vibration measurement and prediction for foundation slab

Research ArticleVibration Measurement and Prediction for Foundation SlabDesign of a High-Tech Lab Based on In Situ Testing

Zhaogang Xu 12 Yu Lou1 and Liu Chen1

1Beijing Engineering Research Center of Micro-Vibration Environment ControlChina Electronics Engineering Design Institute Co Ltd Beijing 100142 China2School of Civil Engineering Harbin Institute of Technology Harbin 150001 China

Correspondence should be addressed to Zhaogang Xu xuzg2009126com

Received 28 June 2020 Revised 19 September 2020 Accepted 4 October 2020 Published 28 October 2020

Academic Editor )anh-Phong Dao

Copyright copy 2020 Zhaogang Xu et al )is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Reduction of road traffic-induced vibrations has gained importance with rapid development of high-tech industry and nano-technology )is study focuses on the in situ vibration measurement and transmissibility-based vibration prediction for thefoundation slab design of a high-tech lab subjected to truck-induced vibrations )e truck-induced vibrations come from aproposed road 30m away from the high-tech lab)e allowable vertical vibration velocity for the foundation slab of the high-techlab was 60 μms in the frequency range of 5ndash50Hz)e truck-induced ground vibrations in the proximity of an existing road withthe same design as the proposed road were taken as the vibration source response used in the foundation design )e groundvibration transmissibility from the proposed road area to the high-tech lab area was determined by conducting frequency sweeptests in the free field Based on the vibration source response and the ground vibration transmissibility two antivibrationfoundation prototypes with different thicknesses were constructed at the site)e vibration transmissibility from the subgrade soilto the surfaces of the two foundation prototypes was obtained bymeasuring the ground vibrations at the high-tech lab area and thesurface vibrations of the two foundation prototypes )e vertical vibration velocities of the two foundation prototypes werepredicted based on the measured transmissibility and the vibration source response )e final thickness of the antivibrationfoundation was determined by comparing the predicted vibration velocities with the allowable vibration velocity After con-struction of the high-tech lab and the road vibration tests were conducted to assess the performance of the actual antivibrationfoundation)e results showed that the actual antivibration foundation was able to reduce the vibration levels at the high-tech labto acceptable levels

1 Introduction

Technological advances in nanotechnology and high-techindustry require an increase in the precision of high-techequipment ie scanning electron microscopes lithographysteppers coordinate measuring machines Such an increasein precision places a severe requirement on the stability ofhigh-tech facilities in which precision equipment is housedbecause even the slightest vibrations can disturb theequipment operation [1] )erefore environmental vibra-tions induced by human activities should be controlled atlow levels over long periods of time for high-tech facilities inwhich precision equipment is housed [2ndash4] Among thehuman activities of interest (railway and road traffic

construction activities [5] operation of heavy machines [6])road traffic has become a major malfunction factor forprecision equipment in urban areas because the distancesbetween the facilities and roads are decreasing due to spacelimitations [7]

An environmental vibration problem can be divided intothree parts the excitation source that generates vibrationsthe medium that transmits the vibrations and the receiverthat must be protected from the vibrations [8 9] Accord-ingly measures to reduce unwanted vibrations can be ap-plied in the proximity of excitation sources in the vibrationpropagation path and at the buildings that should beprotected In general vibration reduction measures appliedaround or at a close distance from the vibration sources are

HindawiShock and VibrationVolume 2020 Article ID 8892597 12 pageshttpsdoiorg10115520208892597

defined as active measures whereas those surrounding thebuildings that are to be protected are defined as passivemeasures [7 10 11] Literature review shows that activemeasures can significantly reduce the intensity of envi-ronmental vibrations and are more effective than passivemeasures especially in reducing the magnitudes of lowfrequency vibrations [12ndash15] However due to cost prob-lems and the uncertainty of vibration sources passivemeasures are usually preferred to control unwanted vibra-tions at high-tech facilities [16]

Passive measures applied at a high-tech facility usuallyinvolve thickening the foundation slab supporting thefoundation slab with piles or improving the subgrade soilBased on a combined finite-element boundary-elementmethod and a semianalytical method Auersch [17] con-ducted a numerical study on the response of thin flexuralplates resting on an elastic half-space to vibrations generatedby harmonic excitation Auersch concluded that slabthickness was the dominant parameter in controlling thevibration levels Gao et al [18] performed field measurementand finite-element prediction on a high-tech electronicsworkshop to study the reduction effect of a pile-raft foun-dation on floor vibrations )e results demonstrated that thepile-raft foundation averaged the gap between the floorvibrations and the VC-B curve showing an overall positivereduction action on the floor vibrations Sanayei et al [19]verified an analytical prediction model of ground vibrationsby performing vibration tests on a full-scale building with aslab-on-grade foundation )e vibration reduction effects ofslabs with different thicknesses were investigated based onthe prediction model )e conclusion showed that athickened slab can be an effective measure for reducingexternal vibrations Amick et al [20] studied the vibrationreduction efficiency of different slab types via vibrationmeasurements and found that the piled-slab foundationperformed better than the slab-on-grade foundation in re-ducing the vertical vibrations generated by external exci-tation sources Persson et al [8 21] conducted a series ofnumerical studies on reducing building vibrations by subsoilimprovement and found that improving the mechanicalproperties of the subgrade soil had a greater effect oncontrolling the vibration levels in a building for both ex-ternal and internal vibration sources Piles are more im-portant in increasing the bearing capacity of soil but the useof a large cement-soil bulk integrated with a concrete slab isimportant to attenuate vibrations that are generated byexternal and internal vibration sources [22]

An advantage of taking vibration reduction measures ata high-tech facility is that the essential construction space ofthe high-tech facility is to be fully used without the need forextra land Particularly thickening a foundation slab as anantivibration foundation is usually preferred for high-techfacilities [23] Determination of the proper thickness of anantivibration foundation requires estimation of the groundvibration levels at the construction area and the surfacevibration levels of the antivibration foundation Due to thecomplexity of the transmission mechanisms of ground vi-brations in soil and of vibrations between the subgrade soiland the foundation slab in situ vibration measurement

appears to be more reliable in determining the vibrationtransmission characteristics than analytical and numericalmethods However literature that systematically demon-strates the design of antivibration foundation for high-techfacilities based on in situ vibration tests is scarce

