岩石碎裂作用的分形尺度(英文)
|
摘要
各种各样的统计幂定律关系经常成功地被用来描述碎屑大小分布和断口形状 (不平整度 )的分级规律 ,表明碎裂作用是一种尺度不变的作用过程。一条新的有关岩石碎裂作用破裂能量的尺度律 ,可以由分形几何以及Griffith能量平衡的概念推导出来 ,而且它与先前三条关于大小缩减或Hall Petch关系的理论是相一致的。从材料强度的观点来看 ,断口形状的分形维数是形状因子和岩石Weibull均质系数的函数。在任何一次采集中 ,如果碎屑都是致密压实的 ,那么大小分布和碎屑不平整度的分形维数是相同的。然而有些地壳碎屑在三维体积上已不再是致密压实的 ,破裂的地壳可被当作分形的多孔物质来处理。在此情况下 ,地壳碎屑形状的分形容量与地壳断口大小分布的分形维数相关 ,可以预期 ,在大地构造及地震强度的分形分析中 ,地壳断口大小分布的分形维数可作为断裂制约条件之一。
A variety of statistical power\|law relations have often been used successfully to describe scaling laws of the size distribution of fragments and shape (surface roughness) of fractures, indicating that fragmentation is a scale invariant process. A new scaling law of the fracturing energy for the rock fragmentation can be derived from the concepts of fractal geometry and the Griffith energy balance and is consistent with three previous theories on size reduction or Hall\|Petchs relation. From the viewpoint of the material strength that the fractal dimension of the fracture shape is a function of shape factor and the Weibulls uniformity coefficient of rocks. If all fragments in any collection are compact, the fractal dimensions of the size distribution and roughness of fragments are equivalent. However,some crustal fragments are no longer compact with the 3\|dimensional volume and the fractured crust might be treated as a fractal porous material. In this case, the fractal capacity dimension of the crustal fragment shape is related to the fractal dimension of the crust fracture\|size distribution, which is expected to be a fracture constraint for the fractal analysis in tectonics and seismicity.
A variety of statistical power\|law relations have often been used successfully to describe scaling laws of the size distribution of fragments and shape (surface roughness) of fractures, indicating that fragmentation is a scale invariant process. A new scaling law of the fracturing energy for the rock fragmentation can be derived from the concepts of fractal geometry and the Griffith energy balance and is consistent with three previous theories on size reduction or Hall\|Petchs relation. From the viewpoint of the material strength that the fractal dimension of the fracture shape is a function of shape factor and the Weibulls uniformity coefficient of rocks. If all fragments in any collection are compact, the fractal dimensions of the size distribution and roughness of fragments are equivalent. However,some crustal fragments are no longer compact with the 3\|dimensional volume and the fractured crust might be treated as a fractal porous material. In this case, the fractal capacity dimension of the crustal fragment shape is related to the fractal dimension of the crust fracture\|size distribution, which is expected to be a fracture constraint for the fractal analysis in tectonics and seismicity.
引文
[ 1] MatsushitaM .Fractalviewpointoffractureandaccretion[J].JPhysSocJapan ,1985 ,5 4:85 7～ 86 0 .
[2 ] MandelbrotBB .TheFractalGeometryofNature[M ].NewYork :WHFreemanandCampany ,1982 .46 8.
[3] TurcotteDL .Fractalsandfragmentation[J]..JGeophysRes ,1986 ,91:192 1～ 192 6 .
[4 ] NagahamaH .Fracturinginthesolidearth[R].SciReptsTohokuUniv .2ndser (Geol) ,1991,6 1:10 3～ 12 6 .
[5 ] GaudinAM .Aninvestigationofcrushingphenomena[J].TransAmerInstMiningMetallPetrolEngrs,192 6 ,73:2 5 3～ 316 .
[6 ] SchuhmannRJr.Principlesofcomminution ,I—Sizedistributionandsurfacecalculations[A].AIMETechPub ,No .1189,MiningEngrs[M ].NewYork :AIME :1940 .
