成果采矿08-1设计

英文原EffectsoffrequencyandgroutedlengthonthebehaviorofguidedultrasonicwavesinrockboltsD.H.Zoua,Y.Cui,V.Madengaa,C.Experimentswereconductedtostudythebehaviorofguidedwavesinandgroutedrockbolts.Ultrasonicwaveswithfrequenciesfrom25to100kHzwereusedasexcitationinputs.Testswerefirstconductedonboltstohelpunderstandthebehaviorofguidedwavesinnon-groutedbolts.Theeffectsofwavefrequencyandgroutedlengthonthegroupvelocityandattenuationoftheguidedultrasonicwaveswerethenevaluated.Thetestresultsindicatedclearbutdifferenttrendsforthegroupvelocityintheandthegroutedbolts.Theattenuationinboltswasnotaffectedbyboltlengthandfrequency.However,ingroutedboltsitincreasedwithfrequencyandgroutedlength.Itwasalsofoundthatthetwomainsourcesofattenuationarethesetupenergyloss,whichhasafixedtyforaspecifictypeoftestsetup,andthedispersiveandspreadingenergylosswhichvarieswithfrequencyandboltlength.2007Elsevier.Allrights :Rockbolts;Guidedwaves;Attenuation;Amplitude;GroupRockboltsarewidelyusedinundergroundandsurfaceexcavationsinminingandcivilengineeringforgroundreinmentandstabilization.Inmanyapplications,rockboltsaregroutedinthegroundwithcementorresin.Testingofthegroutqualityandmonitoringofthebolttensionofrockboltshaslongbeenachallengeinthefield.Conventionally,groutqualityisassessedbypull-outtestandover-coring.Bothmethodsaredestructiveandtimeconsuming.Theusefulnessofpull-outtestresultsasameasureofthegroutqualitycanbelimitedbythecriticallengthofgroutbeyondwhichthesteelboltwillfailfirst.Therefore,othermethods,suchasnon-destructivetestingmethodsusingultrasonicwaveshave eattractive.Inrecentyears,researchinthisareahasbeenveryactive.Itisnoticedthatpropertiesofguidedwaves,suchasvelocityandattenuation,arefunctionsoftheinputwavefrequency.Althoughtheguidedultrasonicwaveseemstobeapromisingmethodformonitoringrockbolts,researchinthisareaisstillintheearlystageandmanytechnicalproblemsremaintobesolved.Inagroutedbolt,wavebehaviorisnotonlyrelatedtothegroutqualitybutalsotothewavefrequency.ThegroutedlengthandthepropertiesofmaterialssurroundingtheboltmayallyanimportantOneoftheimportantcharacteristicsofaguidedwaveisthatitsvelocitynotonlydependsonthematerialpropertiesbutalsoonthethicknessofthematerialandthewavefrequency.Unlikeabulkwave,theguidedwavepropagatesasapacket,whichismadeupofabandofsuperimposedcomponentswithdifferentfrequencies.Itisthegroupvelocitythatdefinesthespeedatwhichthe‘envelope’ofthepacketmovesalong.Ithasbeenshownthatinarockbolt,therateofenergytransferisidenticaltothegroupvelocity.Ourrecentresearchexaminedtheeffectsofwavefrequencyandthecuringtimeofgroutonthegroupvelocityofguidedultrasonicwavesinrockbolts.Wefoundthatthewavegroupvelocityismuchloweringroutedboltsthaninbolts.Thelowerthefrequency,thelowerthevelocity.Ourtestresultsindicatedthattheinputfrequencyforrockbolttestingbelow100kHzwouldprovidebetterresolutionandclearersignals.ThistionissupportedbytheresultsdiscussedfurtheroninthisAttenuationisanotherimportantcharacteristicofaguidedwave.Ingeneral,attenuationreferstothetotalreductioninthesignalstrength.Attenuationoccursasanaturalconsequenceofsignaltransmissionoveradistanceduetowaveenergyloss.Therehavebeenextensiveresearchandexperimentsonattenuationofbulkwaves.Waveattenuationisdefinedbyanattenuationcoefficient.Forexample,thep-waveamplitudedecaycanbeexpressedasafunctionoftravelln

