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GEOPHYSICAL RESEARCH LETTERS, VOL. 17, NO. 12, PAGES 2109-2112, NOVEMBER 1990

FRICTION, OVERPRESSURE AND NORMAL COMPRESSION

J. Byerlee

U.S. GeologicalSurvey, Menlo Park, CA 94025

Abstract. More than twenty-five years ago Miller . In a seriesof experimentsto measurethe strengthof and Low reportedthe existenceof a thresholdpore somewater saturated clays [Radney and Byerlee, 1988], pressuregradient below which water would not flow we found that the effectivestress law for frictional •hroughclay. Recentexperimental observations of the was obeyedand that the tz for montmorillonitewas _>0.2. shearstrength of structuredwater on biotite surfaces Thus even if the San Andreas fault was filled with pure haveprovided a physicalbasis for understaaxdingthis montmorillonite, which seems unlikely, the flow t•o!d gradient. The existenceof this phenomenon constraints would be exceeded. hasprofound implications for the rheologicalproperties The only way for the fault to have the necessarylow of mature fault zones, such as the San Andreas, that strength is for pore pressureto exceed75 percentof the containlarge thicknessesof . For example,a lithostatic stressin the San Andreasfault zonewhile pore day-filledfault zoneabout I km wide at the baseof the pressurefollows the hydrostaticgradient everywhereelse s•mogeniczone decreasing to zero width at the surface (A.H. Lachenbruch,personal commun., 1990). couldsupport core pressureequal to the maximum We will denotean effectivestress component •i = •ri-p principalstress over the entire seismogeniczone. As where p is fluid pressure. Then, for fluid pressures a result, the fault would have near-zero strength and followingthe hydrostat it is commonlyfound [Zoback and t•hemaximum principal stressmeasured on the flanks of Healy,1989] that the maximumand minimumeffective t.•e fault, would be oriented normal to the fault surface. principalstreses are related by •s = •/3. If a• is An.otherconsequence of the threshold gradient is that approximately equal to the lithostatic and the normalhydrostatic fluid pressuresoutside the fault zone densityof the overlyingrock is 2,500kg/m s, thenas = couldcoexist with near-lithostatic fluid pressuresin the 0.6 a•. Thus, from conventionalrock mechanicswe would •nterior of the fault zone without the need for continual expect hydrofracture to occur if ,•, the ratio of pore replenishmentof the overpressuredfluid. In addition,the pressure to lithostatic stress, in the fault zone exceeds porepressure at any point shouldnever exceedthe local 0.6. This wasalso pointed out by Zobacket al. [1987]. minhnumprincipal stressso that hydrofracture will not If the country rock is so strong that hydrofracturedoes not occur, then it is necessaryfor the countryrock to have very low permeabilty to prevent the high pressuresin the introduction fault zone from bleeding off. Calculations by Hanshaw and Bredehoeft,[1963] show that evenif a high pore Recent determinatons of the stress directions indicate pressureregion is surrounded by materiM 1 km thick, thatthe maximumprincipal stress•rx is almostnormal to witha permeabilityof 10-21m2 (whichis anexceedingly ß e SanAndreas fault [Mountand Suppe,1987; Zoback, low permeabilityfor geologicalmaterials) A can not be eta/., 19.87]. This is consistentwith the low shear maintained above 0.75 for more than 10,000 years. This strengthof the fault inferred from the heat flow data. is becausethe specificstorage, which is a functionof the Theseobservations have proven to be very difficult to pore volume and the compressibilityof water and rock, .