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BSEN12504-4:2021
BSIStandardsPublication
Testingconcreteinstructures
Part4:Determinationofultrasonicpulsevelocity
bsi.
BSEN12504-4:2021BRITISHSTANDARD
Nationalforeword
ThisBritishStandardistheUKimplementationofEN12504-4:2021.ItsupersedesBSEN12504-4:2004,whichiswithdrawn.
TheUKparticipationinitspreparationwasentrustedtoTechnicalCommitteeB/517/1,Concreteproductionandtesting.
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◎TheBritishStandardsInstitution2021
PublishedbyBSIStandardsLimited2021
ISBN9780539053500
ICS91.100.30
CompliancewithaBritishStandardcannotconferimmunityfromlegalobligations.
ThisBritishStandardwaspublishedundertheauthorityofthe
StandardsPolicyandStrategyCommitteeon31July2021.
Amendments/corrigendaissuedsincepublication
DateTextaffected
EUROPEANSTANDARD
NORMEEUROPEENNE
EUROP?ISCHENORM
EN12504-4
July2021
ICS91.100.30SupersedesEN12504-4:2004
EnglishVersion
Testingconcreteinstructures-Part4:Determinationofultrasonicpulsevelocity
Essaispourbétondanslesstructures
-Partie4:Déterminationdelavitessedepropagationdesultrasons
PrüfungvonBetoninBauwerken-Teil4:
BestimmungderUltraschall-Impulsgeschwindigkeit
ThisEuropeanStandardwasapprovedbyCENon30May2021.
CENmembersareboundtocomplywiththeCEN/CENELECInternalRegulationswhichstipulatetheconditionsforgivingthisEuropeanStandardthestatusofanationalstandardwithoutanyalteration.Up-to-datelistsandbibliographical
referencesconcerningsuchnationalstandardsmaybeobtainedonapplicationtotheCEN-CENELECManagementCentreortoanyCENmember.
ThisEuropeanStandardexistsinthreeofficialversions(English,French,German).Aversioninanyotherlanguage
madebytranslationundertheresponsibilityofaCENmemberintoitsownlanguageandnotifiedtotheCEN-CENELECManagementCentrehasthesamestatusastheofficialversions.
CENmembersarethenationalstandardsbodiesofAustria,Belgium,Bulgaria,Croatia,Cyprus,CzechRepublic,Denmark,Estonia,Finland,France,Germany,Greece,Hungary,Iceland,Ireland,Italy,Latvia,Lithuania,Luxembourg,Malta,
Netherlands,Norway,Poland,Portugal,RepublicofNorthMacedonia,Romania,Serbia,Slovakia,Slovenia,Spain,Sweden,Switzerland,TurkeyandUnitedKingdom.
EUROPEANCOMMITTEEFORSTANDARDIZATIONCOMITEEUROPEENDENORMALISATION
EUROP?ISCHESKOMITEEFURNORMUNG
CEN-CENELECManagementCentre:RuedelaScience23,B-1040Brussels
◎2021CENAllrightsofexploitationinanyformandbyanymeansreservedRef.No.EN12504-4:2021:E
worldwideforCENnationalMembers
2
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ContentsPage
Europeanforeword iii
1Scope 4
2Normativereferencess 4
3Termsanddefinitions 4
4Principle 4
5Apparatus 4
5.1General 4
5.2Performancerequirements 5
5.3Transducers 5
6Procedures 5
6.1Determinationofpulsevelocity 5
6.1.1Factorsinfluencingpulsevelocitydetermination 5
6.1.2Transducerarrangement 5
6.1.3Pathlengthmeasurement 6
6.1.4Couplingthetransducersontotheconcrete 7
6.1.5Measurementoftransittime 7
7Expressionofresult 7
8Testreport 8
9Precision 8
AnnexA(informative)Determinationofpulsevelocity-indirecttransmission 9
AnnexB(informative)Factorsinfluencingpulsevelocitydetermination 11
AnnexC(informative)Correlationofpulsevelocityandcompressivestrength 14
Bibliography 16
iii
BSEN12504-4:2021
EN12504-4:2021(E)
Europeanforeword
Thisdocument(EN12504-4:2021)hasbeenpreparedbyTechnicalCommitteeCEN/TC104"Concreteandrelatedproducts",thesecretariatofwhichisheldbySN.
