AG US T GUDMUNDSSON,INGRID FJELDSKA AR & OT/LlEGJ ES DA L NGU-BULL 43 9,20 02 - PAGE 61
Fracture-generated permeability and groundwater yield in Norway
AGUST GUDMUNDSSON,INGRIDFJELDSKAAR&OTILlEGJESDAL
Gudmundsson,A.,Fjeldskaar,I.& Gjesdal,O.2002:Fract ure-generated permeability and groundwate ryield in Norway.Norg esqeoloqiskeundersoke/se Bulletin439,61-69.
Thetransportof groundwaterin bedr ockislargelydetermined byinterconnectedfractures and their apert ures.The conditions by whichfract uresbecomeinterconnected are thus ofprimaryimport anceinunderst anding permeabil- ityandgrou ndwateryield.Thisapplies in particulartothe observedlinear correlationbetwee nthe currentpost- glacialupliftrate and groundwateryield inthe bedrockofsouthernNorway.Wepresentboundary-element models ontheform ati onofinterconnected fracturepathways withapplicationtothecoastalareasofWest Norway.In the mod els, weuseexternaltensile st ressandinternalfluid overpressure;loadingconditionsthat arelikely to have been operativeinlargepartsof Nor wayduringtheHolocene.Theext ernaltensile st ressresultsindicate thatmany frac- turepat hwaysformbythe linking upofoffsetjointsthroughtransverse shearfractures.Ot herpath ways, however, areformed bylinkingupof jointsandcontactsthro ughtensile stressesassociatedwiththetips of propagatin g hydrofractures.Howthefractu repathwaysformmay affect the subseq uent permeability.Inparticular,transverse shear fractu resarelikelytohaverelatively smallaperturesandlimitthegroundwatertransport.
AgustGudm undsson,Ingrid Fje/dskaar&OtilieGjesda/. Geologica/ lnstitu te,Universityof Berqen,Allegoten41,N-5007 Berqen,Norway (e-m ail:agust.gudm undsson@geol.uib.no)
Introduction
The observed linear and positive correlat io n between the current rateofpostglacial uplift andyield of ground w ater wells is one of the basic hyd rog eologi cal relation s in Norw ay.This correlatio nwasinitiallypubli shedbyRohr-Torp (1994),usingfive areas of different postglacialuplift rates andincludi ng a total of 1278drilledwells in thebedrock of sout hern Norway.Hisresultswere suppo rted by those of Morland (1997) who used a database of 12,757 bedrock wells,ofwhich8,726areinPrecambrian rocks.
Thiscorr elationmaybe related toincrease in hydraulic conductivity in areas of high uplift rates compared wit h those of low uplift rates(Gud mundsson 1999).High uplift rates would then coincide wit h areasof crustal doming whereassociatedtensile st resses lead to reactiv ation ofold, or formation of new,wate r-conduct ing fractur es.How ever,a fractur e syst em conduct s wate r only if the percolati on thresholdof that system isreached,thatis, only if thefrac- tures form an inte rconnected cluster (Stauffer & Aharony 1994).Thus,in order to understand how uplift-gener ated st ress field scontributeto groundwa te ryield,we must also understand how fractures link up into interconn ected, wat er-conduct ingsyste ms.
Thispaperhasthreeprincipal aims.First,topresentfield examplesofevo lvi ngsmall-scale fracture syste msas anindi- cati on of perm eabilit y development.All the examplesare from theislandof0ygarde n justwest of the cityof Bergen.
Second, to present numericalmodels on how fracture sys- tem slink up in jointed and layered rock masses.Thefocu s is on the propagat ion of the two main types of fractures:
extensionfractures,which includemanyjoints and tension fractu res, andshearfractures,i.e.,fault s.Third,to discussthe postglacialst ressfieldsin Norwayin relatio n tothelinking upoffract ures.
Fracture systems and faults
In many rocks,groundwater flow isprimarily throughfrac- ture syste ms,someof whicheventuallydevelop into large- scalefault s.Thefract urenetworksmaybe primarystr uctures suchas,forexample,manyjointsystemsinsedimentaryand ign eous rocks. Com monl y, these primary fractures form weaknessesfrom which inte rconnected tect oni c fracture systemsand fault sdevelop.