)is paper focuses on the antivibration foundation de-sign of a high-tech lab subjected to truck-induced vibrations)e vibration criterion was that the vertical vibration ve-locity at the surface of the antivibration foundation must notexceed 60 μms in the frequency range of 5ndash50Hz )e roadthat the truck-induced vibrations come from is to be con-structed simultaneously with the high-tech lab )e char-acteristics of such an antivibration foundation design arethat the actual vibration source does not exist prior to thefoundation design and the vibration criterion is stringent Toachieve the antivibration foundation design in an eco-nomical and reliable way a general design process wasproposed based on in situ vibration measurement andprediction To obtain the vibration source response used inthe antivibration foundation design the truck-inducedground vibrations in the proximity of an existing road withthe same design as the proposed road were measured at theconstruction site Two antivibration foundation prototypeswith different thicknesses were constructed at the site Todetermine the corresponding vibration transmissibilityfrequency sweep tests were conducted to measure the free-field ground vibrations and the surface vibrations of thefoundation prototypes Based on the vibration transmissi-bility and the vibration source response the vibration ve-locities of the two foundation prototypes were predicted)ethickness of the actual antivibration foundation was de-termined by comparing the predicted velocities and theallowable vibration velocity After construction of the high-tech lab and the road the vibrations generated by the passageof a heavy truck on the road were measured to assess theperformance of the actual antivibration foundation

2 General Design Process

Because the vibration criterion required for high-tech fa-cilities is more stringent than that normally required for civilengineering analysis of the solutions used in similar facilitiesand their achieved performance is fundamental for a newdesign China Electronics Engineering Design Institute CoLtd has been specialized in providing solutions for thevibration control of high-tech facilities over the past sixdecades such as integrated circuit manufacturing work-shops and high energy photon source facility )e engi-neering experience helped to design the antivibrationfoundation for the high-tech facility in a more economicaland reliable way

)e following steps constitute the general design processused in this study

(1) Site investigation was conducted to evaluate theconditions of the local soil at the construction site

(2) )e truck-induced ground vibrations in the prox-imity of an existing road with the same design as the

2 Shock and Vibration

proposed road were measured to determine the vi-bration source response

(3) Frequency sweep vibration tests were conducted inthe free field to determine the transmissibility ofground vibrations transmitted from the proposedroad area to the high-tech lab area

(4) )e ground vibration transmissibility and the vi-bration source response combined with engineeringexperience led to the constructions of a 10m thickand a 07m thick antivibration foundation prototypeat the construction site

(5) To quantify the transmissibility of vibrationstransmitted via the subgrade soil to the surfaces ofthe antivibration foundation prototypes measure-ments were performed on the two foundation pro-totypes based on frequency sweep testing

(6) Based on the vibration source response obtained instep (2) and the vibration transmissibility obtained instep (3) and step (5) the vibration velocities at thesurfaces of the two foundation prototypes werepredicted

(7) )e predicted vibration velocities of the foundationprototypes were compared with the allowable vi-bration velocity to determine the final thickness ofthe actual antivibration foundation

(8) After construction of the high-tech lab and the roadthe surface vibrations of the actual antivibrationfoundation generated by the passage of a heavy truckon the road were measured to assess the performanceof the actual antivibration foundation

)e flowchart of the general design process of theantivibration foundation is shown in Figure 1

3 Case and Site Descriptions

31 Case Description )e plan size of the foundation slab ofthe high-tech lab is 50mtimes 8m (LtimesW) )e main vibrationhazards for the high-tech lab are truck-induced vibrationscoming from an adjacent road that is to be constructedsimultaneously with the lab )e road runs parallel to thelong side of the high-tech lab and has a width of 6m )edistance between the boundaries of the high-tech lab and theroad is 23m as shown in Figure 2

)e speed limit for vehicles on the road is 30 kmh Forproper operation of precision equipment housed in the high-tech lab the peak velocity of the foundation vibrations of thehigh-tech lab in the vertical direction must not exceed60 μms in the frequency range of 5 to 50Hz

32 Site Characteristics )e construction site of the high-tech lab is located in the northeast part of Beijing city China)e physical and dynamic properties of the local soil weredetermined by a series of geotechnical and geophysical testsIn particular Multichannel Analysis of Surface Waves(MASW) tests were conducted to determine the shear wavevelocities of the subgrade soil Standard Penetration Tests

(SPT) were performed to evaluate the compactness of thesoil strata in terms of the numbers of SPT blows (N635) Inaddition the predominant period of the soil deposit wasdetermined by microtremor tests and was found to be ap-proximately 032 s Figure 3 shows the shear wave velocityprofile of the stratified soil

Site investigation showed that the soil profile consists of15m silty clay over 205m sandy gravel with moderate andhigh compactness )e moderately dense sandy gravelconsists of gravel and approximately 35medium sand)ehigh dense sandy gravel consists of gravel and approximately25 medium sand )e ground material under the sandygravel is moderately weathered granodiorite Because thegeological exploration boreholes did not reach to the bottomof the moderately weathered granodiorite its thickness wasunknown )e groundwater table was observed 20m belowthe ground surface Geotechnical parameters and averageN635 values of the soil are given in Figure 4

4 Antivibration Foundation Prototypes

Two round prototypes of the antivibration foundation withdiameters of 8mwere built at the construction site as shownin Figure 5 )e north foundation prototype was 10m thickand the south foundation prototype was 07m thick asshown in Figure 5(a))e distance between the centers of thetwo concrete foundation prototypes was 60m

First the 15m thick silty clay was dug up in the areaswhere the 10m and 07m thick foundation prototypes wereconstructed and 05m and 08m thick sandy gravel backfillwere filled and packed in a layer-by-layer manner (each layerwas 25 cm thick) with a compaction degree of 095 Next a10m thick and a 07m thick concrete foundation prototypewere constructed and cured for 28 days

5 Measurement Program

Since the proposed road is to be constructed simultaneouslywith the high-tech lab the ground vibrations in the prox-imity of a road with the same design at the site were firstmeasured to determine the vibration source response Twoadditional vibration tests were performed in the designprocess to predict the likely surface vibration response of theantivibration foundation After construction of the high-tech lab and the road measurements were conducted toobtain the vibration level at the surface of the designedantivibration foundation exposed to the passage of a heavytruck on the road

51 Test Plan Test 1 was conducted to obtain the vibrationsource response In test 1 the velocities of the ground vi-brations at a location 1m away from the boundary of anexisting road at the construction site were measured andtaken as the vibration source response)e existing road hadthe same design as the proposed road)e ground vibrationswere generated by the passage of an 18-ton truck on theroad as shown in Figure 6)e truck drove on the road fromnorth to south five times with a speed of 30 kmh

