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How ductile are ductile shear zones? Neil S. Mancktelow* Department of Earth Sciences, Eidgenössische Technische Hochschule Zürich, CH-8092 Zurich, Switzerland ABSTRACT Three premises of ductile deformation in the middle and lower crust are widely accepted: (1) rocks flow with power-law viscous rheology, (2) localization in ductile shear zones involves strain softening, and (3) fluid flows into and is channelized within ductile shear zones. Ductile (viscous) shear zones should therefore initially develop along planes of maximum shear stress, strain soften, and rotate as material planes into the field of progressive extension. However, the mean stress or pressure within a weak, elongate viscous band being stretched is higher than the surrounding matrix, and this is difficult to reconcile with premise (3). In contrast, Mohr-Coulomb brittle faults always have lower pressure within the fault zone. Flow of fluid and melt into high-temperature shear zones therefore implies that ‘‘ductile’’ shear zones are not perfectly viscous but have a pressuredependent viscoplastic rheology. The continued pressure dependence may reflect significant microcracking on the grain scale even when localized deformation does not produce larger-scale discrete fractures. Keywords: faults, shear zones, rheology, pressure, fluids. INTRODUCTION Rock deformation in Earth’s crust is often strongly localized, showing a transition with depth from frictional reactivation of existing planes of weakness, to brittle fracturing of intact rock, and eventually to crystal-plastic flow, due to increasing pressure and temperature. Corresponding structures observed in the field are incoherent fault gouges, fault zones with more coherent cataclasites and locally pseudotachylytes (especially in strong rocks and at greater depths), a mixed brittleductile transition zone (also with pseudotachylytes), and localized ductile shear zones (Sibson, 1977). The change from fracture to flow is commonly referred to as the brittle-ductile (Paterson, 1978) or frictional-viscous (Schmid and Handy, 1991) transition. Rock rheology is correspondingly taken to show a transition from pressure-dependent plasticity, with little dependence on temperature or strain rate, to thermally activated viscous flow, which is controlled by strain rate and temperature but shows little dependence on pressure. Based on experiments from rocks and many other materials, nonassociated Mohr-Coulomb plasticity, with a linear dependence on pressure, is taken as a good approximation for the development of brittle faults or ‘‘shear bands,’’ i.e., near planar zones of highly localized deformation (Vermeer and de Borst, 1984). Viscous flow is approximated by a power-law relationship between stress and strain rate, with the stress exponent generally between 2 and 8 for dislocation creep (Carter and Tsenn, 1987). However, the stress expo*E-mail: [email protected] nent decreases toward 1 as diffusional mechanisms become more important, as proposed for ‘‘superplastic’’ deformation in very finegrained mylonitic shear zones (Schmid et al., 1977). The brittle-ductile transition zone, which is the strongest region of the crust, is sometimes assigned a specific rheology, either a von Mises plasticity (no pressure dependence) or an exponential flow law referred to as the ‘‘Peierls stress mechanism’’ (Regenauer-Lieb and Yuen, 2004). However, crustal deformation can also be described by a more general rheology in which elastic, viscous, and plastic mechanisms compete, depending on the time and length scales involved (Regenauer-Lieb and Yuen, 2003). There has been considerable discussion about appropriate rheological models for the brittle crust, in part because it is not straightforward to include Mohr-Coulomb plasticity in numerical codes. In contrast, pressureindependent, thermally activated power-law viscosity has generally been accepted as appropriate for modeling flow of the lower crust and even as an approximation for the whole buoyant crust (Molnar and Houseman, 2004). However, field studies have established that an interplay between brittle and ductile deformation can still occur at mid- and lowercrustal levels (Simpson, 1985; Segall and Simpson, 1986; Guermani and Pennacchioni, 1998; Mancktelow and Pennacchioni, 2005) and even under conditions of upper amphibolite to granulite facies (Pennacchioni and Cesare, 1997; Kisters et al., 2000) and eclogite facies (Austrheim and Boundy, 1994). The experimental results of Edmond and Paterson (1972) and Fischer