ThisEuropeanStandardshallbegiventhestatusofanationalstandard,eitherbypublicationofanidenticaltextorbyendorsement,atthelatestbyJanuary2022,andconflictingnationalstandardsshallbewithdrawnatthelatestbyJanuary2022.
Attentionisdrawntothepossibilitythatsomeoftheelementsofthisdocumentmaybethesubjectofpatentrights.CENshallnotbeheldresponsibleforidentifyinganyorallsuchpatentrights.
ThisdocumentsupersedesEN12504-4:2004.
Incomparisonwiththepreviousedition,thefollowingchangeshavebeenmade:
-optiontouseequipmentutilizingtransversewaves.
Thisdocumentisoneofaseriesontestingconcrete.
EN12504,Testingconcreteinstructures,consistsofthefollowingparts:
一Part1:Coredspecimens—Taking,examiningandtestingincompression;
一Part2:Non-destructivetesting—Determinationofreboundnumber;
一Part3:Determinationofpull-outforce;
一Part4:Determinationofultrasonicpulsevelocity.
ThisdocumentisbasedontheInternationalStandardISO1920-7,Testingofconcrete-Part7:Non-destructivetestsonhardenedconcrete.Itisrecognizedthattheultrasonicpulsevelocitydeterminedusingthisdocumentisaconventioninasmuchthatthepathlengthoverwhichthepulsetravelsisnotalwaysstrictlyknown.
Themeasurementofpulsevelocitycanbeusedforthedeterminationoftheuniformityofconcrete,thepresenceofcracksorvoids,changesinpropertieswithtimeandinthedeterminationofdynamicphysicalproperties.Thesesubjectswereconsideredtobeoutsidethescopeofthisdocument,butsomeinformationisgiveninAnnexBandmoreinformationcanbefoundinthetechnicalliterature.ThemeasurementcanalsobeusedtoestimatethestrengthofinsituconcreteelementsorspecimensgiveninEN13791,Assessmentofinsitucompressivestrengthinstructuresandprecastconcretecomponents.However,itisnotintendedasanalternativetothedirectmeasurementofthecompressivestrengthofconcrete.
Anyfeedbackandquestionsonthisdocumentshouldbedirectedtotheusers'nationalstandardsbody.AcompletelistingofthesebodiescanbefoundontheCENwebsite
AccordingtotheCEN-CENELECInternalRegulations,thenationalstandardsorganisationsofthefollowingcountriesareboundtoimplementthisEuropeanStandard:Austria,Belgium,Bulgaria,Croatia,Cyprus,CzechRepublic,Denmark,Estonia,Finland,France,Germany,Greece,Hungary,Iceland,Ireland,Italy,Latvia,Lithuania,Luxembourg,Malta,Netherlands,Norway,Poland,Portugal,Republic
ofNorthMacedonia,Romania,Serbia,Slovakia,Slovenia,Spain,Sweden,Switzerland,TurkeyandtheUnitedKingdom.
4
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1Scope
Thisdocumentspecifiesamethodforthedeterminationofthevelocityofpropagationofpulsesofultrasoniclongitudinalwavesorultrasonictransversewavesinhardenedconcrete,whichisusedforanumberofapplications.
2Normativereferences
Thefollowingdocumentsarereferredtointhetextinsuchawaythatsomeoralloftheircontentconstitutesrequirementsofthisdocument.Fordatedreferences,onlytheeditioncitedapplies.Forundatedreferences,thelatesteditionofthereferenceddocument(includinganyamendments)applies.
EN206,Concrete-Specification,performance,productionandconformity
3Termsanddefinitions
Forthepurposesofthisdocument,thetermsanddefinitionsgiveninEN206andthefollowingapply.ISOandIECmaintainterminologicaldatabasesforuseinstandardizationatthefollowingaddresses:
—IECElectropedia:availableat
/
—ISOOnlinebrowsingplatform:availableat
/obp
3.1
transittime
timetakenforanultrasonicpulsetotravelfromthetransmittingtransducertothereceivingtransducer,passingthroughtheinterposedconcrete
NOTETransittimeisreferredtoastimeofflightinENISO5577.
