英文原文EffectsoffrequencyandgroutedlengthonthebehaviorofguidedultrasonicwavesinrockboltsD.H.Zoua,Y.Cui,V.Madengaa,C.ZhangAbstractExperimentswereconductedtostudythebehaviorofguidedwavesinfreeandgroutedrockbolts.Ultrasonicwaveswithfrequenciesfrom25to100kHzwereusedasexcitationinputs.Testswere?rstconductedonfreeboltstohelpunderstandthebehaviorofguidedwavesinnon-groutedbolts.Theeffectsofwavefrequencyandgroutedlengthonthegroupvelocityandattenuationoftheguidedultrasonicwaveswerethenevaluated.Thetestresultsindicatedclearbutdifferenttrendsforthegroupvelocityinthefreeandthegroutedbolts.Theattenuationinfreeboltswasnotaffectedbyboltlengthandfrequency.However,ingroutedboltsitincreasedwithfrequencyandgroutedlength.Itwasalsofoundthatthetwomainsourcesofattenuationarethesetupenergyloss,whichhasa?xedquantityforaspeci?ctypeoftestsetup,andthedispersiveandspreadingenergylosswhichvarieswithfrequencyandboltlength.2021ElsevierLtd.Allrightsreserved.Keywords:Rockbolts;Guidedwaves;Attenuation;Amplitude;Groupvelocity1.IntroductionRockboltsarewidelyusedinundergroundandsurfaceexcavationsinminingandcivilengineeringforgroundreinforcementandstabilization.Inmanyapplications,rockboltsaregroutedinthegroundwithcementorresin.Testingofthegroutqualityandmonitoringofthebolttensionofrockboltshaslongbeenachallengeinthe?eld.Conventionally,groutqualityisassessedbypull-outtestandover-coring.Bothmethodsaredestructiveandtimeconsuming.Theusefulnessofpull-outtestresultsasameasureofthegroutqualitycanbelimitedbythecriticallengthofgroutbeyondwhichthesteelboltwillfail?rst.Therefore,othermethods,suchasnon-destructivetestingmethodsusingultrasonicwaveshavebecomeattractive.Inrecentyears,researchinthisareahasbeenveryactive.Itisnoticedthatpropertiesofguidedwaves,suchasvelocityandattenuation,arefunctionsoftheinputwavefrequency.Althoughtheguidedultrasonicwaveseemstobeapromisingmethodformonitoringrockbolts,researchinthisareaisstillintheearlystageandmanytechnicalproblemsremaintobesolved.Inagroutedbolt,wavebehaviorisnotonlyrelatedtothegroutqualitybutalsotothewavefrequency.Thegroutedlengthandthepropertiesofmaterialssurroundingtheboltmayallplayanimportantrole.Oneoftheimportantcharacteristicsofaguidedwaveisthatitsvelocitynotonlydependsonthematerialpropertiesbutalsoonthethicknessofthematerialandthewavefrequency.Unlikeabulkwave,theguidedwavepropagatesasapacket,whichismadeupofabandofsuperimposedcomponentswithdifferentfrequencies.Itisthegroupvelocitythatde?nesthespeedatwhichthe‘envelope’ofthepacketmovesalong.Ithasbeenshownthatinarockbolt,therateofenergytransferisidenticaltothegroupvelocity.Ourrecentresearchexaminedtheeffectsofwavefrequencyandthecuringtimeofgroutonthegroupvelocityofguidedultrasonicwavesinrockbolts.Wefoundthatthewavegroupvelocityismuchloweringroutedboltsthaninfreebolts.Thelowerthefrequency,thelowerthevelocity.Ourtestresultsindicatedthattheinputfrequencyforrockbolttestingbelow100kHzwouldprovidebetterresolutionandclearersignals.Thisobserva-tionissupportedbytheresultsdiscussedfurtheroninthispaper.Attenuationisanotherimportantcharacteristicofaguidedwave.Ingeneral,attenuationreferstothetotalreductioninthesignalstrength.Attenuationoccursasanaturalconsequenceofsignaltransmissionoveradistanceduetowaveenergyloss.Therehavebeenextensiveresearchandexperimentsonattenuationofbulkwaves.Waveattenuationisde?nedbyanattenuationcoef?cient.Forexample,thep-waveamplitudedecaycanbeexpressedasafunctionoftraveldistance.(1)whereAaistheamplitudeatlocationa,Abistheamplitudeatlocationb,istheattenuationcoef?cient,constant,Listhedistancefromlocationsatob,Ristheamplituderatio,R=Ab/Aa.However,therehasbeenlittleresearchonattenuationofguidedwaves,especiallyingroutedrockbolts.Waveattenuationingroutedrockboltsisverycomplicatedandisoftenaffectedbymanyfactorsincludingthegroutingmaterialandthegroutquality.Eachofthesefactorsmaycausesomeattenuation.Ingeneral,theobservedwaveattenuationmayhaveseveralcomponents,someofwhichmaybefrequency-dependentandsomefrequency-independent.Thetotalattenuationisthesumofthecontributionsofallin?uencingfactors[14],andthisrelationshipappliestobothbulkwavesandguidedwaves:(2)whereistheattenuationcoef?cientoftheithcomponentcausedbytheithfactor,isthetraveldistanceaffectedbytheithfactor,istheamplituderatioafterattenuationoftheithcomponent,Ifisthesameforallfactors,thenwehaveor(3)whereisthetotalattenuationcoef?cient.Accordingtothecause,attenuationmaybegroupedintothefollowingcategories:Dissipativeattenuation:Anenergylossduetonon-elasticresistanceofthemedium.Itincreaseswiththewavetraveldistanceandmaybecomeprofoundoveralongdistancedependingonthematerialproperty.Thistypeofattenuationinsteelisgenerallyverylowcomparedtothatinrocks.Asshownlater,itcanbeignoredinpracticeforguidedwavestravelinginrockboltsduetothelowresistanceofsteelandtheshortboltlength(1–3m).Dispersiveattenuation:Anenergylossduetodeforma-tionofwaveformduringwavepropagation,achar-acteristicthatdistinguishesguidedwavesfrombulkwaves.Thephenomenonofwavedeformationiscalledenergydispersion.Spreadingattenuation:Anenergylosswhichoccursattheinterfacebetweentheboltandthegroutingmaterial.Asaguidedwavereachestheinterface,notallofthewaveenergycanbere?ectedattheinterface.Partoftheenergypassesthroughtheinterfaceandistransmittedintothegroutedmaterial,aphenomenoncalledenergyleakage.Therefore,itcanbereasonablyassumedthatattenuationingroutedrockboltsconsistsoftwomajorcomponents;dispersiveandspreadingattenuation,bothofwhicharefrequency-dependent.ThetotalattenuationingroutedrockboltsshouldthusbethesumofthetwocomponentsandinfuturewillbereferredtoasDISPattenuation.Itshouldbepointedouthowever,thatasobservedduringourlaboratorytests,theamplitudedecayandtheenergylossofguidedwavesrecordedduringtestsofrockboltsinlaboratoryarenotsolelyfromtheDISPattenua-tion.Anotherimportantcomponentistheenergylossduetorefractionatthecontactsurfacesbetweentheboltsampleandtheequipment.Theoretically,whenawavereachesaninterfaceadjoiningamediumwhichdoesnottransmitmechanicalwaves(e.g.,vacuumorair),norefractionoccursandallenergyisre?ectedback.Inarockbolttest,transducersareattachedtotheboltsample,whichisincontactwiththetestingframe(e.g.,atableorarack).Itisatthesecontactsurfacesthatsomeenergyisinevitablyrefracted,causingenergyloss.Thistypeofenergyloss,asshownlater,isexpectedtobeconstantandisofa?xedquantityforaspeci?ctypeoftestsetup.Infutureitwillbecalledsetupenergyloss.Asaresult,therecordedamplitudedecayandenergylossduringrockbolttestswillbegreaterthanwhatisactuallycausedbytheDISPattenuation.AnongoingresearchprogramatDalhousieUniversityisaimedatstudyingthecharacteristicsofguidedwavesingroutedrockbolts.Effectsofwavefrequencyandgroutedlengthonthebehaviorofguidedultrasonicwavesinfreeboltsandgroutedboltshavebeenstudied.Theachievedresultsarestrikinglyconvincing.Thedetailsaregivenbelow.2.ExperimentsofguidedultrasonicwavetestsAnunderstandingoftheultrasonicwavecharacteristicsinfreebolts(non-groutedbolts)isessentialtothestudyofthebehaviorofguidedultrasonicwavesingroutedbolts.Inthisresearch,bothfreeboltsandgroutedboltsweretested.2.1.TestsamplesThetestsamplesincludedtwofreeboltsandthreegroutedboltsofvariouslengths.Thefreeboltswerebaresteelbars.Thegroutedboltsweremadebycastingacylindricalconcreteblockaroundasteelbartosimulatethegroutedrockboltsinthe?eld(Fig.1).Intheseteststheboltswerenottensioned.ThesamplesizesandotherdescriptionsaregiveninTable1.Thetwofreebolts(samples1and2)wereusedtostudytheeffectsofboltlengthandfrequencyonthebehaviorofguidedultrasonicwaves,particularlythesetupenergylossduetoequipmentsetup.Thethreegroutedbolts(samples3–5)withvaryinggroutedlengthswereusedtoinvestigatetheeffectsoffrequencyandgroutedlengthontheattenuationofguidedultrasonicwaves.2.2.TestinstrumentsandexperimentdescriptionTheinstrumentsusedinthestudyincludedaHandy-scopeHS-3(adataacquisitiondevicewithawavegenerator),anampli?er,twotransducers,andacomputer.TheequipmentsetupisillustratedinFig.2.TheHS-3unithasthecapabilityofgeneratingultrasonicsignalswithvaryingfrequencies,aswellasreceivinganddigitizingthereceivedwavesignals.Sinusoidalultrasonicinputsignalswereusedtoexcitethetransmitteratthenon-groutedendofthebolt.Thereceivedsignalattheotherendwasampli?edbeforebeingdigitized.Thecomputerwasusedtorecord,display,andprocessthesignals.Thetransducersusedwerepiezo-electric,typesR6andR15,fromPhysicalAcousticsCorporation.Bothendsofthetestboltsweresmoothedandvacuumgreasewasusedtoprovidegoodcontactwiththetransducers.Theexperimentswereconductedbyexcitingatransmit-ter(R6)withinputsignalsatdifferentfrequenciesintothenon-groutedendofaboltsample.Thesignalarrivingattheotherendwaspickedupbyatransducer(R15)andthewholewaveformwasrecordeddigitally.Duringeachtest,theinputfrequencyrangedfrom25to100kHz.3.ExperimentdataanalysismethodInthefollowing,‘?rstarrival’referstothe?rstwavepacketthatarrivedatthereceivingendand‘echo’referstothesamewavepacketthatreachedthereceivingendforasecondtimeafteritwasre?ectedbackfromtheinputend.Theattenuationwasestimatedbyassessingthewaveamplituderatiooftheechooverthe?rstarrival.3.1.AttenuationestimationAsexplainedearlier,waveattenuationisnotonlyrelatedtothegroutqualitybutalsotothefrequencyandotherfactors.Theamplituderatioofawavepacketthathastraveledsomedistancehasaninverselogarithmrelation-ship,asshowninEq.(1),withtheattenuationcoef?cient.Thehighertheattenuation,thegreatertheenergyloss,andthelowertheamplituderatio.Thereforethemeasuredamplituderatio,Rmasde?nedbelow,isusedasanindirectmeasurementofattenuationinthisstudy:(4)whereA1istheaverageamplitudeofthe?rstarrivalandA2istheaverageamplitudeoftheechoasde?nedbelow.Itisunderstoodthatgoodgroutqualityresultsinhigherenergylossalongtherockboltduetoenergyleakageanddispersion.Itisthereforeverydif?culttostudywaveattenuationingroutedboltsbecausetherecordedwave-formisoftenveryweakandisaffectedbyalotofnoises.Thereceivedwaveformsometimesmaynotbeveryclear,makingitdif?culttoidentifytheboundarybetweenthe?rstarrivalandtheecho.Thisbecomesmoreproblematicwhentheboltisshortorwhendispersionisserious.Themaximumwaveamplitudeinthiscasemaybeaffectedbysuchnoises.Itisthereforecriticaltodevelopasuitableanalysismethodtoanalyzetheattenuationofultrasonicwavesandtogetmeaningfulresults.Inthispaper,amethodtocalculatetheamplituderatiousingtheaverageamplitudeoveratimeintervalissuggestedasfollows:=(5)whereisthetimeintervalcenteredatthemaximumamplitudeofawavepacket,istherecordedwaveamplitude,i=1isforthe?rstarrival,andi=2isfortheecho,kisamaterialconstant.Theparameters,,andtheirde?nitionsareillustratedinFig.3.Becausethismethodconsiderstheaverageamplitudeacrossintervalsofequallengthsoftimeforthe?rstarrivalandtheecho,theeffectsoferrorsandnoisesonthemaximumamplitudewillbeminimized.Toevaluatetheeffectsofthetimeintervallengthandontheaccuracyoftheresults,theamplituderatiosinfreebolts—thoseinwhichtheboundarybetweenthe?rstarrivalandtheechowasveryclear—werecalculatedwithdifferenttimeintervalsasapercentageofthewholewaveformsofthe?rstarrivalandtheecho.Theresultsforsample1atdifferentfrequenciesareshowninFig.4.Itisclearthatifthetimeintervalistoosmall(e.g.,lessthan25%ofthewholewaveform),theamplituderatioasdeterminedbyEq.