Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid I_Boit

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1、TheoryofPropagationofElasticWavesinaFluid-SaturatedPorousSolid.I.Low-FrequencyRangeM.A.BIOTReprintedfromTHEJOURNALOFTHEACOUSTICALSOCIETYOFAMERICA,Vol.28,No.2,pp.168-178,March,1956ReprintedfromTHEJOURNALOFTHEACOUSTICALSOCIETYOFAMERICA,Vol.28,No.2,168-178,March,1956Copyright,1956bytheAcou

2、sticalSocietyofAmerica.PrintedinU.S.A.TheoryofPropagationofElasticWavesinaFluid-SaturatedPorousSolid.I.Low-FrequencyRangeM.A.BIOT*ShellDevelopmentConcpany,RCABuddirg,NewYork,NewYork(ReceivedSeptember1,1955)Atheoryisdevelopedforthepropagationofstresswavesinaporouselasticsolidcontainingac

3、ompressibleviscousfluid.Theemphasisofthepresenttreatmentisonmaterialswherefluidandsolidareofcomparabledensitiesasforinstanceinthecaseofwater-saturatedrock.ThepaperdenotedhereasPartIisrestrictedtothelowerfrequencyrangewheretheassumptionofPoiseuilleflowisvalid.Theextensiontothehigherfrequ

4、encieswillbetreatedinPartII.Itisfoundthatthematerialmaybedescribedbyfournondimen-sionalparametersandacharacteristicfrequency.Therearetwodilatationalwavesandonerotationalwave.Thephysicalinterpretationoftheresultisclarifiedbytreatingfirstthecasewherethefluidisfrictionless.Thecaseofamateri

5、alcontainingaviscousfluidisthendevelopedanddiscussednumerically.Phasevelocitydispersioncurvesandattenuationcoefficientsforthethreetypesofwavesareplottedasafunctionofthefrequencyforvariouscombinationsofthecharacteristicparameters.1.INTRODUCTIONThisisobtainedifadynamiccompatibilityrelatio

6、nisURpurposeistoestablishatheoryofpropagationverifiedbetweentheelasticanddynamicconstants.This0ofelasticwavesinasystemcomposedofaporousisacasewheredissipationduetofluidfrictionwilldisappear.InSec.6thedynamicrelationsarederivedelasticsolidsaturatedbyaviscousfluid.Itisassumedthatthefluidi

7、scompressibleandmayflowrelativetowiththeadditionoffluidviscosityandSec.7derivesthesolidcausingfrictiontoarise.PartIwhichisthepropertiesofthepropagationofthewaveswhendissipationispresent.Itisfoundthatthephasevelocitypresentedhereassumesthattherelativemotionofthefluidintheporesis