Download How ductile are ductile shear zones?

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
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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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Manuscript received 19 September 2005
Revised manuscript received 6 December 2005
Manuscript accepted 16 December 2005
Printed in USA
GEOLOGY, May 2006