•plain in terms of our conventional understanding of is so low that only a very small amount of water needs f•u!t theology. in most regionsof California,faults escapeto drastically lower the pore pressure. • with almost all orientations. If all the faults A clue to explaining the apparent paradox of the 'ma regionhave approximatelythe samecoefficient of of large fault systems comes from crustal friction/•, then elementarycoulomb analysis demands drilling projects and the oil exploration industry. It has :tZatthe maximumangle that ax can make with the been found that overpressuresare commonin the earth most active fault is 45ø , even if /• is zero. It has even in rocks as old as Cambrian. In fact, in some beensuggested, [Zoback ½t al., 1987]that • for sliding casesthe pore pressurecan even exceedthe lithostatic •onthe San Andreas may be very low, but high for stress[Fertl, 1976]. In someoil fieldsthese very high thesubsidiary faults. Calculations(A.H. Lachenbruch,pressures in oil or gascan be explainedby the very high ,personalcommun., 1990) show that/• onthe SanAndreas capillary pressuresthat are required in the non-wetting needs.... to be _• 0.1 to satisfythe heat flow constraints. phase to displacewater from the narrcrwchanne!.ways T• weakestmineral that can be expectedto occurin in the overlyingrocks [Watts, 1987]. In russetplaces, '•y significantquantity in fault zonesis montmorillonite however, water is the only liquid phase present, so we cannot appeal to capillary forcesMone to explainthe his paper is not subject to U.S. copyright. Pub- overpressure. I!s'hedin 1990 by the AmericanGeophysical Union. Threshold Gradient

number 90GL02295 An •planation of howoverpres .sure can be maint•ed !•<94-8276 /90 / 90GL-02295503ßO0 for long comesfrom the r•u!ta of !&borato•

2!• 2110 Byer!ee, J.' Friction, Overpressureand Fault Normal Compression carried out in the field of science. It whentwo surfaces, separated by a liquidare brought has been found that at very low pressure gradients closertogether than about10 timesthe diameterof the water will not flow through dense clay. This is shown molecules,the liquid becomes ordered into discrete lay- schematically in Figure 1. For Darcian flow the flow rate ers. Whenthis occurs the liquidhas a finitestrength. increaseslinearly with pressuregradient. The slope of Furthermorethe normalstress required to expela layer the straight line through the origin is a measure of the of the liquidincreases as the numberof layersdecreases. permeability of the material. With denseclay the flow If a shearstress is applied,shear will not is non-Darcian at low pressure gradients. In this case occurbetween the surfacesuntil the shearstress reaches a thresholdlevel. The magnitudeof the thresholdshear stressincreases as the numberof layersof the liquidde. creases.In addition,the shearstress required to shearthe liquidis •ndependentof the shearvelocity, [Isra•lach•'•i et al., 1988]. With thin filmsof a liquidbetween atomi. callysmooth surfaces the conceptof Newtoninnviscosity breaks down, and attempts to calculate an effectivevis- cositylead to valuesthat are many ordersof magnitude larger than the bulk values. This appliesto water as as all the otherliquids so far studied,[McGuiggan • •., 1989].In the caseof waterits shearstrength is directly proportionalto the normal stressthat canbe supported [Homolaet al., 1989]. It should make no differencewhether shearingof 'the water is caused by a shear displacement of one of the TG surfaces relative to the other or whether the two surfaces are held fixed and the water is forced to move between PRESSURE GRADIENT them by a pressure gradient. The first case requires Fig. 1. A schematic diagram of flow rate as a function a threshold and the secondcase, requires of pressuregradient for flow through a Darcian material, a threshold gradient. Because the threshold stressis and a non darcian material with a threshold gradient TG. zero for greater than 10 layers of moleculesit wouldbe expected that the threshold gradient would not occ-ur when the water-clay ratio is large, but wouldbe man•ffest the zero intercept on the pressuregradient axis is called whenthis ratio is low,as found by Miller andLow, [!