Carlo G. Lai1European Centre for Training and Research inEarthquake Engineering (EUCENTRE) c/oUniversit degli Studi di Pavia,Via Ferrata 1,Pavia, 27100, Italye-mail: carlo.lai@eucentre.itAlberto CallerioStudio Geotecnico Italiano SrL,Via Ripamonti 89,Milano, 20139, Italye-mail: sgi_callerio@studio-geotecnico.itEzio FaccioliDipartimento di Ingegneria Strutturale,Politecnico di Milano,Piazza Leonardo da Vinci 32,Milano, 20133, Italye-mail: faccioli@stru.polimi.itVittorio Morellie-mail: v.morelli@mail.italferr.itPietro Romanie-mail: p.romani@mail.italferr.itItalferr SpA,Via Marsala 53,Roma, 00185, ItalyPrediction of Railway-InducedGround Vibrations in TunnelsThe authors of this paper present the results of a study concerned with the assessment ofthevibrational impact inducedbythepassageof commutertrainsrunninginatunnelplaced underground the city of Rome. Since the railway line is not yet operational, it wasnot possibletomakeadirect measurement of thegroundvibrations inducedbytherailwaytrafcandtheonlywaytomakepredictionswasbymeansofnumericalsimu-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 difculties 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 atareceiverplacedinsideabuilding(e.g.,ahumanindividualorasensitiveinstrument)requiresanevaluationof theroleplayedbythestructureinmodifyingthecomputedfree-eld ground motion. So far, few attempts have been made to model the whole vibra-tionchain(fromthesourcetothereceiver)ofrailway-inducedgroundvibrations, withresults that have been only moderately successful. The numerical simulations performedinthisstudyweremadebyusingasimpliednumerical model aimedtocapturetheessenceofthephysicalphenomenainvolvedintheabovevibrationchainincludingtheinuence of the structural response as well as the dependence of the predicted vibrationspectra on the train speed. DOI: 10.1115/1.2013300Keywords: Ground-Borne Vibrations, Railways, Trains, Tunnels, VibrationModeling,Moving Train1 IntroductionModeling the impact of railway-induced ground vibrations con-stitutesarather difcult problemwhosesolutionrequires, asaminimum,thatthefollowingsubproblemsbeproperlyaddressedand solved see Fig. 1:1. The source problem connected to the denition of the physi-cal mechanisms responsible for the generation of therailway-induced ground vibrations.2. Thepropagationproblemconnectedtothetransmissionofthe ground-borne vibrations from the source to the receiverunder free-eld 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 signicancesincethesolutionofeachoftheabovesub-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 studiesconducted on this topic have focused on deepening a specic as-pect of the vibration chain like, for instance, the source problem,or at most thecombinationof thesourceandthepropagationproblem. The attempts topredict the vibrational response at areceiverlocatedinsideabuildinghavealmostalwaysbeencon-ductedusingempirical or semiempirical approaches whichbytheir intrinsic nature suffer for a lack of generality.Incase of undergroundrailwaylines the source problemisfurther complicated by the presence of the tunnel walls and of itsinteractionwiththetracksystem, themovingtrain, andthesur-rounding soil see Fig. 1. Empirical or semiempirical approachesforsolvingthesourceandpropagationproblemsofundergroundrailwaylines have beenproposedfor instance byRefs. 13.More rigorous formulations using the nite element method havealso been carried out, see, for example, Refs. 46. In the evalu-ationofthevibrationalresponseatthereceiverRef. 5alsoac-counted for the building dynamic response. More recently Ref. 7developed an analytical approach for computing the surfaceground vibrations induced by a moving train in a tunnel based ona simplied two-dimensional model.This paper illustrates the results of a study concerned with theevaluation of the vibrational impact induced by underground rail-way trafc at the receivers located inside two buildings of the cityofRome. Sincetherailwaylineiscurrentlynotyetoperational,thepredictionof theimpact wasmadeusingacombinationofexperimental measurementsandnumerical simulations. Theex-perimental measurements were used to determine at two sectionsof the tunnel, the transfer functions of the transmission chain fromthesourcetothereceiverfreeeldandinsidethebuildings seeFig.1. Thevibrationsourceusedfortheexperimentalmeasure-1Correspondingauthor.FormerlyatStudioGeotecnicoItalianoSrL, ViaRipam-onti 89, Milano, 20139 Italy.Contributed by the Technical Committee on