3.2
onset
leadingedgeofthepulsedetectedbythemeasuringapparatus
3.3
risetime
timefortheleadingedgeofthefirstpulsetorisefrom10%to90%ofitsmaximumamplitude
4Principle
Apulseoflongitudinalortransversevibrationsisproducedbyanultrasonictransducerheldincontactwithonesurfaceoftheconcreteundertest.Aftertraversingaknownpathlengthintheconcrete,thepulseofvibrationsisconvertedintoanelectricalsignalbyasecondultrasonictransducerandanelectronictimingdeviceenablesthetransittimeofthepulsetobemeasured.
5Apparatus
5.1General
Theultrasonictestequipmentconsistsofanelectricalpulsegenerator,apairoftransducers,anamplifierandanelectronictimingdeviceformeasuringthetimeintervalelapsingbetweentheonsetofapulsegeneratedatthetransmittingtransducerandtheonsetofitsarrivalatthereceivingtransducer.
Areferencebarorprismisusedtozerotheinstrumentortoprovideadatumforthevelocitymeasurement.
NOTE1Thisistypicallynecessarywhentheuserchangesthelengthofthecablesbeingused.
BSEN12504-4:2021
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EN12504-4:2021(E)
Threeformsoftheelectronictimingdevicesareavailable:
a)anoscilloscopeonwhichthefirstfrontofthepulseisdisplayedinrelationtoasuitabletimescale;
b)anintervaltimerwithadirectreadingdigitaldisplay;
c)anA-scandisplaybuiltdirectlyintotheinstrument.
NOTE2AnoscilloscopeorintegratedA-scandisplayprovidesthefacilityformonitoringthewaveformofthepulse,whichcanbeadvantageousincomplextestingsituationsorinautomaticsystemmeasurements.
5.2Performancerequirements
Theultrasonictestequipmentshallconformtothefollowingperformancerequirements:
-Itshallbecapableofmeasuringtransittimesinthereferencebarorprismtoalimitdeviationof±0,1μs.
-Theelectronicexcitationpulseappliedtothetransmittingtransducershallhavearisetimeofnotgreaterthanone-quarterofitsnaturalperiod.Thisistoensureasharppulseonset.
-Thepulserepetitionfrequencyshallbelowenoughtoensurethattheonsetofthereceivedsignalisfreefrominterferencebyreverberations.
Theultrasonictestequipmentshallbecapableofdeterminingthetransittimeofthefirstfrontofthepulsewiththelowestpossiblethreshold,eventhoughthismaybeofsmallamplitudecomparedwiththatofthefirsthalfwaveofthepulse.
Theultrasonictestequipmentshallbeusedwithintheoperatingconditionsstatedbythemanufacturer.
5.3Transducers
Thenaturalfrequencyofthetransducersshouldnormallybewithintherange20kHzto150kHz.
NOTEForlongitudinalwaves,frequenciesaslowas10kHzandashighas200kHzcansometimesbeused.Highfrequencypulseshaveawelldefinedonset,but,astheypassthroughtheconcrete,theybecomeattenuatedmorerapidlythanpulsesoflowerfrequency.Itis,therefore,preferabletousehighfrequencytransducers(60kHzto200kHz)forshortpathlengths(downto50mm)andlowfrequencytransducers(10kHzto40kHz)forlongpathlengths(uptoamaximumof15m).Transducerswithafrequencyof40kHzto60kHzarefoundtobeusefulformostapplications.Forultrasonicpulse-echomeasurementsusingtransversewavesthetransducerwithafrequencyof40kHzto60kHzisalsotypical,butinthiscasethepathlengthislimitedtoamaximumofapproximately2,5m.
6Procedures
6.1Determinationofpulsevelocity
6.1.1Factorsinfluencingpulsevelocitydetermination
Inordertoprovideadeterminationofpulsevelocity,whichisreproducible,itisnecessarytotakeintoaccountvariousfactorswhichcaninfluencethemeasurements.ThesearesetoutinAnnexB.
6.1.2Transducerarrangement
Althoughthedirectioninwhichthemaximumenergyispropagatedisatrightanglestothefaceofthetransmittingtransducer,itispossibletodetectpulseswhichhavetravelledthroughtheconcreteinsomeotherdirection.Itisthereforepossibletomakemeasurementsofpulsevelocitybyplacingthetwotransducersonoppositefaces(directtransmission),oronadjacentfaces(semi-directtransmission),orthesameface(indirectorsurfacetransmission;pulse-echotransmission)(seeFigure1)ofaconcrete
6
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structureorspecimen.Inthecaseofpulse-echotransmission,thereceiverdetectspulseswhichhavetravelledthroughtheconcretetotheoppositesurfaceandhavebeenreflectedbacktothefirstsurface.Whereitisnecessarytoplacethetransducersonoppositesurfacesbutnotdirectlyoppositeeachothersucharrangementshallberegardedasasemi-directtransmission(seeFigure1b).