ln(R)

whereAaistheamplitudeatlocationa,Abistheamplitudeatlocationb,istheattenuationcoefficient,constant,Listhedistancefromlocationsatob,Ristheamplituderatio,R=Ab/Aa.However,therehasbeenlittleresearchonattenuationofguidedwaves,especiallyingroutedrockbolts.Waveattenuationingroutedrockboltsisverycomplicatedandisoftenaffectedbymanyfactorsincludingthegroutingmaterialandthegroutquality.Eachofthesefactorsmaycausesomeattenuation.Ingeneral,theobservedwaveattenuationmayhaveseveralcomponents,someofwhichmaybefrequency-dependentandsomefrequency-independent.Thetotalattenuationisthesumofthecontributionsofallinfluencingfactors[14],andthisrelationshipappliestobothbulkwavesandguidedwaves: iLiln(Ri)ln(Ri

where

istheattenuationcoefficientoftheithcomponentcausedbytheithfactor,

istraveldistanceaffectedbytheithfactor,

istheamplituderatioafterattenuationofthecomponent,If

Liisthesameforallfactors,thenwhere

iLtnnisthetotalattenuation

ortinn

Accordingtothecause,attenuationmaybegroupedintothefollowingDissipativeattenuation:Anenergylossduetonon-elasticofthemedium.Itincreaseswiththewavetraveldistanceandmay eprofoundoveralongdistancedependingonthematerialproperty.Thistypeofattenuationinsteelisgenerallyverylowcomparedtothatinrocks.Asshownlater,itcanbeignoredinpracticeforguidedwavestravelinginrockboltsduetothelowofsteelandtheshortboltlength(1–3m).Dispersiveattenuation:Anenergylossduetodeforma-tionofwaveformduringwavepropagation,achar-acteristicthatdistinguishesguidedwavesfrombulkwaves.Thephenomenonofwavedeformationiscalledenergydispersion.Spreadingattenuation:Anenergylosswhichoccursattheinterfacebetweentheboltandthegroutingmaterial.Asaguidedwavereachestheinterface,notallofthewaveenergycanbereflectedattheinterface.Partoftheenergypassesthroughtheinterfaceandistransmittedintothegroutedmaterial,aphenomenoncalledenergyleakage.Therefore,itcanbereasonablyassumedthatattenuationingroutedrockboltsconsistsoftwomajorcomponents;dispersiveandspreadingattenuation,bothofwhicharefrequency-dependent.ThetotalattenuationingroutedrockboltsshouldthusbethesumofthetwocomponentsandinfuturewillbereferredtoasDISPattenuation.Itshouldbepointedouthowever,thatasobservedduringourlaboratorytests,theamplitudedecayandtheenergylossofguidedwavesrecordedduringtestsofrockboltsinlaboratoryarenotsolelyfromtheDISPattenua-tion.Anotherimportantcomponentistheenergylossduetorefractionatthecontactsurfacesbetweentheboltsampleandtheequipment.Theoretically,whenawavereachesaninterfaceadjoiningamediumwhichdoesnottransmitmechanicalwaves(e.g.,vacuumorair),norefractionoccursandallenergyisreflectedback.Inarockbolttest,transducersareattachedtotheboltsample,whichisincontactwiththetestingframe(e.g.,atableorarack).Itisatthesecontactsurfacesthatsomeenergyisinevitablyrefracted,causingenergyloss.Thistypeofenergyloss,asshownlater,isexpectedtobeconstantandisofafixedtyforaspecifictypeoftestsetup.Infutureitwillbecalledsetupenergyloss.Asaresult,therecordedamplitudedecayandenergylossduringrockbolttestswillbegreaterthanwhatisactuallycausedbytheDISPattenuation.AnongoingresearchprogramatDalhousieUniversityisaimedatstudyingthecharacteristicsofguidedwavesingroutedrockbolts.Effectsofwavefrequencyandgroutedlengthonthebehaviorofguidedultrasonicwavesinboltsandgroutedboltshavebeenstudied.Theachievedresultsarestrikinglyconvincing.Thedetailsaregivenbelow.ExperimentsofguidedultrasonicwaveAnunderstandingoftheultrasonicwavecharacteristicsinbolts(non-groutedbolts)isessentialtothestudyofthebehaviorofguidedultrasonicwavesingroutedbolts.Inthisresearch,bothboltsandgroutedboltsweretested.Thetestsamplesincludedtwo