Vibration and Sound for publicationin the JOURNALOF VIBRATIONAND ACOUSTICS. Manuscript received October 11, 2003.Final revision January 6, 2005. Associate Editor: Roger Ohayon.Journal of Vibration and Acoustics OCTOBER 2005, Vol. 127 / 503 Copyright 2005 by ASMEDownloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-usementswasasinusoidal vibrationexciteri.e., aelectrodynamicshaker operatingina frequency-controlledmode inthe range1050 Hz and at a constant frequency step of 0.5 Hz. The numeri-cal simulationswereneededtoextendtheresultsoftheexperi-mental measurements, obtained using a xed point source, to theconditions corresponding to the transit of a train.Section 2 describes the numerical model and the methodologyusedfor thepredictionof thevibrationlevels at thereceivers.Section 3 presents the results obtained fromthe 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 predictionthroughanumericalmodelofthevibrationalimpactinducedbythe railway trafc at a receiver located inside a building requiresat least the denition of the following pieces of information:1 A trainloadingfunctiongivingthevariationinspaceandtimeofthesystemofforcesgeneratedatthebasementofthe track by a train traveling at a uniform velocity V. Pleasenote that dened in this way the train loading function takesinherently into account the dynamic response of the track.2 A dynamic inuence function also called dynamic Greensfunctiondeningthevibrational responseat thereceiverfree eld 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 Adynamicinuencefunctiondeningthevibrational re-sponse at the receiver placed at a specic position inside abuilding as a function of space and time due to a unit im-pulse of vibration acting at the receiver free-eld.Fig. 1 Schematic representation of the vibration-path involved in underground railwaysystemsFig. 2 Methodologyusedfortheevaluationofvibrational impactfromrailwaytrafc from13504 / Vol. 127, OCTOBER 2005 Transactions of the ASMEDownloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-useIncaseofanundergroundrailwaylinethedynamicinuencefunctionofpoint 2accountsalsofortheeffectsinducedatthereceiver free eld by the tunnel lining. Figure 2 shows schemati-cally in a form of a ow 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 sufcient to solve the vibrationalproblemassociatedtothepassageof atrainviaaconvolutionintegral. 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 knownfromthetheoryof linear systems that theimplementationof theaboveprocedureisgreatlysimpliedbysettingtheprobleminthefrequencydomaininwhichcasetheconcept of dynamic inuence function is replaced by that of trans-ferfunction seeFig.2. Thenumericalmodeldevelopedinthisstudyandwhosedetailsarepresentednext isdevelopedinthefrequency domain.2.1 Train Loading Function. Ground vibrations generated bymovingtrains arisefromthecombinationof different types ofmechanisms. The most signicant are the quasistatic deformationofthetracksystemcausedbythesuccessiveaxleloads, thedy-namicforces originatedbytheunevenness of rails andof car-riages wheels, thedynamicforcesresultingfromtheimperfec-tionsofjoints rails, andthedynamiceffectsresultingfromthedeformability 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 mechanism8,10,11 ofground-bornevibrations. Inthisstudythetrainloadingfunctionhasbeendenedwithreferencetothefollowingtwoexcitationmechanisms: a thequasistaticdeformationcausedbytheaxleloadsand bthedynamicforcesarisingfromtheunevennessofthe rails. The loading function associated with the rst mechanismwascomputedusinganumericalmodeldevelopedbytheItalianRailwayCompanyItalferr12. For agiventraincategoryandtrackcharacteristics, this model computes the average verticalpressure at the basement as a functionof frequencyandtrainspeed. The loading spectra are computed by modeling the track asadynamicvertical oscillator restingover axedbasement andconstituted by the rails supported by the rubber pads, the sleepers,theballast bed, andpossiblyavibrationmitigationdevice. TherailsaremodeledasEuler-BernoullielasticbeamswhereastheirsupportsasaseriesofmassesconnectedbyspringanddashpotelementsseeFig. 