NOTE1Theindirecttransmissionarrangementistheleastsensitiveandisusedwhenonlyonefaceoftheconcreteisaccessibleorwhenthequalityofthesurfaceconcreterelativetotheoverallqualityisofinterest.
NOTE2Thesemi-directtransmissionarrangementisusedwhenthedirectarrangementcannotbeused,forexampleatthecornersofstructures.
NOTE3Pulse-echotransmissionisanalternativetoindirecttransmissionwhenonlyonefaceoftheconcreteisaccessible.Thesensitivityiscomparablewithdirecttransmission.
a)
b)
c)
a)Directtransmissionb)Semi-directtransmissionc)Pulse-echotransmissionKey
Risthereceivertransducer
Tisthetransmittertransducer
Figure1—Transducerpositioning
6.1.3Pathlengthmeasurement
Fordirecttransmission,thepathlengthistheshortestdistancebetweenthetransducers.Themeasurementofthepathlengthshallberecordedtothenearest1%ofthemeasureddistance.
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Forsemi-directtransmission,itisgenerallyfoundtobesufficientlyaccuratetotakethepathlengthasthedistancemeasuredfromcentretocentreofthetransducerfaces.Theaccuracyofpathlengthisdependentuponthesizeofthetransducercomparedwiththecentretocentredistance.
Withindirecttransmission,thepathlengthisnotmeasured,butaseriesofmeasurementsismadewiththetransducersatdifferentdistancesapart(seeAnnexA).
Forpulse-echotransmission,thepathlengthistwotimesthedistancefromthesurfacewherethetransducerisplacedandtheoppositesurface.Thepathlengthshallberecordedasfordirecttransmission.
6.1.4Couplingthetransducersontotheconcrete
Thereshallbeadequateacousticalcouplingbetweentheconcreteandthefaceofeachtransducer.Formanyconcretesurfaces,thefinishissufficientlysmoothtoensuregoodacousticalcontactbytheuseofacouplingmediumsuchaspetroleumjelly,grease,softsoapandkaolin/glycerolpasteandbypressingthetransduceragainsttheconcretesurface.
Repeatedreadingsofthetransittimeshouldbemadeuntilaminimumvalueisobtained,indicatingthatthethicknessofthecouplanthasbeenreducedtoaminimum.
Whentheconcretesurfaceisveryroughanduneven,theareaofthesurfaceshouldbesmoothedandlevelledbygrinding,orbytheuseofaquick-settingepoxyresin.
NOTE1Specialtransducersareavailableforuseonveryroughsurfaces.
NOTE2Pulse-echotransducerscanutilizedrypointcontactelementswhichdonotrequireacouplant.Inthiscase,itistypicalforseveraltransducerelementstobeconnectedinparalleltoprovidesufficientsignalstrength.
6.1.5Measurementoftransittime
Usingtheultrasonictestequipmentthetransittimeshallbedeterminedinaccordancewiththemanufacturer'sinstruction(see5.2).
7Expressionofresult
Fordirect,semi-directandpulse-echotransmissionsthepulsevelocityshallbecalculatedfromtheformula:
where
Visthepulsevelocity,inkm/s;
Listhepathlength,inmm;Tisthetransittime,inμs.
Forthevelocitybyindirecttransmission,seeAnnexA.
Theresultantdeterminationofthepulsevelocityshallbeexpressedtothenearest10m/s
8
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8Testreport
Thetestreportshallincludethefollowing:
-areferencetothisdocument,includingitsyearofpublication;—identificationoftheconcretestructureorspecimenstested;
-locationofperformanceofthetest;
-dateofthetest;
-descriptionoftheconcreteincludingmixproportions(ifknown);
-ageofconcrete,attimeoftest(ifknown);
-temperatureoftheconcrete,attimeoftest(whenappropriate,seeB.3);—typeandmakeofapparatusused,including:
一dimensionsofcontactareatransducers;
-naturalpulsefrequencyoftransducers;
-anyspecialcharacteristics;
—transducerarrangementsandtransmissionmethod(sketch,whenappropriate);
-detailsofreinforcingsteelorductsinthevicinityofthetestareas(ifknown);
-surfaceconditionsandpreparationattestpoints;
-measuredvaluesofpathlength,(fordirect,semi-directandpulse-echotransmission)includingthemethodofmeasurement;
-calculatedvaluesofpulsevelocityalongeachpath;
-adeclarationbythepersontechnicallyresponsibleforthetest,thatitwascarriedoutinaccordancewiththisdocument;
-anydeviationfromthemethodssetoutinthedocument.
