Faulting Patterns in North‐Central Nevada and ... - CiteSeerX

VOL. 85, NO. B I

JOURNAL OF GEOPHYSICAL

RESEARCH

JANUARY

10, 1980

Faulting Patternsin North-Central Nevada and Strength of the Crust MARY

LOU ZOBACK AND MARK

D.

ZOBACK

U.S. GeologicalSurvey,Menlo Park, California94025

NNE normalfault trendscharacterize muchof the northernBasinand Rangeprovince.Thesefaults make sharpbendsto NNW and ENE trendsin north-centralNevadain the vicinityof a mid-Miocene rift characterized by a zoneof diabasedike swarms,graben-fillingflows,and a coincidingaeromagnetic anomaly.Despite a roughly45ø changein the leastprincipal stressdirectionsincemid-Miocene time, pre-existingNNW- and ENE-trending faults in the vicinity of the rift accommodatedthe extension whereasregionally,majorcrustalblockswerefaultedalonga NNE trend,approximately perpendicular to the modemleastprincipalstressdirection.An assumed uniformregionalstressfield (derivedfrom geologicandgeophysical indicators of themodemprincipalstress field)andtheobserved obliqueslipon thepre-existing faultswerecombined in an analysis utilizingan empiricallyderivedfrictionalslidinglaw and the Coulombfailurecriterion.This analysisconstrained the ratioof the leastprincipalstressto the greatestprincipalstress(S3/S0 as well as the inherentshearstrengthof intactcrustalrocks,%. While bothparameters, S3/S• and,½,arefunctions of unknowns includingporepressure andthecohesion (frictional strength)of the pre-existingfaults,reasonableassumptions about theseparameterslead to ,½estimatesthatagreewellwith valuesobtainedfromlaboratoryexperiments simulatingcrustalconditions. At a depthof 10kin, the analysisindicatesthattheminimuminherentshearstrengthof intactcrustalrocks mustrangebetween150--450barsfor zeroporepressure and 150-350barsfor hydrostatic porepressure, whereasthecorresponding maximumshearstresses at 10-kindepthare970-1200barsfor zeroporepressureand 640-770 barsfor hydrostaticporepressure.

INTRODUCTION

There is presently a vast amount of laboratory data on the brittle deformationpropertiesof individual rocks and minerals. Experimentson frictional sliding at and above moderate confiningpressures(roughly 1 kbar and larger) yield remarkably uniform coefficientsof static friction independentof the type of fault surface,experimentalconfiguration,or the rock type [Byerlee, 1978]. Field testsin conjunctionwith in situ stressmeasurementsseem to confirm the laboratory friction values [Raleighet al., 1977]. Thus it appearsthat laboratory friction data can be applied to crustal faulting. However, ex-

trapolationof laboratorydata on th'estrengthof rock under crustal conditionsremains a major unresolvedissue.Proper extrapolation requires detailed knowledge of the effects of temperature,pore pressure,and strain rate on strength. Th•s paper describesan investigationof faulting relationshipsin a unique area in the northern Basin and Range province in which there are clear geologicconstraintson the style and timing of deformation. Within this area, it is observed that pre-existingfaultshave beenable to locally accommodate strain by oblique-normal slip whereas regionally favorably oriented-normalfaults were breakingthroughthe upper crust. Assuminga uniform stressfield throughout the region, stress constraintsimposed by utilizing a frictional sliding relationship for thesepre-existingfaults are comparedwith stressratios obtained from a relationshipfor norml fault equilibrium based on the Coulomb criterion for faulting in intact rock. This analysisallows us to place limits on the inherent shear strengthof intact crustalrock (strengthat zero pressure)and also on the maximum FAULTING

shear stresses.

PATTERNS

AND

EXTENSION

DIRECTION

Accumulatinggeologicand geophysicaldata appear to indicate that a simplepattern of displacementsis responsiblefor This paperis not subjectto U.S. copyright.Publishedin 1980 by

theAmerican Geophysical Union. Paper number 9B 1245.