3. Theoscillatingsystemis subjectedtoaseries of point forces representing the wheel loads of a train trav-elingat aparticularspeed. Furtherdetailsofthemodel usedtocompute the train loading spectra can be found by consulting theoriginal Ref. 12whichalsoconsidersthecaseofatracksup-ported by a oating slab system.Reference 12alsoprovidedthebasistoaccount forthedy-namic forces caused by the unevenness of the rails. Their effect ontheloadingspectrawascomputedusingthefollowingempiricalrelation:GD =A av2+ b2v+ a1where GD is the pressure power spectral density, is the angularfrequency, is the train speed, A is a coefcient of quality of thetrack A=1.558 107m rad for track in good conditions, A=8.974 107m rad for track in poor conditions, and a and b areempirical constants whose values are a=0.8246 rad/ mand b=0.0206 rad/ m.Figures4and5showtheloadingemissionspectraofverticalpressure that have been adopted in this study for Freight and TAFtraincategories13. TheacronymTAFstandsforTrenoadAlta Frequentazione that in Italian denotes a special type of com-muter train composed by two-oor carriages. In the gures cap-tion, standardtrackmeansatrackwithout amitigationdevice.The gures show that for both train categories most of the energyassociated to the loading emission spectrum is concentrated in thefrequencyrangebetween0and120Hz. For thetraincategoryTAF see Fig. 4 the maximum value of pressure occurs at about33Hzandisapproximatelyequal to1500 N/ m2. For thetraincategoryFreight theshapeoftheloadingspectrumissimilartothatofTAFcategory, althoughthepressurevaluesassociatedtotheFreight trainareconsistentlyhigherseeFig. 5. Themaxi-mumpressureisabout7500 N/ m2andoccursatafrequencyofapproximately 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.Inthenumericalmodelusedinthisstudyeachsleeperactsasasingle excitation point source and the overall motion caused at theground surface by the moving train is built from the superpositionofthewaveeldsgeneratedbytheactivationofallsleepers. Asmentioned previously this approach to model the train sourcemechanismisrathernatural andit hasbeenusedpreviouslybyotherresearchers 8,9.SometimesthemethodiscalledtheKry-Fig. 3 Dynamic vertical oscillator used to model the multicomponent track system modi-ed from 12Journal of Vibration and Acoustics OCTOBER 2005, Vol. 127 / 505Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-uselovsmodelfromtheresearcherthatinrecenttimeshassystem-atically used it to simulate the vibration generation mechanism oftrains running at the ground surface 8.Theprocedureisformalizedmathematicallybyaconvolutionintegral betweentheforcesdistributedalongthetracki.e., thetrainloadingfunctionandthecorrespondingdynamicinuencefunction. In the frequency domain the convolution integral can bewritten as follows:aFFx, y, =Px, y, , vGFF, dxdy 2where aFFx, y, is the acceleration induced at the receiver freeeld by the moving train along the directions=x,y,zthat are,respectively, transversal, longitudinal, andvertical tothetrack,GFF, is the dynamic inuence function or transfer functionrepresentingtheaccelerationgeneratedat thegroundsurfaceatthe positionx, y, 0 bya unit vertical force oscillatingat theangularfrequencyandplacedat thebasement ofthetrack, =xx2+yy2+z2is the distance between the point of ap-plication of the force along the track at the position x, y, z andthe receiver at the groundsurface havingcoordinates x, y, 0.Last, Px, y, , vrepresentsthetrainloadingspectraanditisgiven by the following relation:Px, y, , v = m=m=+PB, veiy/v y mdx 3where 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 Diracs delta distribution, andPB, v istheaveragevertical pressureat thebasement oftheFig. 4 Loading emission spectrum adopted in the numerical modelVertical pressure at the basement of astandard ballasted trackTrain category TAFTransit velocity: 100 Km/h from 13,12Fig. 5 Loading emission spectrum adopted in the numerical modelVertical pressure at the basement of astandard ballasted trackTrain category freightTransit velocity: 90 Km/h from 13,12506 / Vol. 127, OCTOBER 2005 Transactions of the ASMEDownloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-usetrackcomputedbythenumerical model denedintheprevioussection. Figure 6 shows schematically the various terms appearingin Eq. 2.The dynamic inuence function GFF, was computed usingthe following relationship:GFF, = JEXP*, C ePn4whereJEXP*, istheexperimental transferfunctionbetweenthepointinthetunnelwheretheharmonicvibrationexciterwasplaced and the corresponding point aligned at the ground surface*isthevertical distancebetweenthesetwoparticularpoints.JEXP*, is the acceleration measured at the ground surface andinduced by the oscillations of a unit vertical load generated by theelectrodynamicshakerplacedinsidethetunnelatapointimme-diatelybelowthegroundsurfaceat theangular frequency.ThetermC