Shock and Vibration 3

)e measurement distance for the vibration source re-sponse was determined based on two factors (1) To ensurethat the measured vibration response contains as much realinformation about the vibration source as possible themeasurement distance should be as close to the roadboundary as possible (2) )ere is enough installation spacefor the vibration measurement system In this study 10m isthe most appropriate distance for measuring the vibrationsource response

Because the foundation prototypes and the high-tech labwere constructed at different areas (see Figure 5(a)) test 2

was designed to validate the consistency of the three con-struction areas by measuring and comparing the groundvibration response at test points NP1 SP1 and L1 Test 2 wasnecessary to demonstrate that the three areas show goodconsistency in ground vibrations such that the vibrationtransmissibility between the subgrade soil and the foun-dation prototypes could represent that between the subgradesoil and the actual antivibration foundation In test 2 testpoints NP1 SP1 and L1 were the respective center points of

Site investigation

Measure the truck-induced ground vibrationsin the proximity of an existing road

Measure the free-field ground vibrationsbased on in-situ frequency sweep testing

Determine the vibration source response Determine the ground vibration transmissibilityfrom the proposed road area to the high-tech lab area

Engineering experience

Construct a 10 m thick and a 07 m thick antivibration foundation prototype

Determine the transmissibility of vibrations transmitted viathe subgrade soil to the surfaces of the two foundation prototypes

Predict the vibration velocities at the surfaces of the two antivibration foundation prototypes

Compare the predicted vibration velocities of the two antivibrationfoundation prototypes with the allowable vibration velocity

Determine the final thickness of the antivibration foundation for the high-tech lab

Assess the performance of the actual antivibration foundationafter construction of the high-tech lab and the road

Figure 1 Flowchart of the design process of the antivibration foundation

50 m

23 m

8 m

6 m

High-tech Lab

Building

Concrete road

N

Y

XZ

Figure 2 Layout of the high-tech lab and road

00

2468

101214161820

100 200 300 400 500 600 700 800Shear wave velocity (ms)

Dep

th (m

)

Shear wave velocity

Figure 3 Shear wave velocity profile


the construction areas of the north foundation prototypethe south foundation prototype and the actual antivibrationfoundation As illustrated in Figure 5(a) test points NP1SP1 and L1 had the same distance to the vibration sourcenamely 30m

)e aim of test 3 was to determine the transmissibility offree-field ground vibrations transmitted from the proposedroad area to the high-tech lab area Ground vibrationtransmissibility was determined by measuring and com-paring the ground vibration response at test points S1 and L1

High-tech lab

1m thick northfoundation prototype

Harmonicexcitation

07m thick southfoundation prototype

L1

S1

26 m

26 m26 m8 m 8 m4 m

NP105m thick

Sandy gravel backfill 08 m thickSandy gravel backfill65m thick

Sandy gravel I

15 m thickSilty clay

14 m thickSandy gravel II

SP1

(a)

1 m thick northfoundation prototype

07 m thick southfoundation prototype

(b)

Figure 5 Foundation slab prototypes (a) sketch of the antivibration foundation prototypes (b) aerial photo of the foundation prototypes

15 m

65 m

140 m

Sandy gravel

Sandy gravel

γ = 210 kNm3

γ = 191 kNm3

γ = 221 kNm3

γ = 259 kNm3

Vs = 396 ms

Vs = 571 ms

Vs = 1547 ms

N635ave = 167

N635ave = 248

N635ave = 100

N635ave = 9Vs = 196 msSilty clay

Ground water table

Moderately weatheredgranodiorite

Figure 4 Soil profile of the construction site


in the free field As illustrated in Figure 5(a) test point S1was 4m away from the vibration source and 1m away fromthe boundary of the proposed road Test point L1 was thecenter point of the construction area of the actual anti-vibration foundation)e distance between test point S1 andtest point L1 was 26m

Test 4 was designed to determine the transmissibility ofvibrations transmitted via the subgrade soil to the surfaces ofthe foundation prototypes Vibration transmissibility fromthe subgrade soil to the surfaces of the two foundationprototypes was obtained by measuring the vibration re-sponses at test points NP1 and SP1 and comparing themwith the ground vibration response at test point L1 In test 4test points NP1 SP1 and L1 were the respective centerpoints of the north foundation prototype the south foun-dation prototype and the construction area of the actualantivibration foundation as illustrated in Figure 5(a)

After construction of the high-tech lab and the road test5 was performed to assess the performance of the actualantivibration foundation In test 5 surface vibrations at thecenter point of the actual antivibration foundation generatedby the moving of a heavy truck on the road with a speed of30 kmh were measured as shown in Figure 7 By comparingthe measured vibration responses with the vibration crite-rion the performance of the actual antivibration foundationwas verified It should be noted that test 5 was performed 28days after the antivibration foundation was constructed butbefore the epoxy self-leveling floor was constructed

In the tests that determined the consistency of the threeconstruction areas and the vibration transmissibility anelectromagnetic vibration excitation system was used as avibration source to generate harmonic excitation at fre-quencies varying from 5Hz to 50Hz with steps of 1Hz )eexcitation at each frequency lasted 25 seconds As shown inFigure 8 the excitation system contained four main ele-ments a signal generator a power control cabinet anelectromagnetic exciter and an air-cooled machine

52 Instrumentation and Data Processing )e data acqui-sition system used at a test point mainly contained an ul-tralow frequency vibration sensor (GMS-100HP-T) and one4-channel data acquisition device (INV3062U) to record thevibration velocities in the vertical direction as shown inFigure 9

)e vibration level was evaluated using the peak velocityof the measured velocity time histories )e peak velocitywas obtained from the velocity time histories as

vpeak max|v(t)| (1)

where v(t) is the measured velocity time historiesTo quantify changes in the vibrations transmitted from

one point to the other the transmissibility was used tocalculate the relationship between the vibration levels at twotest points )e transmissibility function represents theoutput-output relationship of a dynamic system as definedbelow

Tij(ω) Xi(ω)

Xj(ω) (2)

where Tij (ω) is the frequency-dependent transmissibilitybetween test points Pi and Pj and Xi (ω) and Xj (ω) are thevibration responses at test points Pi and Pj respectively ω isthe vibration frequency

In this study the ground vibration transmissibility fromthe proposed road area to the high-tech lab area is denotedby TRH

TRH(ω) vH(ω)

vR(ω) (3)

where vR (ω) is the ground vibration velocity at test point S11m away from the boundary of the proposed road vH (ω) isthe ground vibration velocity at the center point L1 of theconstruction area of the high-tech lab vR (ω) and vH (ω)were simultaneously measured in test 3