275

extensionin the northernBasinand Rangeprovincedespite the complexpatternof faulting[Zobackand Thompson, 1978]. Figure 1 showsthe directionsof horizontal extensionand least

principalstressin the northernBasinand Range.Horizontal extensiondirectionsare basedon geologicindicatorsof the senseof fault slip suchas fault groovesand slickensides and also on measureddisplacements from historicearthquakes. Horizontal least principal stressdirectionsare obtained from

T-axesof focalplanemechanisms andin situstress(hydraulic fracturing)measurements. As hasbeennotedpreviously,the general correspondenceof measuredextensiondirectionsand

the focal mechanismT-axes suggestthat the T-axes are reliable indicatorsof least principal stressdirections.The data shownin Figure 1 are tabulatedin Table 1 and presentedin rose diagrams in Figure 2. The mean extensiondirection is N62øW +_14ø while the meanleastprincipalstressdirection inferred from the focal plane mechanismsand in situ stress measurements is N59W

+_ 25 ø. The focal mechanism T-axes

are considerablyscattered;this scattermay be real arising from slipon preexistingfaultsor it may be dueto poorcontrol and the useof composite solutions. Despitethe scatter,a picture of fairly uniform WNW-ESE extensionin the northern Basinand Rangeemerges. WNW-ESE

directed extension is consistent with the overall

NNE trendof basinsand rangeswithinthe Great Basin(Figure 3). A notableexceptionto this pattern of faulting is in north-centralNevadawherea nearlyorthogonalsetof normal faultstrendingNNW and ENE are responsible for the modem ranges.However,measuredslip on thesefaults agrees with the overallpatternof horizontaldisplacements (someof theseslip directionsare includedin Table 1). A possibleinterpretationof thisorthogonalsetof faultsis that theyrepresent pre-existingplanesof weaknessrespondingto the present stressfield. The aeromagneticmap of Nevada indicatesa prominentaeromagnetic high in this regionof north-central Nevada(seeStewardet al. [1975]and inseton Figure3). This NNW-trending high reflectsa zone of graben-fillingbasalts,

276

ZOBACK AND ZOBACK: STRENGTH OF THE CRUST 106ø

122'

120'

118'

Iiti'

llOø

114'

ColorodoI

Plofeou $ierro

Nevodo

• •

EXPLANATION GEOLOGIC EXTENSION EARTHQUAKE T-AXIS

Fig. 1. Extension directions andleastprincipalstress orientations forthenorthernBasinandRangeprovince.

rhyolites, and NNW-trending dike swarms interpreted as a distinct, 250-km-long rift that formed 17-14 m.y. ago [Stewart et al., 1975; Zoback and Thompson, 1978]. A mid-Miocene WSW-ENE least principal stressdirection of broad regional extent may be inferred from the NNW-trending dike swarms in Nevada and parallel contemporaneousfeeder dikes for the Columbia River basalts.The N30ø-35øW trending graben of the western Snake River Plain has been interpreted as forming contemporaneouslywith the eruption of the Columbia River basalts[Mabey, 1976].This mid-Miocene leastprincipal stress direction differs by roughly 45ø from the modern

crust-cutting features but rather as a zone of discontinuous planes of weaknessthat later coalescedto form the modern range-front faults in this region. Alternatively, the ENE trend may representan earlier zone of weakness,possiblyoriginating during the Precambrian, as suggestedby Eaton et al. [1975] for the ENE-trending eastern Snake River Plain-Yellowstone trend.

