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_Journal of Structural Geology 32 (2010) 107–117_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com locate jsg Magnitude of weakening during crustal-scale shear zone development Christopher Gerbi a,*, Nicholas Culshaw b,1, Jeffrey Marsh a,2 a Department of Earth Sciences, University of Maine, Orono, ME 04469, United States b Department of Earth Sciences, Dalhousie University, Halifax B3H 3J5, Canada Article info Article history: Received 17 January 2009 Received in revised form 4 September 2009 Accepted 5 October 2009 Available online 13 October 2009 Keywords: Shear zone Strain weakening Grenville Province Rheology Abstract We describe and apply a field-based approach for calculating the bulk strength of a heterogeneous material to a crustal-scale shear zone defining the margin of the Ma Parry Sound domain in the Grenville Province of southeastern Ontario. Using a numerical method, we calculate bulk strength, defined as effective viscosity, as the ratio between the surface traction needed to deform a square block in simple shear and the velocity gradient across that block. We use natural shear zone geometries to define the internal block structure and assign internal relative viscosities based primarily on textural criteria. The margin of the Parry Sound domain developed into the km-scale Twelve Mile Bay shear zone, accommodating several tens of km of transport, while the domain interior remained rigid. Fracturing and fluid infiltration drove development of an amphibolite facies meter-scale shear zone network that evolved into the Twelve Mile Bay structure. We analyzed three sites across the w5 km-wide strain gradient from near the granulitic domain to the large scale shear zone. The rocks at the shear zone margin weakened by approximately 30%. Those in the core weakened by at least 77% and probably by an order of magnitude. These values lie between but differ substantively from the isostress and isostrain-rate bounds, indicating that a numerical approach such as presented here markedly improves the accuracy of bulk strength calculations. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Spatial and temporal strength variation throughout the crust influences geodynamic processes as disparate as orogenic topographic evolution (e.g., Dahlen et al., 1984; Beaumont et al., 2001; Groome et al., 2008) and post-glacial rebound (Larsen et al., 2005; Wu and Mazzotti, 2007). In addition, and more directly, strength variation affects or controls the strain distribution in a region. Our understanding of crustal strength derives in large part from three sources: experimental deformation, geodesy, and numerical and analogue modeling. From these sources, some general pictures of crustal strength emerge (e.g., Kohlstedt et al., 1995; Handy et al., 2007; Burgmann and Dresen, 2008), but considerable uncertainty remains about the rheological structure in natural orogens (cf., for example, Jackson, 2002; Handy and Brun, 2004). Complicating a general description of rheological structure, processes such as metamorphism, melting and magma migration, fluid infiltration, and deformation all operate during orogenesis. Experimental and theoretical studies can constrain the rheological effects of some of these processes, but thorough understanding requires field-based investigation of synorogenic strength changes. In this contribution, we employ a numerical method for calculating bulk strength based on natural structures, documenting an effective viscosity drop of approximately an order of magnitude at the margins of a granulitic domain where it developed into an upper amphibolite facies km-scale shear zone. Interpretations of spatial strength variation exist (e.g., Houseman et al., 2008), but we are not aware of any field-based study documenting the temporal strength change associated with the development of a shear zone network. 2. Background 2.1. Controls on and calculations of rock strength Rock strength follows many definitions depending on the material type (e.g., viscous, plastic, elastic, and combinations thereof). We frame this study around mechanics in the middle and lower orogenic crust, well below the frictional–viscous transition, so we define strength as effective viscosity: the instantaneous ratio between stress and strain rate. The dominant factors controlling the bulk effective viscosity of a rock include mineralogy, phase or unit geometry (e.g., Handy, 1990, 1994; Ji, 2004; Takeda and Griera, 2006), fluid and or melt content (e.g., Holl et al., 1997; Brown and Solar, 2000; Evans, 2005; Rosenberg and Handy, 2005), and temperature. In general, weaker minerals, a higher degree of weak-phase interconnectivity, higher fluid or melt content, and higher temperatures reduce strength. The strength of polyphase materials lies between the isostress (Reuss, 1929) and isostrain-rate (Voigt, 1928) bounds (e.g., Handy, 1990, 1994; Handy et al., 1999; Tullis et al., 1991; Bons and Urai, 1994; Ji, 2004). The former describes a state in which all phases experience the same stress, usually associated with strong inclusions in a softer matrix. The latter describes a state in which all phases deform at the same rate, usually associated with soft inclusions in a stronger matrix. Handy (1990) described two characteristic microstructures for ductilely deforming polyphase rocks: a load-bearing framework and interconnected weak layers. The latter is markedly weaker, lying close to the isostress bound, and can be stable at high strain. A load-bearing framework is stronger, lying near the isostrain-rate bound, but generally unstable and can evolve into the geometrically more stable interconnected weak layer geometry either mechanically (Handy, 1994; Lonka et al., 1998; Handy et al., 1999), or with the presence of even a small percentage of melt (Rosenberg and Handy, 2005). Calculation of the theoretical isostress and isostrain-rate