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Laboratory determination of fracture aperture, permeability and stress repationships

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Laboratory determination of fracture aperture, permeability and stress repationships

    Laboratory determination of fracture

    aperture, permeability and stress

    repationships

JOURNALOFCOALSC?CE&ENG?幢皿R

    ;(CS~A):SN1006-9097

    ;PP1316VoL9No.2Dec.2o03

    ;Laboratorydeterminationoffractureaperture,permeability

    ;WANGJian-xue(王建学),ZHANGJin-cai(张金才)

    ;(1.HebdImitateotAcblteclxmiSdeB~ndTh

    o,iIaBIQ056038,Chil~;2.CeoperativelnslttuteforResearch

    ;EnvironmentalSdenees,Theualver~0fColorado,Boulder,CO80309?0216,USA) ;AbstractItiswelIknownthattheformationpermeabilityiSnotaconstantbutafunctionof ;theIn-situstressenvironment.Thisstudyhasbeenpdmadlycardedoutnumerically.andtoa ;certainextent,inthefield.However,sincetherockpropertiesaregenerallytestedintheIa- ;boratory.thisIastsituationneedstobemodeledtomaintainconsistentscalesintheanalysis. ;Inthispaper,conceptsandtechniquesoflaboratoryexperimentsarepresentedtodetermine ;relationshipsbetweenfractureapertureandextemaIloadinginsimulatedrocksfconcrete). ;Keywordsfractureaperture,permeability,stressrelationship

    ;Infracturedformations,thepermeabilityvariesasthestressenvironmentismodified….Duringthepast,t

    his

    ;relationshiphasbeenmOlleffectivelydelineatedthroughvariouslaboratoryandfieldtests,representedbydifferent

    ;empiricalforms.Jonespm~dedanempiricalrelationshipforthefracturepermeabilityofcarbonaterocksasfol-

    ;lows[:

    ;=()r,

    ;where,k0istheimtialpermeability;istheeffectivestress;histheeffectivestresswhenk=0. ;Louissuggestedanalternativerelationshipbasedonwellpumpingtestsatdifferentdepths[:

    ), ;k=k0exp(

    ;where,istheeffectivestress,whichCanbeexpressedas:=-pinwhichistheoverburdendensity;here ;Histhedepthofthelocation;Pisthepollpressure;Misacoefficient.

    ;Walshofferedthefollowingempiricalml~onshipderivedfromlaboratorytestdata…:

    ;J}=1()ln()’,

    ;where,isaconstantrelatedtothefracturegeometry;0istheinitialeffectivestress. ;Theparallelplateanaloghasbeenadominantconceptualmodelforfluidflowthroughonidealizedsinglefrac-

    ;}SupportedbyNationalNaturalScienceFoundationofChina(59634030)

;

    ;14JournalofCoalScience&Engineering(China)

    ;ture[5.6]

    ;.InthismodelthatthefractureapertureistheparameterwhichismostIlkelytochangewhenthestress ;conditionsvary.Theempiricalrelationshipcanbegivenasfollows[:

    ;6_60exp(),

    ;where,isthenormalstressactinginsidethefracture;b0istheinitialaperture;isthenormalfracturestiff-

    ;lieS8.

    ;Thisrelationshipwastestedunderdifferentfracturegeometriesusingaconcret~blockofsize4OOmmx ;4OOmmx20011111111.Threedifferenttypesoffracturesweremadeduringtheconstructionoftheblock,i.e.,verti

    ;eal,inclined,andfracturenetwork,asshowninFig.1.Theblockhadtheuniaxialcompressionstrengthof ;39.3lPa.Theloadingandunloadingtestswerebiaxialwheretheratiosofvertical()tohorizontalload() ;rangedfrom1to4.Duringthetests.thechangesinstressesandfractureaperture

    wellasthefracturepropaga-

    ;tionwererecorded.