eP/ nisascalefactorusedfor computingthetransferfunctionsGFF, at thepointsalongthebasement ofthetrackwherenomeasurementsareavailable. Thisfactor ac-counts, even if in a simplied way, of the attenuation of a vibra-tioneldoccurringinadissipativemediumbecauseofmaterialandgeometricdamping. MorespecicallythetermePsimu-latestheeffectofmaterialdampingthroughtheviscousattenua-tion coefcientP= DP/ VP where VP is the velocity of propa-gationofPwavesandDPisthedilatationaldampingratio. Thelatter is usually measured in geotechnical laboratory tests. In un-consolidatedsediments at low-strainlevels DPranges typicallyfrom0.5%2%14. Geometricattenuationisaccountedfor inGFF, bythetermC/ nwhereCandnareparameterscali-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 exponentndependsonitsgeometryandonitspositioninrelationtothegroundsurface. Herethesourceisaverticallyoscillatingforcepositioned inside a cased tunnel surrounded by an heterogeneousmedium. Thus, the geometric attenuation law chosen in this studyrepresentsinevitablyasimplicationofthereal, certainlymorecomplex, attenuation law.For the simplied attenuation lawthe calibration procedureyieldedavalueofnequalto0.4. Figure7showsacomparisonbetween the experimental transfer function measured at theground surface at an horizontal distance of 20 m along the tunnelaxis from the electrodynamic shaker, and that computed using Eq.4. Despite the simplicity of the model used for the attenuation ofthedynamicinuencefunctiontheresultsofthecomparisonareconsidered satisfactory.As a nal remark of this section, it is noted that the innite sumappearinginEq. 3isformalandonlyanitenumberoftermsneed 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 m300.2.3 Propagation of Ground Vibrations in the Far Field. Thevibration measurement campaign conducted in this study hasshownclear evidencethat theattenuationof thevibrationeldinducedat thegroundsurfacebytheelectrodynamicshaker isvirtually negligible up to a distance of about 20 m from the tunnelaxis for the vertical component and it is low to moderate for thetwoothercomponents.Thisexperimentalresultisthoughttobecaused by a geometrical effect due to the relatively low depth ofembeddingofthetunnel atonemeasurementsiteofthetunnel,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-formedintoanexcitationof thetunnel capthat thus becomesitself alargesourceof vibrations. Theweakattenuationof thevibration eld observed experimentally at the ground surfacewithin a certain distance from the tunnel axis is then caused by thepropagation of vibrations radiating away fromthe tunnel capalong cylindrical wave fronts. Although this phenomenon was de-tectedusingapoint source, it isexpectedtobeevenmorepro-nouncedforthecaseofamovingtrainsincethelatteractsgeo-metrically like a nite line source for horizontal distances that aresmall when compared with the train length.In light of these considerations, in the numerical model used forthepredictionof thevibrational impact inducedat thegroundsurfacebytheundergroundrailwaytrafc, itwaspostulatedtheexistence of a near-eld band across the tunnel axis where all thethreecomponent of thewaveelddonot undergoanytypeofspatial attenuation. The size of the near-eld band was assumed tobe20mateachsideofthetunnelaxis.Outsidethisband,here-inafter named far eld, the wave eld was computed according tothe following assumptions:1 The medium where the propagation of ground-borne vibra-tions takes place is weakly dissipative;Fig. 6 Computationschemeadoptedfordeterminingthefree-eldresponseatthereceiverfrom 13Journal of Vibration and Acoustics OCTOBER 2005, Vol. 127 / 507Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use2 The vibration eld is composed exclusively by surfaceRayleigh waves;3 Themovingtrainactsasalinesourceforhorizontal dis-tances from the tunnel axis greater than 20 m and less than1/ times the length of the train 15.As a motivation for assumption2 it is recalled that bulkwaves induced at the free surface of a homogeneous half space byalineloadattenuategeometricallywithafactorproportional to1/ r1.5withrbeingthedistancefromthesource,whereasRay-leighwavesdonot sufferanygeometrical attenuation 16. Theassumption2 is well substantiated also by other studies onrailway-induced ground vibrations 17.Basedontheseassumptions, thespatialattenuationofgroundvibrationsinthefareldinducedbyundergroundrailwaytrafcwas computed for all three components, via a term proportional toeRrwhere r is the distance measured at the ground surface fromthe tunnel axis, and R=R is the Rayleigh attenuation coef-cient. Inastratiedmedium, Risgivenbythefollowingrela-tionship 16:R =VR2 iNVPiVRVPiDPi + iNVSiVRVSiDSi5where VR=VR is the velocity of propagation of Rayleighwaves, VSiVPiare, respectively, thetransversal andlongitudinalwave velocity of each of the N layers of the soil deposit, and DSi,DPi are the corresponding damping ratios. It is important to recallthatsinceVRandthepartialderivativesappearinginEq. 