15

The behavior of rocks in the shallow crust (fig.7) has been extensively investigated with rockmechanics laboratory experiments. Theresults of experiments on the failure of intactrocks are graphically expressed using Mohrdiagrams that relate principal stresses actingon a rock volume to shear stresses acting onplanes differently oriented within the body. In Mohr diagrams (figs. 8, 9, 10), the composi-te failure envelope for intact isotropic rock iscontructed by merging the Griffith and

Coulomb criteria (JAEGER & COOK, 1979;SIBSON, 1998). Three failure modes of intactrock have been recognized (ENGELDER, 1999;SIBSON, 1998): tensional fracturing, transitio-nal-tensional fracturing (also called in literatu-re extensional-shear fracturing, e.g., SIBSON,1998) and compressional failure (also called inliterature compressional shear failure, e.g.,SIBSON, 1998). The first two failure modesoccur when the effective minimum stress istensional and are generally considered tooccur only for fluid pressures greater thanlithostatic in thrust regimes or at shallowdepths in normal fault regions (SIBSON, 1998).Tensional fracturing mainly controls the deve-lopment of extensional fractures in rocks,whereas the compressional failure applies todevelopment of faults and is governed by theCoulomb fracture criterion: t=C+sm wheret is the shear stress, C is the cohesive shearstress, s is the normal stress and m is the angleof rock internal friction. The slope of theCoulomb envelope is controlled by the coeffi-cient of internal friction of rocks involved inthe deformation. Laboratory strength tests ona wide range of rock types have shown that

Fig. 7 - Plumose structure on a fracture in lavas at Colcuc(Dolomites). Note on the left the center of nucleation of thefracture.

2. Fault mechanics: some basic aspects

the internal friction coefficient ranges bet-ween 0.5 and 1.0 (e.g., JAEGER & COOK, 1979).It has been shown that in isotropic bodies(quite a rare situation in the Earth's crust),thrust faults are most likely to form from

intact rocks at an angle of about 30° to s1 (fig.11). ANDERSON (1905) used the Coulomb-Mohr theory to explain conjugate faults andthe different mean dip of the various types offaults. The Anderson's theory applies close tothe Earth's surface, where one of the principalstresses needs to be vertical and the two remai-ning horizontal (due to the fact that, being asolid-air interface, the Earth's surface cannotsustain shear stresses). The main compressio-nal stress s1 is vertical in extensional regimesand consequently normal faults normallydevelop with high (dip around 60°) angle,whereas it is horizontal in contractional areasand thrust faults consequently develop withlow angle (around 30°). In strike slip settingss2 is vertical and strike-slip faults are mainlysubvertical. Important classes of faults thatappear to contradict the Anderson's theoryare low angle normal faults and high anglereverse faults. Fluid (e.g., water and hydrocarbons) pressureaffects significantly the mechanics of faulting(fig. 12). High fluid pressures (caused by rapidburial of impermeable strata, thermal waterpressuring and dehydration reactions occur-ring during burial and metamorphism) reducedrastically the stress needed to generate rockfracturing and formation of faults, since it sup-ports part of the normal stress that wouldotherwise act across rock grain boundaries.The normal stress is then reduced to a lowereffective normal stress. Extremely high porefluid pressure will promote hydrofracturing (aprocess normally induced in oil wells toincrease the permeability of reservoir rocks)and vein development. Normally, faults areassociated with hydrothermal extensional veinsystems (fig. 13). Veins are mainly horizontalwhen associated to thrust faults and subverti-cal for normal faults.Reactivation of existing faults accounts formost of the deformation within the frictionalseismogenic crust (fig. 14). In Mohr diagrams,the frictional failure envelope follows the

Structural Style & Dolomites Field Trip16

Fig. 9 - Generic Mohr diagram showing a composite Griffith-Coulomb failure envelope for intact rocks. The three shown cri-tical stress circles represent different failure modes: tensionalfracturing, transitional-tensional fracturing (also called in lite-rature extensional-shear fracturing) and compressional failure(also called in literature compressional shear failure).