    ;(c)

    ;毋蛋1S曲旧岫tcwI矗咖re,i珊娜nedandnetwork矗拟加re

    ;(a)vertical~(b)inclined;(c)network

    ;1.1Verltiealtraetm-e

    ;ThreesectionsoftheverticalfractureashowninFig.1(a),withorigi~aperturesbeing11.25,11.25 ;and8.25mill,respectively.(1)Uniaxialloadingandunloadingperpendiculartothefractureplane.Asshownin

    ;Fig.2(a)uniaxialloading(inthedirection),resultsinfractureaperturestodecreasetlItheloadincrease ;inallthreesection8.Thedecayisexponential;andreversiblefortheunloadingca8e.However,thewidthoforigi-

    ;(+,MPa

    ;(c)

    ;2Aperture舭眦Ii曩虹aIloadingperpendieular,l~l’alleltothefracture

    ;jnseeliolls1and2andIiplP/tm,elndIb萱衄湖lo_m

    ;halaperturecanneverberecove.(2)Uniaxialloadingandunloadingparalleltothefractureplane.Forthe ;loadingparalleltothefractureplane(inthe,

    direction),theaperture-loadrelationshipsareoppositetothe

    ;casetlIloadingperpendiculartothefractureplane,andareshowninFig.2(b).Duringunloading,theaperture

    ;changesremainfluctuatingbutwithminimumamplitude.(3)Uniformbiaxialloading..I1lewidthofthefraetttre

    ;

    ;t?【II,IIIA

    ;

    ;WANGJian-xue.eta1.L~boratorydeterminationoffractureaperture15

    ;decreasesastheloadingincreasesforallthreesections

    ;,

    ;asshowninFig.2

    ;(C).(4)Unevenbiaxialloading.Fordifferentloadingratios.tlIein. ;Cre&~ofstressagainresultsinadecreaseinfractureaperture.Incompari. ;sonwiththepreviousbiaxialloadingcase,thenegativeexponentialrela- ;tionshipofaperture,stressbecomeslessrelevant,evidencedbythemuch ;lowerrelativecorrelationcoefficients.Thisi8partlyduetotheeffectofnew ;fracturescreatedduringtheloadinginFi$3.

    ;1.2Inclinedfracture

    ;Theinclinedfracturealongwiththreemeasuringsectionsaredepicted ;inFig.1(b).Theoriginalwidthsofthesesectionsare6.10,6.95,7.60

    mm,respectively.Forvariousloading

    ;ratios,Fig.4indicatetheapparentnegativeexponentialdecayrelationshipsbetweenfractureaperturean

    dload.

    ;8.O

    ;7.5

    ;7.O

    ;6.5

    ;6.O

    ;:

    ;s.s

    ;(+/SPa

    ;4.O

    ;.o

    ;

    ;6”51

    ;I+

    ;5-s

    ;5.0-6___O

    ;(a)(b)

    ;4ApertureandnnitOl’lllblaxiall~~lhg,apertureandbimdall~~lhg(=4y)

    ;Duringthetests,newfractureswereinitiallydeveloped,andpropagated ;untilfinalfailureoftheblock,asshowninFig.5.

    ;1.3Fracturenetwork

    ;Thisgeometrymaybeabetterrepresentationofthenaturalfractures ;inrockmasses.AsshowninFig.1(C),sixsectionswereselectedtlI ;thewidthsof7.15,10.90,7.4o,12.25,7.85and8.0omm,respec-

    ;tively.Thetrendofaperture-stressrelationshipforthefracturenetworkis ;againsimilarastheaperturedecreaseswhenthestressincreases,asshown ;inFig,6.However,newfracturedevelopmentsappeartobecompletely ;awayfromtheoriginalfracturepaths,inthedirectionsperpendiculartotheoriginalfractureplanes.Asare

    sult,a

    ;circularringtypefractureprofilebecomesthedominantfeature(Fig.7). ;g7.6

    ;童墨’2

    ;6?81

;.O2.O3.04.0

    ;(a+a)/IV[Pa

    ;(a)

    ;g7.6

    ;童墨

    ;7_2

    ;.-_.——_??6097-7ffp[-6.