Referring to the physiographicmap (Figure 3), it is apparent that the NNW- and ENE-trending planes of weakness presumedto have developedduring mid-Miocenerifting were able to accommodateextensionas the least principal stressdiWNW-ESE extension direction. rection changed •45 ø in a clockwisesense,whereasin the surThus, it is clear why the NNW trend shouldconstitutepre- roundingregion major crustalblockswere faulted with an oriexisting planes of weakness.A detailed examination of geo- entation approximately perpendicular to the modern least logic features along the northern Nevada rift zone in the principal stressdirection. The observationthat WNW-ESE Midas trough region (arrow on Figure 3) suggestsan origin (modern) extensionwas accommodatedby slip on pre-existfor the ENE-trending planes of weakness.A prominent, seg- ing faults of markedly oblique trendsin a restrictedregion in mented NNW-trending rhyolite dike associatedwith the rift- the vicinity of the mid-Miocene rift while new, more favoring was found in this region.This feature has been previously ably oriented NNE-trending faults were being formed in the discussedin detail [Zoback and Thompson,1978], however, surroundingregion allows us to place limits on the inherent the conclusionsare summarized here becausethey bear di- shearstrengthof the crust and the relative magnitudesof the rectly on early evidence for faulting along the ENE trend. principal stresses. Lack of evidence for faulting outside of the dike segments THEORY (Figure 4) as well as the orientation of a small segmentbetween the two major segmentssupporta leaky transform oriTo investigatethe oblique slip of the ENE-trending faults gin for the feature [Zoback and Thompson,1978].Recent nu- responsiblefor most of the modern physiographyin northmerical studies by Fujita and Sleep [1978] predict a central Nevada, regional stressesare resolvedon a fault plane reorientation of stressesconsistentwith the pattern shown in where frictional sliding relationshipsare assumedto apply; Figure 4b caused by drag along the transform fault. Thus this permits calculation of a range of allowable stressstates. there is an indication that ENE-trending planes of weakness These values are compared with principal stressratios obmay have developedas transformsduring massivedike intru- tained from a relationshipfor normal fault equilibrium based sion in mid-Miocene time. Obviously, the transform faults on the Coulomb criterion for faulting in intact rock. This criwould be expected to have a 90ø dip whereas the modern terion is considered valid because new normal faults were faults have approximately a 60ø dip at the surface.Thus these forming in the surroundingregion as the rift zone faults conpostulatedENE-trending transformsare not viewed as major tinued to slip.

ZOBACK AND ZOBACK: STRENGTH OF THE CRUST

277

TABLE 1. Stress Orientations andExtension Directions for theNorthernBasinandRangeProvince Location

T-axis

Type of

Solution*

Type of

N. Latitude

W. Longitude

EventS-

Azimuths

35.92 ø 36.0ø 36.6ø 36.81o

117.80 ø 114.7 ø 116.27 ø 115.88 o

S C S S

36.92ø

115.98 ø

C

SS

N45W

37.13 ø 37.2ø 37.2ø 37.4ø 37.47 ø 37.5ø 37.73 o 37.75 ø 38.3ø 38.5ø 38.58 ø 39.2ø 39.2ø 39.2ø 39.6ø 39.7ø 39.8ø 41.8ø 41.8ø 41.83ø 42.17 ø 43.0ø

117.32 ø 116.5 ø 116.5 ø 114.2 ø 117.87 ø 118.5 ø 115.05 o 116.0 ø 118.4 ø 117.8 ø 112.83 ø 118.0 ø 118.1 o 118.1 o 111.9 ø 118.4 ø 118.0 ø 111.8 ø 112.9 ø 118.48 ø 119.92 ø 111.4 ø

S C C S S C S C C C C C S C S C C S S C S C

N/SS N/SS SS SS N/SS SS N SS N+SS N/SS N/SS N N+SS N+SS N/SS N N/SS N N N N+SS N/SS

N50W ~N45W ~N45W -•N30W N88W N90W N51W N6W ~N75W NI00W N75W N44W N64W N66W N74W N56W N 14W N74W ~N 105W ~N80W N60W N8IW

Focal Mechanism

SS SS N/SS SS

Plunge

Reference

Data

N66W N46W N6W N67W

0ø 20øSE 3øNW ? ?

