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1、FELLENIUS,B.H.,1984.Waveequationanalysisanddynamicmonitoring.DeepFoundationsJournalSpring1984,DeepFoundationsInstitute,Springfield,NewJersey,Vol.1,No.1,pp.49-55.WAVEEQUATIONANALYSISANDDYNAMICMONITORINGAPresentationattheDeepFoundationsInstitute'sMcGil
2、lUniversitySymposium,Montreal,September1983BengtH.FelleniusTheadventofthewaveequationanalysisduringthe1960sthroughthe1970swasaquantumleapinmodernfoundationengineering.Forthefirsttime,thefullcomplexofpiledrivingcouldbeconsidered,thatis,velocitydepende
3、ntaspects(damping),soildeformationcharacteristics,soilresistance(totalaswellasitsdistributionofresistancealongthepileshaftandbetweenthepileshaftandthepiletoe),hammerefficiency,hammerandpilecushionsparameters,andother.However,whilethewaveequationisthe
4、oreticallycorrect,whenusedwithoutfactualdata,theresultsareonlyqualitativelycorrect,notquantitatively.Eachinputdatumisreallyavariablewithacertainrangeofpossiblevalues.Astherearemanyinputparameters,thecombinedeffectisthattheresults(forinstance,abearing
5、graph)isonlysomewherenearthequantitativelycorrectvalue.Therefore,oneshouldneverjustbesatisfiedwithoneanalysis(computerrun),butrunseveralanalysestodeterminethewidthofprobableconditionsthroughapplyingrangesofinputvalues.Theresultsarethenpresentednotaso
6、newelldefinedcurve,butasrepresentativeareasorbands,whichwidthsdefinethedegreeofconfidenceinthevalidityoftheanalysistotheactualbehavior,asshowninFig.1.Morethanoneconfidencebandcouldexist,dependingonwhether,forexample,theanalysisaddressesend-of-initial
7、-drivingorrestrikingconditions.RANGEOFULTIMATEMOSTLYTOESTATICRESISTANCEATRESISTANCETERMINATIONOFDRIVINGCOMBINEDTOEANDSHAFTRESISTANCEMOSTLYSHAFTRESISTANCERANGEOFPENETRATIONRESISTANCEATTERMINATIONOFDRIVINGFig.1BearingGraphfromWEAPAnalysisPage2Often,the
8、bearinggraphcanbecombinedwithempiricalinformationandparedwith"engineeringjudgment"tonarrowthewidthoftheconfidenceband.Usually,though,onceonehasrealizedthatthewaveequationdoesnotgivesinglelineorsimpleanswers—ineffectrealizedthenecessityofproducingaban