Asanexample ofalargelyunconnectedfract uresyste m, one may considerexfo liat ionfract ures (sheetjoints)inlay- ered gneiss on the island of0ygarden (Fig.1).These frac- tures,subparallelwit h the freesurface,for masa result of rapid unloadin g of thesurface dueto erosionand deglacia- tion. Remova lof theoverburden leadstothesurface-parallel compressivest resses exceedingthevertica lst ress.The result isfractur edevelopment paralleltothemaximum compres- sivest ress and, therefore,parallel wit h thesurface.Thehor i- zontalexfo liation fractures giverisetomechanicallayering which part lyfoll owsthe origi nal layering in thegneiss,but is partl y independent of that layering(Fig.1).Thus, therock becomes divided into sheets which, however, decrease rapidl yin frequency wit h depth (Fig.1,cfJ ohn son1970).
Exfoli ation fract uresthat become interconnected may cont ribute tobedrock permeabilityatshallow dept hs.They, like other fractures, becomeinterconnectedthrough either
NGU-BULL 439,2002 - PAGE 62 AGU STGUOMUNO SSON,INGRJOFJEL O SKA A R&OT/LlE GJESOAL
Fig. 1. Suhorizontal exfoliation fractures in gneissonthe island of 0ygarden (Toft ey). West Norway.Spacing of the exfolia - tion fractures increases rapidly with depth.View northeast;the subver tica l nor mal fault west of the person istheone inFig.3.
extensio nfracturesorshear fractures.Inan extensionfrac- ture the displacement is primarily perpendicular to,and away from, the fracture plane(Fig. 2).whereas in a shearfrac- ture the main displacement is parallel with the fracture plane(Fig. 3).
Fig.2. Linking up of exten sion fractures in gneiss on the island of 0ygarden (Toft ey).View northeast;the fracture apertu re tends to increasewhen meetingwit h the horizontalexfoliationfractures,at the contacts wit h the dark amphib olitelayers.The steeltapeis 1 mlong.
Fig.3.Steeply dipping normalfaultinterconnecti ng subhorizontalexfo- liatio nfractu resinthe gneissof 0ygarden(Toft oy)(Fig.1).Maximum verti cal displacem ent is 4cminthecent re ofthe fault.but decreasesto zero at the tips.Viewnortheas t;theperson s providea scale.
Extension fractures
Ext ension fractures (Fig. 2) are either tension fractures or hydrofra ctures.Tension fractures form when the minimum principal compressive st ress(considered posit ive)is nega- tive,that is,when there is an absolute tension in the crust.
AG US T GUDMUN D SSO N,/NGRID FJELDSKAAR& OT/LlEGJESDAL NGU-BULL439, 2002 - PAGE63
Fig. 4. Well intercon nected, orth ogo nal jointsystemingneiss on the island of 0ygarden (Toftey), View southwest;theper- son providesascale.
They aremostly limitedto areasundergoing active exte n- sion,suchas areas ofrifti ng and those ofgreat postg lacial uplift such as in the central part ofFenn o scandia(M6rner 1980,Gudmund sson 1999).The maximumdepthto whicha tensionfracturecanpropagate
a.:
from the surface(before it changesinto anorm alfault) isgiven by (Gudm undsson 1992, 1999):dm"
-R
- p,g (1)whereToistheinsit u tensilestrength,
P,
the densit y of the hostrock, and 9the accelerat ion dueto gravity.The jointsin Figs. 2 and4are ina crustal layerwith an averagedensityof around 2500kgrn'(Hansen1998).lf these joi ntsaretension fractures,theirmaximumdepthscanbeestim atedfrom Eq.(1). Typical in sit u st rengt hs of bedrock are 0.5-6 MPa (Amadei& Step hansson1997),and the acceleration due to gravity at the surfaceis 9=9.8 m s'.Substit ut ing theseval- uesin Eq.(1),we obtain
a .:
as around60m(fo rTo=0.5 MPa) and 700 m(forTo=
6 MPa).Thepresum edtensionjoints inFigs.2 and4 are unlike ly to reach the above maxim um depth becausethe horizontal exfo liat ion fractu res wouldtendto arrest the joint tip s.Also, thereis a correlat ion bet w een ope ningofatensionfracture at the sur faceand itscontrollin gdimension,defi ned asthe smalle r of the fractu re dip and strike dimensions (Gudmundsson2000).For a mechanically layeredhost rock, the controll ing dimen sion ofafracture is normallyits dip dimension (Gud m undsson 1992, 2000).Thus,tension frac- tures wit h maximum surfaceopenings of afew mill imetres normally have dip (cont rolling) dimensions of several metr es or,at most,a few tensofmetr es.Theinterconn ect ed jointsystem in Fig.4isthereforelikelyto belimitedtothe upp erm osttens of metresor, at most,afewhundredmet res, bot h as regards the depth of the exfoliatio nfractures as well
asthe depth of the vertical tension joints.