5aremodal quantities, in this study they were computed with referencetothefundamental modeofpropagation.Accountingforhighermodes 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. FROMfree-eldgroundmotioninthe proximityof thebuilding TO vibration eld at the basement of the buildingi.e., dynamic effect of ground-foundation coupling;2. FROM vibration eld at the basement of the building TOvibrationeldat aspecicoorofthebuildingandat aposition close to the perimeter wall i.e.,dynamiceffectofvertical-resisting structure;3. FROM vibration eld at a specic oor of the building andat a position close to the perimeter wall TO vibration eldat the center of a specic oor of the building i.e., dynamiceffect of oor diaphragms.Eachofthesecomponentsofthevibrationchaincanbecharac-terizedinthefrequencydomain byits owntransfer functionHj j =1, 3; =x, y, z. Computationof these transfer func-tions via numerical modelingconstitutes a rather difcult taskmainly due toFig. 7 Comparison between experimental and computed transfer functions from 13508 / Vol. 127, OCTOBER 2005 Transactions of the ASMEDownloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use The variability of structural resisting frame systems; Difcultiesinassessingtheeffectsofcladdingandingen-eral of not structural components; Difculties 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 transferfunctions must be dened.In light of these difculties and of the problems associated to theevaluation of the dynamic response of different categories ofbuildings, a more practical approachtodetermine the transferfunctionsHjisbywayofasuitablenumberofexperimentalmeasurements. 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 19561960, withcon-crete resisting structure moment-resisting frame, four-stories, piled-foundations; BuildingB: Residential andcommercial, relativelyrecent19651970, with concrete resisting structure moment-resisting frame, four-stories, shallow foundations.Thenexttwosectionswilldescribethepositionwherethemea-surementsweremadeinsidethetwobuildingsandwillillustratethe modulus of the measured transfer functionsHj.2.4.1 BuildingA. Themeasurement deviceswereplacedatthe following locations: Seismometer S3wasset tomeasurethefree-eldgroundmotion and thereby positioned in the courtyard in proximityof the building; SeismometerS4waspositionedinsidethebuilding, at thebasement near a column; SeismometerS5waspositionedinsidethebuilding, at thecenter of the second oor diaphragm.With the seismometers placed in these positions it was possible tomeasure the following transfer functions:H1A =aS3aS4A6H2+3A =aS4aS5A7where aSK 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 H1A 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 oftheelectrodynamicshaker. Asthegureclearlyshows, allthreecomponentsof H1Ahaveanirregulartrend. Rapidchangesalternate to narrow spikes that may denote the existence oflocalresonancephenomena. Forthisreasontheyhavebeensmoothedusing a piece-wise straight-line approximation throughout the en-tire frequency range of denition using a conservative criterion.Fig. 8 Measuredtransfer functionsof ground-foundationcouplingeffect inbuildingA:Experimental thin line and piece-wise straight-line approximation thick line from 13Journal of Vibration and Acoustics OCTOBER 2005, Vol. 127 / 509Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-useFromFig. 