30øNW 0ø ~0ø ~ 16øSE 3øW 0ø 30øSE 15øSE ~0ø 21øW 34øNW 5øNW 2øNW 3øNW 20øSE 5øNW 1øNW 13øNW ~30øNE 0ø 13øSE 10øNW

SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] Carr[1974] Carr[1974] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] Smith andLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] Smith andLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978] SmithandLindh[1978]

Horizontal Extension

Location

N. Latitude

W. Longitude

36.1ø 36.75o 36.85ø 37.5ø 38.2ø 39.0ø 39.3o 39.7ø 40.2ø 40.3ø 40.6ø

116.8 ø 118.2 ø 116.0 ø 118.3 ø 118.15 ø 119.8 ø 119.6ø 118.0 ø 116.5 ø 117.6 ø 116.75 ø

Typeõ

Direction

Reference

NW-SE N57W N55W N60W N82W E-W N60W N55W N55W N60-65W N77W

Wrightetal. [1974] Bateman[1961] Carr[1974] Russell [1977] Speed andCogbill [1979] Thompson andBurke[1973] Thompson andBurke[1973]

GeologicSlip Data

DeathValley,CA OwensValley,CA NevadaTestSite WhiteMt, CA Candelaria Hills,NV Genoa,NV Comstock Lode,NV DixieValley,NV Cortez,NV Pleasant Valley,NV ArgentaRim,NV

Grooves Eq Grooves Grooves Grooves Grooves Grooves Grooves Grooves Eq Grooves

Thompson andBurke[1973] Muffler[1964];Zoback[1979] R. Wallace(personal communication, 1977) Zoback[1979]

HorizontalLeastPrincipal

Location

N. Latitude

NevadaTestSite DinkeyCreek,CA

36.85 ø 37.15 ø

W. Longitude

Stress Direction

Reference

Hydrofrac Data

~ 116ø -• 119ø

N40W(avg.of 2) N65W

Haimson etal. [1974] Haimson [1977]

*S, singleeventsolution;C, compositesolution.

•-N,normal;SS,strikeslip,N/SS - predominately normal;N+ SS,approximately equalnormalandstrike-slip movement. :•Azimuthresolvedto NW quadrant.

[}Grooves, basedon faultgrooves andslickensides; Eq, basedon historical earthquake offsets.

A tensortransformation canbe usedto resolvethe regional tion(Sl vertical, positive downandS3horizontal, N60øW). stresses to shearand normalstresses actingin the slip direcThe generallyNNE-trendingfaultswhichcharacterize the tion on the fault plane.This analysisrequiresthat the orienta- NevadaBasinand Rangechangeabruptlyto NE to ENE tion of the regionalprincipal stresses, as well as the orienta-

trendsin the vicinityof the mid-Miocene rift. (We haveas-

tion of the fault plane and slip direction be known. As

sumed that slip on thesefaults will occur such that the hori-

presentedearlier, earthquakefocal mechanismT-axes as well

zontalcomponent of slipis in theleastprincipalstress direc-

as in situ stressmeasurementssuggestan orientation of tion.) Using an averagetrend of N65øE for thesemodern N60W-S60E for S3 (least principal stress).Active normal faultsanda dip of 60ø (dipsof 60-65ø are commonly ob-

faultingthroughout the provincesuggests that $1 (maximum served onBasinandRangenormalfaults[Thompson, 1959]) principalstress) is vertical.Thus,a right-handcoordinate sys- asrepresentative of thecross-faulting trend,theslipdirection tem requires that S2 be horizontal and be in a S30øW direc- hasan azimuthof N60øWanda plungeof 55øNW.

278

ZOBACKAND ZOBACK:STRENGTHOF THE CRUST

Mean

Mean '

N•W

N62W

w

s

(a)

(b)

Fig. 2. Rosediagramsfor data presentedin Figure 1. (a) extensiondirectionsdeterminedfrom geologicevidence;(b) focal mechanism

T-axes and in situ stress data.