boltsandthreegroutedboltsofvariouslengths.Theboltswerebaresteelbars.Thegroutedboltsweremadebycastingacylindricalconcreteblockaroundasteelbartosimulatethegroutedrockboltsinthefield(Fig.1).Intheseteststheboltswerenottensioned.ThesamplesizesandotherdescriptionsaregiveninTable1.Thetwobolts(samples1and2)wereusedtostudytheeffectsofboltlengthandfrequencyonthebehaviorofguidedultrasonicwaves,particularlythesetupenergylossduetoequipmentsetup.Thethreegroutedbolts(samples3–5)withvaryinggroutedlengthswereusedtoinvestigatetheeffectsoffrequencyandgroutedlengthontheattenuationofguidedultrasonicwaves.TestinstrumentsandexperimentTheinstrumentsusedinthestudyincludedaHandy-scopeHS-3(adataacquisitiondevicewithawavegenerator),anamplifier,twotransducers,andacomputer.TheequipmentsetupisillustratedinFig.2.TheHS-3unithasthecapabilityofgeneratingultrasonicsignalswithvaryingfrequencies,aswellasreceivinganddigitizingthereceivedwavesignals.Sinusoidalultrasonicinputsignalswereusedtoexcitethetransmitteratthenon-groutedendofthebolt.Thereceivedsignalattheotherendwasamplifiedbeforebeingdigitized.Thecomputerwasusedtorecord,disy,andprocessthesignals.Thetransducersusedwerepiezo-electric,typesR6andR15,fromPhysicalAcousticsCorporation.Bothendsofthetestboltsweresmoothedandvacuumgreasewasusedtoprovidegoodcontactwiththetransducers.Theexperimentswereconductedbyexcitingatransmit-ter(R6)withinputsignalsatdifferentfrequenciesintothenon-groutedendofaboltsample.Thesignalarrivingattheotherendwaspickedupbyatransducer(R15)andthewholewaveformwasrecordeddigitally.Duringeachtest,theinputfrequencyrangedfrom25to100kHz.ExperimentdataysisInthefollowing,‘firstarrival’referstothefirstwavepacketthatarrivedatthereceivingendand‘echo’referstothesamewavepacketthatreachedthereceivingendforasecondtimeafteritwasreflectedbackfromtheinputend.Theattenuationwasestimatedbyassessingthewaveamplituderatiooftheechooverthefirstarrival.AttenuationAsexinedearlier,waveattenuationisnotonlyrelatedtothegroutqualitybutalsotothefrequencyandotherfactors.Theamplituderatioofawavepacketthathastraveledsomedistancehasaninverselogarithmrelation-ship,asshowninEq.(1),withtheattenuationcoefficient.Thehighertheattenuation,thegreatertheenergyloss,andthelowertheamplituderatio.Thereforethemeasuredamplituderatio,Rmasdefinedbelow,isusedasanindirectmeasurementofattenuationinthisstudy:R

1whereA1istheaverageamplitudeofthefirstarrivalandA2istheaverageamplitudeoftheechoasdefinedbelow.Itisunderstoodthatgoodgroutqualityresultsinhigherenergylossalongtherockboltduetoenergyleakageanddispersion.Itisthereforeverydifficulttostudywaveattenuationingroutedboltsbecausetherecordedwave-formisoftenveryweakandisaffectedbyalotofnoises.Thereceivedwaveformsometimesmaynotbeveryclear,makingitdifficulttoidentifytheboundarybetweenthefirstarrivalandtheecho.This esmoreproblematicwhentheboltisshortorwhendispersionisserious.Theumwaveamplitudeinthiscasemaybeaffectedbysuchnoises.Itisthereforecriticaltodevelopasuitableysismethodtoyzetheattenuationofultrasonicwavesandtogetmeaningfulresults.Inthispaper,amethodtocalculatetheamplituderatiousingtheaverageamplitudeoveratimeintervalissuggestedasfollows:titikv2i12i t= ti2v(t)dt,i1,=i(ti2ti1 i