In contrast to tension fractures ,hydrofractures can occur at any crustaldepth. Hyd rofractu res areopened up by a fluid pressurethat isgreate r thanthe normal stress on the frac- ture plane. Most hyd rof ract ures are extension fractures (Gudmundssonet al.2001),inwhic h casethe norma l stress on thehydrofractureplane istheminimum principal com-
Fig.5.Dolerit edyke, of Perm ian age,on theislandofTysnesoy,southof Bergen,WestNorway.Viewnortheast;thedykeis0.7mthick anddips
n ONw.
NGU-BULL439 ,200 2 - PAGE 64 AGUSTGUDMUNDSSON,INGRID FJELDSKA AR &OT/LlEGJESDAL
pressivestress.Thenormal condition for hydrofra cture for- mation canthus be given as(Jaeger&Cook1979):
Fault s
Faultsmay initiateassma ll-scale shear fractu res(Fig.3)or, perhaps more commonly,develop during the linking up of small fract ures of various types (Fig.6).In vertical sections, shear fractures (like tension fractures)norma lly have diffi- cult y inprop agat ingthrou g h horizontal discontinuities such as openexfol iationfractures(Fig.3).At such discontinu it ies, ashearfract ure may either becom e offset orarrested.
where P,isthetotal fluidpressure, 0",istheminimumcorn- pressive principalstress(normal to the hydrofracture),andTo isthe in situtensile streng t hof the host rock.
Becausehydr ofracturescan form at any crustaldepth, theyare likelytobegenerally moreim por tan t forthe devel- opmentoffracturepathwaysand permeabilityin rocks than tension fract ures.For examp le,manyjoints (Figs.2, 4)may form as hydrofractu reswhere the fluid disappears subse- quentto the joint formation.In general,where groundwater or gas isthefluid that drives a fractureope n,itisdifficu lt to confirm that the fract ure was generate d by afluid.Other fractures,however,are generated by fluidsor magma that freeze in the fracture subseque nt to its formation.Well known exam p lesare dykes, sills, incli ned sheets and mineral- filled veins. Com monly, mineral veins form networks of ext inct geot hermal system s that provide important infor- mat ion onpermeabi litygeneratio nthroug h their em place- ment (Gudm undsson et al. 2001).Some veins may reach leng th sofseveralhun d red metres, butmost have lengthsof severalmet resor less (Gudmu ndsson et al. 2001
L
and are thusindividuallytoo small to have much effecton ground- waterflow.Thicksil ls canhave considera bleeffectsongroundwa te r flow, but generally the most important 'f rozen' hydrofrac- tures for groundwater flow are regional dykes (Fig. 5). In Norw ay,dykes are commo nalong the westcoastandinthe Osloreg ion (Thon 1985,Sundvoll& Larsen 1993, Torsvik et al. 1997,Fossen & Dunlap 1999).Many dykes are of dense basalt or doleritewit h low matrix permeability and act as barrierstotransverse flow of groundwater. Others,particu- larly thick and fractured dykes,may be sources of ground wa- ter (Sing hal&Gupta1999).
Perhapsthe mostimportanteffect of dykes on groun d- water flow in Norway, however, is that the basalticdyke rock has nor mally very different mechanicalproperties from it s host rock(Fig. 5).It follow sthat stresses tendto concentrate atthe contact between the dykerock and the host rock and generatefract uresthat may conduct groundwater.Dykes form theirpathwaysina similarway to thatin the mode lsof hydrof ract ure formation below.It followsthat groundwater conduit s at contacts betw een dyke rock and host rock will followthese same pathways.
Inlateral sect ions (Fig.6),shear fractures (andexte nsion fractures) normally grow by the linki ng up of gradually larger segm ents . These segment s may initially be offset joints formed early in the evolu ti on of the host rock.
