaker. As the figure clearly shows, all threecomponents of �H�

1����A have an irregular trend. Rapid changesalternate to narrow spikes that may denote the existence of localresonance phenomena. For this reason they have been smoothedusing a piece-wise straight-line approximation throughout the en-

-foundation coupling effect in building A:-line approximation „thick line… „from †13‡…

undght

tire frequency range of definition using a conservative criterion.

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From Fig. 8 it is noted that the ground-foundation couplingcauses an attenuation of about 7 dB in the range 10–40 Hz of thelongitudinal component of �H�

1����A. The transversal componentshows a similar trend with an attenuation of about 5 dB in therange 10–25 Hz. The vertical component attenuates in the fre-quency range from 12 to 24 Hz and from 30 to 40 Hz. Goodagreement is found between these results and data from the litera-ture �18�.

Figure 9 shows the three components of the transfer function�H�

2+3����A which describes the combined effect of the vertical-resisting structure and of diaphragm vibration. The horizontalcomponents of �H�

2+3����A show an attenuation that increases withfrequency from 5 to 15 dB. Conversely, the vertical componentshows an amplification in the range 12–45 Hz.

The transfer functions of Figs. 8 and 9 have been extended fromthe frequency range 10–50 Hz to the range 1–80 Hz to make themsuitable for a computation of the vibrational impact according tothe Standard ISO 2631 �19,20�. The extension was made by inte-grating the results obtained with the electrodynamic shaker with aseries of independent measurements carried out on two identicalbuildings exposed to the ordinary road traffic. The process hasbeen facilitated by the use of the Campbell diagrams to identifyand reject possible outliers �see next section for more details�. Theresults of these measurements have shown that the transfer func-tion �H�

1����A does not essentially modify the free-field groundmotion, whereas for �H�

2+3����A it is observed an attenuation of 4dB for the horizontal components. The vertical component re-mains essentially unchanged. More details about the experimentalmeasurements on road traffic can be found in the original

Fig. 9 Measured transfer functions of comand of diaphragm vibration in building A: Exline approximation „thick line… „from †13‡…

reference �13�.

510 / Vol. 127, OCTOBER 2005

2.4.2 Building B. The building is located in a highly popu-lated area with only neighboring roads breaking the building con-tinuity. The measurement devices were installed at the followinglocations:

• Seismometer S3 was set to measure the free-field groundmotion and thereby positioned in the courtyard in proximityof the building;

• Seismometer S2 was positioned inside the building, at thebasement floor, near a column;

• Seismometer S5 was positioned inside the building, at thecenter of the second floor diaphragm.

Due to unfavorable conditions at the measurement site for back-ground noise �the basement is used as a parking lot and car re-pairing facility�, it was found convenient to measure directly thecombined effect of the three measured transfer functions H�

j ����j=1,3 ;�=x ,y ,z� thereby obtaining

�H�1+2+3����B = � a�

S3���a�

S5����B

�8�

Figure 10 shows the three components of �H�1+2+3����B plotted

together with the piece-wise straight-line approximation of thesecurves. As for the transfer functions associated to building A, thespectra of Fig. 10 were conservatively extended below 10 Hz andabove 50 Hz to cover the frequency range 1–80 Hz. Both thehorizontal components show a similar tendency with an attenua-tion of about 15 dB in the frequency range 10–50 Hz. At higherfrequencies however, the longitudinal component show a null at-

1+2+3

ed effect of the vertical-resisting structurerimental „thin line… and piece-wise straight-

binpe

tenuation. The vertical component of �H� ����B exhibits a

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thic

more irregular behavior within the operational frequency range ofthe electrodynamic shaker with an alternation of positive �attenu-ation� and negative �amplification� values. Below 10 Hz for all thethree components and above 50 Hz for the vertical component, itwas conservatively assumed a null attenuation.

3 Experimental MeasurementsThe testing sites were located in correspondence of two sec-

tions of the railway tunnel Cassia-Montemario in Rome, Italy.

Fig. 10 Measured transfer functions of covertical-resisting structure, and diaphragm vand piece-wise straight-line approximation „

Fig. 11 Testing site at the Cassia-M

Journal of Vibration and Acoustics

The two sections along the tunnel, whose total length is 4381 m,were identified as section A �located at the progressive distance24+035 km� and section B �located at the progressive distance24+610 km� and include the homonymous buildings selected forthe vibration measurement campaign. Figure 11 shows the loca-tion of seismometers in section A. The top of the tunnel cap ispositioned at about 6 m below the ground surface in section A and10 m in section B.