titi2

isthetimeintervalcenteredattheumamplitudeofawavevi(t

istherecordedwaveamplitude,i=1isforthefirstarrival,andi=2isfortheecho,kismaterialconstant.The

vi(t)

andtheirdefinitionsareillustratedinFig.3.Becausemethodconsiderstheaverageamplitudeacrossintervalsofequallengthsoftimeforthefirstarrivalandtheecho,theeffectsoferrorsandnoisesontheumamplitudewillbeminimized.Toevaluatetheeffectsofthetimeinterval

ontheaccuracyofthetheamplituderatiosinbolts—thoseinwhichtheboundarybetweenthefirstarrivalandtheechowasveryclear—werecalculatedwithdifferenttimeintervalsasapercentageofthewholewaveformsofthefirstarrivalandtheecho.Theresultsforsample1atdifferentfrequenciesareshowninFig.4.Itisclearthatifthetimeintervalistoosmall(e.g.,lessthan25%ofthewholewaveform),theamplituderatioasdeterminedbyEq.(5)varieswiththelengthofthetimeinterval.Whenthetimeintervalisgreaterthan25%ofthewholewaveform,theresultsvaryverylittleandarenearlythesameasthatat100%(thewholewaveform).Inthe

t1=t2=100

wereusedincalculationoftheaverageamplitudefortests.Withaninputsignalof25kHz,thistimeintervalcorrespondedto45%fthewholewaveforminbolts,andat100kHz,itcovered95%ofthewholewaveform.Itisapparentthatalthoughasmallpartofthewholewaveformhasnotbeenconsideredinthismethod,thecalculatedamplituderatiocanstillreflectthetotalenergylossinarockbolt.Thismethodhowevermakesitmucheasierinpracticetoestimatetheenergyloss,especiallywhentheboundarybetweenthefirstarrivalandtheechoingroutedrockboltsisdifficulttoidentifybecauseofdispersion.GroupvelocityThewavetraveltimeintherockboltisdefinedasthetimelapsefromthebeginningoftheexcitationsignal,whichwasrecordedfromtheinputendofthebolt,tothefirstarrival,whichwasrecordedfromtheotherendofthebolt.However,determinationofthebeginningofthefirstarrivalandtheechoisoftencomplicatedbythedispersioncharacteroftheguidedwave.Dispersionincreaseswithfrequency.Therecordedrawwaveformsthereforeneedtobefilteredfirstbyabandfiltertonarrowthefrequencybandaroundeachtestingfrequency[5].Thiswasachievedbyusingafilteringprogramdesignedin.Alltherecordedwaveformswerefilteredusingthisprogramtogiveanarrowbandof75kHz.Thearrivaltimedeterminedbythefilteredwaveformsisfoundtobemorerepresentativeoftheanticipatedactualwavetraveltimeataspecificfrequency.Withtheboltlengthandthetraveltimedeterminedusingthismethod,thegroupvelocityofguidedultrasonicwavescanbecalculated.Thecalculatedgroupvelocityisfoundtofollowdifferenttrendsintheandthegroutedbolts,asexinedlater.Forpartiallygroutedbolts,thegroupvelocityinthesegmentisconsideredthesameasthatinthebolts.EffectsoffrequencyandboltlengthonthebehaviorofguidedwavesinExperimentswereconductedonboltsusingfre-quenciesfrom25to100kHz.Fig.5a)showsthetypicalwaveformrecordedinsample1ataninputfrequencyof25kHz.Itwasobservedduringdataysisthatwiththeincreaseoftheinputfrequency,thetraveltimeofthefirstandtheechoreachingthereceivingendincreasedslightly,andthewaveamplitudereductionoftheechofromthefirstarrivalisalmostthesameatallinputfrequencies.AttenuationinThemeasuredamplituderatio,Rm,determinedfromthetwobolts(samples1and2)areshowninFig.6.Itcanbeconcludedfromthechartthatthetotalattenuationintheboltsdidnotchangewithfrequency.Theaverageamplituderatiois0.79forsample1and0.81for2.Thusitisalsoclearthattheamplituderatioisnotaffectedmuchbytheboltlengthandthattheverysmalldifferenceforthetwoboltsisnegligible.Thisconfirmsthatthedissipativeattenuationcanbeignoredforrockboltsbecauseoftheshorttravelingdistance.Sincethereislittleornodispersioninwaveforms,noristhereenergyleakagetoothermediums,theDISPattenuation,whichwasexpectedtochangewithfrequencyanddistance,isnegligibleinthebolts.Theenergylossforbothboltswasnearlyconstantanddidnotchangewithfrequencyorboltlength.Asdiscussedearlier,thispartoftheenergylosshasafixedamount,andismainlycausedbysetuploss,mostlyfromrefractionatthecontactsurfacesoftheboltsampleswithotherobjects.Thesetuplossishoweverexpectedtochangefordifferenttestsetups.IftheamplituderatioaftertheDISPattenuationisassumedasR1andafterthesetuplossasR2,thenthemeasuredamplituderatio,Rm,accordingtoEq.(2),willbe:Rm

