Engineering Structures 77 (2014) 119–128

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Engineering Structures

journal homepage: www.elsevier .com/ locate /engstruct

Measurement and prediction of train-induced vibrations in a full-scalebuilding

http://dx.doi.org/10.1016/j.engstruct.2014.07.0330141-0296/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 (617) 627 4116.E-mail addresses: masoud.sanayei@tufts.edu (M. Sanayei), AnishKP@linboston.

com (A. Kayiparambil P.), jmoore@acentech.com (J.A. Moore), CRBrett@sgh.com(C.R. Brett).

1 Tel.: +1 (781) 333 9588.2 Tel.: +1 (617) 499 8011.3 Tel.: +1 (781) 907 9270.

Masoud Sanayei a,⇑, Anish Kayiparambil P. b,1, James A. Moore c,2, Cory R. Brett d,3

a Department of Civil and Environmental Engineering, Tufts University, Medford, MA, United Statesb Tufts University, Medford, MA, United Statesc Acoustics & Vibrations, Acentech Inc., Cambridge, MA, United Statesd Simpson Gumpertz & Heger Inc., Waltham, MA, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 20 August 2013Revised 23 May 2014Accepted 24 July 2014Available online 23 August 2014

Keywords:Train-induced vibrationImpact hammer testingImpedance modelingFloor vibrationVibration mitigationBlocking floor

Buildings located close to transportation corridors experience structure-borne sound and vibration due topassing traffic which can be disruptive to operation of sensitive equipment in manufacturing, andmedical facilities. Structure-borne sound and vibrations, when high may also be annoying to humanoccupants in residential, office, and commercial buildings. Hence, there is a growing need for cost effec-tive sound and vibration predictions to evaluate the need for mitigation.

The research focuses on in-situ testing of a full-scale building for verification of a previously developedimpedance-based methodology and to create a prediction model to study ground-borne vibrations in thetest building. A mitigation methodology was also examined using the verified prediction model.

Impedance modeling involves the propagation of axial waves through columns combined with theimpedance of the intermediate floor slabs. The vibration transmission in the building was characterizedand predicted using a single column model with attached floors.

Train-induced floor vibrations in an existing four-story building in Boston were measured andcompared with predictions of the impedance model. The impedance model predictions closely matchedwith the measured floor responses.

A previously suggested mitigation method was investigated analytically using the impedance model. Athickened floor referred as the ‘‘blocking floor’’ was used on the lower elevation of the building and thereduction in vibration at the upper floors of the building was compared for various thicknesses of theblocking floor, to study its efficiency. The blocking floor has high impedance and reflects a major portionof the vibration transmitting in the columns preventing it from reaching the upper floors. The blockingfloor was found to mitigate the transmission of ground-borne vibrations to upper floors.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In major cities around the world, urbanization and rising landprices have been driving an increase in real estate developmentadjacent to, and above in some cases, railway lines and othertransportation corridors. Structure-borne sound and vibrationsfrom traffic can not only be annoying to human occupants, theycan also be disruptive to the operation of manufacturing facilities,

medical facilities, and research laboratories. As awareness ofstructure-borne sound and vibrations issues grow among develop-ers, owners, designers, and building occupants, there is a corre-sponding increase in demand for cost effective sound andvibration predictions to evaluate the need for mitigation. Ifdesigners could predict the vibration response of buildings withreasonable accuracy, cost-effective vibration mitigation strategiescould be incorporated into initial stages of structural design.

1.1. Background

Transmission of train-induced ground borne vibrations can bebroadly classified into three different stages. The vibration genera-tion at the source, ground borne transmission and the vibrationtransmission from the ground into the building and within thebuilding. Previous researchers have investigated in detail to

Fig. 1. Axial wave propagation model for a column segment.

120 M. Sanayei et al. / Engineering Structures 77 (2014) 119–128

identify the source of vibration from railway lines and to find pos-sible solutions to mitigate the effect of train-induced vibrations inbuildings. Cox and Wang [1] summarized the track geometry andthe rail head roughness as possible causes of vibration. Vibrationstransmit from the rail to the track structure and then to thesurrounding ground, propagate through the ground and eventuallyentering into the building through the foundations and transmit-ting to the upper floors.

