StructuralsafetycriteriaforblastingvibrationbasedonwaveletpacketenergyspectraZhongGuoshenga,b,*,LiJianga,ZhaoKuiaaSchoolofResources&EnvironmentalEngineering,JiangxiUniversityofScience&Technology,Ganzhou341000,ChinabSchoolofCivil&Transportation,SouthChinaUniversityofTechnology,Guangzhou510641,ChinaarticleinfoArticlehistory:Received24May2010Accepted2July2010Keywords:BlastingvibrationWaveletpackettransformResponseenergySafetycriteriaabstractGivenmulti-resolutiondecompositionofwaveletpackettransforms,waveletpacketfrequencybandenergyhasbeendeducedfromdifferentbandsofblastingvibrationsignals.Ourdeductionreflectsthetotaleffectofallthreekeyelements(intensity,frequencyanddurationofvibration)ofblastingvibration.Weconsideredanddiscussthedynamicresponseofstructuresandtheeffectofinherentcharacteristicsofcontrolledstructurestoblastingvibration.Frequencybandresponsecoefficientsforcontrolledstructuresbyblastingvibrationhavebeenobtained.Weestablishedmulti-factorblastingvibrationsafetycriteria,referredtoasresponseenergycriteria.Thesecriteriareflectthetotaleffectofintensity,frequencyanddurationofvibrationandtheinherentcharacteristics(naturalfrequencyanddampingratio)ofdynamicresponsesfromcontrolledstructuresthemselves.Feasibilityandreliabilityofthecriteriaarevalidatedbyanexample.CopyrightÓ2011,ChinaUniversityofMining&Technology.Allrightsreserved.
1.IntroductionWhenweassesssafetyinblasting,weshouldfirstofallestablishsafetycriteria,whichreflectfactorsimpactingonseismicblasting.Practiceshowsthatinmanycases,asingleparticlevelocityastheonlyindicatortomeasureseismicintensityofblastingdoesnotreflectaccuratelytheactualbreakagethatoccursinstructures,becausethefrequencyofseismicwaves,durationofvibrationandotherfactorswerenotconsidered[1e3].Researchshowsthat,damagetostructurescausedbyblastingvibrationistheresultfromavarietyoffactors,suchasintensity,frequencyanddurationofvibrationaswellasthecharacteristicsofadynamicresponseofthecontrolledstructuresthemselves[4,5].However,currentsafetystandardshaveneitherconsideredthedurationofblastingvibra-tionnortheinherentpropertiesofthecontrolledstructures(i.e.,naturalfrequencyanddampingratio).Itisinevitablethattherearesomedefectsandshortcomingsincarryingoutsafetymeasures.Inordertoadvancenewsafetycriteriatoreflectallthefactorsinvolvedinblastingvibration,shouldbeputontheagendaassoonaspossible[6,7].Waveletpackettechniqueshavebeenusedtoanalyzeblastingvibrationsignals.Basedonwaveletpacketenergyspectraandthestructureofdynamicresponses,newsafetycriteriahavebeenestablished,whichreflectthetotaleffectoftheintensity,frequencyanddurationofvibrationandthecharacteristicsofdynamicresponsesofthecontrolledstructuresthemselves.Itisoftheoret-icalandpracticalimportancetoassessaccuratelyandrationallytheseismiceffectofblastingbythesecriteria.Thefeasibilityandreliabilityofthesecriteriaarevalidatedbylivedataofblastingvibration.
2.Waveletpacketenergyspectrumanalysisofblastingvibration2.1.CharacteristicsofwaveletpacketanalysisWaveletanalysisdecomposessignalsintotwoparts:low-frequencyandhigh-frequency.Informationlostinthelow-frequencypartcouldbeobtainedfromthehigh-frequencypart.Inturn,thelow-frequencypartisdecomposedintotwopartsandthisdecompositioncanbecontinuedtoanumberofdeeperlevels.Fromthestructureofwaveletdecompositionitcanbeseenthatthefrequencyresolutionofthewavelettransformreduceswithincreasedfrequency.Waveletpacketanalysis(WPD)isdifferent.Itdecomposessignalsnotonlyintolow-frequencysignals,butalsointoahigh-frequencypart.WPDcanadaptivelyselecttheappropriatefrequencyspectrumtomatchthesignalspectrumfromtheanalysisofthesignalcharacteristicsandrequirements,itisrelativelyrefinedmethod.Manypublicationsdwellonits*Correspondingauthor.Tel.:þ867978312259.E-mailaddress:zgs1001@163.com(Z.