8it is notedthat theground-foundationcouplingcauses an attenuation of about 7 dB in the range 1040 Hz of thelongitudinalcomponentof H1A. Thetransversalcomponentshowsasimilartrendwithanattenuationofabout 5dBintherange1025Hz. Thevertical component attenuates inthefre-quencyrangefrom12to24Hzandfrom30to40Hz. Goodagreement is found between these results and data from the litera-ture 18.Figure9showsthethreecomponentsofthetransferfunctionH2+3Awhichdescribesthecombinedeffect ofthevertical-resisting structure and of diaphragmvibration. The horizontalcomponents of H2+3A show an attenuation that increases withfrequencyfrom5to15dB. Conversely, thevertical componentshows an amplication in the range 1245 Hz.The transfer functions of Figs. 8 and 9 have been extended fromthe frequency range 1050 Hz to the range 180 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 aseriesofindependentmeasurementscarriedoutontwoidenticalbuildingsexposedtotheordinaryroadtrafc. TheprocesshasbeenfacilitatedbytheuseoftheCampbelldiagramstoidentifyand reject possible outliers see next section for more details. Theresults of these measurements have shown that the transfer func-tionH1Adoesnot essentiallymodifythefree-eldgroundmotion, whereas for H2+3A it is observed an attenuation of 4dBfor the horizontal components. The vertical component re-mains essentially unchanged. More details about the experimentalmeasurements on road trafc can be found in the originalreference 13.2.4.2 BuildingB. Thebuildingislocatedinahighlypopu-lated area with only neighboring roads breaking the building con-tinuity. Themeasurementdeviceswereinstalledatthefollowinglocations: Seismometer S3wasset tomeasurethefree-eldgroundmotion and thereby positioned in the courtyard in proximityof the building; SeismometerS2waspositionedinsidethebuilding, at thebasement oor, near a column; SeismometerS5waspositionedinsidethebuilding, at thecenter of the second oor diaphragm.Duetounfavorableconditionsatthemeasurementsiteforback-groundnoise thebasement isusedasaparkinglot andcarre-pairingfacility,itwasfoundconvenienttomeasuredirectlythecombinedeffect ofthethreemeasuredtransferfunctionsHjj =1, 3; =x, y, zthereby obtainingH1+2+3B =aS3aS5B8Figure10showsthethreecomponentsofH1+2+3Bplottedtogetherwiththepiece-wisestraight-lineapproximationofthesecurves. As for the transfer functions associated to building A, thespectra of Fig. 10 were conservatively extended below 10 Hz andabove50Hztocover thefrequencyrange180Hz. Boththehorizontalcomponentsshowasimilartendencywithanattenua-tionofabout15dBinthefrequencyrange1050Hz. Athigherfrequencies however, the longitudinal component show a null at-tenuation. The vertical component of H1+2+3Bexhibits aFig. 9 Measuredtransferfunctionsofcombinedeffectofthevertical-resistingstructureand of diaphragm vibration in building A: Experimental thin line and piece-wise straight-line approximation thick line from 13510 / Vol. 127, OCTOBER 2005 Transactions of the ASMEDownloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-usemore irregular behavior within the operational frequency range ofthe electrodynamic shaker with an alternation of positive attenu-ation and negative amplication values. Below 10 Hz for all thethree components and above 50 Hz for the vertical component, itwas conservatively assumed a null attenuation.3 Experimental MeasurementsThetestingsiteswerelocatedincorrespondenceof twosec-tions of therailwaytunnel Cassia-MontemarioinRome, Italy.The two sections along the tunnel, whose total length is 4381 m,wereidentiedassection A locatedat theprogressivedistance24+035 km andsectionBlocatedat theprogressivedistance24+610 km and include the homonymous buildings selected forthevibrationmeasurementcampaign. Figure11showstheloca-tionofseismometersinsectionA. Thetopofthetunnel capispositioned at about 6 m below the ground surface in section A and10 m in section B.At both sections, the measurements were made at ve stationsFig. 10 Measuredtransferfunctionsof combinedeffect of ground-foundationcoupling,vertical-resisting structure, and diaphragm vibration in building B: Experimental thin lineand piece-wise straight-line approximation thick line from 13Fig. 11 Testing site at the Cassia-Montemario underground railway line inRome, ItalyPosition of seismometers in section A from 13Journal of Vibration and Acoustics OCTOBER 2005, Vol. 127 / 511Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-usesee Fig. 11 each of them composed by a seismometer made upof three particle velocity transducers i.e., geophones oriented inthedirectionsparallel, andperpendiculartothetunnelaxis.Theseismometerswerehighsensitivitygeophones 1V/1mm/sca-pable of operating in the frequency range of 1 to 100 Hz.The excitation inside the tunnel was provided by an electrome-chanical shakeroperatinginafrequency-controlledmodeintherange 1050 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 andBandsetforverticaloscillations.Thetimevariationofthedy-namic load generated by the shaker was sinusoidal with an ampli-tudethat variedquadraticallywithfrequencyuptoamaximumvalue of 20 kN at 50 Hz.Measurementsatsections A andBweremadeintwoseparatesessions. By varying the frequency of excitation from 10 to 50 Hzthe vibrations generated by the shaker were measured by the net-work of ve seismometers positioned in and out of the tunnel seeFig. 