Fig. 8 - Mohr diagram showing the state of effective stress atfailure for various experiments (varying the confining and theaxial load) with intact Fredrick Diabase. Each circle representsthe state of stress at failure at a different mean stress([s1+s2+s3]/3). The locus of stress states that bounds thefield of stable and unstable stresses is called the Mohr envelo-pe (after SUPPE, 1985).

linear Amonton's law and, for faults characte-rised by cohesive strength, is a form of theCoulomb envelope (fig. 15). The slope of theAmonton envelope is controlled by the sli-ding coefficient of friction of the fault, whichhas been shown to have typical values as highas 0.85 in the shallow crust (BYERLEE, 1978).The frictional resistence along pre-existingplanes is expressed by the Byerlee's law:t=0.85s. The Byerlee's law is broadly litho-logy-insensitive. Fault surfaces that contain alayer of gouge also obey Byerlee's law and dis-play a frictional behavior similar to clean rocksurfaces involving either strong and weaklithologies. The only silicatic minerals thatdisplay significant lower friction thanByerlee's law are montmorillonite, vermiculi-te and illite. Other platy minerals (e.g., chlori-te, kaolinite and serpentine) display normalfrictional properties. The existence of near optimally oriented faults(at an angle close to 30° from s1) normallyinhibits the development of new planes bybrittle failure. As the orientation of existingfaults becomes less favourable, reactivationoccurs for increasingly higher effective stressesuntil the angle of frictional lockup is reachedand Coulomb mode rupture is expected tooccur (HANDIN, 1969). For example, in com-pressional settings characterised by pre-exi-sting normal faults unfavourably oriented

with respect to s1 pre-existing normal faultsare expected to remain unsheared and newfault planes may develop. Domino tilting offaults in extensional and compressional areasmay progressively rotate the active fault planeso that they may acquire an unfavourableorientation for re-shearing, may lock-up andbe abandoned. Further deformation willrequire the nucleation of new, favourablyoriented faults.Most of the theory on fault mechanics is basedon the assumption of isotropic rock. Thisassumption is largely inconsistent with theobservations both in sedimentary and base-ment rocks, where stratification, schistosityand other metamorphic and igneous foliationsoccur. In strongly anisotropic rocks, theorientation of the forming fractures is gene-rally influenced by the foliation. Only in caseof planes of anisotropy nearly perpendicularto the s1 direction, unisotropy is unimpor-tant in localizing fractures (fig. 16).The displacement distribution along normaland thrust faults is maximum at the fault cen-ter and dies out to the fault margins. Thethickness of the fault gouge is direct functionof total slip along the surface (fig. 17).The mechanics of thrust faulting has been thesubject of animated discussion since whenlarge thrust sheets were recognized. Themechanical problem is that thrust sheets are

FAULT MECHANICS 17

σn

τ Mohr envelope

2θ σ1 σ3

τ0

φ

σ1 σ3 +

2

σ3 σ3

σ1

σ1

θ θ

Fig. 10 - Mohr-Coulomb failure criterion for isotropic intact rocks (left panel). The point of tangency of the Mohr circle represents thestate of stress on the plane which is at an angle Q from the s1 axis of the right panel.

Structural Style & Dolomites Field Trip18

σ3

σ3

σ1 σ1

30°σ2

σ2

60°

σ3 σ3

σ2

σ2

σ1

σ1

σ2

σ2 σ1

σ1

90°σ3

σ3

Fig. 11 -Anderson'stheory of faul-ting. The struc-tures associatedto fault planes(i.e., stylolites,extensional frac-tures and veins)are also shown.

very thin relative to their apparent frictionalresistence. When thrust faulting is reduced tothe elementary physics problem of pushing arigid block over a rigid base, the force withwhich the thin sheet has to be pushed deter-mines stresses that are even an order of magni-tude larger than the yield stress of communrocks.Several solutions were proposed to solve thisenigma: 1) the basal resistence is not expressedby Coulomb friction but is viscous or plastic(i.e., lower than expected); 2) thrusts are notpushed from behind but slide along dippingplanes; 3) fluid pressures may lower the fric-tional resistence along the basal surface andenhance thrusting; 4) mountain belts are pla-stic masses that flow outward under their own

weight; 5) mountain belts may be modelled ascritical tapers, similar to the deformed wedgesof snow or sand developing in front of a bull-dozer.At present the two more accepted explana-tions invoke the role of fluids and the criticaltaper behavior of thrust faults. Two lines ofevidence suggest that fluid pressures play asignificant role: 1) pumping of fluids in reser-voirs near active faults produces small earth-quakes; 2) fluid pressure measurements in acti-ve regions show that major thrusts are confi-ned to overpressured rock volumes. The critical taper theory suggests that fold-and-thrust belts and accretionary prisms arefirst characterised by internal deformation anddevelopment of a topographic gradient

FAULT MECHANICS 19

Fig. 12 - Mohr stress diagram showing the effects of pore fluidpressure on the state of stress of a rock volume. An increase ofpore fluid pressure p lowers the principal stresses acting on thebody and shifts the corresponding Mohr circle to the left. In thisexample, the dry rock is stable (i.e., it does not fracture since itdoes not reach the Mohr envelope) whereas the same rock volu-me, when subject to fluid pressure, may be unstable, i.e, cha-racterised by a Mohr circle tangent to the Mohr envelope. sn isthe normal stress.