The characteristics, frequency range and magnitude, oftrain-induced vibrations have been well identified by researchers.Vibration energy levels are observed to be in the frequency rangeof 10–250 Hz [2]. One of the challenges is to develop a methodol-ogy to predict floor vibration levels in a building based on theground-borne vibration input at the base of the building, at thefoundation level. A prediction model will also facilitate the studyand comparison of different design alternatives for floor vibrationmitigation.

Current guidelines for predicting train-induced vibrations inbuildings, published by FTA [19], rely on a heuristic predictivemodel. The FTA’s recommendations for estimating floor-to-floorvibration attenuation are �2 dB per floor (1–5 floors above grade)and �1 dB per floor (5–10 floors above grade). However offsettingthis attenuation are resonances of the building structure, particu-larly the floors, walls and ceilings which will create amplificationin the vibration levels.

There have been several attempts to develop predictive finiteelement models ([3,4]). However, a detailed finite element modelrequired to accurately replicate the dynamic behavior of the build-ing from low to high frequency ranges is not available at initialstages of design.

Study of train-induced floor vibrations and its mitigation is anarea of ongoing research at Tufts University and Acentech Inc.We have developed a simplified impedance-based analyticalmodel for train-induced vibration predictions [5]. An axial wavepropagation model with a single column and associated floorswas considered to predict floor vibration levels based on measuredground-borne vibration input at the base of the column. Theimpedance of columns and slabs representing stiffness, mass anddamping properties constitute the basic elements of the model.The prediction model was validated using tests on a four-storyscale model building and the robustness and efficiency of the mod-eling technique was demonstrated by comparison with finite ele-ment models [6].

Mitigation of train-induced vibration has been investigated byvarious researchers by considering methods applied at the sourceor along the transmission path or at the building structure. Reduc-ing wheel and rail irregularities, noise isolation pads [7], soilreplacement below tracks [8], and specialized track structuredesign [9] have been found to reduce level of vibrations transmit-ted from the track to the surrounding ground. The use of open andfilled trenches [10], wave barrier of lime-cement columns [11] andgas cushion screens [12] have been investigated and found to beeffective in reducing vibration transmission between the railwaytrack and nearby buildings. Base isolation in buildings using resil-ient foundations or elastomeric bearings [13], compacted sand fillbelow foundation [14] were also found effective in reducing vibra-tion transmission into buildings.

The researchers at Tufts University and Acentech Inc. haveinvestigated the use of a thickened ‘‘blocking floor’’ for vibrationmitigation at the building. The blocking floor has high impedanceand reflects down a major portion of the vibrations transmittingfrom the columns to the upper floors. Use of lower floors of thebuilding as a blocking floor for mitigation of ground-borne vibra-tions was successfully investigated using a four-story scale modelbuilding designed and constructed at Tufts University with andwithout the blocking floor [15].

1.2. Scope of research

A continuation of the earlier work at Tufts University in theareas of vibration prediction and mitigation, the original contribu-tions of this research are (1) verification of train-induced vibrationcharacteristics and its propagation within a full-scale building (2)to study the axial wave propagation between floors through col-umns, examination of impedance of complex floor systems andverification of composite slab properties using in-situ impact ham-mer testing (3) prediction of train-induced ground-borne vibra-tions using the impedance model and comparison with measuredresponse of the actual building (4) examination of the blockingfloor concept using the verified impedance model.

2. Impedance model

Impedance modeling involves the propagation of axial wavesthrough columns combined with the impedance of the intermedi-ate floor slabs. A previously developed impedance-based predic-tion model representing a single column and the connectedfloors was used to simulate the dynamic behavior of the test build-ing and predict floor responses to train-induced vibration inputmeasured at the base of a column. The train-induced vibrationsat a floor are the sum of the incoherent contributions from individ-ual columns surrounding the floor. Hence, a single column-floormodel can be treated as an independent system to represent thevibration transmission in the building. A detailed explanationand validation for the same is provided in Section 5.

Impedance represents stiffness, mass and damping propertiesof the system. The finite column segment between floors is repre-sented as impedances at the top and bottom of the column and theimpedance of the floor slabs are included at the junction betweencolumn segments above and below.

A summary of the impedance-based modeling concept, theassociated wave propagation equations, and the blocking floor the-ory that are used in this paper is presented in this section for com-pleteness. Previous research [15] has shown that axial vibrationsare the dominant mode of ground-borne vibration transmissionin columns to upper floors of the building, hence the analysispresented here is limited to transmission due to axial wave prop-agation in columns.