At both sections, the measurements were made at five stations

ined effect of ground-foundation coupling,ation in building B: Experimental „thin line…k line… „from †13‡…

temario underground railway line in

mbibr

on

OCTOBER 2005, Vol. 127 / 511

�see Fig. 11� each of them composed by a seismometer made upof three particle velocity transducers �i.e., geophones� oriented inthe directions parallel, and perpendicular to the tunnel axis. Theseismometers were high sensitivity geophones �1 V/1 mm/s� ca-pable of operating in the frequency range of 1 to 100 Hz.

The excitation inside the tunnel was provided by an electrome-chanical shaker operating in a frequency-controlled mode in therange 10–50 Hz at a constant frequency step of 0.5 Hz. The elec-trodynamic shaker was anchored at the center of the basement ofthe track inside the tunnel �see Fig. 11� at the two sections A andB and set for vertical oscillations. The time variation of the dy-namic load generated by the shaker was sinusoidal with an ampli-tude that varied quadratically with frequency up to a maximumvalue of 20 kN at 50 Hz.

Measurements at sections A and B were made in two separatesessions. By varying the frequency of excitation from 10 to 50 Hzthe vibrations generated by the shaker were measured by the net-work of five seismometers positioned in and out of the tunnel �seeFig. 11�. The magnitude of the dynamic forces generated by theshaker was chosen so as to satisfy a good signal-to-noise ratio atthe receivers. More details on the testing equipment used to per-form the vibration measurements can be found by consulting theoriginal Ref. �13�. The time histories recorded at each seismom-eter were used to compute the transfer functions associated toeach component of the vibration chain from source to receiver�see Fig. 11�. Computation of the experimental transfer functionswas guided by the use of the Campbell’s diagrams which allowedto assess the influence of background noise on the signals gener-ated by the electrodynamic shaker at various frequencies �see Fig.12�.

Concerning the geological and geotechnical features of the test-ing sites, the area of Rome relevant to the passage of the Cassia-Montemario underground railway line is characterized by thepresence of three main geological formations described as follows�13�:

• Monte Mario Unit �Lower Pleistocene age� constitutedmostly by silty sand and clayey sandy silt, medium perme-able, with an high peak friction angle and a low to nullcohesion.

• Monte Vaticano Unit �Pliocene-Lower Pleistocene age� con-stituted by clayey silty sediments, slightly permeable, with amoderate value of the peak friction angle and a modestcohesion.

• Paleotevere Alluvial Unit �Medium Pleistocene age� consti-tuted by fluvial alluvial deposits.

Fig. 12 Testing site at the Cassia-Montemario undergrSection A—Seismometers S2 and S3 „from †13‡…

At the ground surface along the tunnel, the subsoil includes also a

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stratum of fill �thickness varying from 0 to 15 m�. A geotechnicalinvestigation campaign which included several types of in situ andlaboratory tests was conducted along the underground railway linefor geotechnical site characterization �13�. The results of this in-vestigation were used to determine the geotechnical parametersrequired by the numerical model to predict the railway-inducedground vibrations. More specifically, the transversal wave velocityprofile ranged from 150 to 350 m/s, the Poisson ratio from 0.2 to0.45, and the damping ratios ranged from 0.01 to 0.02. The massdensity of the sediments was assumed to vary from 1850 to1950 kg/m3.

4 Results of Numerical SimulationsThe numerical model described in Sec. 2 was used to predict

the vibrational impact resulting from the reactivation of the un-derground railway line Cassia-Montemario in Rome, Italy. In thisstudy, by vibrational impact it is meant the particle accelerationspectrum measured at a receiver located either at the ground sur-face or inside a building and it is denoted by �a�

RC����. By re-ceiver, it is meant a human individual or a sensitive instrument.By recalling the nomenclature of Sec. 2, the vibrational responseat the receiver can be computed by means of the followingrelationships:

�a�RC����A = a�

FF����H�1����A�H�

2+3����A �9�

�a�RC����B = a�

FF����H�1+2+3����B �10�

where �a�RC����A denotes the acceleration spectrum predicted at a

receiver located at the center of the second floor of building typeA, and �a�

RC����B denotes the acceleration spectrum predicted at areceiver located at the center of the second floor of building typeB. To evaluate the impact �aRC����, the values of the three com-ponents �=x, y, z of the acceleration spectrum are combined to-gether using the following relation �19,20�:

�aRC����A/B = �axRC����A/B

2 + �ayRC����A/B

2 + �azRC����A/B

2

�11�The numerical simulations were conducted considering the pas-sage of trains of categories TAF and Freight �see Sec. 2� bothtraveling at a speed of 100 km/h.