Ascanbeseen,theattenuationrelationshipdefinedinEq.(1)appliesonlytoR1,nottothedirectlymeasuredRm,sinceR2isindependentfromtraveldistance.ForaboltR1≈1.0,themainenergylosswillbethesetuplossandRm≈R2.Itcanbeinferredthatforgroutedrockbolts,thenon-groutedlengthwillhaveverylittleeffectontheresultofattenuationbecauseofitsshortlengthandthemajorenergylosswillbeinthegroutedlength.ItcanalsobereasonablyconcludedfromFig.6thattheamplituderatio,R2,afterthesetuploss(approximay20%)forthetestsetupinthisresearchisabout0.8.GroupvelocityinAsindicatedabove,beforeestimatingthearrivaltime,therawwaveformswerefilteredwithabandfilter.Atypicalfilteredwaveformofsample1isillustratedinFig.5b),whichshowsamorewell-definedsignalthantherawwaveform.Thedeterminedgroupvelocitiesforthetwobolts(samples1and2)areshowninFig.7togetherwiththetheoreticalgroupvelocitysolution,whichwasdeterminedfromAchenbach’ssolutioninasteelbarof19.5indiameter[3].Itcanbeseeninthechartthattheresultsfromthefiltereddatafitwellwiththetheoreticalsolutioninthetestedfrequencyrange.Asthefrequencychangedfrom25to100kHz;thegroupvelocitydroppedbyabout10%.Thegroupvelocitywasapparentlynotaffectedbytheboltlength.EffectsoffrequencyandgroutedlengthonbehaviorofguidedExperimentswerealsoconductedonthegroutedrockboltsusingfrequenciesfrom25to100kHz.Thetypicalrawwaveformforsample4ataninputfrequencyof35kHzisdisyedin3.Itwasobservedfromtherecordeddatathatthewaveformsingroutedboltsshoweddispersion,apparentlymoreseriousathigherfrequencyranges.Atthesametime,astheinputfrequencyincreasedthelengthsoftimeforthefirstarrivalandtheechotoreachthereceivingenddecreasedsignificantly,followinganoppositetrendfromthatobservedinthebolts.ThewavereductionoftheechofromthefirstarrivalalsobecamemoreAttenuationingroutedrockTheresultsofthemeasuredamplituderatio,Rm,forthegroutedboltsatdifferentfrequenciesareshowninFig.8.ItisalreadyknownfromtheexperimentresultsofboltsinFig.6thattheamplituderatioafterthesetuploss,R2,is0.8andisindependentfromfrequency.Becausetheequipmentsetupandtestconditionsforthegroutedrockboltsarethesameasthoseforthebolts,itisassumedthattheamplituderatio,R2,isalso0.8inthegroutedbolts.ThustheamplituderatioR1aftertheDISPattenuationcanbecalculatedbyre-writingEq.(6)asR1=Rm/R2.Rmcanbecalculatedfromtherecordedwaveformsfollowingthesameprocedureasforbolts.TheresultsofR1ofthegroutedrockboltswithdifferentfrequenciesareshowninFig.9.Itcanbeseenthattheratio,R1,ofthegroutedrockboltsvariesinverselywithfrequencyandgroutedlength.Atfrequencieslessthan65kHz,R1decreasedlinearlywithfrequencyanditalsodecreasedwithgroutedlength.Itisnoticeablethatatfrequencieshigherthan65kHz,thedatawerescatteredandthelineartrendbecameunclear.Theexnationisthatbothdispersiveandspreadingattenuationincreasedwithfrequency.Thehigherthefrequency,thegreatertheenergyloss.Hence,thereceivedsignalbecameveryweakwhentheinputfrequencywasabove75kHz.Theweaksignalnotonlyintroducesmoremeasuringerrors,butalsoaggravatestheeffectsofnoises,makingtheresultslessreliable.GroupvelocityingroutedrockForthegroutedbolts,theresultsofgroupvelocitycalcu-latedfromtherawwaveformdataweretotallymeaningless.Onlyafterfilteringcouldmeaningfulresultsbeobtained.Thefilteringmethodandthearrivaltimeestimationmethodarethesameasthosepreviouslydiscussedforthe