Guosheng).ContentslistsavailableatScienceDirectMiningScienceandTechnology(China)
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10.1016/j.mstc.2010.12.016MiningScienceandTechnology(China)21(2011)35e40mathematicalmethodologyandnumericalcalculations[8,9].Theycannotallbediscussedhereforlackofspace.2.2.WaveletpacketanalysisofblastingvibrationThelevelofdecompositionisdeterminedbythesignalsthem-selvesandspecializedinstrumentationisusedforacquiringblast-ingvibrationdata.TheequipmentusedinourtestwasanIDTS3850blastingvibrationrecorder,manufacturedbytheChengduVIDTSDynamicInstrumentCo.Ltd.Itsminimumoperatingfrequencyis1Hz.Themainvibrationfrequencyofblastingvaria-tionisgenerallybelow200Hz.Accordingtosamplingtheory,thesignalsamplingfrequencyissetto2000Hz,inwhichcaseitsNyquistfrequencyis1000Hz[10].Asaresult,giventhealgorithmofwaveletpacketanalysisusingbinary-scaletransformation,signalscanbedecomposedintosevenlevels,correspondingtothelowestband,i.e.,0e7.8125Hz.Frequencybandsofreconstructedsignalsatalllevelsofdecomposedblastingvibrationsignalsbywaveletpacket,areshowninTable1.2.3.WaveletpacketenergyspectrumanalysisofblastingvibrationsignalsWhenwedecomposesignals(t),usingawaveletpacket,toleveli,wecanobtainthe2isub-band,i.e.,s(t)canbedenotedasfollows.sðtÞ¼X2iÀ1j¼0fi;jÀtjÁ¼fi;0ðt0Þþfi;1ðt1Þþ/þfi;2iÀ1t2iÀ1
j¼0;1;2;/;2iÀ1(1)wherefi;jðtjÞisthereconstructedsignalatnode(i,j).Ifthelowestandmaximumfrequencyofs(t)are0andum,thenthefrequencywidthattheithlevelisum=2i.AccordingtotheParsevaltheorem[9]inspectrumanalysis,wecanobtainthewaveletpacketenergyspectrumofsignals(t):Ei;jÀtjÁ¼ZTjfi;jÀtjÁj2dt¼Xmk¼1jxj;kj2(2)wherexj;k(j¼0;1;2;/;2iÀ1;k¼1;2;/;m;mdenotesthenumberofdiscretesamplingpointsofseismicblasting)isthediscretepointamplitudeofthereconstructedsignalfi;jðtjÞ.Ei;jðtjÞisthefrequencybandenergywhenthesignaldecomposestotheithlevelatthejthnode.Thetotalenergyofs(t)isobtainedfromEquation(2):E¼X2iÀ1j¼0Ei;jÀtjÁ(3)Theratio,accountingfortheenergyofeachbandtototalenergyisPi;j¼Ei;jÀtjÁEÂ100%(4)Equations.(1)and(2)showthattheblastingvibrationsignals,decomposedbythewaveletpacketintodifferentfrequencycomponents,reflecttheeffectofthefrequencyofblastingvibration,aswellasthebandenergy,whilesimultaneouslyindicatingblast-ingvibrationintensityandduration.Asaresult,thewaveletpacketbandenergyobtainedonthisbasisisabletoreflecttheeffectofthreeelementsofblastingvibration(vibrationintensity,frequencyandduration).
3.Criteriaofsecurityresponseenergyofseismicblasting3.1.AnalysisofconstructionresponsetoseismicblastingSeismicblastingwavescanbeseenfromthesynthesisofaseriesofsinewaves,i.e.:AðtÞ¼Xni¼1Aisinðuitþ4iÞ(5)whereAi,uiand4idenoteamplitude,frequencyandinitialphaseoftheithsinewaverespectively.Inordertosimplifythecalculation,thestructureofthesystemisusuallyassumedtohaveasingledegreeoffreedom,accordingtotheprincipleofthebalanceofpower[11]:€xþ2xu0_xþu20x¼Fimsinuit(6)whereu0¼ffiffiffiffiffiffiffiffiffik=mpandx0¼c=2mu0arethenaturalfrequencyanddampingratioofastructure.GiventheseismicblastingloadingcomponentforceFisinuit,thetheory[12]ofstructuraldynamicsindicatesthatthemagnifi-cationfactorb,whencomparedtocorrespondingdisplacementx,isthemaximumconstructiondisplacementandcalculatedas:b¼1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiÀ1Àu2=u20Á2þ4x20$Àu2=u20Áq(7)whereuisthemotivationfrequencyofseismicblasting;u0andx0arethenaturalfrequencyanddampingratiosofastructure.Thisshowsthatthemagnificationfactorb,theresponsecoef-ficienttoblastingvibrationofastructure,isanon-dimensionalphysicalquantity.Equation(7)tellsusthatresponsefactorofacontrolledstructureiscloselyrelatedtoitsownnaturalfrequencyanddampingratio.Whenthemotivationfrequencyofblastingvibrationisclosetothenaturalfrequencyandthedampingratiooftheconstructionsmall,itcanbeconcludedthatthegreaterthevibrationresponsefactor,thegreaterthevibrationresponse,butontheotherhand,therewillbelessvibrationresponsefactor.
AsTable1Rangeforfrequencybandsofreconstructedblastingvibrationsignalsbywaveletpacketanalysis(Hz).LevelSi;0Si;1Si;2.Si;jÀ1Si;j10e500500e100020e250250e500500e750750e100030e125125e250250e375.750e875875e100040e62.562.5e125125e187.5.875e937.5937.5e100050e31.2531.25e62.562.5e93.75.937.5e968.75968.75e100060e15.62515.625e31.2531.25e46.875.968.75e984.375984.375e100070e7.81257.8125e15.62515.625e23.4375.984.375e992.1875992.1875e1000Note:sijdenotesreconstructedsignalsattheithlevelforthejthwaveletpacketdecompositioncoefficient.i¼1;2;/;7;j¼0;1;2;/;2jÀ1.Z.Guoshengetal./MiningScienceandTechnology(China)21(2011)35e4036