The fault plane coordinate systemis defined with the normal to the fault and the slip direction in the fault as the coordinateaxesx l' and x2', respectively,and the normal to the slip direction in the fault plane as x3'. Rotation of the princi-

principalstress to themaximumprincipalstress) asa function of P, So,Sl, and/•fwiththeboundsS• -- S: andS: = S3:

S3/S• = I•P-Sl(0.50/• So-S•(0.52/•0.40) S2= S• (5a) + 0.43)

pal stresses Sii(whichdefinethe unprimedcoordinatesystem) to the new coordinate system is accomplishedby a tensor

and

transformation:

S3/S•-I•P- Sl(0.77/•f So-S•(0.25/•0.40) q-0.43)

S•a'= a•,,aoS,./

The directioncosinematrix aii for the transformationcan be determined from angles between the coordinate axes measuredon an equal area projection(Figure 5).

s: = s

(5/,)

Frictionalslidingon pre-existingfault planeshasbeen the

subjectof numerouslaboratoryinvestigations. Byedee[1978] summarizesthesedata and suggests that for normal stresses

up to 2 kbarthe shearstress requiredto causeslidingon preX]

X2

existingfaultsis givenapproximatelyby

X3

•' = 0.85o•v

Xl !

cos 120 ø

cos 121 ø

cos45 ø

X2t

cos 37 ø

cos 90 ø

cos 53 ø

In thiscase,So-- 0 and/• -- 0.85.For normalstresses above2

X3t

cos 107.5 o

cos 31 o

cos 65.5 o

kbar the shear stressfor frictional sliding is given approximately by

The normal stressacrossthe fault plane (S•v)is givenby

0.5 + 0.6o•v kbar

SN• SIIt = al12Slq-a122S2 q-a132S3 (1) S•v= 0.25S1 + 0.27S2 + 0.50S3

whereSo-- 500barsand/• = 0.6.However,thelinearrelation • = 0.67o•v, with So= 0, appearsto fit the data equallywell in the 2-13 kbar range.

The shearstress(•) alongthe slipdirectionis givenby •' = -S•2' = a•a2•Si + a•2a22S2+ a13a23S3

• =0.40S• - 0.43S3

Byedee[1978]concludesthat thesefrictionalcoefficients -- 0.85for low normalstressi.e., lessthan about2 kbar, and/• = 0.6-0.67 for normal stressesgreater than 2 kbar) are valid (2) regardless of the type of fault surface,the rock type (with the

Theseequationscan be combinedwith the linear law for frictional slidingpre-existingfaults[Jaeger,1962,p. 76]:

? = So+/•f(S•v- P)

(3)

where Sois cohesion(strengthon pre-existingfaults due to a healingmechanism),P is pore pressure,and/•f is the coefficient of friction for frictional sliding. Substituting(1) and (2) into (3), we cansolvefor slipon the ENE-trendingfaults:

So-/•P + (0.25/• - 0.40)S,+ (0.27/•)S• + (0.50/•f+ 0.43)S3= 0

(4)

This equationcan be solvedfor S3/S• (the ratio of the least

possibleexceptionof montmori!lonitegouge),or the experimentalconfiguration.His data alsolimit the cohesivestrength (So)on pre-existingfaultsbetween0 and 500 bars.Accordingly,we havechosen0.6-0.8 asa reasonable rangefor/•f and have allowed Soto vary between0 and 500 bars. The correspondingrange of S3/S• calculatedby (5a) and

(5b) canbe comparedwith S3/S•valuesfor normalfault equilibrium based on the Coulomb criterion [Jaeger and Cook, 1969].Sucha comparisonisjustifiedbecausenormalfaults in the surroundingregionwere formedstrikingperpendicularto the least principal stressdirection as the rift faults continued to slip.