11.Themagnitudeofthedynamicforcesgeneratedbytheshaker was chosen so as to satisfy a good signal-to-noise ratio atthereceivers.Moredetailsonthetestingequipmentusedtoper-form the vibration measurements can be found by consulting theoriginalRef. 13.Thetimehistoriesrecordedateachseismom-eter wereusedtocomputethetransfer functions associatedtoeachcomponent of thevibrationchainfromsourcetoreceiversee Fig. 11. Computation of the experimental transfer functionswas guided by the use of the Campbells diagrams which allowedto assess the inuence 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 follows13: Monte Mario Unit Lower Pleistocene age constitutedmostly by silty sand and clayey sandy silt, medium perme-able, withanhighpeakfrictionangleandalowtonullcohesion. Monte Vaticano Unit Pliocene-Lower Pleistocene age con-stituted by clayey silty sediments, slightly permeable, with amoderate value of the peakfrictionangle anda modestcohesion. Paleotevere Alluvial Unit Medium Pleistocene age consti-tuted by uvial alluvial deposits.At the ground surface along the tunnel, the subsoil includes also astratum of ll 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 lineforgeotechnicalsitecharacterization 13. Theresultsofthisin-vestigationwereusedtodeterminethegeotechnical parametersrequiredbythenumerical model topredict therailway-inducedground vibrations. More specically, the transversal wave velocityprole 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 from1850 to1950 kg/ m3.4 Results of Numerical SimulationsThenumerical model describedinSec. 2wasusedtopredictthevibrational impact resultingfromthereactivationoftheun-derground railway line Cassia-Montemario in Rome, Italy. In thisstudy, byvibrationalimpactitismeanttheparticleaccelerationspectrum measured at a receiver located either at the ground sur-faceor insideabuildingandit isdenotedbyaRC. Byre-ceiver, itismeantahumanindividualorasensitiveinstrument.By recalling the nomenclature of Sec. 2, the vibrational responseat the receiver can be computed by means of the followingrelationships:aRCA = aFFH1AH2+3A9aRCB = aFFH1+2+3B10where aRCA denotes the acceleration spectrum predicted at areceiver located at the center of the second oor of building typeA, and aRCB denotes the acceleration spectrum predicted at areceiver located at the center of the second oor of building typeB. To evaluate the impact aRC, the values of the three com-ponents=x,y,zof the acceleration spectrum are combined to-gether using the following relation 19,20:aRCA/B = axRCA/B2+ ayRCA/B2+ azRCA/B211Thenumerical simulationswereconductedconsideringthepas-sageof trainsof categoriesTAFandFreight seeSec. 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 oor.The acceleration spectra are plotted as RMS root mean squarevalues in one-third octave frequency scale in the range 180 Hz.Fig. 12 Testingsiteat theCassia-MontemarioundergroundrailwaylineinRome, ItalyCampbellsdiagramsinSection ASeismometers S2 and S3 from 13512 / Vol. 127, OCTOBER 2005 Transactions of the ASMEDownloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-useFor both buildings A and B and for both categories of trains TAFandFreight, the predictedaccelerations are, at all frequencies,belowthelimitsfordiscomfort prescribedbytheStandardISO2631-2 thin line19. However the values of aRC predictedfor theFreight traindashedline areconsistentlyhigher thanthoseofthe TAFtrain boldline.Figures13and14putalsoinevidencethat althoughthedepthofembeddingofthetunnel insection B is greater than in section A about 10 m against 6 m,theaccelerationvaluespredictedbythemodelatbuildingBarehigher thanthoseof buildingA. Thisresult hasalsobeencon-rmed experimentally by comparing the magnitude of the transferfunctions measured with the electrodynamic shaker at sections AandB, andithasbeeninterpretedasthegrosseffectyieldedinsection 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, atthecenterofthesecondoor,isabout60dBatbuilding A i.e.,103m/ s2and80dBat buildingB i.e., 102m/ s2withbothpeaks 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-sentationof theresults, theinterestedreader is referredtotheoriginal Ref. 13.5 Concluding RemarksThispaperillustratedtheresultsofanumerical model devel-oped for the predictions of the vibrational