随机故障网络的幂律连通性 断层长度分布

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1、WATERRESOURCESRESEARCH,VOL.33,NO.7,PAGES1567-1583,JULY1997ConnectivityofrandomfaultnetworksfollowingapowerlawfaultlengthdistributionOlivierBourandPhilippeDavyG6osciencesRennes,UPR4661CNRS,Rennes,FranceAbstract.Wepresentatheoreticalandnumericalstudyoftheconnectivityoffaultnetworksfollowingpowerla

2、wfaultlengthdistributions,n(l)--•al-a,asexpectedfornaturalfaultnetworks.Differentregimesofconnectivityareidentifieddependingona.Fora>3,faultssmallerthanthesystemsizerulethenetworkconnectivityandclassicallawsofpercolationtheoryapply.Ontheopposite,fora<1,theconnectivityisruledbythelargestfaultinth

3、esystem.For1

4、rticular,wepredicttheexistenceofacriticalscaleatwhichfaultnetworksarealwaysconnected,whateverasmallerthan3,andwhatevertheirfaultdensity.Introductionlength[Englmanetal.,1983;Robinson,1983,1984;Balbergetal.,1984,1991;Gu•guenandDienes,1989].ForsuchsystemsInfracturedrocksofverylowmatrixpermeability,

5、suchasthepercolationthreshold,thecriticaldensityofcracksneces-crystallinerocks,fluidflowisoftenveryheterogeneousandsarytoconnecttheboundariesofthesystem,iswellknown,focusedinfewfractures,asshownbyhydraulicfieldexperi-andRobinson[1984]andBalberg[1986]alsodemonstratethements[Neretnieks,1985,1994;L

6、ong,1994].Inthiscase,clas-generalapplicabilityofpercolationtheorythroughthemea-sicaltheoriesofhydrogeologythatconsideranequivalentpo-surementsofsomeuniversalexponents.rousmediaareoftendifficulttoapply.ThecomplexityoffluidAlargedistributionoffaultlengthintroduceslong-rangeflowinfracturedrocksisma

7、inlyduetothecomplexgeometryspatialcorrelationinthesystem,particularlyinthecaseofaoffaultpatternswheresuperposedstructuresofvarioussizespowerlawdistribution,whichhasintrinsicallynocharacteristicmayallhavenonnegligiblecontribu