According to theCoulomb theory,faultingin intactrock

ZOBACK AND ZOBACK:

STRENGTH

279

OF THE CRUST

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Fig. 3. Physiographic map of Nevada. LettersA and B mark the extentof the mid-Miocenerift. Locationof Sawtooth dike/Midas trougharea is indicatedby the arrow. Inset indicatesoutline of aeromagnetichigh associatedwith the rift.

occurs when the Mohr circle describing the state of stressis tangentto a linear failure envelope.In this case•c is the inherent shearstrengthof tntact crustalrocks(strengthat zero pressure), oNis effectivestress(S•-P), 0 is the dip of the fault, and 4, is the angle of internal friction. The failure envelopeis given by

Defining •, = tan 4,,where •i is the coefficientof internal friction, •[.•i is thusrelatedto 0, the dip of the fault, since4, -- 20 -

ß = • + oN tan 4,

1/2(•i -- 0•)= 1/2(o,+ o•)sin4'+ •'•cos4'

•r/2. The Coulomb criterion for shear failure in intact rock

[Jaegerand Cook, 1969, p. 93, equation 2] can be written in terms of the principal stresses as

(6)

280

ZOBACK AND ZOBACK.' STRENGTH OF THE CRUST

sameasthe rangeof pf, the coefficientof frictionfor frictional sliding. Thus in order to reduce the number of variables we

assume that/• =/•f = p. Within therangeof p to be considered in the analysis, experimental resultsappearto supportthisas-

S3

sumption[seeHandin, 1969]. RESULTS

occupied by dike

• • S3 S3 local c•S3

Fig. 4. Diagrammaticmaps showingpostulatedstressregimeat the time of intrusion of Sawtooth dike (mid-Miocene). (a) 'Leaky transform'origin;(b) local reorientationof stressfield resultingfrom shearalong the transform fault.

where 1/2(o• - 03)is the maximum shearstress,1/2(o• + 03) is the mean stressin the Ol, 03plane, and •c is the inherent shear strengthof the material. Substitutingthesevaluesinto (6) and replacingo with effectivestress(S-P) yields S3/S 1 =

1 + sin•b

1- sin•+ •-i sin•+ -•-i cos •] 2P 2•c

(7)

Thus we can solve (7) as a function of •c, P, and • for given values of S•.

Figures6 and 7 plot S3/S1as a functionof p, the coefficient of friction, at a depth of 10 km (S3/S l valuesfor normal fault equilibriumare a functionof $l, henceare depth dependent). A depth of 10 km wasusedsincemostBasinand Rangeearthquakesfall in the depth range of 5-15 km [Smith and $bar, 1974], although the depth estimatesare poorly constrained. Two casesare considered,zero pore pressureand hydrostatic pore pressure. In all casesslip will not occur on the ENEtrending faults unlesstheir cohesivestrength($o) is lessthan tc, the inherent shear strengthof intact crustal rock; that is, these ENE-trending faults must be pre-existing planes of weakness.The range of possiblestressstatescalculated from the linear frictional slidinglaw for slip on the ENE faults (4) is given by the ruled region. The solid lines denotenormal fault equilibrium for various values of rc for intact crustal rock basedon the Coulomb criteria (6). These valuesrepresenta lower limit for S3/S•. Smaller values(which correspond to higher shearstresses) are not possible,becausefaulting occurs when the shear stress1/2(Sl -- S3) exceedsthe equilibrium value. The heavy solid bar representsthe rangeof reasonablevaluesof p, 0.6-0.8. An important additional constraint can be placed on the above analysisfor caseswith pore pressure.For shear failure to occur,the leastprincipal stress($3) must be larger than the pore pressure;if not, the pore pressurewould hydro-frac the rock along vertical fractures striking perpendicular to $3. Thus in the hydrostaticpore pressurecase(Figure 7), $3 cannot be less than the hydrostatic head pwgz,where pw is the densityof water (1 g/cm3),g is gravity, and z is depth.The greatestprincipal stress,$l, however,has been assumedequal to the lithostatic load, prgZ,where Pr is the density of crustal