[7] ZhaoZY ,WangY ,LiuXH .Fractalanalysisappliedtocataclasticrocks[J].Tectonophysics,1990 ,178:373～377.
[8] NagahamaH .Fractalfragmentsizedistributionforbrittlerocks[J].IntJRockMechMinSci&GeomechAbstr ,1993,30 :46 9～ 471.
[9] NagahamaH ,YoshiiK .Fractaldimensionandfractureofbrittlerocks[J].IntJRockMechMinSci&GeomechAbstr ,1993,30 :173～ 175 .
[10 ] NagahamaH ,YoshiiK .Scalinglawsoffragmentation[A].KruhlJH ,ed .FractalandDynamicalSystemsinGeosciences[M ].Berlin :Springer Verlag ,1994.2 5～ 36 .
[11] RittingerPRv .LehbuchderAufbereitungskunde[M ].Berlin :ErnstundKorn ,186 7.
[12 ] KickF .DasGesetzderproportionalemWiderstandundseineAnwendung[M ].Leipzig :ArthusFelix ,1885 .
[13] BondFC .Thethirdtheoryofcomminution[J].TransAmerInstMiningMetallPetrolEngrs,195 2 ,193:484～494.
[14] BergstromBH ,CrabtreeDD ,SollenbergerCL .Feedsizeeffectsinsingleparticlecrushing[J].TransAmerInstMiningMetallPetrolEngrs ,196 3,2 2 6 :433～ 44 1.
[15 ] WalkerWH ,LewisWK ,McAdamsWH ,etal.PrinciplesofChemicalEngineering[M ].London :McGraw Hill,1937.
[16 ] CharlesRJ .Energy sizereductionrelationshipsincomminution[J].TransAmerInstMiningMetallPetrolEn grs,195 7,2 0 8:80～ 88..
[17] SchuhmannRJr.Energyinputandsizedistributionincomminution[J].TransAmerInstMiningMetallPetrolEngrs,196 0 ,2 17:2 2～ 2 5 .
[18] TartaronFX .Ageneraltheoryofcomminution[J].TransAmerInstMiningMetallPetrolEngrs,196 3,2 2 6 :183～ 190 .
[19] GriffithAA .Thetheoryofruptureandflowinsolids[J].PhilTransRoySoc,SerA ,192 0 ,2 2 1:16 3～ 198.
[2 0 ] GriffithAA .Thetheoryofrupture[A].BiezenoCB ,BurgersJM ,eds.Proceedingsofthe 1stInternationalCongressofAppliedMechanics[M ].[s .l.]:BoekhandelenDrukkerijJ .WalterJr,192 4.5 4～ 6 3.
[2 1] MandelbrotBB ,PassojaDE ,PaullayAJ .Fractalcharacteroffractalsurfacesofmetals[J].Nature ,1984,30 8:72 1～ 72 2 .
[2 2 ] BrownSR ,ScholzCH .Broadbandwidthstudyofthetopographyofnaturalrocksurfaces[J].JGeophysRes ,1985 ,90 :12 5 75～ 12 5 82 .
[2 3] ScholzCH ,AvilesCA .Thefractalgeometryoffaultsandfaulting[A].DasS ,BoatwrightJ ,ScholzCH ,eds .EarthquakeSourceMechanics[M ].MauriceEwingVolume 6 .Washington ,D .C .:AGU ,1986 .47～ 5 5 .
[2 4] NagahamaH .Afractalcriterionforductileandbrittlefracture[J].JApplPhys,1994,75 :32 2 0～ 32 2 2 .
[2 5 ] NiiY ,NakamuraK ,ItoK ,etal.Thefractaldimensionoffracturefragmentsinrelationwithfracturingenergy[A].Proceedingsofthe 18thISASLunarandPlanetarySymposium[C],1985 .5 8～ 5 9.
[2 6 ] MandelbrotBB .Fractals:Form ,ChanceandDimension[M ].SanFrancisco :Freeman ,1977.