and Paterson (1989) have demonstrated that dilatancy can still occur at high temperatures and confining pressures, which implies continued pressure dependence under mid- to lower-crustal conditions. This study analyzes the pressure distribution in and around brittle faults and ductile shear zones. It questions the fundamental assumption that the ductile crust, and specifically heterogeneous ductile shear zones, can be modeled by a pressure-independent viscous rheology. Pressure dependence of lower-crustal rock rheology can more readily explain both the observed strain localization and the pattern of fluid flow into shear zones. MODELING STRAIN LOCALIZATION AND PRESSURE IN FAULT ZONES The most striking characteristic of fault zones is the degree of strain localization, which occurs over a broad range of conditions, from near-surface to mantle depths. Although broader anastomosing zones may develop in both brittle and ductile regimes, localization on the scale of individual faults even within these broader patterns is often extreme. Natural shear zones are long relative to their width and thus approach the geometry of ‘‘shear bands,’’ where variation in strain along their length is very much less than that perpendicular to the band (Ramsay and Graham, 1970). For viscous rheology, without pressure dependence, strain rate is directly proportional to the effective viscosity. Localization within a shear band therefore implies lower effective viscosity within the band. This strain softening may be due to grain size reduction, min- 䉷 2006 Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or [email protected]. Geology; May 2006; v. 34; no. 5; p. 345–348; doi: 10.1130/G22260.1; 3 figures; Data Repository item 2006071. 345 Figure 1. Localization in viscous material, developed around an initial isolated perturbation (viscosity 10% less than the matrix). A: Plots of normal stress xx in lower left element of model, presented for (1) powerlaw material (n ⴝ 6) without strain softening, (2) linear viscous (n ⴝ 1) with strain softening determined by a bell-shaped curve, and (3) power-law material (n ⴝ 3) with same strain softening behavior. Note that localization only occurs in (3) and then only after an initial amount of bulk strain (~1.5%). B: Central third of model for case (3), showing strong localization developed at 3% bulk shortening. eral reaction, or development of crystallographic preferred orientation. Power-law viscosity entails a decrease in effective viscosity with increasing strain rate, which in itself can promote localization. However, as discussed by Mancktelow (2002), power-law viscous rheology or strain softening in linear viscous materials is not sufficient for strong localization. An interplay between both effects is necessary, as can be seen from the results of finite-element numerical models (see GSA Data Repository1) presented in Figure 1. The numerical experiment (1) in Figure 1A is for power-law rheology with n ⫽ 6, 1GSA Data Repository item 2006071, finite element modeling methods, is available online at www.geosociety.org/pubs/ft2006.htm, or on request from [email protected] or Documents Secretary, GSA, P.O. Box 9140, Boulder, CO 803019140, USA. 346 Figure 2. Pressure distribution in a ductile stretching shear zone, modeled as a weak elliptical viscous inclusion in a viscous matrix, with viscosity ratio of 10, ellipticity of the inclusion R ⴝ 50, angle to horizontal shortening direction of 60ⴗ, pure-shear boundary conditions, and power-law exponents from 1 to 50. Pressure is normalized against background value of compressive normal stress xx (ⴝ 1 in the far field). A–D: For a single elliptical shear zone. E–F: For three parallel elliptical shear zones, separated by a horizontal distance equal to ten times the minor axis of the ellipse. without material strain softening, and shows a constant flow stress at the boundary without structural weakening due to localization. Material strain softening for experiments (2) and (3) is modeled with a bell-like strain softening curve. This is considered to be a reasonable approximation to natural behavior in that it requires some small amount of initial deformation to develop, then weakens rapidly, but is asymptotic at very high strains. Experiment (2), with a linear viscous rheology, exactly follows the bell curve for the overall material strain softening and shows no significant localization. However, for experiment (3) with power-law rheology (n ⫽ 3), there is strong localization after an initial amount of distributed strain (⬃1.5% shortening), as can be