The axial wave propagation model shown in Fig. 1 is consideredto represent a typical column segment. Where, f1 and f2 representthe axial forces and u1 and u2 represent the axial displacements atthe ends of the column segment, which are frequency dependent.

The dynamic relationship between forces and displacements atthe ends of the column segment is represented by the dynamicstiffness matrix of the column given by Eq. (1). It accounts forthe stiffness, mass, and damping properties of the column.

½k� ¼ qAcx

sinðbLÞ

� �cosðbLÞ �1�1 cosðbLÞ

� �ð1Þ

where L is the length of the column, A is the cross-sectional area thecolumn, x is the driving frequency, b is the wave number defined interms of the wave speed, c and material density, q [16] and given byEqs. (2) and (3).

b ¼ xc¼ x

ffiffiffiffiqE

rð2Þ

M. Sanayei et al. / Engineering Structures 77 (2014) 119–128 121

c ¼

ffiffiffiffiEq

sð3Þ

where E is the complex modulus of elasticity of the column definedby Eq. (4).

E ¼ Eð1þ igÞ ð4Þ

where E is modulus of elasticity of the column and g is the materialloss factor.

Axial vibrations in the columns induces bending deformationsin the floors at the connections. The axial load transmitted throughthe column is transferred as a point load to the floors which aremodeled as thin infinite plates as per Kirchhoff plate theory. Thepoint impedance of thin plates is resistive. Energy propagates awayfrom the drive point at the column interface. This drive pointimpedance is defined by Cremer et al. [16] and given in Eq. (5) rep-resenting stiffness, mass, and damping properties of the floor.

z ¼ 8ffiffiffiffiffiffiffiffiffiffiqDh

qð5Þ

where q is the slab material density, h is the slab thickness and D isthe bending stiffness of the slab given by Eq. (6).

D ¼ Eh3

12 1� m2ð Þ ð6Þ

where m is the Poisson’s ratio of the slab material and E is thecomplex modulus of elasticity of the slab. The dynamic mass ofthe floor depends on the driving frequency and is given by Eq. (7).

m ¼ zix

ð7Þ

Fig. 2 shows the simplified one-column impedance model of thefour-story full-scale building used for testing. The model consistsof four axial degrees of freedom, one per floor in the axial direction.

The dynamic stiffness matrices of the column elements, Eq. (1),are assembled into global matrix [K] and the dynamic mass of thefloors, Eq. (7), are assembled into global matrix [M]. The stiffnessand the mass matrices are functions of frequency. The excitationis represented by the load vector {F} and the steady state response

Fig. 2. Impedance model: simplified column and floor slab model of the teststructure.

of the system is shown as {U}. The system relationship is repre-sented by Eq. (8), [17].

½K�fUg �x2½M�fUg ¼ fFg ð8Þ

For train-induced excitations, the load vector of external forces{F} comprises of a non-zero force at the column base and zeroexternal forces at all other floors as shown in Fig. 2. Since themodel considers force input at the column base, the grade slaband the foundation system are not included in the impedancemodel. The frequency dependent steady state response for allfloors is given by Eq. (9) and the corresponding velocity given byEq. (10).

fUg ¼ ½K �x2M��1fFg ð9Þ

fVg ¼ ixfUg ð10Þ

If the forces at the column base are known, the frequencydependent response is determined using Eq. (9). In the case ofmeasured vibrations at the column base, velocity ratios establishedbetween various floors with reference to the base are used in con-junction with the measured floor vibrations at the column base.This is explained in detail in Section 6.

3. Test building

A four-story building in Boston, Massachusetts was selected todevelop and verify the predictive capability of the impedance-based analytical model considered in this research. Four floors ofthe building were considered for the test plan and identified frombottom to top as loading dock, plaza floor, second floor, and thirdfloor. Two tracks of the commuter rail line pass through the build-ing tunnel at the loading dock level. Fig. 3 shows a train exiting thetest building.