[2 7] FederJ .Fractals[M ].NewYork :Plenum ,1988.
[2 8] MatsuiT ,WazaT ,KaniK ,etal.LaboratorysimulationofPlanetesimalcollision[J].JGeophysRes,1982 ,87:10 96 8～ 10 982 .
[2 9] WeibullW .Astaticaltheoryofthestrengthofmaterials[Z].IngVetenskapsAkad ,StockholmHandlingar ,No .15 0 ,1939.
[30 ] WeibullW .Thephenomenonofruptureinsolids[Z].IngVetenskapsAkad ,StockholmHandlingar ,No .15 3,1939.
[31] YokoboriT .Strength ,FractureandFatigueofMaterials[M ].TheNetherlands :Wolters Noordhoff.Co .,196 5 .
[32 ] JaegerJC ,CookNGW .FundamentalsofRockMechanics[M ].NewYork :JohnWiley&Sons,Inc,196 9.5 85 .
[33] MogiK .Theinfluenceofthedimensionsofspecimensonthefracturestrengthofrocks:comparisonbetweenthestrengthofrockspecimensandthatoftheEarth scrust[J].BullEarthqResInst ,196 2 ,40 :175～ 185 .
[34 ] KandaY ,YashimaS ,ShimoiizakaJ .Sizeeffectsandenergylawsofsinglespherecrushing[J].JourMiningMetallInstJapan ,196 9,85 :987～ 992 (JapanesewithEnglishabstract) .
[35 ] PatersonMS .ExperimentalRockDeformation :TheBrittleField[M ].BerlinHeidelberg :Springer Verlag ,1978.
[36 ] OkaY ,MajimaH .Energyrequirementsinsizereduction[J].TransSocMiningEngrsAIME ,196 9,2 44 :2 49～2 5 1.
[37] KandaY ,YashimaS ,ShimoiizakaJ .Sizeeffectsandenergylawsofsinglediskcrushing[J].JourMiningMetallInstJapan ,1970 ,86 :435～ 44 0 (JapanesewithEnglishabstract) .
[38] GudenbergB ,RichterCF .SeismicityoftheEarthandAssociatedPhenomena[M ].2nded .Princeton :PrincetonUnivPress ,195 4.
[39] KingG .TheaccommodationoflargestrainsintheupperlithosphereoftheEarthandothersolidsbyself similarfaultsystems:Thegeometricoriginofb value[J].PAGEOPH ,1983,12 1:76 1～ 815 .
[4 0 ] TurcotteDL .Afractalmodelforcrustaldeformation[J].Tectonophysics,1986 ,132 :2 6 1～ 2 6 9.
[4 1] DuboisJ ,NovailiL .Quantificationofthefracturingoftheslabusingafractalapproach[J].EarthPlanetSciLett ,1989,94:97～ 10 8.
[4 2 ] NagahamaH .FractalStructuralGeology[J].MemGeolSocJapan ,1998(5 0 ) :13～ 19.
[4 3] MainIG ,MeredithPG ,JonesC .Areinterpretationoftheprecursoryseismicb valueanormalyfromfractureme chanics[J].GeophysJ ,1989,96 :131～ 138.
[4 4] MainIG ,PeacockS ,MeredithPG .Scatteringattenuationandthefractalgeometryoffracturesystems[J].PA GEOPH ,1990 ,133:2 83～ 30 4.
[4 5 ] KanamoriH ,AndersonDL .Theoreticalbasisofsomeempiricalrelationsinseismology[J].BullSeismolSocAm ,1975 ,6 5 :10 73～ 10 95 .
[4 6 ] TeisseyreR .Earthquakeprocessesinamicromorphiccontinuum[J].PAGEOPH ,1973,10 2 :15～ 2 8.