Common dips on Basin and Range normal faults that have not been tilted or are tilted only slightly are 600-65 ø [Thompson, 1959].While there is growing evidencethat listric normal faulting may locally be important in the Basinand Range, the small tilts (60-8 ø) of 15-16 m.y. basalt flows capping the rangesin the vicinity of the mid-Miocenerift appearto preclude large rotationsresultingfrom slip on listric faults. Thus the major range-boundingfaults in this region are considered to be steep,relatively planar faults with dips of 600-65ø (the range of measuredsurfacedips). This dip range corresponds rock(-•2.7 g/cm3);thusa minimumvaluefor S3/Sl underhyto a/ti between 0.57 and 0.84. This range is essentiallythe drostaticpore pressureconditionsis 0.37. The shadedline indicatesthis level on Figure 7. Note that the constraintthat S3 > P limits cohesion(So) on the pre-existingfaults to a maxiN mum value of 300 bars for the hydrostaticcase.The value of So -- 500 bars for cohesionsuggestedby laboratory frictional slidingexperimentsabove2 kbar confiningpressure[Byedee, 1978] appearsto be too large. Obviously, this rationale cannot be applied to the zero pore pressurecase(Figure 6). It should also be noted that the actual state of stress in the

Basin and Range should be closer to the lower limit of the E ruled region, when S: -- S 1. If the intermediate stresswere very low (S: = S3) we would not expect the uniform NNESSW fault pattern observed,i.e., faults could open in either the S2 or the S3 direction. Consistent with the idea that S2 = Si, earthquake focal mechanismsin the northern Basin and Range yield both normal and strike-slip solutions (as indicated in Table 1) with similar T-axes [seealso Hamilton et al., 1969].The strike-slipmechanismsare mostcommonalong the westernmargin of the northern Basinand Range. +S2 S By comparingthe range of allowable stressstates(deterFig. 5. Equal-areaprojectionshowingorientations of the princimined from (5a) and (5b)) with normal fault equilibrium valpal stresses andthe fault planecoordinatesystem(primed)described in the text. Solidcirclesdenotelowerhemisphere points,opencircles ues, some limits on the inherent shear strengthof intact crusdenoteupper hemispherepoints. tal rocks, •c, can be obtained. Laboratory data on the shear

ZOBACKAND ZOBACK: STRENGTHOF THE CRUST

COHESION - 0 BARS

0.4

I

0.3

0.4

281

COHESION - 100 BARS

I

I

/x

I

o.3

S3/S1 0.2

•

•

•

0.1

/

I

I

I

I

0.5

0.6

0.7

0.8

COHESION

0.4

0.2 / /

-

o.• o • I

0.9

200

0

1.0

BARS

/

o

•

I

0.5

0.6

0.7

COHESION

018

-

400

I

l

0.9

1.0

BARS

0.4

;

I

0.3

0.3

S3/S1

S3/S1

0.2

0.2

0.1

0.1

0.5

0.6

0.7

0.8

0.9

1.0

0.5

0.6

0.7

0.8

0.9

1.0

Fig. 6. Ratio of greatestto leastprincipalstress(S3/S•) versuscoefficientof friction,/4 for zero pore pressureand for variousvaluesof cohesionon the pre-existingfaults.The heavysolidlinesrepresentnormal fault equilibriumfor various valuesof •c, inherentstrengthof intact crustalrock (7). Ruled regiongivesrangeof allowablestressstatesbound by the dottedlinesdeterminedfrom (Sa) and (Sb).The heavybar givesthe rangeof reasonablevaluesof/•, 0.6-0.8.