The test structure selected is a convention center with largeopen halls and a limited number of partition walls, an ideal choicefor creating a simplified model as the alternate vibration propaga-tion paths are avoided and vertical transmission of vibrations ismainly through the columns. The building, originally constructedin the 1960s and substantially renovated in the 1980s, contains amix of concrete and steel-frame construction, one-way slabs onwide-flange beams and two-way waffle slabs. The superstructureis founded on pile caps that distribute load to steel piles. The mainstructural columns are located on a square grid of size 9.144 m(30 ft). To ensure stronger train-induced excitation and avoid floor

Fig. 3. Train passing through test building.

Fig. 4. Test building plan and section.

122 M. Sanayei et al. / Engineering Structures 77 (2014) 119–128

complexities, a column located close to the train tracks and awayfrom any masonry walls or large floor openings was selected.Fig. 4 shows the plan and section of the building identifying thetest column. The foundation system below the column consistsof an isolated pile cap supported on four steel-encased concrete,end bearing piles.

3.1. Modeling of composite columns

The chosen column consists of three finite segments betweenthe four floors. The two lower segments between loading dock-plaza floor and plaza floor-second floor are reinforced concreteand the third segment between second floor and third floor is steelsection encased in concrete, hence a composite column model isconsidered for these segments. The train-induced vertical vibrationis assumed to be uniform across the cross-section of the compositecolumn. The concrete and steel portions are assumed to experiencethe same axial motion corresponding to the train-induced vibra-tion with no shear slippage occurring between them. The dynamicstiffness of a column defined in Eq. (1) depends on the materialwave speed and the area density of the column. Hence an equiva-lent wave speed and equivalent area density are considered for thecomposite column cross-section as per Eqs. (11) and (12),respectively.

ceq ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAsEs þ AcEc

qsAs þ qcAc

sð11Þ

ðqAÞeq ¼ qsAs þ qcAc ð12Þ

Eqs. (11) and (12) use composite column material propertiesthat are; the density of reinforcing bars or steel section qs, densityof concrete qc, cross-sectional area of steel As, cross-sectional areaof concrete Ac, complex elastic modulus of reinforcing bars or steelsection Es and complex elastic modulus of concrete Ec.

3.2. Modeling of composite slabs

The plaza and second floor have concrete waffle slab construc-tion. The waffle slab consists of 0.4826 m � 0.4826 m (1900 � 1900)domes at every 0.6096 m (2 ft) with 0.0889 m (3.500) thick slaband 0.0254 m (100) topping layer. The third floor, a composite slabwith light-weight concrete over metal decking is supported on agrid of steel beams and girders spanning in perpendiculardirections, hence composite slab models are considered for thesefloors. The impedance, z, of the floor slab defined in Eq. (5) and

the bending stiffness of the slab, D defined in Eq. (6) can also berepresented as shown in Eqs. (13) and (14),

z ¼ 8ffiffiffiffiffiffiffiffiffiffiffiffiffiqDhm

qð13Þ

D ¼ Eh3k

12ð1� m2Þ ð14Þ

where hk and hm are respectively the slab thicknesses consideringan equivalent homogeneous flat plate with the same plate bendingstiffness and mass of the actual composite slab.

For the plaza and second floors, equivalent flat slab thicknesseshk and hm were computed based on waffle slab properties availablein CRSI design handbook [18]. For the third floor, equivalent flatslab thicknesses were computed for the floor system consideringcontribution of the concrete slab, steel beams and girders.

Tables 1 and 2 summarize the properties of relevant structuralelements of the building which serve as building blocks for theimpedance model. m is the Poisson’s ratio of the material, E is themodulus of elasticity of the material, q is the density of the mate-rial and g is the material loss factor.

In Table 1, all three column segments have the same grosscross-sectional area, however the reinforcement contents of thereinforced concrete sections are different. The equivalent wavespeed is dependent on the complex modulus of elasticity andhence has an imaginary component related to damping, whichresults in a decay during propagation. Damping is accounted bymaterial loss factor, g, the values for which are obtained from stan-dard literature. In Table 2, the waffle slabs are normal weight con-crete and the third floor is lightweight concrete over metaldecking. In these tables LD is abbreviation for Loading dock, PL isPlaza level, SF is Second floor, and TF is Third floor.

4. Measurement of floor impedance

Impact hammer tests were performed at several locations oneach floor level to study the individual floor responses. The imped-ance associated with a constant impedance, analytical floor whichbest represents the measured floor response is considered as theimpedance of the floor in the analytical model.