Alternat ively,later-formed tectonicfracturesmaypropagat e andlinkupintolarger,segme nte d fract ures(Fig.6). lndoing so,they form anint erco nnecte d syste m of fractu res or seg- mentsthat has the potential of conducting groundw ater alongits entire leng t h.
The linking up of small-scalejoi nt sand fract uresinto larger shear fractures or fracturesystems is,in detai l,a com- plexprocess that is still only part ly under stoo d(Cox &Scho lz 1988, Gudmundsson 1992,Acocella etal. 2000,Mansfield&
Cartwright 2001).This process,however, largel y controls whet her or not thepercolat ionthreshold of a fract uresys- temis reachedand,thereby,thebed rockperme abilit y.Some general aspects of linking up of fractures into segmented extension fracturesand shearfractu res are illustrate d by the follo w ingnumer icalmodels.
Fig.6 .Extension fractureslinkedup through transver se shear fractures, modelled in Figs.7-8.ViewNNE;thelengt hof thesteel tape is0.8 m.
Num erical models of fracture growth
All the modelsaremade using thebound ary-elem ent pro- gramBEASY(1991
L
themethod beingdescribed in detailby(2)
Pr"'O",+ToAGUSTGU DM U N DSSON, ING RID FJEL D SKA A R& OT/ LlEGJ ESDA L NGU - BULL 439, 2002 - PA GE 65
Fig. 7. Bound ary-elementmod el show ing thetensile st ress,inmega- pascals as absolute values,between thenearbytips oftwo extension fracturesof equal lengthsubject to 6 MPa tensileloading (indicated by horizontalarrows).In this model,the offset(horizontal distance)and underlapp ing (vertica ldistance) between thenearby tips arebot h equalto half thefract ure length.
Fig. 8.Bound ary-elementmod el showi ng the shearst ress,in meqa-pas- cals,forthesame fractur e config urat io nandloadingasinFig.7.
Brebbia&Dom in gu ez (1989). The program makesit possi- ble, for given bound arycondition s,to calculate the stresses and displacements at any points of interest inside the model.The resultsare most convenientlypresentedas con- tours ofequalstress magnit ude,given in mega-pascals,as wellas openingup of discontinuitiessuch asfract ures and contacts.The models are divided int o one or more zones (correspondi ng, for example,to mechanical layers), each with uniformmechanical properties;here Young'smodulus (also referredto as stiffness)and Poisson'sratio.
Thefirstmod els (Figs.7, 8) indicate how offset fractu res may linkupto form an interconnectedsystemof en echelon segments (Fig. 6).Inthese models,the only loading on the offset fract ures isafracture-perpendicul artensile stressof 6 MPa,a value similartothemaximum insit u tensile strength
of gneiss (Amadei&Stephansson 1997).Thisload is applied as tension perp endicu lar to the two bound aries of the model that run parallel wit h thefract ures (Figs.7, 8).A uni- form Poisson'sratio of 0.25,used inall the models,is appro- priate for gneiss (Jumikis 1979, Bell 2000).The uniform Young'smodulus used inthe firstmodels, 10GPa, is in the lower range of laborato ry valuesof Young's modulusfor gneiss(Jumikis 1979,Bell 2000).Because in situ rocks nor- mallyhavemuchlower Young'smoduli than small-scale lab- oratory measurements of the same rocktyp es (Goodma n 1989),thisvalue is appropriate. The fractures are modelled asinternal springs, each with a stiffness of 6 MPa/m .The unitsof fractur e st iffn ess differfrom those of rockstiffness (Young'smodul us) becausethe stiffnessof a solid rock is determinedfrom a stress-straincurve whereas that of a frac- ture is determined from a stress-displacement curve (Hudson&Harrison 1997).
The result sshow zones of high tensile(Fig.7)and shear (Fig.8) st resses between the nearbytips ofthe fractures. For the given loading of6MPatensile stress, thesezones gener- ate potent ialtensile stresses in excessof 11 MPa(Fig. 7)and potential shearst resses in excessof 13 MPa (Fig.8).Theseare the relevant values, but much higher potential stresses occurat the fract uretips.A tensile stressof 11 MPa isaround double the maximum in situ tensile strength of gneiss (Amadei & Stephansson 1997), so that tensile fractur es would be expected to form inside the high-stress zone.