seen from Figure 1B, plotted at 3% bulk shortening. Viscous shear zones initiate parallel to planes of maximum shear stress (i.e., 45⬚ to the shortening direction; Mancktelow, 2002). GEOLOGY, May 2006 shortening direction. This is close to the value of 37.5⬚ predicted by the relationship proposed by Vermeer (1990), namely, ⫽ 45⬚ ⫺ ( ⫹ )/4, where is the angle of the shear band to the shortening direction, is the angle of internal friction (30⬚), and is the angle of dilatancy (0⬚). The slightly higher angle in Figure 3 also reflects the 1.5% bulk shortening, which will increase the angle . Figure 3. Localization and pressure distribution in nondilatant Mohr-Coulomb material after 1.5% shortening in pure shear. Only central third of model is shown. A: Second invariant of plastic strain rate, normalized against the imposed value. B: Pressure in MPa (imposed background pressure of 100 MPa). In this orientation, there is no difference in pressure between shear band and matrix, regardless of any rheological contrast (Mancktelow, 1993). With ongoing deformation, ductile shear zones rotate into the field of incremental extension and should in general represent ‘‘positive stretching faults’’ (Means, 1989). In Figure 1B, for example, the shear band already makes an angle of 47.6⬚ to the shortening direction after 3% bulk shortening. Localization in a viscous shear zone implies lower effective viscosity in the band, and strong localization suggests a large viscosity contrast relative to the matrix. Extension of a weaker layer produces higher pressure in the layer and, for high viscosity contrast, this tectonic overpressure is effectively equal to the radius of the Mohr stress circle for the stronger matrix, i.e., (1 ⫺ 2)/2 (Mancktelow, 1993, 2002). Localization in experiments such as Figure 1B produces strain-softened zones narrower than a single finite element, and the pressure distribution within the shear zone cannot be characterized in any detail. It is instead analyzed by representing the localized and weakened viscous shear zone as an ellipse with length-to-width ratio of 50 and long axis oriented at 60⬚ to the shortening direction of the imposed pure shear (Figs. 2A–2D). The effective viscosity ratio between matrix and inclusion for the background strain rate is 10, and models are presented for power-law stress exponents of 1 (linear viscous), 3, 10, and 50. As expected, pressure inside the elongate GEOLOGY, May 2006 weak zone is always higher than in the matrix. For linear viscous materials, the pressure inside the inclusion is constant (Schmid and Podladchikov, 2003). For nonlinear viscosity, it is not constant, but the gradient along the weaker zone (toward lower values at the tips) is small. At higher values of the stress exponent, the average pressure in the inclusion increases slightly, and a marked high-pressure zone develops, flanking the length of the inclusion (Fig. 2D). For multiple zones, the flanking high-pressure zone is restricted to the boundary of the outermost elliptical weak zones, and the pressure internally between the zones is approximately the same as that in the far field (Figs. 2E and 2F). The stretching weak zones themselves, however, always have a pressure higher than the far-field value. Strong localization is typical of pressuredependent rheology, such as Mohr-Coulomb plasticity, due to the positive feedback effect of decreased pressure in the shear band. This could be expected for dilatant plasticity (angle of dilatancy ⬎ 0⬚), but it is also true for nondilatant but pressure-sensitive plasticity (Vermeer and de Borst, 1984, 1990), as in the numerical model of Figure 3. A background pressure of 100 MPa, appropriate to ⬃3–4 km depth, was assumed, leading to a matrix pressure effectively double this value at MohrCoulomb failure (Petrini and Podladchikov, 2000). As can be seen from Figure 3B, pressure in the shear bands is always lower than in the matrix, and the dominant MohrCoulomb shear band is oriented at 38.5⬚ to the DISCUSSION Many publications have established that both brittle faults and ductile shear zones are preferential conduits for fluid flow (McCaig, 1987; Kisters et al., 2000). This is often reflected in hydrating mineral reactions, the most common example being phyllonitic shear zones in granitic rocks. However, fluid flow into active shear zones is also important for promoting metamorphic reactions even where these reactions do not involve hydration—for example, local eclogitization of dry rocks (Pennacchioni, 1996; Austrheim and Engvik, 1997). Changes in minor-element