9Precision
Therearenoprecisiondataavailableforthistest.
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AnnexA
(informative)
Determinationofpulsevelocity-indirecttransmission
A.1Withindirecttransmissionthereissomeuncertaintyregardingtheexactlengthofthetransmissionpathbecauseofthesignificantsizeoftheareasofcontactbetweenthetransducersandtheconcrete.Itis,therefore,preferabletomakeaseriesofmeasurementswiththetransducersatdifferentdistancesaparttoeliminatethisuncertainty.
A.2Todothis,thetransmittingtransducershallbeplacedincontactwiththeconcretesurfaceatafixedpointxandthereceivingtransducershallbeplacedatfixedincrementsxnalongachosenlineonthesurface.Thetransmissiontimesrecordedshouldbeplottedaspointsonagraphshowingtheirrelationtothedistanceseparatingthetransducers.AnexampleofsuchaplotisshowninFigureA.1.
A.3Theslopeofthebeststraightlinedrawnthroughthepoints(1/tan?)shallbemeasuredandrecordedasthemeanpulsevelocityalongthechosenlineontheconcretesurface.Wherethepointsmeasuredandrecordedinthiswayindicateadiscontinuity,itislikelythatasurfacecrackorsurfacelayerofinferiorqualityispresent(seeB.Z)andavelocitymeasuredinsuchaninstanceinunreliable.
Risthereceivertransducer
Tisthetransmittertransducerttransittime
BSEN12504-4:2021
EN12504-4:2021(E)
10
Xidistancebetweentrasnmitterandreceivertransducers中angleofslope
xdistancefromtransmittertransducer
FigureA.1-Exampleofthedeterminationofpulsevelocitybyindirect(surface)transmission
11
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AnnexB
(informative)
Factorsinfluencingpulsevelocitydetermination
B.1General
Inordertoprovideadeterminationofpulsevelocitywhichisreproducibleandwhichdependsessentiallyonthepropertiesoftheconcreteundertest,itisnecessarytoconsiderthevariousfactorswhichcaninfluencepulsevelocityanditscorrelationwithvariousphysicalpropertiesoftheconcrete.
B.2Moisturecontent
Themoisturecontenthastwoeffectsonthepulsevelocity,onechemical,andtheotherphysical.Theseeffectsareimportantintheproductionofcorrelationsfortheestimationofconcretestrength.Betweenaproperlycuredstandardcubicalorcylindricalspecimenandastructuralelementmadefromthesameconcrete,therecanbeasignificantpulsevelocitydifference.Muchofthedifferenceisaccountedforbytheeffectofdifferentcuringconditionsonthehydrationofthecement,whilesomeofthedifferenceisduetothepresenceoffreewaterinthevoids.Itisimportantthattheseeffectsarecarefullyconsideredwhenestimatingconcretestrength(seeAnnexC).
B.3Temperatureoftheconcrete
Variationsoftheconcretetemperaturebetween10℃and30℃havebeenfoundtocausenosignificantchangeofvelocitieswithouttheoccurrenceofcorrespondingchangesinstrengthorelasticproperties.Correctionstopulsevelocityvaluesshouldbemadeonlyfortemperaturesoutsidethisrangeusingguidanceintherelevantliterature.