(5)varieswiththelengthofthetimeinterval.Whenthetimeintervalisgreaterthan25%ofthewholewaveform,theresultsvaryverylittleandarenearlythesameasthatat100%(thewholewaveform).Inthefollowing,==100wereusedincalculationoftheaverageamplitudeforalltests.Withaninputsignalof25kHz,thistimeintervalcorrespondedto45%fthewholewaveforminfreebolts,andat100kHz,itcovered95%ofthewholewaveform.Itisapparentthatalthoughasmallpartofthewholewaveformhasnotbeenconsideredinthismethod,thecalculatedamplituderatiocanstillre?ectthetotalenergylossinarockbolt.Thismethodhowevermakesitmucheasierinpracticetoestimatetheenergyloss,especiallywhentheboundarybetweenthe?rstarrivalandtheechoingroutedrockboltsisdif?culttoidentifybecauseofdispersion.3.2.GroupvelocityestimationThewavetraveltimeintherockboltisde?nedasthetimelapsefromthebeginningoftheexcitationsignal,whichwasrecordedfromtheinputendofthebolt,tothe?rstarrival,whichwasrecordedfromtheotherendofthebolt.However,determinationofthebeginningofthe?rstarrivalandtheechoisoftencomplicatedbythedispersioncharacteroftheguidedwave.Dispersionincreaseswithfrequency.Therecordedrawwaveformsthereforeneedtobe?ltered?rstbyaband?ltertonarrowthefrequencybandaroundeachtestingfrequency[5].Thiswasachievedbyusinga?lteringprogramdesignedinMatlab.Alltherecordedwaveformswere?lteredusingthisprogramtogiveanarrowbandof75kHz.Thearrivaltimedeterminedbythe?lteredwaveformsisfoundtobemorerepresentativeoftheanticipatedactualwavetraveltimeataspeci?cfrequency.Withtheboltlengthandthetraveltimedeterminedusingthismethod,thegroupvelocityofguidedultrasonicwavescanbecalculated.Thecalculatedgroupvelocityisfoundtofollowdifferenttrendsinthefreeandthegroutedbolts,asexplainedlater.Forpartiallygroutedbolts,thegroupvelocityinthefreesegmentisconsideredthesameasthatinthefreebolts.4.EffectsoffrequencyandboltlengthonthebehaviorofguidedwavesinfreeboltsExperimentswereconductedonfreeboltsusingfre-quenciesfrom25to100kHz.Fig.5a)showsthetypicalwaveformrecordedinsample1ataninputfrequencyof25kHz.Itwasobservedduringdataanalysisthatwiththeincreaseoftheinputfrequency,thetraveltimeofthe?rstarrivalandtheechoreachingthereceivingendincreasedslightly,andthewaveamplitudereductionoftheechofromthe?rstarrivalisalmostthesameatallinputfrequencies.4.1.AttenuationinfreeboltsThemeasuredamplituderatio,Rm,determinedfromthetwofreebolts(samples1and2)areshowninFig.6.Itcanbeconcludedfromthechartthatthetotalattenuationinthefreeboltsdidnotchangewithfrequency.Theaverageamplituderatiois0.79forsample1and0.81forsample2.Thusitisalsoclearthattheamplituderatioisnotaffectedmuchbytheboltlengthandthattheverysmalldifferenceforthetwoboltsisnegligible.Thiscon?rmsthatthedissipativeattenuationcanbeignoredforrockboltsbecauseoftheshorttravelingdistance.Sincethereislittleornodispersioninwaveforms,noristhereenergyleakagetoothermediums,theDISPattenuation,whichwasexpectedtochangewithfrequencyanddistance,isnegligibleinthefreebolts.Theenergylossforbothfreeboltswasnearlyconstantanddidnotchangewithfrequencyorboltlength.Asdiscussedearlier,thispartoftheenergylosshasa?xedamount,andismainlycausedbysetuploss,mostlyfromrefractionatthecontactsurfacesoftheboltsampleswithotherobjects.Thesetuplossishoweverexpectedtochangefordifferenttestsetups.IftheamplituderatioaftertheDISPattenuationisassumedasR1andafterthesetuplossasR2,thenthemeasuredamplituderatio,Rm,accordingtoEq.