    ;06~i(

    ;/h~7,4193=a_.?.?..???-,J,:

    ;6-0_]?——=.o

    ;(+),MPa

    ;(b)

    ;6Apertureandbiaxialloading

    ;(a)O”x=2;(b)O”x=3o’y

    ;?I?,a=Il

    ;?I?,a=Il

    ;霎嚣

    ;

    ;16JournalofCoalScience&Engineering(China)

    ;TheaperturestressrelationshipforvarioustypesoffracturestlIdifferentinitialaperturesandsubjectedto

    ;differentloadingconditionscanbesummarizedasfollows:

    ;(1)Fortheuniaxialloadingperpendiculartothefractureplane,theaperturedecreasesasthesincrea- ;ses,whichcanbedefinedby:b=boexp(Atry),hereisthestressperpendiculartothefractureplane.

    ;(2)Fortheuniaxialloadingparalleltothefractureplane,theapertureincreasesasthestressincreases, ;whichcanbedefinedby:b=boexp(Btr),hereisthestressparalleltothefractureplane.

    ;(3)Foruniaxialunloading,theaperture?stressmayshowtheoppositetrendfromtheloadingeases,butthe ;originalaperturewidthcan,ingeneral,notberecovered.Forthebiaxialloadingwithdifferentloadingratios,the

    ;aperturedecreasesasthestressincreases,whichcanbecharacterizedas:b=boexp[C(+)],hereand

    ;,arethebiaxialloads;A,B,Carethetestingconstant(A,B,C>0).

    ;(4)Underbiaxialload,newfracturesdevelopduringtheloading.Thesenewfracturesdonotfollowthe8alne

    ;pathsastheoriginalfractures.Instead,theytendtobepositionedindirectionsperpendiculartotheoriginalfracture

    ;planes,nearthefracturetips.Foraninitialfracturenetwork,acircularringtypefractureenclosingtheor

    iginal

    ;fracturesisfrequentlytheendproduct.Fracturesareprobablytheresultofthesenewimemalfracturedisplacement

    ;combinedwiththeindueedtensionnearthefracturetips.

    ;Experimentalworkofstress?dependentpermeabilityprovidesstrongevidencethatpermeabilitycannotbeacon-

    ;stantbutafunctionofstresses.Inthispermeability?stressrelationship,exponentialformisadominantfeature,

    ;whichcomplieswiththefieldobservationsreportedintheliterature.Thetrendandmagnitudesofthepermeability

    ;variationsseemtobecontrolledbytheinitialmagnitudesoffractureaperture,externalloadconfigurations,andfail-

    ;uremodesofthetestedmaterials.

    ;BaiM,ElsworthD.Modelingofsubsidenceandstress-dependenthyd,~dicconductivityofintactandfracturedporousmedia.

    ;[J].RockMech.andRockEngng.,1994,27(4):209234.

    ;JonesF0.Alaboratorystudyoftheeffectsofconfiningpressureonfractureflowsndstoragecapacityincarbonaterocks.[J].

    ;J.Petro.Technol,1975.2127.

    ;LouisC.Gmundwaterflowinrockm

    s8esanditsinfluenceonstability[R].RockMech.ResearchReport.ImperialCol-

    ;legc,UK,1969,10.

    ;WalshJB.Effectofporepressureandconfiningpressureonfracturepermeability[J].Int.J.RockMech.Min.Sci.and

    ;Geomech.Abstr.,1981,18(3):429~435.

    ;BearJ.Dyusmie8offluidsinporousmedia[M].AmericanElsevierPublishingCompany,Inc.,1972.764. ;WitherspeonPAeta1.VMidityofCubiclawforfluidflowinadeformablerockfracture[J].WaterResour.Res.,1980,16

    ;(6):10161024.

    ;张金才,刘天泉,张玉卓.裂隙岩体渗透特征研究[J].煤炭学报,1997,22(5):481485.

    ;ZhangJC,TQ,ZhangYZ.Thestudyofpermeabilitybehaviorsforfracturedrockmas8es[J]-J.ofChinaCoalSociety,

    ;1997.22(5):481485.

    ;瓤巍

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