Figures 13 and 14 show the results obtained from the numericalsimulations for building A and B, respectively �at the center of thesecond floor�.

The acceleration spectra are plotted as RMS �root mean square�

d railway line in Rome, Italy—Campbell’s diagrams in

values in one-third octave frequency scale in the range 1–80 Hz.

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For both buildings A and B and for both categories of trains TAFand Freight, the predicted accelerations are, at all frequencies,below the limits for discomfort prescribed by the Standard ISO2631-2 �thin line��19�. However the values of �aRC���� predictedfor the Freight train �dashed line� are consistently higher thanthose of the TAF train �bold line�. Figures 13 and 14 put also inevidence that although the depth of embedding of the tunnel insection B is greater than in section A �about 10 m against �6 m�,the acceleration values predicted by the model at building B arehigher than those of building A. This result has also been con-firmed experimentally by comparing the magnitude of the transferfunctions measured with the electrodynamic shaker at sections Aand B, and it has been interpreted as the gross effect yielded in

Fig. 13 Results of numerical simulations at the Cassia-Montemario underground railway line in Rome, Italy—Magnitude of acceleration spectrum in one-third octave scaleat the center of the second floor of building A—Comparisonwith standard ISO 2631 for the evaluation of human responseto vibrations „from †13‡…

Fig. 14 Results of numerical simulations at the Cassia-Montemario underground railway line in Rome, Italy—Magnitude of acceleration spectrum in one-third octave scaleat the center of the second floor of building B—Comparisonwith standard ISO 2631 for the evaluation of human response

Journal of Vibration and Acoustics

section B by the presence of underground structures and lifelineswhich amounts in reducing the attenuation of ground-borne vibra-tions �13�. The maximum acceleration predicted by the model, atthe center of the second floor, is about 60 dB at building A �i.e.,10−3 m/s2� and 80 dB at building B �i.e., 10−2 m/s2� with bothpeaks occurring at a frequency of 50 Hz.

The numerical model used to make these calculations was alsoadopted to predict the vibrational impact at other buildings up to adistance from the tunnel axis of about 80 m. For a complete pre-sentation of the results, the interested reader is referred to theoriginal Ref. �13�.

5 Concluding RemarksThis paper illustrated the results of a numerical model devel-

oped for the predictions of the vibrational impact induced by therailway traffic resulting from the reactivation of the undergroundrailway line Cassia-Montemario in Rome, Italy. For the predictionof the free-field ground vibration the model was calibrated usingthe results of experimental measurements conducted with a elec-tromechanical shaker.

One of the objectives of the vibration measurement campaignwas also to determine the experimental transfer functions to assessthe effects of the building dynamic response on the free-fieldground motion. Although the results of the numerical simulationsdisplay a rather favorable vibrational scenario, a direct compari-son of the predicted vibration climate with the vibration levelsmeasured after the reactivation of the underground railway line isrequired for a definitive validation of the model.

AcknowledgmentsThe work of the first two authors has been sponsored by Studio

Geotecnico Italiano Srl. The support of Italferr S.p.A. which pro-vided the experimental data is also acknowledged. Finally theauthors would like to express a special word of appreciation toIng. Natoni of Italferr S.p.A. for his valuable suggestions.

References�1� Kurzweil, L. G., 1979, “Groundborne Noise and Vibration From Underground

Rail Systems,” J. Sound Vib., 66�3�, pp. 363–370.�2� Melke, J., 1988, “Noise and Vibration From Underground Railway Lines:

Proposals for a Prediction Procedure,” J. Sound Vib., 120�2�, pp. 391–406.�3� Hood, R. A., Greer, R. J., Breslin, M., and Williams, P. R., 1996, “The Cal-

culation and Assessment of Ground-Borne Noise and Perceptible VibrationFrom Trains in Tunnels,” J. Sound Vib., 193�1�, pp. 215–225.