Similarly,thein situ shear strength of rock, which is com- monly roughly twice its tensile st rengt h (Jumikis 1979, Farmer 1983), is also normally much less than 13 MPa,in whichcaseshearfractures wouldbe expectedto form in the high -st ress zone.
TheESE-WNW-t rend ing and straight transverse fractures connecti ng the main NNE-SSW-trending fractures in Fig.6 arelikely to be mostlyshearfract ures.Shear fractu res tend to be st raig ht and forminside the zone of maximumshear st ress(Fig.8), whereasmost tensilefractures generated in such a high-stresszonearegentl y curvingand for mhook- shaped fractures (Gud mu ndssonet al.1993,Acocella et al.
2000).
The othermodels(Figs.9-12) show how ahydrofract ure, drivenby an internalfluidoverpr essure, opensup discont i- nuities (joint sand contacts) in the host rock ahead of the hydrofracture tip.Inall thesemodels, the hyd rofractu re is model led as a vertica lext ension (mo de I)fractu re with an internal fluid overpressurethatvaries from 10 MPa at the bottom of thefracture to0MPa atthefluid front. The fluid frontcoincideswiththe fractur etipin themodels in Figs.9- 11,but in Fig.12the fluidfront is 0.1 units belowthe fracture tip.Each model hasa unit height;all the dim ensions are givenas a fraction of this unit.Onlytheupperhalf ofeach hydrofractureismodelled, andthe modelsare fastenedat the lower corners, so as to avoid rigid bod y translatio nand rotation.
As in the earlier models (Figs.7,8),a uniform Poisson's
NGU-B ULL439,20 0 2 - PAGE 66 AGUSTGUD M UN DSS ON,INGRID FJ ELDSKA A R
s
OT/LlE GJESDALSurface
Tension fractures
/ \ '"
Fig.9. Boundary-element model showing how the tensile st ress,in mega-pascals, aroundthetip of a vertical hyd rofractu re opens upverti- cal jointsanda weakcontact int o tensionfract ures.Figs.8-12showonly tensilestressesinthe range1.5-10MPa.
Fig.10.Same model asin Fig. 9,exceptthat athirdjoint has beenadded (in the centre)and the weak contact ishere tw iceaslong as in thepre- vious(Fig. 9)model.
Surface
Fig.11. Boundary-element model showing how the tensile stress, in mega-pascals,around the tipof avert ical hydrofractureopensupverti- cal joints intotension fractures.Thejoi nts arelocated in asohlayer B (Young's modulus5 GPa)embedded in a stifferlayer A(Young'smodu- lus 10 GPa).The soh layer reducesthe tensile st resses associated wit h the hydrofracturetip.
modulusof 5GPa,is embedded ina layer A of 10GPa, both ofwhich haveaPo isson'sratio of0.25.Thereare twovert ical discon tinuit ies,each of length 0.4 units and present ed by internalspring s ofst iff ness 6MPa/m that reach the surface.
Fig. 11 show s that, evenifthediff erencein stiffn ess betwee n
A
A ensionfractu res B
ratioof 0.25isused and,for the firsttwo models(Figs.9-10), alsoauniformYoung's modulusof 10 GPa.Inthethird and fourth models(Figs.11-12),how ever,there isa softerlayerof 5GPa embeddedinthestifferlayerof 10 GPa,representing layering wit hi n thegneiss (Figs.1-3).As before,thejoints and horizontal contacts in the rock are mod ell ed as int ern al springswitha stiffnessof6MPa/m.Here, this stiffness may be taken as representative of asoft,but elastic, infil linajoint and aweak sed imentaryor soilmaterial at a contact. For comparison, sma ll-scale labor ato ry samples of clay and weak mudsto nehave Young'smodu li so low as3 MPa(Bell 2000).Nearlyide nt ical result s were obtained inmodel runs wherethe contacts andjoints were open (em pt y)andthus wit hzero materialstiffness.