)e vibration transmissibility from the subgrade soil to afoundation prototype is denoted by TSF

TSF(ω) vF(ω)

vH(ω) (4)

where vF (ω) is the surface vibration velocity at the centerpoint (NP1 or SP1) of a foundation prototype vH (ω) is theground vibration velocity at the center point L1 of theconstruction area of the high-tech lab vF (ω) and vH (ω)were simultaneously measured in test 4

)e velocity time histories vF (t) of a foundation pro-totype were predicted as

vF(t) IFFT FFT vVS(t)( 1113857 middot TRH(ω) middot TSF(ω)( 1113857 (5)

Test point

Figure 6 Measurement of the vibration source response


where vVS(t) is the velocity time histories of the vibrationsource used in the antivibration foundation designmeasuredin test 1 FFT () means to perform fast Fourier transformIFFT () means to perform inverse fast Fourier transform

6 Results and Discussion

61 Vibration Source Response )e 8-second velocity timehistories of the ground vibrations before and after the truckpassed the test location were taken to determine the vi-bration source response used in the antivibration foundationdesign In this study the vibration frequency that was ofinterest was 5Hz to 50Hz )us 5ndash50Hz bandpass filteringwas first performed on the 8-second velocity time historiesas shown in Figure 10 )e results showed that the peak

velocities were notably similar )e mean of the peak ve-locities is 1236 μms for the five truck pass-by events Inaddition the velocity for any one of the five truck pass-byevents peaked at the moment when the truck passed the testlocation )us it is rational to adopt the data around thepeak velocity to design the antivibration foundation

)e consistency of the peak velocities in the time domainof the vibration source responses for the five truck pass-byevents confirmed that the vibration measurement to obtainthe vibration source response by measuring the groundvibrations in the proximity of a road was repeatable)erefore the measured velocity time histories of theground vibrations were reliable for use as the vibrationsource response in the antivibration foundation design ofthe high-tech lab In this study the 1-second data around the

Test point

(a) (b)

Figure 7 Vibration measurement of the designed antivibration foundation (a) high-tech lab (b) passage of a heavy truck on the road

Signal generatorPower control cabinetElectromagnetic exciterAir-cooled machine

(1)(2)(3)(4)

2

3

14

Figure 8 Electromagnetic vibration excitation system

(a) (b)

Figure 9 Data acquisition instruments (a) GMS-100HP-T sensor (b) data acquisition device


peak value of the velocity time histories with the mean peakvelocity (1236 μms) was selected as the vibration sourceresponse as shown in Figure 11(a) To understand thefrequency characteristic of the vibration source response thefast Fourier transform with a frequency resolution of 1Hzwas performed on the selected 1-second velocity time his-tories in Figure 11(a) )e velocity spectrum of the selectedvibration source data is shown in Figure 11(b) )e velocityspectrum of the selected vibration source data was used toguide test 3 and test 4

62 Consistency of the 4ree Construction AreasConsistency verification of the construction areas of thenorth foundation prototype the south foundation proto-type and the actual antivibration foundation was achievedvia test 2 Free-field ground vibrations generated by har-monic excitation at the center points NP1 SP1 and L1 of thethree construction areas were measured simultaneously )evertical velocities of the free-field ground vibrations at thethree construction areas are shown in Figure 12 )e ve-locity-frequency curves of the three construction areas werealmost exactly the same for the free-field ground vibrations)is result demonstrated that the construction areas of thenorth and south foundation prototypes were of good con-sistency with that of the high-tech lab in vibration response

Figure 13 shows the difference in the vertical velocities ofthe three construction areas )e maximum difference in thevelocities between the north and south foundation prototypeareas was 201 μms at 19Hz)emaximum difference in thevelocities between the north foundation prototype and thehigh-tech lab areas was 204 μms at 30Hz )e maximumdifference in the velocities between the south foundationprototype and the high-tech lab areas was 191 μms at 36HzAs was expected the difference in the vertical velocities ofthe three construction areas was small )is is because thethree construction areas are adjacent and the strata from thevibration source to the three areas are relatively uniform

)e results described above confirmed that the vibrationpropagation path was similar for the construction areas ofthe north foundation prototype the south foundationprototype and the high-tech lab and thus the three con-struction areas had good consistency and could be used ascontrol subjects for subsequent tests

63 Transmissibility of Ground Vibrations In determinationof the ground vibration transmissibility via test 3 the ve-locity spectrum of the vibration source response inFigure 11(b) was used to adjust the output energy of theexcitation system to guarantee that the vibration sourceresponse generated by the excitation system was similar tothe truck-induced vibration response Figure 14 shows thevelocity-frequency curves of the vibration source and thehigh-tech lab areas)e transmissibility of ground vibrationstransmitted from the vibration source point S1 to the centerpoint L1 of the high-tech lab area was calculated by equation(3) and is shown in Figure 15

It was observed from Figure 15 that the transmissibilityof ground vibrations transmitted from the proposed roadarea to the high-tech lab area was frequency-dependent Inother words the propagation characteristics of ground vi-brations at different frequencies were different )is em-phasized that it is essential to determine the groundvibration transmissibility via the frequency sweep tests

64 Vibration Transmissibility between the Foundation Pro-totypes and Subgrade Soil In determination of the vibrationtransmissibility via test 4 the velocity spectrum of the vi-bration source response in Figure 11(b) was used to adjustthe output energy of the excitation system to guarantee thatthe vibration source response generated by the excitationsystem was similar to the truck-induced vibration response)e transmissibility between a foundation prototype and thesubgrade soil represents the ability of the foundation

30times103

25

15

ndash15

20

ndash20

10

ndash10

05

ndash0500

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(μm

s v

ertic

al)

Peak velocity 1238 μmsPeak velocity 1236 μmsPeak velocity 1237 μmsPeak velocity 1232 μmsPeak velocity 1235 μms

Figure 10 Velocity time histories of the vibration source


15

41 42 43 44 45403938373635ndash15

10

ndash10

05

ndash05

00

Time (s)

Velo

city

(μm

s v

ertic

al)

Vibration source response

times103

(a)

05 10 15 20 25 30 35 40 45 50

50100150200250300350400450

Frequency (Hz)

Velo

city

ampl

itude

(μm

s v

ertic

al)

Peak velocity 1236 μms

(b)

Figure 11 Vibration source response used in the antivibration foundation design (a) velocity time history (b) velocity spectrum

160

140

120

100

80

60

40

20

0

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

(μm

s v

ertic

al)