• the thresholdgradient {TG). At pressuregradients below With dense clay it has been found that the TG starts the TG, flow does not occur so that the permeability of to be measurablewhen the , the volumeof the the material is zero. The experiments to measurethe TG voids to the volume of the ,is about 2 and increases are very difficult to carry out, and somehydrologists have to 0.5MPa/m at a voidratio of about0.75 [Ping, 1963]. assumedthat the observedTG is an experimental artifact From physical considerationsall that shouldbe re- mainly becausein some experiments no TG is observed, quiredfor a TG to existin fault gougeis that thewidth of whereas in others it is, even with the same material the passagewaysoccupied by water not exceedten although of different . In addition, until now the diameter of a water molecule. If this is true, then there has been no satisfactory physical explanation for it may not be necessaryfor the walls of the passageways the phenomena.It has been suggestedœu•z and Kemper throughwhich the watermoves to be perfectlyparallel [1959],that the streamingpotential generated by the flow they are in clays,such as montmorillonite,illire, s•- can producesmall countercurrents along the pore walls tine, etc. Thusa TG mayalso exist in a gougewith pa•- in a direction opposite to the main flow, and it may be clesof claysize regardless of theircomposition, possiblefor this mechanismto reduce the flow rate at experimentsare required to confirmthis. In anycase it low pressuregradients, but it can not explain why flow doesappear reasonable at this stageto assumethat ceasesaltogether below the TG. Others[Miller andœow, manygouges the TG is real andwe canproceed to Inv• 1963, Vo• E•gelhardt a•d Tun, 1955 and Swartzendruber, tigatewhether the existenceof TG leadsto a resolutic• 1962]have suggested that non-Darcianbehavior can be of someof the hithertopuzzling tectonic observations. attributed to a non-Newtonian shear rate dependent liquid viscositycaused by clay-water interactions. But, Model here again, this mechanismcan not explain why flow ceasesalthogether below the TG. Hansbo[1960], Mitchell In our modelof the fault zone(Figure 2) we and Younger[1967], have suggested that there may be that in countryrock the effectivemaximum prin•p:al a rearrangementat high pressuregradients to stress,• = •r• - p• is equalto threetimes the et!ectiv•: allow water to flow only when the TG is exceeded,but it minimumprincipal stress •s wherep• isthe hydrostarve is difficult to see how this mechanism would operate in porepressure. a• is assumed tobe normal to the pl• e"•' dense clay. thefault containing gouge 2D + d thick.For equilibrium A soundphysical explanation for the TG phenomena cqmust remain constant through the gouge zone. comesfrom the results of recent experimentscarried out TG isassumed tobe (a•-p•)/D sothat the pore pr.ess•:•um in the field of . It has been found that p increasesfrom hydrostatic at the gouge country Byerlee,J.: Friction,Overpressure and Fault NormalCompression 2111

dr1I P -- Ph example, in the Mecca Hills area in southern California Ph ø'1 Sylvester[1988]. Anotherconsequence of our modelis ---> ø'3 , the fact that, regardlessof the orientationof the fault //•7ZX///////////////// T X,.•.".....,,i zoneto the far field stressesthe fault will yield in sucha D way as to forcethe near field maximum principal stress to rotate until it is sub-normal to the fault. This effect whichis a consequenceof the lowstrength of the fault, is o'1 = o'3 - p d similar to the stress field rotation near the surface of an /////////////////// open crack since,in that case,the free surfacerequires D zero shear tractions on the crack walls. Observations of stress orientations in California are consistent with this prediction[Zoback eta/., 1987]. -.