B.4Pathlength
Thepathlengthoverwhichthepulsevelocityisdeterminedshouldbelongenoughnottobesignificantlyinfluencedbytheheterogeneousnatureoftheconcrete.Itisrecommendedthat,exceptfortheconditionsstatedinB.5,theminimumpathlengthshouldbe100mmforconcreteinwhichthenominalmaximumsizeofaggregateis20mmorlessand150mmforconcreteinwhichthenominalmaximumsizeofaggregateisbetween20mmand40mm.Thepulsevelocityisnotgenerallyinfluencedbychangesinpathlength,althoughtheultrasonictestequipmentcanindicateatendencyforvelocitytoreduceslightlywithincreasingpathlength.Thisisbecausethehigherfrequencycomponentsofthepulseareattenuatedmorethanthatlowerfrequencycomponentsandtheshapeoftheonsetofthepulsebecomesmoreroundedwithincreaseddistancetravelled.Thus,theapparentreductionofpulsevelocityarisesfromthedifficultyofdefiningexactlytheonsetofthepulseandthisdependsontheparticularmethodusedforitsdetermination.Thisapparentreductioninvelocityisusuallysmallandwellwithinthetoleranceoftransittimemeasurementaccuracygivenin5.2,butparticularcareneedstobetakenwhentransmittingoverlongpathlengths.
B.5Shapeandsizeofspecimen
Thevelocityofshortpulsesofvibrationsisindependentofthesizeandshapeofspecimeninwhichtheytravel,unlessitsleastlateraldimensionislessthanaminimumvalue.Belowthisvalue,thepulsevelocitymaybereducedappreciably.Theextentofthisreductiondependsmainlyontheratioofthewavelengthofthepulsevibrationstotheleastlateraldimensionofthespecimenbutisinsignificantiftheratioislessthanunity.TableB.1givestherelationshipbetweenthelongitudinalpulsevelocity
12
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intheconcrete,thetransducerfrequencyandgivesrecommendationsfortheminimumpermissiblelateraldimensionofthespecimenwhenmeasuringwithlongitudinalwaves.
Iftheminimumlateraldimensionislessthanthewavelengthoriftheindirecttransmissionarrangementisused,themodeofpropagationchangesand,therefore,themeasuredtransittimevelocitywillbedifferent.Thisisparticularlyimportantincaseswhereconcreteelementsofsignificantlydifferentsizesarebeingcompared.
TableB.1—Effectofspecimendimensionsonpulsevelocityoflongitudinalwaves
TransducerfrequencyPulsevelocityinconcrete
km/s
kHzVc=3,50Vc=4,00Vc=4,50
Minimumrecommendedlateralspecimendimensionmm
24
54
82
150
146
65
43
23
167
74
49
27
188
83
55
30
B.6Effectofreinforcingbars
Whenpossible,measurementsincloseproximitytosteelreinforcingbars,paralleltothedirectionofpulsepropagationshouldbeavoided.
Whenanultrasonicpulsetravellingthroughconcretemeetsaconcrete-steelinterface,roughly40%to50%oftheenergyisreflected.Inthecaseofpulseechotransmission,thismaybeusedtoestimatethedepthandlocationofreinforcingbars,metalpipesandtendonducts.
B.7Cracksandvoids
Whenanultrasonicpulsetravellingthroughconcretemeetsaconcrete-airinterface,thereisnegligibletransmissionofenergyacrossthisinterface.Thus,anyair-filledcrackorvoidlyingimmediatelybetweentwotransducerswillobstructthedirectultrasonicbeamwhentheprojectedlengthofthevoidisgreaterthanthewidthofthetransducersandthewavelengthofsoundused.Whenthishappens,thefirstpulsetoarriveatthereceivingtransducerwillhavebeendiffractedaroundtheperipheryofthevoidandthetransittimewillbelongerthaninsimilarconcretewithnovoid.
Dependingonthedistanceseparatingthetransducersitispossibletomakeuseofthiseffectforlocatingflaws,voidsorotherdefectsgreaterthanabout100mmindiameterordepth.Relativelysmalldefectshavelittleornoeffectontransmissiontimes,butequallyareprobablyofminorengineeringimportance.Plottingcontoursofequalvelocityvaluesoftengivessignificantinformationregardingthequalityofaconcreteunit.Examinationofthesignalattenuationmayalsoprovidehelpfulinformation.
Incrackedmembers,wherethebrokenfacesofthemembersareheldtightlytogetherinclosecontactbycompressionforces,theultrasonicpulsesmaypassunimpededacrossthecrack.Asanexample,thiscanoccurincrackedverticalbearingpiles.Ifthecrackisfilledwithliquidwhichtransmitstheultrasonicenergy,e.g.inmarinestructuresorifthecrackispartiallyfilledwithsolidparticles,thecracki
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