North foundation prototype areaSouth foundation prototype areaHigh-tech lab area

Figure 12 Velocity of free-field ground vibrations

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

North-south foundation prototype areasNorth foundation prototype area-lab area

00

05

10

15

20

25

30

South foundation prototype area-lab area

Diff

eren

ce in

velo

city

(μm

s)

Figure 13 Difference in the velocities of free-field ground vibrations


prototype to reduce vibrations transmitted from the soilunderneath

Figure 16 shows the velocity-frequency curves of thesurface vibrations at the center points (NP1 and SP1) of thetwo foundation prototypes and the ground vibrations at thecenter point (L1) of the high-tech lab area )e velocities ofthe surface vibrations of the north foundation prototype with10m thickness were smaller than those of the ground vi-brations at the high-tech lab area in the whole analyzed rangeof frequency implying continued vibration reduction abilityof the north foundation prototype in the whole analyzedrange of frequency However the south foundation prototypewith 07m thickness caused amplification of the vibrations atfrequencies of 8 to 13Hz In addition the velocity-frequencycurves of the north and south foundation prototypes weredifferent implying different frequency response characteris-tics due to their different thicknesses

)e transmissibility between the foundation proto-types and the subgrade soil was calculated by equation (4)and is shown in Figure 17 )e transmissibility of vi-brations transmitted via the subgrade soil to the northfoundation prototype with 10 m thickness was lower

than 1 explaining the continued reduction action of thenorth foundation prototype in the whole analyzed rangeof frequency However the transmissibility of vibrationsat frequencies of 8 to 13 Hz transmitted to the surface ofthe south foundation prototype with 07 m thickness washigher than 1 explaining the amplification effects of thesouth foundation prototype on the vibrations at 8 to13 Hz

65VibrationPrediction forFoundationPrototypes )e timehistories of the vibration velocities of the two foundationprototypes were predicted based on the velocity spectrum ofthe vibration source response in Figure 11(b) the groundvibration transmissibility in Figure 15 and the vibrationtransmissibility from the subgrade soil to the foundationprototypes in Figure 17 as shown in equation (5) )epredicted velocity time histories of the two foundationprototypes are shown in Figure 18 )e peak velocities of thesurface vibrations of the north and south foundation pro-totypes were 475 μms and 605 μms respectively )e peakvelocity of the surface vibrations of the north foundationprototype was smaller than that of the south foundationprototype because the vibration reduction ability of thenorth foundation prototype with 10m thickness wasstronger than that of the south foundation prototype with07m thickness Based on the vibration control criterion of60 μms it was concluded that the final thickness of theactual antivibration foundation should be 1m

66 Vibration Responses of the Actual AntivibrationFoundation After construction of the high-tech lab and theroad vibration tests were conducted to measure the surfacevibrations at the center point of the actual antivibrationfoundation )e 8-second velocity time histories of thesurface vibrations before and after the truck passed by thetest point were recorded Figure 19 shows the 5ndash50Hzbandpass-filtered velocity time histories of the surface vi-brations for five truck pass-by events )e peak velocities

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)

Truck-induced vibration sourceHarmonic vibration sourceHigh-tech lab area

Figure 14 Ground vibrations at the vibration source area and high-tech lab area

000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction

Figure 15 Transmissibility of ground vibrations transmitted fromthe vibration source area to the high-tech lab area


were approximately 38 μms for the five truck pass-byevents smaller than the vibration criterion of 60 μms

)e consistency of the peak velocities of the surfacevibrations of the designed antivibration foundation for thefive truck pass-by events confirmed that vibration mea-surement used to obtain the response of truck-inducedvibrations for the designed antivibration foundation wasrepeatable In other words the measured vibration velocitiesof the designed antivibration foundation were reliable forassessing the performance of the antivibration foundation)e test results showed that the designed antivibrationfoundation for the high-tech lab satisfied the required vi-bration control criterion

7 Conclusions

Road traffic-induced vibration is a potential hazard for high-tech facilities in which precision equipment is housed)ickening the foundation slab is an effective measure tocontrol the unwanted vibrations at a high-tech facility Inthis study the design process of the foundation slab for ahigh-tech lab exposed to truck-induced vibrations wasdiscussed in detail Prediction of the likely surface vibrationlevels of the antivibration foundation of the high-tech labwas achieved using the corresponding vibration transmis-sibility obtained by in situ frequency sweep tests Based onthe results of this case study on the antivibration foundationdesign for a high-tech lab the following conclusions weredrawn

(1) )e measurement process used to obtain the vi-bration source response by measuring the groundvibrations in the proximity of a road was repeatable)e measured responses of the ground vibrationswere reliable for use as the vibration source data inthe antivibration foundation design of high-techfacilities

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)

North foundation prototypeSouth foundation prototypeHigh-tech lab area

60

70

80

50

40

30

20

10

0

Figure 16 Velocities of ground vibrations at the high-tech lab areaand surface vibrations of the foundation prototypes

15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

North foundation prototypeSouth foundation prototype

Figure 17 Transmissibility of vibrations transmitted to thefoundation prototypes from subgrade soil

00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)

ndash80ndash60ndash40ndash20

020406080

100

Time (s)

North foundation prototype South foundation prototype

Figure 18 Predicted velocity time histories of the surface vibra-tions of the two foundation prototypes

0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)

Figure 19 Velocity time histories of the surface vibrations of theactual antivibration foundation


(2) )e transmissibility of ground vibrations transmit-ted from the proposed road area to the high-tech labarea and the transmissibility of vibrations trans-mitted via the subgrade soil to the surfaces of thefoundation prototypes were both frequency-depen-dent )e frequency dependence of vibrationtransmissibility confirmed the necessity of deter-mining the vibration transmissibility by in situfrequency sweep testing

(3) Measurements conducted after construction of thehigh-tech lab and the road showed that the designedantivibration foundation was able to reduce the vi-bration level at the high-tech lab to an acceptablelevel )us the thickened foundation slab furtherproved to be an effective vibration reduction mea-sure for high-tech facilities

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is study was supported by the National Key Research andDevelopment Project of China (2018YFC0705700) )e fi-nancial support is gratefully acknowledged

References

[1] K A Salyards and R J F Iii ldquoReview of generic and man-ufacturer design criteria for vibration-sensitive equipmentrdquoin Proceedings of the IMAC-XXVII Orlando FL USA Feb-ruary 2009

[2] A Guo Y Xu and L Hui ldquoRoad vehicle-induced vibrationcontrol of microelectronics facilitiesrdquo Earthquake Engineeringand Engineering Vibration vol 4 pp 139ndash151 2005