bounds simply requires knowledge of the strengths of the individual phases and their volume fraction; these bounding definitions take no explicit account of the phase distribution. But because the phase distribution controls where between the strength bounds the bulk strength lies, it is a fundamental determinant of rock strength. Ji (2004) modified the isostress and isostrain-rate formulations to include a parameter, J, to account for the phase geometry. Similarly, Bons and Urai (1994) suggested that the distance between the bounds is proportionally constant, relative to volume fraction, for a given microstructure that they defined as related to the percolation threshold. Unfortunately, no robust a priori method exists to derive either J or the percolation threshold for complex natural structures, limiting the value of those approximations. Treagus (2002) calculated the bulk viscosity of two-phase mixtures with various idealized geometries based on conglomerates and concluded that both volume fraction and shape fabric are critical controls on the aggregate strength. Her results, however, which are based on an inclusion-matrix structure, do not directly apply to more general structural geometries in naturally deformed rocks. Tullis et al. (1991) developed a numerical approach to calculate bulk flow properties based on digitizing the phase or unit distribution and providing a flow law for each component. Their approach works well if the individual flow laws are well-characterized, but it is also a time-consuming methodology. To date, analytical approaches to calculating bulk rock strength are too imprecise for most situations, which therefore require a numerical approach such as used by Tullis et al. (1991) or the one described below. Both numerical and analytical approaches require knowing the individual phase properties accurately. 2.2. Magnitude of weakening Rocks can weaken either uniformly or through the development of localized high strain zones. Both mechanisms can develop for similar reasons, but local feedback and rate relationships influence which dominates at which scale. In the upper crust, faults appear to be up to five to ten times weaker than their host rocks (Zoback, 2000). Rutter (1999) has postulated up to a 50% decrease in strength at the regional scale due to shear zone development. Parallel to the factors that control rock strength, the dominant factors that affect the degree of strength change include metamorphic reactions (e.g., Rubie, 1983; Wintsch et al., 1995; Groome et al., 2006; Upton and Craw, 2008), structural or textural evolution (e.g., Handy, 1994; Johnson et al., 2004), fluid flux, melting, and temperature changes. Of these factors, melting induces the greatest strength change, as melt viscosities may be up to 14 orders of magnitude lower than their solid counterparts (Cruden, 1990; Pinkerton and Stevenson, 1992). During most tectonism, the strength drop is significantly less, as the deforming rocks would likely host only a small melt percentage, but still could be more than an order of magnitude (Rosenberg and Handy, 2005). Using the strengths of the constituent phases in addition to analytical flow laws generated for polyphase materials and mylonites (e.g., Jordan, 1987; Hueckel et al., 1994; Handy, 1994; Handy et al., 1999; Treagus, 2002; Ji et al., 2004), some studies estimate the strength change during shear zone formation, but with little direct application to natural systems. For example, based on the analytical equations of Handy et al. (1999), an analysis by Park et al. (2006) implies strength drops of approximately 25% and 70% for nonmicaan_ Ключевые слова: mile bay shear zone, effective viscosity, orogenic belt, mechanical evolution, dogleg island, study area, two-phase mixture, panel strength, process, evans, drop, aggregate, calculation, weakening, sound domain, geological, belt, shear zone, tel, minimum strength, dresen, boomerang, factor, grenville, journal, bay shear, island, yield, science, rate, contrast, upper, time, journal geophysical, strength, matches island, mile, parry, numerical method, study, boundary, lie, mile bay, order magnitude, jamieson, percolation threshold, load-bearing framework, gneiss, gerbi, margin, protolith, rgmann, viscosity contrast, wu mazzotti, facies, greater, bound, scale, deformed, handy, result, journal structural, minimum, sound, simple shear, rheological, geology, islands, deformed panel, boomerang island, strain, based, tectonics, dogleg islands, america abstracts, approach, transport, crust, rutter, elsevier, numerical, table, dogleg, nature, springer, proportional distance, crustal, development, law, structural, geometry, numerical calculation, method, dogleg boomerang, isostress bound, jessell, handy handy, gerbi journal, hirth, shear, matches, granulite, temperature, isostress, core, granulitic domain, transposed fabric, houseman, effective, journal structural geology, craw, johnson, layer, volume fraction, area, strength contrast, variation, numerical approach, metamorphic, structural geology, solid earth, petrological observation, relative strength, canadian, mechanical property, magnitude, rock, zoback, tectonophysics, bulk, viscosity, tullis, textural, earth, bulk viscosity, experimental, rybacki, transposed, solid, relict, order, jordan, weaker, phase, domain, isostrain-rate, treagus, boomerang islands, mile bay shear, geophysical, deformation, bulk strength, undeformed, ?ow, magnitude weaker, structure, unit, relative, strength drop, der, park, transposed gneiss, comparable, davidson, localization, selected area, granulitic, material, bay, calculated, strength change, model, zone, isostrain-rate bound, bulk weakening, viscosity map, site, bay shear zone, culshaw, weak, panel, wa, transport direction, parry sound, bons, property, change, granulitic protolith, temperature change, estimate, grenville province, comparable strength, koons, lithological boundary