(2),willbe:(6)Ascanbeseen,theattenuationrelationshipde?nedinEq.(1)appliesonlytoR1,nottothedirectlymeasuredRm,sinceR2isindependentfromtraveldistance.ForafreeboltR1≈1.0,themainenergylosswillbethesetuplossandRm≈R2.Itcanbeinferredthatforgroutedrockbolts,thenon-groutedfreelengthwillhaveverylittleeffectontheresultofattenuationbecauseofitsshortlengthandthemajorenergylosswillbeinthegroutedlength.ItcanalsobereasonablyconcludedfromFig.6thattheamplituderatio,R2,afterthesetuploss(approximately20%)forthetestsetupinthisresearchisabout.GroupvelocityinfreeboltsAsindicatedabove,beforeestimatingthearrivaltime,therawwaveformswere?lteredwithaband?lter.Atypical?lteredwaveformofsample1isillustratedinFig.5b),whichshowsamorewell-de?nedsignalthantherawwaveform.Thedeterminedgroupvelocitiesforthetwofreebolts(samples1and2)areshowninFig.7togetherwiththetheoreticalgroupvelocitysolution,whichwasdeterminedfromAchenbach’ssolutioninasteelbarof19.5indiameter[3].Itcanbeseeninthechartthattheresultsfromthe?ltereddata?twellwiththetheoreticalsolutioninthetestedfrequencyrange.Asthefrequencychangedfrom25to100kHz;thegroupvelocitydroppedbyabout10%.Thegroupvelocitywasapparentlynotaffectedbytheboltlength.5.EffectsoffrequencyandgroutedlengthonbehaviorofguidedwavesExperimentswerealsoconductedonthegroutedrockboltsusingfrequenciesfrom25to100kHz.Thetypicalrawwaveformforsample4ataninputfrequencyof35kHzisdisplayedinFig.3.Itwasobservedfromtherecordeddatathatthewaveformsingroutedboltsshoweddispersion,apparentlymoreseriousathigherfrequencyranges.Atthesametime,astheinputfrequencyincreasedthelengthsoftimeforthe?rstarrivalandtheechotoreachthereceivingenddecreasedsigni?cantly,followinganoppositetrendfromthatobservedinthefreebolts.Thewaveamplitudereductionoftheechofromthe?rstarrivalalsobecamemoresevere.5.1.AttenuationingroutedrockboltsTheresultsofthemeasuredamplituderatio,Rm,forthegroutedboltsatdifferentfrequenciesareshowninFig.8.ItisalreadyknownfromtheexperimentresultsoffreeboltsinFig.6thattheamplituderatioafterthesetuploss,R2,is0.8andisindependentfromfrequency.Becausetheequipmentsetupandtestconditionsforthegroutedrockboltsarethesameasthoseforthefreebolts,itisassumedthattheamplituderatio,R2,isalso0.8inthegroutedbolts.ThustheamplituderatioR1aftertheDISPattenuationcanbecalculatedbyre-writingEq.(6)asR1=Rm/R2.Rmcanbecalculatedfromtherecordedwaveformsfollowingthesameprocedureasforfreebolts.TheresultsofR1ofthegroutedrockboltswithdifferentfrequenciesareshowninFig.9.Itcanbeseenthattheratio,R1,ofthegroutedrockboltsvariesinverselywithfrequencyandgroutedlength.Atfrequencieslessthan65kHz,R1decreasedlinearlywithfrequencyanditalsodecreasedwithgroutedlength.Itisnoticeablethatatfrequencieshigherthan65kHz,thedatawerescatteredandthelineartrendbecameunclear.Theexplanationisthatbothdispersiveandspreadingattenuationincreasedwithfrequency.Thehigherthefrequency,