The excitation force is an impulse generated by striking theimpact hammer on the floor slab at a location away from thecolumn and floor beams. The resulting force spectrum is fairly con-stant in the frequency range of 10 Hz to 300 Hz. The correspondingresponse of the floor is measured using an accelerometer placed

Table 1Column properties based on construction drawings.

Column Length (m) Cross-sectional area (m2) Construction Equivalent wave speed (m/s) Equivalent area density (kg/m)

LD ? PL 6.528 0.372 Reinforced concrete 3.74E+3 + 86.33i 980.62PL ? SF 6.121 0.372 Reinforced concrete 3.57E+3 + 99.84i 914.83SF ? TF 8.249 0.372 Concrete encased steel column 3.54E+3 + 83.81i 963.18

Table 2Floor slab properties based on construction drawings.

Floor Construction hk (m) hm (m) m E (GPa) q (kg/m3) g

LD Grade slab 0.330 0.330 0.12 23.0 2400 0.06PL Waffle slab 0.340 0.267 0.12 23.0 2400 0.06SF Waffle slab 0.340 0.267 0.12 23.0 2400 0.06TF Concrete over metal decking 0.205 0.132 0.12 15.4 1842 0.06

M. Sanayei et al. / Engineering Structures 77 (2014) 119–128 123

adjacent to the point of excitation. The response is an exponen-tially decaying function and depends on the impedance of the sys-tem. The measurements are recorded and analyzed using adynamic signal analyzer. The test equipment is shown in Fig. 5.

Fig. 6 shows the comparison between measured transfer func-tion cross spectra or accelerance defined using Eq. (15) and analyt-ical accelerance spectra calculated for a constant impedance floorslab using Eq. (16).

Acceleranceðf Þ ¼ Floor response accelerationðf ÞExcitation forceðf Þ ð15Þ

Acceleranceðf Þ ¼ ixzðf Þ ð16Þ

Floor impedance z for a thin floor in bending is constant, thereforethe accelerance is directly proportional to frequency and hence isseen as a straight line with constant slope in dB scale in Fig. 6.

Fig. 6 shows accelerance of four floor slabs with three differentconstruction types. The loading dock accelerance is shown inFig. 6(a). It is a normal-weight concrete grade slab. It shows thatfor most frequencies the constant analytical impedance behaviorassociated with an infinite flat plate approximates the measuredaccelerance of the loading dock grade slab. The plaza floor andthe second floor accelerance are shown in Fig. 6(b) and (c), respec-tively. These are normal-weight concrete waffle slabs. The acceler-ance computed analytically fairly replicates the measuredaccelerance plots on the corresponding floors. The analytical graphline for each floor follows the trend associated with the best fit linethrough the measured data points, which represents the actualimpedance of the waffle floor slabs. Measurements of these twofloors above 200 Hz were not considered for comparison due to

Fig. 5. Impact hammer test equipment.

low coherence. The third floor accelerance is shown in Fig. 6(d).It is a light-weight concrete slab on metal deck supported on a gridof steel beams and girders. The agreement between the analyticalslab model behavior and the measurements is good. The analyticalslab model at this location considers only the concrete slab portion.The lower accelerance observed in the measurements below 30 Hzand above 150 Hz, can be associated to the presence of the metaldeck, surrounding beams and girders which increased the localstiffness of the slab at the test location.

Comparison of the analytical and measured accelerance plotsindicate that the slab impedance models used for modeling of allfour floors with different construction types, replicate the mea-surements. Hence the idealized constant impedances of thesefloors are computed using Eqs. (5) and (13) and utilized in theimpedance model of the building to represent the floor behavior.

5. Train-induced vibration measurements in the building

Train-induced floor vibrations were measured to study thecharacteristics of the train-induced excitation at the base of thebuilding and its propagation to higher floors. The measurementswere also used to validate the impedance modeling assumptionsand to verify the prediction model developed in this research.Vibrations were measured simultaneously on all floors using accel-erometers placed near the column floor junctions. Fig. 7 shows thetest setup for measuring vertical components of the train-inducedvibrations.