Thegroupvelocityinthegroutedlengthofapartiallygroutedrockboltwascalculatedusingthetraveltimeinthegroutedlengthonly.Thetraveltimeinthegroutedlengthwasdeterminedbysubtractingthetraveltimeinthe length,whichisassumedtohavethesamevelocityasthebolt,fromthetotaltraveltime.Themeasuredgroupvelocityinthegroutedlengthforsamples3–5areshowninFig.7,togetherwiththatfromtheItcanbeseenfromFig.7thattheresultsofthethreegroutedboltsareconsistenttoeachother.Thegroupvelocityinthegroutedboltsfollowedanoppositetrendasdidthatinthebolts;anditsvaluewasnotaffectedbythegroutedlength,butbythefrequency.Itisinterestingtonotethatatthelowfrequencyend(i.e.,25kHz),thegroupvelocityinthegroutedboltswasabouthalfofthatinthebolts;atfrequencieshigherthan75kHzthevelocityincreaseinthegroutedboltssloweddown,andatthehighfrequencyend(i.e.,100kHz),thevelocitywasapproachingthatofthebolts.Infact,athighfrequencies,itwasmoredifficulttoseparatethegroutedlengthandthelengthfromtherecordedsignals.Therefore,frequencieshigherthan75kHzaremendedfortheDiscussionsandThisresearchexaminedtheattenuationandgroupvelocityoftheguidedultrasonicwavesinrockbolts.Thetestresultsshowedvariationswithfrequencyandgroutedlength.Itwasdeterminedthatduetotheshortlengthofrockboltsusedinthefield,thedissipativeattenuationcanbeignored.Inbolts,thedispersiveandspreadingattenuationalongtheboltisnegligibleandthemainsourceofattenuationisfromthesetuplossofenergy,whichreducedtheamplitudeby20%inoneroundtripfortheequipmentsetupinthisresearch.Thesetuplossisconsideredtobefromfrequencyandboltlength,butdepen-dentuponthespecificequipmentsetup.Thegroupintheboltsdecreasedbyabout10%asthefrequencyincreasedfrom25to100Ingroutedbolts,thesetuplossisassumedtobethesameasthatintheboltsbecausethetestsetupwasthesame.However,thedispersiveandspreading(DISP)attenuationincreasedwithfrequencyandgroutedlength,anditwasmoreseverethanthatfromthesetuploss.TheamplituderatioduetotheDISPattenuationdecreasedasthefrequencyandgroutedlengthincreased.Thegroupwavevelocityinthegroutedlengthofthetestboltsincreasedsteadilyasthefrequencyincreasedto75kHzwhiletheincreasesloweddownatahigherfrequency.However,at25kHz,thegroupvelocitywasnearly50%lowerinthegroutedlengththanthatinthebolts.Asthefrequencyapproached100kHz,thevelocitydifferencebetweentheboltsandthegroutedlengthwasreducedtolessthan10%.Asindicatedearlier,theexperimentsinthisstudywereconductedusingatransmission-throughsetup(i.e.,withsensorsonbothendsofthetestedbolts).Thistypeofsetupisnotapplicabletothefieldwhereonlyoneendofarockboltisaccessible.Thenextstepofthisresearchwillbetoconductsimilartestsusingatransmission-echosetup(i.e.,withasensoratoneendonly).Thiswillrequireadifferenttestingdevice,whichisbeingcustom-builtforthespecifictestingrequirements.Duringthenextstageofresearch,tensionwillalsobeappliedtotheboltsamplestostudythetensioneffects.Theultimategoalofthisresearchwillbetodevelopanon-destructivetestingdeviceusingguidedultrasonicwavesforfieldmonitoringofgroutedrockbolts,particularlythegroutquality,groutedlength,boltfailure,andbolttension.ThisresearchwassupportedbyaresearchgrantfromtheNaturalSciencesandEngineeringResearchCouncilofCanada.中文译