[3] C G Gordon ldquoGeneric criteria for vibration-sensitiveequipmentrdquo in Proceedings of the SPIEmdash4e InternationalSociety for Optical Engineering (Proceedings of SPIE)pp 193ndash5 San Jose CA USA February 1992

[4] H Amick and M Gendreau ldquoConstruction vibrations andtheir impact on vibration-sensitive facilitiesrdquo in Proceedings ofthe Construction Congress VI Orlando FL USA February2000

[5] J Wu L Ma J Shi Y Sun J Ke and DWang ldquoInvestigationof ground vibration of full-stone foundation under dynamiccompactionrdquo Shock and Vibration vol 2019 Article ID2631797 11 pages 2019

[6] Y Tian Q Shu Z Liu and Y Ji ldquoVibration characteristics ofheavy-duty CNC machine tool-foundation systemsrdquo Shockand Vibration vol 2018 Article ID 4693934 12 pages 2018

[7] D Ulgen and O Toygar ldquoScreening effectiveness of open andin-filled wave barriers a full-scale experimental studyrdquoConstruction and Building Materials vol 86 pp 12ndash20 2015

[8] P Persson K Persson and G Sandberg ldquoNumerical study onreducing building vibrations by foundation improvementrdquoEngineering Structures vol 124 pp 361ndash375 2016

[9] A Garinei G Risitano and L Scappaticci ldquoExperimentalevaluation of the efficiency of trenches for the mitigation oftrain-induced vibrationsrdquo Transportation Research Part DTransport and Environment vol 32 pp 303ndash315 2014

[10] F Yarmohammadi R Rafiee-Dehkharghani C Behnia andA J Aref ldquoDesign of wave barriers for mitigation of train-induced vibrations using a coupled genetic-algorithmfinite-element methodologyrdquo Soil Dynamics and Earthquake En-gineering vol 121 pp 262ndash275 2019

[11] E Ccedilelebi S Fırat G Beyhan I Ccedilankaya I Vural andO Kırtel ldquoField experiments on wave propagation and vi-bration isolation by using wave barriersrdquo Soil Dynamics andEarthquake Engineering vol 29 no 5 pp 824ndash833 2009

[12] J T Nelson ldquoRecent developments in ground-borne noiseand vibration controlrdquo Journal of Sound and Vibrationvol 193 no 1 pp 367ndash376 1996

[13] P Jayawardana R Achuhan G H M J S De Silva andD P )ambiratnam ldquoUse of in-filled trenches to screenground vibration due to impact pile driving experimental andnumerical studyrdquo Heliyon vol 4 no 8 Article ID e007262018

[14] L Liang X Li J Yin D Wang W Gao and Z Guo ldquoVi-bration characteristics of damping pad floating slab on thelong-span steel truss cable-stayed bridge in urban rail transitrdquoEngineering Structures vol 191 pp 92ndash103 2019

[15] Z Zeng J Wang H Yin S Shen A A Shuaibu andW Wang ldquoExperimental investigation on the vibration re-duction characteristics of an optimized heavy-haul railwaylow-vibration trackrdquo Shock and Vibration vol 2019 ArticleID 1539564 17 pages 2019

[16] D Ulgen O L Ertugrul and M Y Ozkan ldquoMeasurement ofground borne vibrations for foundation design and vibrationisolation of a high-precision instrumentrdquo Measurementvol 93 pp 385ndash396 2016

[17] L Auersch ldquoResponse to harmonic wave excitation of finite orinfinite elastic plates on a homogeneous or layered half-spacerdquo Computers and Geotechnics vol 51 pp 50ndash59 2013

[18] G Gao J Chen J Yang and Y Meng ldquoField measurementand FE prediction of vibration reduction due to pile-raftfoundation for high-tech workshoprdquo Soil Dynamics andEarthquake Engineering vol 101 pp 264ndash268 2017

[19] M Sanayei P A Kayiparambil J A Moore and C R BrettldquoMeasurement and prediction of train-induced vibrations in afull-scale buildingrdquo Engineering Structures vol 77 pp 119ndash128 2014

[20] H Amick N Wongprasert J Montgomery P Haswell andD Lynch ldquoAn experimental study of vibration attenuationperformance of several on-grade slab configurationsrdquo inProceedings of the SPIE Bellingham WA USA August 2005

[21] P Persson Analysis of Vibrations in High-Tech Facility LundUniversity Lund Sweden 2010

[22] R T Neuenschwander L Liu S R MarquesA R D Rodrigues R M Seraphim andR T Neuenschwander ldquoEngineering challenges of futurelight sourcesrdquo in Proceedings of the 6th International ParticleAccelerator Conference pp 1308ndash1313 Richmond VA USAMay 2015

[23] B R Barben and L M Hanagan Investigation of a Slab onGrade Supporting Sensitive Equipment Springer InternationalPublishing Berlin Germany 2014


defined as active measures whereas those surrounding thebuildings that are to be protected are defined as passivemeasures [7 10 11] Literature review shows that activemeasures can significantly reduce the intensity of envi-ronmental vibrations and are more effective than passivemeasures especially in reducing the magnitudes of lowfrequency vibrations [12ndash15] However due to cost prob-lems and the uncertainty of vibration sources passivemeasures are usually preferred to control unwanted vibra-tions at high-tech facilities [16]

Passive measures applied at a high-tech facility usuallyinvolve thickening the foundation slab supporting thefoundation slab with piles or improving the subgrade soilBased on a combined finite-element boundary-elementmethod and a semianalytical method Auersch [17] con-ducted a numerical study on the response of thin flexuralplates resting on an elastic half-space to vibrations generatedby harmonic excitation Auersch concluded that slabthickness was the dominant parameter in controlling thevibration levels Gao et al [18] performed field measurementand finite-element prediction on a high-tech electronicsworkshop to study the reduction effect of a pile-raft foun-dation on floor vibrations )e results demonstrated that thepile-raft foundation averaged the gap between the floorvibrations and the VC-B curve showing an overall positivereduction action on the floor vibrations Sanayei et al [19]verified an analytical prediction model of ground vibrationsby performing vibration tests on a full-scale building with aslab-on-grade foundation )e vibration reduction effects ofslabs with different thicknesses were investigated based onthe prediction model )e conclusion showed that athickened slab can be an effective measure for reducingexternal vibrations Amick et al [20] studied the vibrationreduction efficiency of different slab types via vibrationmeasurements and found that the piled-slab foundationperformed better than the slab-on-grade foundation in re-ducing the vertical vibrations generated by external exci-tation sources Persson et al [8 21] conducted a series ofnumerical studies on reducing building vibrations by subsoilimprovement and found that improving the mechanicalproperties of the subgrade soil had a greater effect oncontrolling the vibration levels in a building for both ex-ternal and internal vibration sources Piles are more im-portant in increasing the bearing capacity of soil but the useof a large cement-soil bulk integrated with a concrete slab isimportant to attenuate vibrations that are generated byexternal and internal vibration sources [22]