strength of intact rock samples vary widely. Handin [1966] summarizesstrength data and concludesthat the •'cof intact material is of the order of 100-200 bars for sedimentaryrocks and about 500 bars for crystalline rocks. However, Byerlee [1971]reporteda shearstrengthof 700 barsfor intact Weber B sandstoneand a shear strength on the order of 1 kbar for Westerly Granite [Byedee, 1967]. Our results,summarizedin Table 2, generally support these laboratory data and indicate that inherent shear strength of intact crustal rock, %, is between 150 and 600 bars for zero pore pressureand between 150 and 400 bars for hydrostatic pore pressure.The upper limit for •'c in the hydrostatic case is provided by the constraint that S3 must be greaterthan P. 'Maximum' shear stress(I/2(Si -- S3)) can also be determined from the calculatedrange of allowable stressstates.We have done this for/• -- 0.6 correspondingto a favorably oriented normal fault with a 60ø dip and a coefficientof frictional slidingof 0.6 (as suggestedby Byerlee[1978] for conditions at a 10-km depth). These values are also given in Table

2. As the cohesionon the ENE faults increases,the values of •'c also increaseas expected;in addition, the effect of introducing pore pressuretends to reduce the values of shear

stress,that is, to increaseS3/Si. Since,as suggested above,the actual state of stressmust be closerto S2 = Si than S2 -- S3,

the highermagnitudeend of the rangesof bothstrengthand shear stressare preferred.The actual upper limit for shear stressin the hydrostaticcaseis providedby the constraintthat S3 > P which leadsto a minimum allowable value of S31Si -0.37 and a maximum sheerstress(I/2(Si - S3)) of 850 bars at 10-km depth. In situ measurementsof the magnitudesof S• and S3 have providednumerousvaluesfor 'maximum'shearstress(I/2(Si - S3)) to depths of 2-2.5 km with a few values down to 5 km [see McGarr and Gay, 1978]. These results indicate shear stresses between 100 and 275 bars at 2-2.5 km depths.Maximum shear stressat 2.25-km depth predicted by the present

analysisrangesbetween215 and 305 barsfor zeropore pressureand from 135to 190barsfor hydrostaticporepressure.

282

ZOBACK AND ZOBACK: STRENGTHOF THE CRUST COHESION

-

0

BARS

,

0.6

•

.•

0.5

/

COHESION

-

1 O0

BARS

0.6

0.5

•..

0.4

•_3•

S3/s•0.3

S3/si 0.2

0.2

1000

1000

0.1

0.1

I

!

0

i

,

0

,

COHESION

-

300

BARS

COHESION

0.6•

•' •

0.5

500

BARS

0.6 0.5

0.4

/ /'7'".

S 0.3 1

0.4

S$/si 0.3

$/SI

I

o

o.1

o

-

o.1

....

0.5 0.6 0'.7 0.8 0.9 110

o

Fig. 7. Ratioof greatest to leastprincipalstress (S3/S•) versuscoefficient of friction,/t,for hydrostatic porepressure andfor variousvaluesof cohesion on the pre-existing faults.The lightlyshadedline marksthe minimumallowablelevel

of S3/S•determined by therequirement, forshearfailure,that$3mustbegreaterthantheporepressure. Otherdesignationsthe sameasin Figure 6.

ZOBACKAND ZOBACK: STRENGTHOF THE CRUST

283

TABLE 2. Resultsof Analysis Assumed

Cohesion on ENE Assumed Pore Pressure 0

Hydrostatic 0

Hydrostatic 0

Hydrostatic 0

Hydrostatic

Inherent Crustal Shear

'Maximum' Crustal Shear

Strength(•c), bars

Stress•($1 - $3), bars

Magnitude, $o/•'c

0

150-450

970-1200

0

0

300

150-350 250-550 250-400 350-650 =400

640-770 1025-1250 690-840 1080-1325 800-850

0 0.40-0.18 0.40-0.25 0.57 -0.30 0.75

400

550-750

1200-1350

0.73-0.53

Faults ($o), bars

100

100 200

500

Relative

impossible,S3