Train passage events were identified by reviewing the vibrationtime histories, removing events that were significantly corruptedby vibration from other sources such as vehicular traffic and mov-ing equipment. Ambient measurements collected provide a senseof the robustness of the measured data. Thirty second long ambientmeasurements were simultaneously recorded from all accelerom-eters in each setup. Train pass by were transient events varyingfrom 15 to 25 s in duration. Sampling rate of 2000 Hz was usedfor train-induced vibration measurements. The time histories wereprocessed in one second intervals to obtain a ‘‘peak hold’’ ormaximum value of the spectra at each frequency during the trainpassage. The acceleration spectrum obtained was converted tothe corresponding floor vibration velocity in decibel scale using areference velocity of 1 � 10�8 m/s recommended by FTA [19].FTA also recommends one-third octave band frequency spectra torepresent the detailed analysis of building response and perfor-mance of vibration mitigation methods. One-third octave bandwere computed by summing narrow band spectral energies lyingwithin each one third octave band. The velocity levels obtainedare represented in decibel scale. A set of measurements for fivetrain passage events were recorded and the mean of the processed

(a) loading dock (b) plaza floor

(c) second floor (d) third floor

Fig. 6. Floor slab accelerance based on impact hammer test and slab properties.

Fig. 7. Train-induced floor vibration measurement setup.

Fig. 8. Train-induced vibrations at base of the test column at the loading dock floor.

124 M. Sanayei et al. / Engineering Structures 77 (2014) 119–128

vibration amplitudes was used as the measured floor vibrationvelocity on each floor.

The train-induced measurements recorded at the base of thetest column serve as the source of vibration input for validationof the impedance model considered in this research. Fig. 8 showsthe measurements recorded at the column base using a tri-axialtest setup.

The solid lines represent the train-induced vibration measure-ments and the dotted lines represent the ambient vibration mea-surements. It is seen that the important part of the train-inducedvibration spectrum lies between 30 and 200 Hz with a broad peakaround 50 Hz. Researchers ([2,20]) have also reported similarconclusions regarding the frequency range of interest fortrain-induced vibrations based on a large number of

measurements carried out along railway lines in Boston and Stock-holm, respectively. The ambient vibration measurements werewell below the train-induced vibrations in the frequency range40–150 Hz. Measurements recorded below 30 Hz in this test setupwere ignored due to significant ambient noise present in the build-ing associated with moving equipment, vehicles, and the ventila-tion system. The vertical component of vibration at the base ofthe test-column was observed to be lower than the horizontalcomponents.

Train-induced vibrations originate from the interactionbetween the train wheel and track. Individual wheel sets act asindependent sources of vibration. Two adjacent columns in abuilding which are equidistant from the rail track, receive vibra-tions primarily generated at different sources of the rail trackand from different wheel sets. The sources of vibration at the baseof two adjacent columns are statistically independent of each otherand so is the vibration that propagates up through them. A

(a) loading dock

(b) plaza floor

(c) second floor

Fig. 9. Coherence plots between train-induced vibration measurements at twoadjacent columns.

M. Sanayei et al. / Engineering Structures 77 (2014) 119–128 125

statistical analysis performed on the vibrations measured due to atrain passage event, on the same floor at two adjacent columnlocations verified this phenomenon. The coherence betweenmeasurements from two adjacent columns is shown in Fig. 9.

A high signal to noise ratio observed in these train-inducedvibrations suggest robust measurements. Low coherence observedindicates that the measurements are statistically independent.Also, high frequency waves in slabs do not travel far from theirsources at the column-slab connection [15], reducing the influence

(a) loading dock

(c) second floor

Fig. 10. Train-induced floor vibration predic

of the vibrations observed at one column location over thevibrations measured at the adjacent column location. Hence, aone column mathematical impedance model shown in Fig. 2 canbe treated as an independent system to represent the propagationof train-induced vibrations in the building.

6. Train-induced vibration predictions using impedance model

Train-induced floor vibration velocity can be predicted on eachfloor at the column junction using Eqs. (9) and (10). This howeverrequires measurement of the force at the base of the test columndue to train-induced excitation, which was not essentially feasible.The vibration relationship between floors in the impedance modelwas established by the application of a unit harmonic load at thefoundation level. The vibration relationship is the velocity ratiobetween the vibration at an upper floor at the junction with thecolumn relative to the vibration at the loading dock adjacent tothe same column. The vibration velocity levels obtained were usedto predict the train-induced vibrations on upper floors by multiply-ing them with the train-induced vibration velocity measured onthe loading dock floor at the base of the column.