An advantage of taking vibration reduction measures ata high-tech facility is that the essential construction space ofthe high-tech facility is to be fully used without the need forextra land Particularly thickening a foundation slab as anantivibration foundation is usually preferred for high-techfacilities [23] Determination of the proper thickness of anantivibration foundation requires estimation of the groundvibration levels at the construction area and the surfacevibration levels of the antivibration foundation Due to thecomplexity of the transmission mechanisms of ground vi-brations in soil and of vibrations between the subgrade soiland the foundation slab in situ vibration measurement

appears to be more reliable in determining the vibrationtransmission characteristics than analytical and numericalmethods However literature that systematically demon-strates the design of antivibration foundation for high-techfacilities based on in situ vibration tests is scarce

)is paper focuses on the antivibration foundation de-sign of a high-tech lab subjected to truck-induced vibrations)e vibration criterion was that the vertical vibration ve-locity at the surface of the antivibration foundation must notexceed 60 μms in the frequency range of 5ndash50Hz )e roadthat the truck-induced vibrations come from is to be con-structed simultaneously with the high-tech lab )e char-acteristics of such an antivibration foundation design arethat the actual vibration source does not exist prior to thefoundation design and the vibration criterion is stringent Toachieve the antivibration foundation design in an eco-nomical and reliable way a general design process wasproposed based on in situ vibration measurement andprediction To obtain the vibration source response used inthe antivibration foundation design the truck-inducedground vibrations in the proximity of an existing road withthe same design as the proposed road were measured at theconstruction site Two antivibration foundation prototypeswith different thicknesses were constructed at the site Todetermine the corresponding vibration transmissibilityfrequency sweep tests were conducted to measure the free-field ground vibrations and the surface vibrations of thefoundation prototypes Based on the vibration transmissi-bility and the vibration source response the vibration ve-locities of the two foundation prototypes were predicted)ethickness of the actual antivibration foundation was de-termined by comparing the predicted velocities and theallowable vibration velocity After construction of the high-tech lab and the road the vibrations generated by the passageof a heavy truck on the road were measured to assess theperformance of the actual antivibration foundation

2 General Design Process

Because the vibration criterion required for high-tech fa-cilities is more stringent than that normally required for civilengineering analysis of the solutions used in similar facilitiesand their achieved performance is fundamental for a newdesign China Electronics Engineering Design Institute CoLtd has been specialized in providing solutions for thevibration control of high-tech facilities over the past sixdecades such as integrated circuit manufacturing work-shops and high energy photon source facility )e engi-neering experience helped to design the antivibrationfoundation for the high-tech facility in a more economicaland reliable way

)e following steps constitute the general design processused in this study

(1) Site investigation was conducted to evaluate theconditions of the local soil at the construction site

(2) )e truck-induced ground vibrations in the prox-imity of an existing road with the same design as the


























Site investigation












50 m

23 m

8 m

6 m

High-tech Lab

Building

Concrete road

N

Y

XZ


00

2468

101214161820


Dep

th (m

)

Shear wave velocity





High-tech lab


Harmonicexcitation


L1

S1

26 m

26 m26 m8 m 8 m4 m

NP105m thick


Sandy gravel I



SP1

(a)



(b)


15 m

65 m

140 m

Sandy gravel

Sandy gravel

γ = 210 kNm3

γ = 191 kNm3

γ = 221 kNm3

γ = 259 kNm3

Vs = 396 ms

Vs = 571 ms

Vs = 1547 ms

N635ave = 167

N635ave = 248

N635ave = 100


Ground water table










vpeak max|v(t)| (1)



Tij(ω) Xi(ω)

Xj(ω) (2)



TRH(ω) vH(ω)

vR(ω) (3)



TSF(ω) vF(ω)

vH(ω) (4)




Test point








Test point

(a) (b)



(1)(2)(3)(4)

2

3

14


(a) (b)










30times103

25

15

ndash15

20

ndash20

10

ndash10

05

ndash0500

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(μm

s v

ertic

al)




15

41 42 43 44 45403938373635ndash15

10

ndash10

05

ndash05

00

Time (s)

Velo

city

(μm

s v

ertic

al)


times103

(a)

05 10 15 20 25 30 35 40 45 50

50100150200250300350400450

Frequency (Hz)

Velo

city

ampl

itude

(μm

s v

ertic

al)


(b)


160

140

120

100

80

60

40

20

0

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

(μm

s v

ertic

al)



Frequency (Hz)5 10 15 20 25 30 35 40 45 50


00

05

10

15

20

25

30


Diff

eren

ce in

velo

city

(μm

s)









5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)



000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction





7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References

















































Site investigation












50 m

23 m

8 m

6 m

High-tech Lab

Building

Concrete road

N

Y

XZ


00

2468

101214161820


Dep

th (m

)

Shear wave velocity





High-tech lab


Harmonicexcitation


L1

S1

26 m

26 m26 m8 m 8 m4 m

NP105m thick


Sandy gravel I



SP1

(a)



(b)


15 m

65 m

140 m

Sandy gravel

Sandy gravel

γ = 210 kNm3

γ = 191 kNm3

γ = 221 kNm3

γ = 259 kNm3

Vs = 396 ms

Vs = 571 ms

Vs = 1547 ms

N635ave = 167

N635ave = 248

N635ave = 100


Ground water table










vpeak max|v(t)| (1)



Tij(ω) Xi(ω)

Xj(ω) (2)



TRH(ω) vH(ω)

vR(ω) (3)



TSF(ω) vF(ω)

vH(ω) (4)




Test point








Test point

(a) (b)



(1)(2)(3)(4)

2

3

14


(a) (b)










30times103

25

15

ndash15

20

ndash20

10

ndash10

05

ndash0500

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(μm

s v

ertic

al)




15

41 42 43 44 45403938373635ndash15

10

ndash10

05

ndash05

00

Time (s)

Velo

city

(μm

s v

ertic

al)


times103

(a)

05 10 15 20 25 30 35 40 45 50

50100150200250300350400450

Frequency (Hz)