D.H.Zoua,Y.Cui,V.Madengaa,C.25100千赫的超声波作为励磁输入，研究超声波在自由和锚固锚杆中传引ln

ln(R)

其中Aa，Bb分别是位置a，b处的振幅；是衰减系数且是常数；L是从a到bR是振幅比率，R=Ab/Aa iLiln(Ri)ln(Ri

n其中i是受第i个因素影响的第i个分量的衰减系数；Li是受第i个因素影响的距离；Ri是第iLi都相同，则有nnniLt其中t

或

i

中跟在岩石中相比普遍很低，如后面所述，在实践中由于钢的低阻力和锚杆长度(1~3m),超声导波测试的实了解超声波在自由锚杆（非锚固）试验样1锚杆试件的几何特征样锚杆长度锚杆直径锚固长度锚固直接100200345试验仪器和实验描在研究中所用的工具，包括一个手提示波器S3(有产生波的器)，一个放器，两个传感器和一台电脑。设备安装的说明图，见图2。单一的手提示波器S3有发不同频率的超声波信号的能力，以及接收和数字化接收波的信号。超声波正弦输入信号被用来激发在锚杆非锚固末端的发射机。在另一端接收到的信号先是被扩增，然后被数字化。电脑被用来记录，显示和处理信号。实验的进行通过激发一个发射机（6），在锚杆样品非锚固的末端输入不同频率的输入信号,在信号到达的另一端被一个传感器15）次试验中，输入频率的范围介于25至100千赫。实验数据的分析方衰减估Rm1

其中A1是首次到达的平均振幅，A2是回声的平均振幅算，如下：titikv2i1 t2i 2 t)tiv2ii

其中(ti2ti1vi(t是波的振幅，i=1表示首次到达，i=2表示回声；k参数it)、ti2、ti1和它们的含义如图3所示。因为这个方法考虑两个相同时间间隔中首次到达和回声的平均振幅，所以误差和噪音对最大振幅的影响最小。为了说明时间间隔的长度对结果准确度的影响，用不同时间间隔计算自由锚杆中的振幅比(首次到达和回声的界限很明显)4的看出：当时间间隔很小时(25%)，由方程5得到的振幅比随间隔时间的长短而变化。当时间间隔超过这个波形的25%时，结果变化就非常小，几乎达到100%。估算群自由锚杆中频率和锚杆长度对导波行为的影自由锚杆中的衰中，跟频率和距离有关的色散衰减在自由锚杆中也就可以忽略假设色散衰减后的振幅比是R1，安装损耗后的振幅比是R2，则由方程2得到实测振RmR1

对于自由锚杆11.0时，主要的能量损失是安装损耗，此时m2固锚杆中非锚固端的长度对衰减影响很小，因为距锚杆自由端很短，主要的能量损失在锚固端。从图6中可得出，这项研究中受安装损耗(大约20%)