�4� Balendra, T., Chua, K. H., Lo, K. W., and Lee, S. L., 1989, “Steady-StateVibration of Subway-Soil-Building System,” J. Eng. Mech., 115, pp. 145–162.

�5� Chua, K. H., Balendra, T., and Lo, K. W., 1992, “Groundborne Vibrations dueto Trains in Tunnels,” Earthquake Eng. Struct. Dyn., 21, pp. 445–460.

�6� Jones, C. J. C., and Block, J. R., 1996, “Prediction of Ground Vibration FromFreight and Trains,” J. Sound Vib., 193�1�, pp. 205–2l3.

�7� Metrikine, A. V., and Vrouwenvelder, A. C. W. M., 2000, “Surface GroundVibration due to a Moving Train in a Tunnel: Two-Dimensional Model,” J.Sound Vib., 234�1�, pp. 43–66.

�8� Krylov, V., and Ferguson, C., 1994, “Calculation of Low-Frequency GroundVibrations From Railway Trains,” Appl. Acoust., 42, pp. 199–213.

�9� Castellani, A., and Valente, M., 2000, “Vibrazioni Trasmesse da Veicoli suRotaia all’Ambiente Circostante,” Ingegneria Sismica, Anno XVII-N.1 �inItalian�.

�10� Lai, C. G., Callerio, A., Faccioli, E., and Martino, A., 2000, “MathematicalModeling of Railway-Induced Ground Vibrations,” Proceedings, 2nd Interna-tional Workshop WAVE 2000-Wave Propagation-Moving Load-Vibration Re-duction, Ruhr University Bochum, December 13–15, 2000, Balkema, Bochum,Germany, pp. 99–110.

�11� Paolucci, R., Maffeis, A., Scandella, L., Stupazzini, M., and Vanini, M., 2003,“Numerical Prediction of Low-Frequency Ground Vibrations Induced byHigh-Speed Trains at Ledsgaard, Sweden,” Soil Dyn. Earthquake Eng. 23, �6�,pp. 425–433.

�12� Italferr S. p. A., 2000, “Linee Guida per la Progettazione e la Posa in Opera diArmamento Antivibrante” Internal Report No. XXXX 00 0 IF PF SF 00 00001 A, Italian National Railway Company, Rome, Italy �in Italian�; for moreinformation, see http://www.italferr.it/

�13� Italferr S. p. A., �2001�, “Progetto Esecutivo Messa in Sicurezza ed in Sagoma

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23+500 al Km. 25+000 - Relazione Generale,” Internal Report No. REE1 00E 15 RG IM0006 001 A, Italian National Railway Company, Rome, Italy �inItalian�; for more information, see http://www.italferr.it/

�14� Ishihara, K., 1996, Soil Behaviour in Earthquake Geotechnics, Oxford SciencePublications, Oxford, UK.

�15� Gutowski, T. G., and Dym, C. L., 1976, “Propagation of Ground Vibration: AReview,” J. Sound Vib. 49�2�, pp. 179–193.

�16� Aki, K., and Richards, P. G., 1980, Quantitative Seismology: Theory andMethods, W. H. Freeman and Company, San Francisco.

�17� Hung, H-H., and Yang, Y-B., 2001, “A Review of Researches on Ground-

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Borne Vibrations With Emphasis on Those Induced by Trains,” Proc. Natl. Sci.Counc., Repub. China, Part A: Appl. Sci Vol. 25, No. 1, pp. 1-16.

�18� Saurenmann, H. G., Nelson, G. T., and Wilson, G. P. �1982�, Handbook ofUrban Rail Noise and Vibration Control, edited by DOT USA Department ofTransportation, Washington, DOT Washington; for more information, seehttp://www.fta.dot.gov/

�19� ISO 263l, �l989�, “Evaluation of Human Exposure to Whole-Body Vibration.Part 2: Continuos and Shock-Induced Vibration in Buildings �1 to 80 Hz�.”

�20� ISO 2631, l997, “Mechanical Vibration and Shock Evaluation of Human Ex-posure to Whole-Body Vibration. Part 1: General requirements.”

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