Velo

city

ampl

itude

(μm

s v

ertic

al)


(b)


160

140

120

100

80

60

40

20

0

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

(μm

s v

ertic

al)



Frequency (Hz)5 10 15 20 25 30 35 40 45 50


00

05

10

15

20

25

30


Diff

eren

ce in

velo

city

(μm

s)









5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)



000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction





7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References



























High-tech lab


Harmonicexcitation


L1

S1

26 m

26 m26 m8 m 8 m4 m

NP105m thick


Sandy gravel I



SP1

(a)



(b)


15 m

65 m

140 m

Sandy gravel

Sandy gravel

γ = 210 kNm3

γ = 191 kNm3

γ = 221 kNm3

γ = 259 kNm3

Vs = 396 ms

Vs = 571 ms

Vs = 1547 ms

N635ave = 167

N635ave = 248

N635ave = 100


Ground water table










vpeak max|v(t)| (1)



Tij(ω) Xi(ω)

Xj(ω) (2)



TRH(ω) vH(ω)

vR(ω) (3)



TSF(ω) vF(ω)

vH(ω) (4)




Test point








Test point

(a) (b)



(1)(2)(3)(4)

2

3

14


(a) (b)










30times103

25

15

ndash15

20

ndash20

10

ndash10

05

ndash0500

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(μm

s v

ertic

al)




15

41 42 43 44 45403938373635ndash15

10

ndash10

05

ndash05

00

Time (s)

Velo

city

(μm

s v

ertic

al)


times103

(a)

05 10 15 20 25 30 35 40 45 50

50100150200250300350400450

Frequency (Hz)

Velo

city

ampl

itude

(μm

s v

ertic

al)


(b)


160

140

120

100

80

60

40

20

0

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

(μm

s v

ertic

al)



Frequency (Hz)5 10 15 20 25 30 35 40 45 50


00

05

10

15

20

25

30


Diff

eren

ce in

velo

city

(μm

s)









5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)



000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction





7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References































vpeak max|v(t)| (1)



Tij(ω) Xi(ω)

Xj(ω) (2)



TRH(ω) vH(ω)

vR(ω) (3)



TSF(ω) vF(ω)

vH(ω) (4)




Test point








Test point

(a) (b)



(1)(2)(3)(4)

2

3

14


(a) (b)










30times103

25

15

ndash15

20

ndash20

10

ndash10

05

ndash0500

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(μm

s v

ertic

al)




15

41 42 43 44 45403938373635ndash15

10

ndash10

05

ndash05

00

Time (s)

Velo

city

(μm

s v

ertic

al)


times103

(a)

05 10 15 20 25 30 35 40 45 50

50100150200250300350400450

Frequency (Hz)

Velo

city

ampl

itude

(μm

s v

ertic

al)


(b)


160

140

120

100

80

60

40

20

0

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

(μm

s v

ertic

al)



Frequency (Hz)5 10 15 20 25 30 35 40 45 50


00

05

10

15

20

25

30


Diff

eren

ce in

velo

city

(μm

s)









5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)



000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction





7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References






























Test point

(a) (b)



(1)(2)(3)(4)

2

3

14


(a) (b)










30times103

25

15

ndash15

20

ndash20

10

ndash10

05

ndash0500

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(μm

s v

ertic

al)




15

41 42 43 44 45403938373635ndash15

10

ndash10

05

ndash05

00

Time (s)

Velo

city

(μm

s v

ertic

al)


times103

(a)

05 10 15 20 25 30 35 40 45 50

50100150200250300350400450

Frequency (Hz)

Velo

city

ampl

itude

(μm

s v

ertic

al)


(b)


160

140

120

100

80

60

40

20

0

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

(μm

s v

ertic

al)



Frequency (Hz)5 10 15 20 25 30 35 40 45 50


00

05

10

15

20

25

30


Diff

eren

ce in

velo

city

(μm

s)









5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)



000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction





7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References
































30times103

25

15

ndash15

20

ndash20

10

ndash10

05

ndash0500

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(μm

s v

ertic

al)




15

41 42 43 44 45403938373635ndash15

10

ndash10

05

ndash05

00

Time (s)

Velo

city

(μm

s v

ertic

al)


times103

(a)

05 10 15 20 25 30 35 40 45 50

50100150200250300350400450

Frequency (Hz)

Velo

city

ampl

itude

(μm

s v

ertic

al)


(b)


160

140

120

100

80

60

40

20

0

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

(μm

s v

ertic

al)



Frequency (Hz)5 10 15 20 25 30 35 40 45 50


00

05

10

15

20

25

30


Diff

eren

ce in

velo

city

(μm

s)









5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)



000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction





7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References

























15

41 42 43 44 45403938373635ndash15

10

ndash10

05

ndash05

00

Time (s)

Velo

city

(μm

s v

ertic

al)


times103

(a)

05 10 15 20 25 30 35 40 45 50

50100150200250300350400450

Frequency (Hz)

Velo

city

ampl

itude

(μm

s v

ertic

al)


(b)


160

140

120

100

80

60

40

20

0

Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

(μm

s v

ertic

al)



Frequency (Hz)5 10 15 20 25 30 35 40 45 50


00

05

10

15

20

25

30


Diff

eren

ce in

velo

city

(μm

s)









5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)



000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction





7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References































5 10 15 20 25 30 35 40 45 50Frequency (Hz)

0

100

200

300

400

500

600

Velo

city

ampl

itude

(μm

s v

ertic

al)



000

005

010

015

020

025

030

5 10 15 20 25 30 35 40 45 50Frequency (Hz)

Tran

smiss

ibili

ty o

f gro

und

vibr

atio

ns

Vertical direction





7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References



























7 Conclusions



Frequency (Hz)5 10 15 20 25 30 35 40 45 50

Velo

city

ampl

itude

(μm

s v

ertic

al)


60

70

80

50

40

30

20

10

0


15

12

09

03

06

00

Vibr

atio

n tr

ansm

issib

ility

Frequency (Hz)5 10 15 20 25 30 35 40 45 50



00 01 02 03 04 05 06 1007 08 09

Velo

city

(μm

s v

ertic

al)


020406080

100

Time (s)



0 1 2 3 4 5 6 7 8Time (s)


100

ndash40

120

20

ndash60

80

ndash20

60

0

40

Velo

city

(μm

s v

ertic

al)





Data Availability




Acknowledgments


References



























Data Availability




Acknowledgments


References

























vibration measurement and prediction for foundation slab

Documents