In thefirstmodel(Fig.9),ahydrofractu retip at a depthof 0.5 unitsbelo w the surfac e approachesthree discontinu- iti es,presentedbytwo vertical joi nts anda hori zon tal co n- tact,eachwith a length of 0.2 units.Thismod el reflects,for examp le,the mechan icaleffectsof avertical hyd rofractu re appro aching the sur facein Fig.4.Allthethreediscontinu- ities open up, andtensile stressesconcent rate around the tip s of theco nt act and the low er tipsof the join ts.These stressconcentrations ind icateatendenc yforthe jointsand thecontactto link up,asisseenin the nextmodel(Fig. 10).
whereanewcentra ljoint has alsobeen added.Thecont act has the greatest opening,followed by that of thecentral joint(Fig. 10)and,then, the jointstoeachside.All joi nt s have the greatest opening s intheirdeep erpart s.
The next two models (Figs.11-12) show the effectsof mechan icallayering on discontinuiti es openi ng ahead of a prop agat ing hydro fract ure.A
soh
layer B, with a Young'sAGUSTGUDMUNDSSON,ING RID FJELDSKAAR & OT/Ll EGJESDA L NGU- BULL 439,2002 -PAGE 67
urface
A
Hydrofracture~
Fig.12.Same modelasin Fig.11except thatthetipofthe hydrofra ctur e heremeets withthebott om ofthesoftlayerB.
layers A and B is only by a factor of 2, thetensile st ress relatedtothe hydrofracture is muchdimin ishedin the soft layer.Thereis a small opening ofthe verticaljoints intheir deepest parts whilethe near-surfacepart s remain closed.
When,however, the hydrof ractur e has propagated an additiona l0.1 unittowardsthe surface,thatis,tothe bottom of the soft layer B,there is considerable opening of the joints,the maximumbeing at the freesurface(Fig. 12).Thus, for the givenloading conditions, when thehydrofractur e is at 0.4 unit sbelowthefree surface,the geomet ry of theverti- cal discontinuiti es changes from the maximum opening being in their deepest parts to itsbeing atthe surface.The apertu reofanexte nsionfract urecommonlybecomes much larger atafree surface,oratan open, sliding discontinuity, because of thelack ofelasticconstraint(Fig.2).
Stress fields in Norway
The num erical models aboveconsider two loading condi- tion s: exte rnal tensile st ressand internalfluid overpressure.
Here we explore briefly howtheseloading conditionsmatch withcurrent ideas on the stress fieldin Norway.
The present- daystressfield in Norway has recently been subject to adetailed st udy, usingfocalmechanisms, overcor- ing and boreholebreakout data(Feje rskovetal. 2000, Hicks etal. 2000). ForWest Norway,themainst ressis aWNW-ESE- trending compression offshoreanda weaker NE-SW-t rend- ingexte nsiononshore.The offsho re horizont al compression is widely att ributed to ridge push (Fejerskov & Lindholm 2000).Boththe onshoreext ension as wellas the offshore compressioncan, however,partly be explained in terms of the inferred glacialerosion and postglacialuplift,depending
on where the margin of theupliftedcrustalplate is takento be(Gudmundsson1999).Thus,thepresent -day st ressfieldin Nor way dependsonitslate-glacialhist ory.
There is considerableevidence thatthe whole ofNorway becamedeglaciatedduringthe period from8000 to 12,000 B.P. Thedeglaciation began in thecoastal areas(Mangerud 1991,Sejrup et al.2000) and continued to the highl and s where it was essentially complete some 8000 yearsago (Mangerud 1991,Nesje & Dahl 2002).InWest Norway,the postglacial stre ss field generated neotect onic activity (Anundsen et al. 2002,Helle et al. 2000).The best docu- ment edneotectonic activityin Norwa y,howev er,isfromthe Laplandprovincein the farnorth whereseveralreverseand norm alfaultshave been active in theHolocene,some up to the present (Olesen 1992,Dehls etal.2000), andgivenriseto hyd rological changes(Olesen etal.2000).
During deglaciation in thecoastal areas,temporaryten- sile stresses may have followed the initial comp ressive st resses associated with the formation of the horizontal exfoliationfractures(Fig.1).Becauserocks are muchweaker in tension than in compression,the linking up of existing joints and fractures subject to suita bly orient ed tensile stresses (Figs.7, 8)ismuch morelikely than for an equally large compressivestress.Extensi on isstilloccurrin g in some coasta l parts of West Norway(Hicks etal.2000). Postglacial tensile stressesat shallow crustaldepth sarethu slikely to have been common,thereby supporting the use of tensile loading in some of thenumerical models(Figs.7,8).