[4 7] ShimboM .Ageometricalfoundationoftheanalysisofgranularbehavior[A].CowinSC ,SatakeM ,eds .ProceedingoftheUS JapanSeminaronContinuum MechanicalandStatisticalApproachesintheMechanicsofGranularMaterials[M ].Tokyo :GakujyutsuBunkenFukyukai,1978.2 72～ 2 81.
[4 8] IesanD .Someapplicationsofmicropolarmechanicstoearthquakeproblems[J].IntJEngngSci,1981,19:85 5～86 4.
[4 9] NagahamaH ,TeisseyreR .Micromorphiccontinuum ,rotationalwaveandfractalpropertiesofearthquakesandfaults[J].ActaGeophysPolon ,1998,46 :2 77～ 2 94.
[5 0 ] NagahamaH ,TeisseyreR .MicromorphiccontinuumandfractalfracturingintheLithosphere[J].PAGEOPH ,2 0 0 0 ,15 7,inpress .
[5 1] SatakeM .Compatibilityconditionsforgranularassembly[A].KatoT ,TakakiR ,ToriwakiJ,eds.ScienceonForm :ProceedingsoftheFirstInternationalSymposium forScienceonForm[M ].Tokyo :KTKSciPubl,1986 ..191～ 199.
[5 2 ] OnodaGY ,TonerJ .Fractaldimensionsofmodelparticlepackingshavingmultiplegenerationsofagglomerations[J].CommAmCeramicSoc ,1986 ,6 9:C2 78～C2 79.
[5 3] NanjoK ,NagahamaH ,SatomuraM .Ratesofaftershockdecayandthefractalstructureofactivefaultsystems[J].Tectonophysics,1998,2 87:173～ 186 .
[2 ] MandelbrotBB .TheFractalGeometryofNature[M ].NewYork :WHFreemanandCampany ,1982 .46 8.
[3] TurcotteDL .Fractalsandfragmentation[J]..JGeophysRes ,1986 ,91:192 1～ 192 6 .
[4 ] NagahamaH .Fracturinginthesolidearth[R].SciReptsTohokuUniv .2ndser (Geol) ,1991,6 1:10 3～ 12 6 .
[5 ] GaudinAM .Aninvestigationofcrushingphenomena[J].TransAmerInstMiningMetallPetrolEngrs,192 6 ,73:2 5 3～ 316 .
[6 ] SchuhmannRJr.Principlesofcomminution ,I—Sizedistributionandsurfacecalculations[A].AIMETechPub ,No .1189,MiningEngrs[M ].NewYork :AIME :1940 .
[7] ZhaoZY ,WangY ,LiuXH .Fractalanalysisappliedtocataclasticrocks[J].Tectonophysics,1990 ,178:373～377.
[8] NagahamaH .Fractalfragmentsizedistributionforbrittlerocks[J].IntJRockMechMinSci&GeomechAbstr ,1993,30 :46 9～ 471.
[9] NagahamaH ,YoshiiK .Fractaldimensionandfractureofbrittlerocks[J].IntJRockMechMinSci&GeomechAbstr ,1993,30 :173～ 175 .
[10 ] NagahamaH ,YoshiiK .Scalinglawsoffragmentation[A].KruhlJH ,ed .FractalandDynamicalSystemsinGeosciences[M ].Berlin :Springer Verlag ,1994.2 5～ 36 .
[11] RittingerPRv .LehbuchderAufbereitungskunde[M ].Berlin :ErnstundKorn ,186 7.
[12 ] KickF .DasGesetzderproportionalemWiderstandundseineAnwendung[M ].Leipzig :ArthusFelix ,1885 .
[13] BondFC .Thethirdtheoryofcomminution[J].TransAmerInstMiningMetallPetrolEngrs,195 2 ,193:484～494.
[14] BergstromBH ,CrabtreeDD ,SollenbergerCL .Feedsizeeffectsinsingleparticlecrushing[J].TransAmerInstMiningMetallPetrolEngrs ,196 3,2 2 6 :433～ 44 1.