chemistry (Marquer et al., 1994; Rolland et al., 2003) and stable isotopes (Kerrich et al., 1984) are also clear evidence for strong fluid flow into many shear zones. Preferential channeling within shear zones implies a gradient of decreasing pressure into and along the shear zone, and presumably also enhanced permeability, at least transiently (Kisters et al., 2000; Kolb et al., 2004). As demonstrated in Figures 2 and 3, there is a characteristic difference between plastic (i.e., brittle) and viscous (i.e., ductile) shear zones—plastic shear zones have lower pressure compared to the surrounding matrix, whereas viscous zones have higher pressure. This has fundamental consequences for the direction of fluid flow. Fluid and rock pressures cannot necessarily be linked in a simple and direct manner, but the gradient in fluid pressure is unlikely to be opposite to that in rock pressure. This implies that fluid flow into ductile shear zones is only promoted if shear zones involve a component of pressuresensitive plastic (i.e., brittle) rheology and not just a (power-law) viscous rheology, as has commonly been assumed for lower-crustal shear zones. Observations from high-grade shear zones support this contention. Direct field evidence suggests that highly localized ductile shear zones may have a brittle precursor, and that in this case their geometry is largely predetermined by that of the initial brittle fracture pattern (Segall and Simpson, 1986; Guermani and Pennacchioni, 1998; Mancktelow and Pennacchioni, 2005). Ductile shear zones developed from brittle precursors have been observed not only under lowmetamorphic-grade conditions close to what is 347 traditionally taken as the brittle-ductile transition, but also under amphibolite to granulite facies (Pennacchioni and Cesare, 1997; Kisters et al., 2000) and even eclogite facies (Austrheim and Boundy, 1994). Mutual overprinting relationships between brittle fractures and ductile shear zones indicate that the process is not a single event, but involves multiple cycles of fracturing and subsequent localized ductile shearing (Pennacchioni and Cesare, 1997; Kisters et al., 2000; Kolb et al., 2004). The transition from brittle fracture to ductile shearing could be explained by a drop in fluid pressure in the brittle fault zone, together with promotion of more ductile mechanisms by the introduction of water itself, mineralogical changes due to fluid-rock interaction, and grain size reduction due to cataclasis. However, causes for a transition back to brittle behavior are less clear, since localized ductile shearing implies both lower deviatoric stress due to strain softening and higher pressure within the zone, both of which move the stress state away from the MohrCoulomb failure envelope. Renewed brittle failure would require an increase in pore-fluid pressure, possibly also together with strain hardening and/or increased strain rate in the shear zone (Kolb et al., 2004). CONCLUSIONS The fundamental difference in pressure distribution associated with plastic (brittle) and viscous (ductile) shear band formation suggests that fluid should flow into brittle faults and should be expelled from ductile shear zones. Studies of natural ‘‘ductile shear zones’’ have established that there is a clear tendency for fluid to flow into and along shear zones. This is not consistent with predicted higher pressures in viscous shear zones, leading to the conclusion that strain localization in heterogeneous ductile shear zones involves an important component of pressure-dependent plastic behavior. This conclusion requires a dramatic reevaluation of the appropriate rheology for tectonic modeling of localized ductile shear zones in the middle and lower crust, below what has traditionally been taken as the ‘‘brittle-ductile transition’’ at 10–15 km depth. Isolated fluid-filled porosity, even in relatively dry rocks, will be close to lithostatic pressure, so that microcracking at the grain scale may be quite ubiquitous, even under high-grade metamorphic conditions. Pressure-dependent microcracking, enhanced in zones of high strain rate, could result in a pressuredependent viscoplastic rheology in deep, ‘‘ductile’’ shear zones, without any overall loss of cohesion or development of linked macroscopic fractures. 348 ACKNOWLEDGMENTS Development of the finite-element code benefited greatly from discussions with Yuri Podladchikov, Dani Schmid, Guy Lister, and Boris Kaus. Reviews by Gideon Rosenbaum and Jochen Kolb are gratefully acknowledged. 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