The ambient vibration measurements, measured train-inducedfloor vibration velocities and the corresponding predictions fromthe impedance model are shown in Fig. 10.

High signal to noise ratio observed for the train-induced vibra-tion measurements indicate robust measurements in the fre-quency range of interest. The measured vibration velocity levelsat the loading dock level serve as the input to velocity ratios fromthe impedance model in computing the velocity spectra at theupper floors. Comparison of the measured floor vibrations levelsbelow 50 Hz at all floors reveal similar amplitudes, indicating thatthe higher floors have the same motion as measured at the columnbase. Below 50 Hz, a reasonably good match is observed betweenthe predictions and measurements on higher floors. Above 50 Hz,

(b) plaza floor

(d) third floor

tions superimposed on measured data.

126 M. Sanayei et al. / Engineering Structures 77 (2014) 119–128

the floor vibration predictions on higher floors tend to deviate fromthe measurements. In the impedance model, the resonant behaviorof the columns was observed at 70 Hz and above.

The impedance model is a simplified representation of thecomplex building system. A difference in interpretation of theactual behavior of the composite columns would in turn affectthe floor vibration predictions and may have been a possible rea-son for the deviation in the predictions observed at higher fre-quencies. A sensitivity analysis performed on the impedancemodel by considering various structural and material parameterswas not successful in identifying a definite cause for the variationobserved in the results. The authors acknowledge that a mea-surement error at the loading dock level could also potentiallyresult in significantly lower vibration levels measured at theloading dock floor. The impedance model considers the loadingdock floor as an input for vibration predictions at upper floorsof the building. A lower input to the model would result inunderestimating the floor vibration levels on upper floors. Theimpedance model considers a single column with the associatedfloors as a statistically independent system with no influencefrom the adjacent columns. However, the transmission acrossthe floors from the surrounding columns, although not very highfor columns spaced further apart, can influence the responsemeasured at the column considered for the test. This modelingerror can lead to underestimation of the single column responsesubjected base excitations.

Overall, the reasonable match observed between thepredictions and the measured floor velocities in the frequencyrange of interest from 10 Hz to 250 Hz, shows the capability ofthe impedance-based analytical model to predict the floor vibra-tion velocities of a real building subjected to train-inducedexcitations.

(a) loading dock

(c) second floor

Fig. 11. Predicted reduction of floor vibratio

7. Impedance modeling as a potential floor vibration predictiontool

For a building located close to a train-induced vibration source,impedance modeling can offer a simplified and computationallyefficient approach to predict vibration levels at various floors withreasonable accuracy. Considering a target area of interest in thebuilding, only column and floor dimensions, material properties,boundary conditions and vibration measurements at the base ofthe column are required to assemble the impedance model of thetest building.

For new buildings impedance modeling has the potential topredict train-induced floor vibrations based on open field measure-ments. The authors acknowledge that open field measurementspotentially differ from the actual vibration levels that would beobserved at the grade slab level after the building has beenconstructed [2], in particular at the base of a column and awayfrom the column on the grade slab. The vibrations at the base ofa column in the constructed building would also be influencedby the column and foundation system. The effect of these factorsneeds to be investigated further.

The impedance model developed for an existing building can beused for studying retrofit scenarios and for comparison of differentdesign alternatives to mitigate ground-borne floor vibrations.

In general building owners are interested in prediction of floorvibrations anywhere on the floors in addition to locations near col-umns. Train-induced vibration predictions using the impedancemodel are obtained for a floor at a location near the column. Thetotal response of the floor is a sum of incoherent contributionsfrom individual columns surrounding the floor. Hence, the totalresponse at an arbitrary point on the floor can be obtained byconsidering the sum of the vibration energy contributions from

(b) plaza floor

(d) third floor

ns as a function of plaza floor thickness.

M. Sanayei et al. / Engineering Structures 77 (2014) 119–128 127

individual columns. The transfer functions between the nearestfour columns and the point on the floor are multiplied with theresponse measured at the respective column locations and thevibration energy contributions are summed up. For existing build-ings, the transfer function can be estimated using impact hammertests on the floor, with excitation at the individual columns and thecorresponding responses at the same point of the floor in the baybetween the four columns.