[15 ] WalkerWH ,LewisWK ,McAdamsWH ,etal.PrinciplesofChemicalEngineering[M ].London :McGraw Hill,1937.
[16 ] CharlesRJ .Energy sizereductionrelationshipsincomminution[J].TransAmerInstMiningMetallPetrolEn grs,195 7,2 0 8:80～ 88..
[17] SchuhmannRJr.Energyinputandsizedistributionincomminution[J].TransAmerInstMiningMetallPetrolEngrs,196 0 ,2 17:2 2～ 2 5 .
[18] TartaronFX .Ageneraltheoryofcomminution[J].TransAmerInstMiningMetallPetrolEngrs,196 3,2 2 6 :183～ 190 .
[19] GriffithAA .Thetheoryofruptureandflowinsolids[J].PhilTransRoySoc,SerA ,192 0 ,2 2 1:16 3～ 198.
[2 0 ] GriffithAA .Thetheoryofrupture[A].BiezenoCB ,BurgersJM ,eds.Proceedingsofthe 1stInternationalCongressofAppliedMechanics[M ].[s .l.]:BoekhandelenDrukkerijJ .WalterJr,192 4.5 4～ 6 3.
[2 1] MandelbrotBB ,PassojaDE ,PaullayAJ .Fractalcharacteroffractalsurfacesofmetals[J].Nature ,1984,30 8:72 1～ 72 2 .
[2 2 ] BrownSR ,ScholzCH .Broadbandwidthstudyofthetopographyofnaturalrocksurfaces[J].JGeophysRes ,1985 ,90 :12 5 75～ 12 5 82 .
[2 3] ScholzCH ,AvilesCA .Thefractalgeometryoffaultsandfaulting[A].DasS ,BoatwrightJ ,ScholzCH ,eds .EarthquakeSourceMechanics[M ].MauriceEwingVolume 6 .Washington ,D .C .:AGU ,1986 .47～ 5 5 .
[2 4] NagahamaH .Afractalcriterionforductileandbrittlefracture[J].JApplPhys,1994,75 :32 2 0～ 32 2 2 .
[2 5 ] NiiY ,NakamuraK ,ItoK ,etal.Thefractaldimensionoffracturefragmentsinrelationwithfracturingenergy[A].Proceedingsofthe 18thISASLunarandPlanetarySymposium[C],1985 .5 8～ 5 9.
[2 6 ] MandelbrotBB .Fractals:Form ,ChanceandDimension[M ].SanFrancisco :Freeman ,1977.
[2 7] FederJ .Fractals[M ].NewYork :Plenum ,1988.
[2 8] MatsuiT ,WazaT ,KaniK ,etal.LaboratorysimulationofPlanetesimalcollision[J].JGeophysRes,1982 ,87:10 96 8～ 10 982 .
[2 9] WeibullW .Astaticaltheoryofthestrengthofmaterials[Z].IngVetenskapsAkad ,StockholmHandlingar ,No .15 0 ,1939.
[30 ] WeibullW .Thephenomenonofruptureinsolids[Z].IngVetenskapsAkad ,StockholmHandlingar ,No .15 3,1939.
[31] YokoboriT .Strength ,FractureandFatigueofMaterials[M ].TheNetherlands :Wolters Noordhoff.Co .,196 5 .
[32 ] JaegerJC ,CookNGW .FundamentalsofRockMechanics[M ].NewYork :JohnWiley&Sons,Inc,196 9.5 85 .
[33] MogiK .Theinfluenceofthedimensionsofspecimensonthefracturestrengthofrocks:comparisonbetweenthestrengthofrockspecimensandthatoftheEarth scrust[J].BullEarthqResInst ,196 2 ,40 :175～ 185 .
[34 ] KandaY ,YashimaS ,ShimoiizakaJ .Sizeeffectsandenergylawsofsinglespherecrushing[J].JourMiningMetallInstJapan ,196 9,85 :987～ 992 (JapanesewithEnglishabstract) .