-•i1\ - o-3 Ph (71 Another consequenceof this model is that the mini- o'a| P - Ph mum width of the gougelayer will dependon depth for this mechanismto operate throughoutthe seismogenic Fig.2. A schematicdiagram showing how •rx,•r3and zone. The pressuregradient will be the differencebe- P varieswithin a fault zone containing material with tween the pressurein the central zone crlz and the hy- a thresholdgradient of t•/D. The dashedand dotted drostaticpressure phz at depth z divided by the width t•es are the values for •r3 when the strength of the clay of the zoneDz. If the TG is 0.5 MPa/m independentof go•e is suchthat the ration of •/•3 is equalto 3 and , effectivepressure and compositionthen 2 respectively. _>2z), = (4) interface,to lithostatic in the central zone of width d and where Tz is the thicknessof the gougezone. If the f&fiowsthe relationship, densityof the overlyingrocks is 2,500 Kg/ms then Tz = 60 m/kin. At the surface,the gougezone can have zero width and at a depth of 15 km it only needs P-- Ph '•' (cr• D- Ph) X (1) to be 900 m wide to satisfy our model. The central whereX is the distance from the gouge country rock zone can be any width. By measuring the reflection interface.if •r• = 2.5ph and •3 = « P• inthe gouge zone along profiles across the San Andreas fault thenby substitution, in the ChalomeValley region Shedlocket al. [1990] determined that the width of the fault zone is less than X 50 m wide near the surfacebut it apparently widenswith = + (2) depth. Unfortunately, reflection data is not accurate wMchis shown as the dashed line in Figure 2. If the enough to make a more precise statement than this. gougeisweaker so that •3 - « • then, With subsidiary faults that are less mature than the San Andreas, it would be expected that the width of X their gouge zones would be much smaller, even though = .75 + (3) the same physical mechanism may operate on them whi& is shown• the dotted line in Figure 2. • both as , they will be much stronger becausethe pore c.• • = •t = p in the central region. pressurein their fault zonescannot build up to lithostatic Thee •e three importer consequencesof this model values. Thus, movement on secondaryfaults will be tMt helpto resolvethe fault mech•ics paradoxprevi- minor comparedto what it is on the San Andreas,even •'•!y described.First, the porepress•e in the central though they are subjectedto highershear stress because mne•c•ß be • high • the lithostatic pressure,•d can of their more favorable orientation. • maintMnedat this levelindefinitely. Second, •he pore We would expect that the mechanismthat we have p•e never exceedsthe minimum principal stressr• proposed here would be more effective on the long g•dl• of the strengthof the gougeso the water c•not straightsection of the creepingzone in centralCalifornia. •ape by hydrofracturingthe countryrock. Finally, the In the lockedregions of northern and southernCalifornia, f•ulttone h• zeroshe• strengthso that movementcan could still occur if most of the normal c•curon the fault with normal or subnodal compres• stress on the fault is supported by gouge with high $•o2.Therefore, the constraintsof the heat flowdata pore pressure,but the fault is hinderedfrom sliding •d the orientation of the stress directions are satisfied. by one or more interlocked asperitiesthat result in an R theTG is a functionof the effectivepress•e, then earthquakewhen they fail, as simulatedin the laboratory tmthe central zone p maybe lessth• •! •d the central experimentscarried out by ff,ockner and Byeflee, [1989]. z•.e will have a finite strength. So that in this c•e, In this casetrl may in generalbe normalto the fault, but farslip to occuron the fault •x will make• angleof locallywhere the asperitiesinterlock it may 'be45 ø to the • • 90ø to the pl•e of thefault. In otherwords, fault. Alternatively,in the lockedregions the gougemay •k•e will be subnodal fault zonecompriion. • the not be wide enoughfor the pore press.ure in its central c.;mtr•zone h• a ve• low shearstrength, it will