impact induced by therailway trafc resulting from the reactivation of the undergroundrailway line Cassia-Montemario in Rome, Italy. For the predictionof the free-eld ground vibration the model was calibrated usingtheresultsofexperimentalmeasurementsconductedwithaelec-tromechanical shaker.Oneoftheobjectivesofthevibrationmeasurementcampaignwas also to determine the experimental transfer functions to assessthe effects of the buildingdynamic response onthe free-eldground motion. Although the results of the numerical simulationsdisplayaratherfavorablevibrationalscenario, adirectcompari-sonof thepredictedvibrationclimatewiththevibrationlevelsmeasured after the reactivation of the underground railway line isrequired for a denitive validation of the model.AcknowledgmentsThe work of the rst two authors has been sponsored by StudioGeotecnico Italiano Srl. The support of Italferr S.p.A. which pro-videdthe experimental data is alsoacknowledged. Finallytheauthorswouldliketoexpressaspecial wordofappreciationtoIng. Natoni of Italferr S.p.A. for his valuable suggestions.References1 Kurzweil, L. G., 1979, Groundborne Noise and Vibration From UndergroundRail Systems, J. Sound Vib., 663, pp. 363370.2 Melke, J., 1988, Noise andVibrationFromUndergroundRailwayLines:Proposals for a Prediction Procedure, J. Sound Vib., 1202, pp. 391406.3 Hood,R.A.,Greer,R.J.,Breslin,M.,andWilliams,P.R.,1996,TheCal-culationandAssessment of Ground-BorneNoiseandPerceptibleVibrationFrom Trains in Tunnels, J. Sound Vib., 1931, pp. 215225.4 Balendra, T., Chua, K. H., Lo, K. W., andLee, S. L., 1989, Steady-StateVibration of Subway-Soil-Building System, J. Eng. Mech., 115, pp. 145162.5 Chua, K. H., Balendra, T., and Lo, K. W., 1992, Groundborne Vibrations dueto Trains in Tunnels, Earthquake Eng. Struct. Dyn., 21, pp. 445460.6 Jones, C. J. C., and Block, J. R., 1996, Prediction of Ground Vibration FromFreight and Trains, J. Sound Vib., 1931, pp. 2052l3.7 Metrikine, A. V., andVrouwenvelder, A. C. W. M., 2000, SurfaceGroundVibrationduetoaMovingTraininaTunnel: Two-Dimensional Model,J.Sound Vib., 2341, pp. 4366.8 Krylov, V., andFerguson, C., 1994, CalculationofLow-FrequencyGroundVibrations From Railway Trains, Appl. Acoust., 42, pp. 199213.9 Castellani, A., andValente, M., 2000, Vibrazioni TrasmessedaVeicoli suRotaiaallAmbienteCircostante,IngegneriaSismica, Anno XVII-N.1inItalian.10 Lai, C. G., Callerio, A., Faccioli, E., andMartino, A., 2000, MathematicalModeling of Railway-Induced Ground Vibrations, Proceedings, 2nd Interna-tional WorkshopWAVE2000-WavePropagation-MovingLoad-VibrationRe-duction, Ruhr University Bochum, December 1315, 2000, Balkema, Bochum,Germany, pp. 99110.11 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. 425433.12 Italferr S. p. A., 2000, Linee Guida per la Progettazione e la Posa in Opera diArmamento AntivibranteInternal Report No. XXXX000IFPFSF0000001 A,ItalianNationalRailwayCompany,Rome,Italy inItalian;formoreinformation, see http://www.italferr.it/13 Italferr S. p. A., 2001, Progetto Esecutivo Messa in Sicurezza ed in SagomaDella Galleria Cassia-MontemarioStudio Vibrazionale dal Km.Fig. 13 Results of numerical simulations at the Cassia-Montemario underground railway line in Rome, ItalyMagnitudeofaccelerationspectruminone-thirdoctavescaleat thecenterof thesecondoorof buildingAComparisonwithstandardISO2631fortheevaluationofhumanresponseto vibrations from 13Fig. 14 Results of numerical simulations at the Cassia-Montemario underground railway line in Rome, ItalyMagnitudeofaccelerationspectruminone-thirdoctavescaleat thecenterof thesecondoorof buildingBComparisonwithstandardISO2631fortheevaluationofhumanresponseto vibrations from 13Journal of Vibration and Acoustics OCTOBER 2005, Vol. 127 / 513Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use23+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. 492, pp. 179193.16 Aki, K., andRichards, P. G., 1980, Quantitative Seismology: Theory andMethods, W. H. Freeman and Company, San Francisco.17 Hung, H-H., andYang, Y-B., 2001, AReviewof ResearchesonGround-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., andWilson, G. P. 1982, HandbookofUrban Rail Noise and Vibration Control, edited by DOT USA Department ofTransportation, Washington, DOTWashington; 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.514 / Vol. 127, OCTOBER 2005 Transactions of the ASMEDownloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 08/04/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use