[35 ] PatersonMS .ExperimentalRockDeformation :TheBrittleField[M ].BerlinHeidelberg :Springer Verlag ,1978.
[36 ] OkaY ,MajimaH .Energyrequirementsinsizereduction[J].TransSocMiningEngrsAIME ,196 9,2 44 :2 49～2 5 1.
[37] KandaY ,YashimaS ,ShimoiizakaJ .Sizeeffectsandenergylawsofsinglediskcrushing[J].JourMiningMetallInstJapan ,1970 ,86 :435～ 44 0 (JapanesewithEnglishabstract) .
[38] GudenbergB ,RichterCF .SeismicityoftheEarthandAssociatedPhenomena[M ].2nded .Princeton :PrincetonUnivPress ,195 4.
[39] KingG .TheaccommodationoflargestrainsintheupperlithosphereoftheEarthandothersolidsbyself similarfaultsystems:Thegeometricoriginofb value[J].PAGEOPH ,1983,12 1:76 1～ 815 .
[4 0 ] TurcotteDL .Afractalmodelforcrustaldeformation[J].Tectonophysics,1986 ,132 :2 6 1～ 2 6 9.
[4 1] DuboisJ ,NovailiL .Quantificationofthefracturingoftheslabusingafractalapproach[J].EarthPlanetSciLett ,1989,94:97～ 10 8.
[4 2 ] NagahamaH .FractalStructuralGeology[J].MemGeolSocJapan ,1998(5 0 ) :13～ 19.
[4 3] MainIG ,MeredithPG ,JonesC .Areinterpretationoftheprecursoryseismicb valueanormalyfromfractureme chanics[J].GeophysJ ,1989,96 :131～ 138.
[4 4] MainIG ,PeacockS ,MeredithPG .Scatteringattenuationandthefractalgeometryoffracturesystems[J].PA GEOPH ,1990 ,133:2 83～ 30 4.
[4 5 ] KanamoriH ,AndersonDL .Theoreticalbasisofsomeempiricalrelationsinseismology[J].BullSeismolSocAm ,1975 ,6 5 :10 73～ 10 95 .
[4 6 ] TeisseyreR .Earthquakeprocessesinamicromorphiccontinuum[J].PAGEOPH ,1973,10 2 :15～ 2 8.
[4 7] ShimboM .Ageometricalfoundationoftheanalysisofgranularbehavior[A].CowinSC ,SatakeM ,eds .ProceedingoftheUS JapanSeminaronContinuum MechanicalandStatisticalApproachesintheMechanicsofGranularMaterials[M ].Tokyo :GakujyutsuBunkenFukyukai,1978.2 72～ 2 81.
[4 8] IesanD .Someapplicationsofmicropolarmechanicstoearthquakeproblems[J].IntJEngngSci,1981,19:85 5～86 4.
[4 9] NagahamaH ,TeisseyreR .Micromorphiccontinuum ,rotationalwaveandfractalpropertiesofearthquakesandfaults[J].ActaGeophysPolon ,1998,46 :2 77～ 2 94.
[5 0 ] NagahamaH ,TeisseyreR .MicromorphiccontinuumandfractalfracturingintheLithosphere[J].PAGEOPH ,2 0 0 0 ,15 7,inpress .
[5 1] SatakeM .Compatibilityconditionsforgranularassembly[A].KatoT ,TakakiR ,ToriwakiJ,eds.ScienceonForm :ProceedingsoftheFirstInternationalSymposium forScienceonForm[M ].Tokyo :KTKSciPubl,1986 ..191～ 199.
[5 2 ] OnodaGY ,TonerJ .Fractaldimensionsofmodelparticlepackingshavingmultiplegenerationsofagglomerations[J].CommAmCeramicSoc ,1986 ,6 9:C2 78～C2 79.
[5 3] NanjoK ,NagahamaH ,SatomuraM .Ratesofaftershockdecayandthefractalstructureofactivefaultsystems[J].Tectonophysics,1998,2 87:173～ 186 .
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心