tend regionto be muchgreater than hydrostaticand in this • be•truded up •d out of thefault zone.Structures region the fault could be strong almost everywhere,so •:• • this•e co--on alongthe S• Andre• fault,for that trl may be closeto 45ø to the fault everywhere.The 2112 Byeflee, J' Friction, Overpressureand Fault Normal Compression compilationof the databy Zobacket al. [1987]shows that Miller,R.J., and P.F. Low, Threshold gradient for there is a large variation in the direction of the maximum flowin claysystems, Proc. Soil Sci. Am., 27, horizontal stressalong the San Andreasfault, but it is not 609, 1963. clear that this is real or simply an artifact of the methods Ping,L.S., Measuring extremely low flow of used in their determination. Thus our presentconfidence water in clays,,95, 410-413. 1963. •n the data is not sufficient to distinguishbetween the P•adney,B., and J. Byeflee,Laboratory studies of the two possibilities set out above. shearstrength of montmori1!onite(abstract), Finally, it should be pointed out that the mechanism Trans. AGU, 69, 1463, 1988. that we have proposed here to explain the rheo!ogy Shedlock,K.M., T.M. Brocher,and S.T. Harding, Shal- of some strike-slip faults may also explain how pore low structureand deformationalong the San pressures close to lithostatic can be maintained in fault dreasfault in ChalomeValley, California, based on zones,for geologicallysignificant lengths of to allow high-resolutionreflection profiling, J. Geoph!ts. Res., slip on large overthrusts and on very low angle normal 95, 5003-5020, 1990. faults without grossfailure of the overlyingrocks. Swartzendruber,D., Non-darcy flow behavior ofliquid saturatedporous media, J. Geophys.Res., 67, 5205- References 5213, 1962. Fertl, W.H., Abnormal formation pressures,382 pp., Sylvester,A.G., Strike-slip faults, Geol. Soc. Am. Bull., 100, 1666-1703, 1988. Elsevier, New York, 1976. Von Engelhardt,W., and W.L.M. Tunn,The flowof Hansbo, S., Consolidationof clay with specialreference ids throughsandstones. (Translated by P.A. to the influenceof vertical drains, 160 pp., Pro- ceeding18, SwedishGeotechnical inst., Stockholm, erspoonfrom Heidelbeger Beltrage Zur Mineralo•ie 1960. undPetro•lraphie 2,12-25, 1954), illinois State Surve!tCir., 194, 1-16, 1955. Hanshaw, B.B., and J.D. Bredehoeft, On the mainte- Watts, N.L., Theoreticalaspects of cap-rockfluid seals nance of anomalousfluid pressures:II Sourcelayer at depth, Geol. Soc. Am. Bull., 79, 1107-1122, 1968. for singleand two phasehydrocarbon columm, Homola, A.M., J.N. Israelachvili,M.L. Gee, and P.M. Marine and PetroleumGeolog!I, 4, 274-307,1987. McGuiggan, of and relation between Zoback,M.D., and J. Healy, Overviewof In-situ stress measurementsin the Cajon Pass scientificdrill h0h the adhesionand friction of two surfacesseparated by molecularlythin liquidfilms, Journal of Tribolog•/, to a depthof 3.5 kin, (abstract)Eos Trans. AGU• 70, 480, 1989. 111, 675-682, 1989. Israelachvili,J.N., P.M. McGuigganand A.M. Homola, Zoback,M.D., M.L., Zoback,V.S. Mount,J. Suppe,J.P. Dynamicproperties of molecularlythin liquid films, Eaton,J.H. Healy,D. Oppenheimer,P. Reasenberg, Science,240, 189-191, 1988. L. Jones,C.B. Raleigh,I.G. Wong,O. Scotti,and Wentworth, New evidence on the state of stress Locknet,D., and J. Byerlee,An exampleof slip insta- the San Andreasfault system,Science, 238, 1!05- bility resultingfrom displacementvarying strength, 1111, 1987. PAGEOPH, 133, 269-281, 1990. Lutz, 2.F., and W.D., Kemper,Intrinsic permeability of clay as affectedby clay water interactions,Soil J. Byerlee(U.S. GeologicalSurvey, Menlo Park,CA Science,88, 83-90, 1959. 94025) McGuigan, P.M., $.N. Israelachvili,M.L. Gee and A.M. Homola,Measurements of static and dyn•znicinter- (Received:July 13, 1990 actionsof molecularlythin liquid filmsbetween l•evised: September6, 1990 surfaces,Mat. Res. Soc.Sitrap., 140, 79-88, 1989. accepted:September 11, 1990)