Theothernumericalmodels useinternal fluid overpres- sureasthe only loadin g mechanism (Figs.9-12).Thistypeof loading emphasisesthe basic condit io nsfor thepropaga- tion of vertical hydrofractures.Themodels inFigs. 9-12 also indicate that atleast some ofthe horizontalexfoliat ionfrac- tures (Figs.1-3)mayhave opened up duringflow of an over- pressured groundwater associated wit h the hyd rof ract ure propagation.Similarsuggestions havebeen made forhori- zontalfracturesin Sweden,some of whichare thoug ht to be partl y generated byfluid overpressurebeneath the retreat- ing icefrontdurin g deglaciation(Talbot 1999).
Discussion
The relat ionshi pbetwee ncurrent postglac ialupliftratesand yieldof groundwa terwells(Rohr-Torp 1994)isof fundamen- tal importance inthe bedrockhyd rog eology ofNorway.To understand this relationship in mechanical term swemust explain how the rate of uplift aff ects the yield.The most likelyphysicalparameterto be affected by postglacialuplift and associatedstressesis thehydraulicconductivity.In the bedrock of Norway, hydraulic conductivit y is commonly almost entirely determined by interconn ected fract ures.
How these fract ures become interconn ected and grow is thusperhapsthe keyto understanding this empirical rela- tionship.
In this paper we use numerical models toindicate some of thebasicways bywhichinte rconnected fracture systems
NGU-BU L L 439,20 0 2 -PAGE 68 AGUSTGUDMUNDSSON,IN GRID FJELDSKA A R
s
OT/LlE GJESD ALmay develop, using fract ures from the coastal areas of Norwayasexamples(Figs.1-4).Howthese fract uresystems grow affectstheir effectivenessin transporting groundwa- ter. For example,when the initially offset fractures link up throughtransverse shear fract ures (Figs.7, 8)thetransverse fractures may limitthe groundwater transport ofthesyst em.
This follows because the normal compressive st ress on a shear fracture is greate r than the minimum compressive principal stress so that the overpressure of ground water flowing through a transverse fracture is usually less than thatof ground wat erflowingthrough anexte nsionfracture.
Also,for a given controlli ng dimens ion of a fracture,the apertu reof such a transversefracture is normallyless than that ofaneq ual-sizedexte nsion fractur e.Inmineral vein
sys-
tems in Norway andelsew here,veins in shear fractur esare normally thinner than veins in extension fractu res (Gud mundssonetal. 2001).
When thegroundwaterpathwayis formed by propagat- ing hydrofractu res(Figs.9-12),thedirect ion ofsubsequent groundwater flow along the pathway dependson several parameters. For example,once the hyd rofracture reaches the contact in Fig.10,the groundwater could,theoretica lly, flow into any ofthe verticaljoints.Although the openingof the centra ljoint isthe greatest,and would thusnormally favour the ground water flow,the pressure gradient also influencestheflow direction.For hydrofractures inanelastic crust, thepressure gradient depends on the stateof st ressin the host rock (Gudmundsson et al. 2001,Gudmundsson 2001).By contrast,if therock behavedin a rigidmannersub- sequent tothe openingofthediscont inuit ies, the event ual flowdirection of groundwater would be partly determined bythe hydraulicgradient.
In conclusion,the data and models presented in this paper indicate that rapid erosion and postglacial upliftare likely to have generated stressfields suitab leforthe link ing upandgrowt hof interconnected fract ure systemsin various parts of Norway.In particular,temporary tensilestressesand associated fracturegrowthmay havesignificant lyincreased the hyd raulic conduc tivity in the bedrock of Norway.The poten tial tensile stressesincrease wit h increasing rate of postglacialuplift (Gudmundsson 1999)so that the fract ure- generated permeabil ity and associated yield of bedrock groundwater wells would beexpected to follow empirical relatio nshipssimilar to those proposedby Rohr-Torp(1994).
Ackno wledgements
Wethank AlvarBraath enand Helg e Ruistu enfor helpful commentson the manuscript.Thi s wo rkwas su pporte d by several grant s from the Norway Research Council as well as a grant from the European Commissio n(cont ract EVR1-CT-1999-40002).
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