8. Train-induced floor vibration mitigation using blocking floor

The impedance model can also be used to study mitigationmeasures to reduce train-induced floor vibration levels. Theimpedance of a floor slab, defined by Eq. (5), increases with thesquare of the floor thickness. Increasing the thickness of a singlefloor in the model significantly increases its impedance with thepotential to reduce the vibration velocity level on that floor andthe floors above as vibration energy is reflected by the thickened‘‘blocking floor’’ back down towards the foundation. The methodis more effective when lower floors of the building above groundare treated as blocking floors. This way it reduces the vibrationson all floors above and also keeps the heavy floor as close as pos-sible to the ground. Two different cases of the analytical modelof the test building with the plaza floor slab thickened by twotimes (2�) and three times (3�) in the impedance model were con-sidered to observe the sensitivity to this phenomenon. The readershould note that only the plaza floor which is the lowest floorabove ground in the building is thickened. The train-induced floorvibration predictions using the impedance model with and withoutthe blocking floors are compared in Fig. 11.

These predictions were obtained by varying only the plaza floorthickness. Hence the order of magnitude of the results shown inFig. 11 can be used for a relative comparison between the casesanalyzed. Comparison of the results from the three cases revealsthe effectiveness of the thickened plaza floor to reduce the train-induced vibration levels on the higher floors of the building. Thefloor vibrations levels above 30 Hz on the plaza and higher floorlevels are lowered by 5 dB or more for the 2� case and 10 dB ormore for the 3� case when compared to the vibration levels with-out the blocking floor action. Hence, a thicker lower floor can pro-vide significant floor vibration mitigation at the blocking floor andthe floors above.

The observations indicate that the blocking floor has the poten-tial to mitigate vibration transmission to floors above the blockingfloor level. A thickened blocking floor is a simple method that canbe easily integrated into the design of the structure with less impacton the overall design, construction and cost of the building. In manybuildings lower floors which functionally serve as parking garagesare thicker and designing them as blocking floors would be an easierand cost-effective train-induced vibration mitigation solution.

The blocking floor is a floor with high impedance that is a com-bination of higher stiffness, damping, and mass properties. Floorsystems such as waffle slabs or composite slabs offer higher bend-ing stiffness that are more efficient for their use as a blocking floor.

9. Conclusions

An impedance-based analytical model was used to simulate thedynamic behavior of a four-story full-scale building and to predictthe floor responses to train-induced vibration. The predictionswere compared to the measured building responses. A floor vibra-tion mitigation methodology was also evaluated using the devel-oped impedance model.

The following conclusions have been made from the findings ofthe research presented in this paper:

1. Train-induced vibrations measured at the base of the test col-umn serve as ground-borne vibration input into the building.The important part of the train-induced vibration spectrumwas found to lie between 30 and 200 Hz with a broad peakaround 50 Hz.

2. Individual column responses to train-induced vibrations werefound to be statistically independent, justifying the use of a sin-gle column analytical model with floor impedances to representthe building.

3. Waffle slab and concrete slab on metal deck floors can be mod-eled based on standard composite floor approaches, in that themeasured accelerance values for the floors agreed well withcomposite model predictions.

4. Impedance-based modeling offers a simple and quick approachfor reasonably accurate prediction of train-induced vibrationwith small computational requirements.

5. Based on the impedance model, blocking floor used at a lowerlevel above ground, has the potential to reduce train-inducedvibration levels on higher floors of the building.

10. Future work

The results from this work form the foundation for future full-scale building investigations. The continuation of this research willinclude the following:

1. Study relationship between open field measurements and mea-surements after construction of the building, both at columnlocations and away from columns on grade slabs.

2. Study vibration prediction on building floors away fromcolumns based on vibration contributions from the surroundingcolumns.

3. Full-scale testing of buildings to study the effectiveness ofblocking floor concept as a floor vibration mitigationmethodology.

4. Development of design guidelines for the prediction andmitigation of building vibrations.

Acknowledgements

The authors would like to thank Jack Haley and his team fromMass Convention Center Authority and Scott J. DiFiore fromSimpson Gumpertz & Heger for providing access to the test build-ing. Sincere thanks to Gladys Unger from Acentech Inc. for lendingvibration measurement and impact test equipment.

The authors would also like to thank former graduate studentsat Tufts University Pradeep Maurya, Jesse Sipple, Ang Li and SagarShetty for their assistance with the test equipment and during fieldtesting.

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