thegreatertheenergyloss.Hence,thereceivedsignalbecameveryweakwhentheinputfrequencywasabove75kHz.Theweaksignalnotonlyintroducesmoremeasuringerrors,butalsoaggravatestheeffectsofnoises,makingtheresultslessreliable.5.2.GroupvelocityingroutedrockboltsForthegroutedbolts,theresultsofgroupvelocitycalcu-latedfromtherawwaveformdataweretotallymeaningless.Onlyafter?lteringcouldmeaningfulresultsbeobtained.The?lteringmethodandthearrivaltimeestimationmethodarethesameasthosepreviouslydiscussedforthefreebolts.Thegroupvelocityinthegroutedlengthofapartiallygroutedrockboltwascalculatedusingthetraveltimeinthegroutedlengthonly.Thetraveltimeinthegroutedlengthwasdeterminedbysubtractingthetraveltimeinthefreelength,whichisassumedtohavethesamevelocityasthefreebolt,fromthetotaltraveltime.Themeasuredgroupvelocityinthegroutedlengthforsamples3–5areshowninFig.7,togetherwiththatfromthefreebolts.ItcanbeseenfromFig.7thattheresultsofthethreegroutedboltsareconsistenttoeachother.Thegroupvelocityinthegroutedboltsfollowedanoppositetrendasdidthatinthefreebolts;anditsvaluewasnotaffectedbythegroutedlength,butbythefrequency.Itisinterestingtonotethatatthelowfrequencyend(i.e.,25kHz),thegroupvelocityinthegroutedboltswasabouthalfofthatinthefreebolts;atfrequencieshigherthan75kHzthevelocityincreaseinthegroutedboltssloweddown,andatthehighfrequencyend(i.e.,100kHz),thevelocitywasapproachingthatofthefreebolts.Infact,athighfrequencies,itwasmoredif?culttoseparatethegroutedlengthandthefreelengthfromtherecordedsignals.Therefore,frequencieshigherthan75kHzarenotrecommendedforthetest.6.DiscussionsandconclusionsThisresearchexaminedtheattenuationandgroupvelocityoftheguidedultrasonicwavesinrockbolts.Thetestresultsshowedvariationswithfrequencyandgroutedlength.Itwasdeterminedthatduetotheshortlengthofrockboltsusedinthe?eld,thedissipativeattenuationcanbeignored.Infreebolts,thedispersiveandspreadingattenuationalongtheboltisnegligibleandthemainsourceofattenuationisfromthesetuplossofenergy,whichreducedtheamplitudeby20%inoneroundtripfortheequipmentsetupinthisresearch.Thesetuplossisconsideredtobeindependentfromfrequencyandboltlength,butdepen-dentuponthespeci?cequipmentsetup.Thegroupvelocityinthefreeboltsdecreasedbyabout10%asthefrequencyincreasedfrom25to100kHz.Ingroutedbolts,thesetuplossisassumedtobethesameasthatinthefreeboltsbecausethetestsetupwasthesame.However,thedispersiveandspreading(DISP)attenuationincreasedwithfrequencyandgroutedlength,anditwasmoreseverethanthatfromthesetuploss.TheamplituderatioduetotheDISPattenuationdecreasedasthefrequencyandgroutedlengthincreased.Thegroupwavevelocityinthegroutedlengthofthetestboltsincreasedsteadilyasthefrequencyincreasedto75kHzwhiletheincreasesloweddownatahigherfrequency.However,at25kHz,thegroupvelocitywasnearly50%lowerinthegroutedlengththanthatinthefreebolts.Asthefrequencyapproached100kHz,thevelocitydifferencebetweenthefreeboltsandthegroutedlengthwasreducedtolessthan10%.Asindicatedearlier,theexperimentsinthisstudywereconductedusingatransmission-throughsetup(i.e.,withsensorsonbothendsofthetestedbolts).Thistypeofsetupisnotapplicabletothe?eldwhereonlyoneendofarockboltisaccessible.Thenextstepofthisresearchwillbetoconductsimilartestsusingatransmission-echosetup(i.e.,withasensoratoneendonly).Thiswillrequireadifferenttestingdevice,whichisbeingcustom-builtforthespeci?ctestingrequirements.Duringthenextstageofresearch,tensionwillalsobeappliedtotheboltsamplestostudythetensioneffects.Theultimategoalofthisresearchwillbetodevelopanon-destructivetestingdeviceusingguidedultrasonicwavesfor?eldmonitoringofgroutedrockbolts,particularlythegroutquality,groutedlength,boltfailure,andbolttension.AcknowledgmentsThisresearchwassupportedbyaresearchgrantfromtheNaturalSciencesandEngineeringResearchCouncilofCanada.

中文譯文頻率和錨固長度對超聲波在錨桿中傳播行為的影響D.H.Zoua,Y.Cui,V.Madengaa,C.Zhang摘要以頻率從25至100千赫的超聲波作為勵磁輸入，研究超聲波在自由和錨固錨桿中傳播的特性。首先對自由錨桿進行實驗來了解導(dǎo)波在非錨固時的行為。從波的頻率和錨固長度上對群速度和衰減超聲導(dǎo)波的影響進行評估。實驗結(jié)果表明，在自由和錨固錨桿中，群速度有不同的趨勢。在自由錨桿中，波的衰減不受錨桿長度和波頻的影響。但是，在錨固錨桿中衰減隨著頻率和錨固長度的增加而增加。同時還發(fā)現(xiàn)設(shè)置能量損失引起衰減的兩個主要來源，一是對某一特定類型的測試體系的一個固定量，二是色散和傳播能量損耗隨波的頻率和錨桿長度的變化而變化。關(guān)鍵詞：巖石錨桿；導(dǎo)波；衰減；振幅；群速度1引言錨桿被廣泛應(yīng)用在采礦和土木工程中的地下和地表開挖后加固和穩(wěn)定地面。在許多應(yīng)用中，錨桿用水泥或樹脂錨固。測試錨桿錨固質(zhì)量和監(jiān)測錨桿預(yù)緊力長期以來一直是該領(lǐng)域中的一個挑戰(zhàn)。通常用拉拔實驗和應(yīng)力解除法來測試錨固質(zhì)量。這兩種方法都是破壞性和耗時的實驗。用拉拔實驗結(jié)果來衡量錨固質(zhì)量，受錨桿初次破壞后關(guān)鍵錨固長度的限制。因此，像利用超聲波這種非破壞性測試方法已經(jīng)受到了關(guān)注。近年來，這一領(lǐng)域的研究已經(jīng)非?；钴S。導(dǎo)波的性質(zhì)，如速度和衰減，受輸入波頻率的作用影響。雖然超聲導(dǎo)波是一個很有前景的監(jiān)測錨桿的方法，但是在這一領(lǐng)域的研究仍尚處于初期階段，許多技術(shù)問題仍待解決。在錨桿中，波的行為不僅與錨固的質(zhì)量，而且與波的頻率有關(guān)，也受錨桿周圍巖體的特性和錨固長度的影響。導(dǎo)波的一個重要的特征是其速度不僅取決于材料性能，而且取決于材料的厚度及波的頻率。導(dǎo)波不像體波，而是由一個束具有不同頻率的成分波疊加組成。群速度決定其傳播速度，波整體以該速度傳播。在錨桿中，能量傳遞速率與群速度相同。我們最近研究測試錨桿中波的頻率和固化時間對超聲導(dǎo)波群速度的影響。我們發(fā)現(xiàn)群速度在錨固錨桿中低于在自由錨桿中。頻率越低，速度越低。實驗結(jié)果表明，為錨桿實驗輸入低于100千赫的頻率會提供更好的分辨率和更清晰的信號。本文將進一步討論這個實驗結(jié)果。導(dǎo)波的另一個重要特點是衰減。一般來說，衰減是指信號強度的減弱。衰減是信號長距離傳輸過程中波能損失的自然結(jié)果。在體波的衰減方面已經(jīng)有廣泛的研究和試驗。波的衰減是由一個衰減系數(shù)定義的。舉例來說，縱波振幅衰減可以表示為一個距離函數(shù)。(1)其中Aa，Bb分別是位置a，b處的振幅；是衰減系數(shù)且是常數(shù)；L是從a到b的距離；R是振幅比率，R=Ab/Aa。然而,很少有研究導(dǎo)波的衰減，特別是在錨桿錨固方面。在錨固錨桿中波的衰減是非常復(fù)雜并且常常受包括錨固材料和錨固質(zhì)量在內(nèi)的多種因素的影響。這些因素都可能造成一些衰減。通常，波的衰減可能有幾個部分組成，其中一些隨頻率變化一些與頻率無關(guān)?？偹p是所有因素影響的結(jié)果，這也適用體波和導(dǎo)波：(2)其中是受第i個因素影響的第i個分量的衰減系數(shù)；是受第i個因素影響的距離；Ri是第i個分量衰減后振幅的比；如果對所有的因素都相同，則有或(3)其中是所以衰減系數(shù)的和。根據(jù)起因，衰減可分為以下幾類：(a)耗散衰減：一種由非彈性介質(zhì)阻礙引起的能量損耗。它隨波的傳播距離的增加而增加，并可能根據(jù)物質(zhì)的性質(zhì)在長距離傳播時成為很顯著的原因。這類型的衰減在鋼材中跟在巖石中相比普遍很低，如后面所述，在實踐中由于鋼的低阻力和錨桿長度(1~3m),導(dǎo)波在錨桿中傳播時,這種衰減可以被忽視。(b)色散衰減：一種由于傳播過程中波形變形導(dǎo)致的能量損耗。這也是導(dǎo)波在波傳播中區(qū)別于體波的一個特點。這種波變形的現(xiàn)象稱為能量色散。(c)傳播衰減：一種發(fā)生在錨桿與錨固材料界面間的能量損失。作為一個導(dǎo)波的到達界面，并不是所有的波能都可以在界面上反射的。一部分能量會穿過界面，并傳到錨固材料，這種現(xiàn)象稱為能量泄漏。因此，可以合理地假設(shè)在錨固錨桿中衰減由兩部分組成:色散衰減和傳播衰減，這兩者都是跟頻率