Fig. 13 - Hydrothermal extensional vein systems associated toAnderson style fault systems (after SIBSON, 1990).

without sliding on the basal surface (or decol-lement) and developing a wedge shape (figs. 18,19, 20). Only when the wedge attains its criti-cal taper (given by the sum of a, the surfaceslope dip, and b, the basal decollement dip),the belt starts sliding stably, continuing togrowth at constant taper as additional material

enters the belt at the front. If, at a specificpoint, the critical taper of a wedge is less thanthe critical value (because of erosion, forexample), then the material will deform inmore internal sectors (for example with thedevelopment of out of sequence thrusts) untilthe critical value is once again attained. At this

Structural Style & Dolomites Field Trip20

Fig. 14 - Fracturing of intact rocks vs. frictional reactivation ofpre-existing faults. The frictional reactivation envelope for pre-existing faults is lower than that for faulting of intact rocks. Thestress required for frictional sliding along pre-existing fracturesis significantly less than the fracture strength. Two circles forfracture of intact rock (i.e., tangent to the Mohr envelope label-led as "faulting of intact rock") are shown. For the stress distri-butions associated to the two circles, frictional sliding on pre-existing fractures should anticipate the development of a newfault plane provided that such fractures have orientations com-prised in the 2b angles shown in figure

Fig. 15 - Measurements of maximum friction in sandstone, limestone and graywake. The frictional resistence along pre-existing pla-nes is expressed by the Byerlee's law: t=0.85s. Notice that, in the shallow crust (for lithostatic pressure lower than 0.2 GPa) the cohe-sion is null. The Byerlee's law is broadly lithology-insensitive and is valid for fault surfaces involving either strong and weak litholo-gies that may contain a layer of gouge as well. The only silicatic minerals that display significant lower friction than Byerlee's law aremontmorillonite, vermiculite and illite (after BYERLEE, 1978).

point migration of the belt and accretion ofmaterial at the thrust front will start again. Typical values of surface slope dips are bet-ween 1° and 10°, whereas decollement dips

may be as high as ca. 20°. When the basaldecollement runs within low-friction or ducti-le rocks, then the surface slope becomes abouthorizontal and plateaus develop.

FAULT MECHANICS 21

Fig. 17 - Fault gouge thickness (T) vs. total slip (D) for faultsmainly developed in crystalline rocks (after SCHOLZ, 1990).

Fig. 16 - Fracturing in anisotropic rocks. The effect of the orientation of the plane of slaty cleavage on a fracture orientation is inve-stigated in compressive fracture experiments on Martinsburg Slate. The orientation of the forming fractures is generally influencedby the foliation. For inclination of the slaty cleavage to the 1 of as much as 45°, the fracture always lay parallel to the cleavage.Only in cases for which the plane of anisotropy is nearly perpendicular to the s1 direction, anisotropy is unimportant in localizingfractures (after SUPPE, 1985).

Fig. 18 - Maximum length (l), as a function of fluid pressureratio (l=Pf/Pl, where Pf is the fluid pressure and Pl is the litho-static pressure) of a rectangular thrust sheet that can be pushedalong a horizontal decollement without fracturing. l is the fluidpressure within the thrust sheet and lf is the fluid pressurealong the fault (after SUPPE, 1985).

s

Fig. 19 - Contractional belts are normallymodelled as purely brittle critical tapersdeforming internally and spreading underthe action of body (gravity) and surface (tec-tonic) forces (upper panel). These modelssuccessfully reproduce large scale topogra-phic signatures of several wedge-shapeddeformed regions (accretionary wedges)overlying a basal décollement. Surface slopeand basal decollement dips predicted forsubmarine and subaerial accretionary wed-ges worldwide are shown in the bottompanel (after DAVIS et alii 1983).

Plateau

DecollementFrictional

DecollementPlastic

x

B/P transition

Frontal Ramp

Fig. 20 - The topographic features of moun-tain belts are controlled by the rheologicalbehavior of the basal decollement. Low-anglesurface slopes, typical of frontal sectors ofwedges deforming with a purely brittle (fric-tional) behavior, are interrupted by relativelysteeper slopes, where the lowermost part ofthe wedge (wedge base) crosses thebrittle/plastic transition and starts creepingwhile the basal décollement, deforming athigher strain rates, still behaves frictionally.Further to the rear, where both the wedge baseand the décollement are plastic, the surfaceslope flattens (plateau). After CARMINATI &SILETTO (1997).

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