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_Journal of Structural Geology 32 (2010) 1732–1741_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com locate jsg_ _Unlocking the effects of friction on fault damage zones_ _Heather M. Savage a,*, Michele L. Cooke b_ _a Earth and Planetary Science Department, University of California, Santa Cruz, CA 95064, USA_ _b Geosciences Department, University of Massachusetts, Amherst, MA, USA_ _article info_ _Article history: Received 30 January 2009; Received in revised form 10 August 2009; Accepted 25 August 2009; Available online 11 September 2009_ _Keywords: Fault zone evolution Slip-weakening friction Off-fault damage Boundary element modeling_ _abstract_ _Two-dimensional, numerical models of a linear fault embedded within a linear elastic medium show the generation of off-fault tensile failure that results from inelastic slip along the fault. We explore quasistatic models with slip-weakening friction to assess the effects of spatially and temporally variable friction on the damage patterns. Tensile fractures form where tangential normal stresses along the fault exceed the tensile strength of the rock. These stresses result from locally high slip gradients at the rupture tip. Because faults of different displacement history and rock type could have varying slip-weakening distances, we examine the effect of changing the slip-weakening distance on the damage pattern and find that this parameter is important in determining off-fault fracture intensity and continuity along strike. Faults with short slip-weakening distance produce greater off-fault damage and significantly greater seismic radiated energy than faults with longer slip-weakening distances. We also investigate the effect of pre-existing damage on the subsequent development of fractures in second generation slip episodes and find that damage localizes onto pre-existing patches. These results could guide field studies of small faults as to whether the fault failed in one slip event or multiple small events._ _© 2009 Elsevier Ltd. All rights reserved._ _1. Introduction_ _Halos of pervasive cracking around faults, called damage zones, are ubiquitous features (e.g., Brock and Engelder, 1977; Chester and Logan, 1986; Faulkner et al., 2006). Although damage zones have important implications for rupture dynamics (Rice et al., 2005) and fluid flow in fault zones (Caine et al., 1996), our understanding of their initiation and development is limited. The processes at work during fault slip that could contribute to damage of the host rock include: change in the quasi-static stress field, ground shaking due to seismic waves, fault geometry (such as fault bends), and frictional variability along the fault due to the frictional evolution of fault surfaces and or gouge layers. However, damage zones nucleate and evolve from repeated deformation and displacement along faults (Sibson, 1977; Chester and Logan, 1986; Cowie and Shipton, 1998; Shipton and Cowie, 2003; Kim et al., 2004; Okubo and Schultz, 2005) and the overprinting of multiple events obscures how damage is generated in a single event, when the host rock is relatively intact. In order to understand how the damage zone develops in early stages of fault displacement when damage patterns should be more straightforward, we perform numerical experiments of the incipient stages of off-fault fracture._ _* Corresponding author. Tel.: +1 831 459 5263. E-mail address: hsavage@pmc.ucsc.edu (H.M. Savage)._ _0191-8141 $ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2009.08.014_ _development, on several-meter long faults that slip fractions of centimeters._ _This study highlights some potential differences in macroscopic damage patterns and intensity between faults with varying initial roughness. Surface roughness will determine the critical slip distance, which is the slip distance required for a fault to renew asperity contacts so that friction can evolve between steady-state values. In this paper we are specifically modeling this process solely as a function of slip and will refer to this distance as the slip-weakening distance (L). This distance is most likely a function of fault maturity on natural faults. Incipient faults have rougher surfaces that smooth with shear displacement (Sagy et al., 2007). For faults with gouge layers, localization of slip into shear bands will have smaller critical slip distances compared to gouge zones in which the entire layer participates in shear (Marone and Kilgore, 1993). The length of the critical slip distance affects the variability of friction along the fault during failure. As the fault begins to slip, patches of the fault that have slipped more than the critical slip distance will be weaker than patches that have not and therefore faults with small critical slip distances will have greater difference in friction between adjacent segments. This frictional variability will in turn influence the slip gradient along the fault (e.g., Burgmann et al., 1994). When slip gradients are high enough, local tensile stresses can arise and off-fault fracturing commences (Cooke, 1997). Although critical slip distances may scale non-linearly with displacement along faults at large slips (Ohnaka, 2000; Abercrombie and Rice, 2005), they should be constant in terms of displacement for the small slip events we discuss in this paper._ _Previous models of damage zone generation show that tensile tail cracks form in the tensile quadrants of the fault during displacements (e.g., Rispoli, 1981; Martel, 1997). Quasi-static models predict that fractures generally form at crack tips, which we refer to as fault tips in this paper in order to distinguish from the crack tips associated with off-fault damage. If present, an inelastic process zone can allow cracks to form inboard of the fault tip due to the slip gradient created at this change in frictional strength (e.g., Burgmann et al., 1994; Cooke, 1997). Dynamic slip studies have shown that the slip gradient preceding a rupture front produces fractures far inboard of the fault tip (Yamashita, 2000; Dalguer et al., 2003; Andrews, 2005). In these models, the zone of damage generated is thinnest where the rupture begins and widest at the end of the rupture in the tensile quadrants. The angle of the tail crack with respect to the main shear fracture can be a function of the strength of the process zone (Cooke, 1997) or in the case of dynamic rupture, slip velocity (Broberg, 1999). Yamashita (2000) predicted that joints formed in the tensile quadrant make a more oblique angle to the fault than joints formed in the compressive quadrant, however their fractures must fall along a prescribed regular mesh. These models predict that the generation of off-fault damage slows rupture propagation during an earthquake, as energy is absorbed through the creation of new fractures (e.g., Andrews, 2005)._ _In this paper, we directly simulate off-fault damage in the form of tensile fractures generated along small faults. Our model is quasistatic and has fault elements with a slip-weakening failure criterion. By studying a quasi-static slip-weakening frictional fault, we can isolate the effects of friction from the effects of dynamic stresses included in elastodynamic rupture models (e.g., Dalguer et al., 2003; Rice et al., 2005). We investigate fracture patterns for different slip-weakening lengths in an effort to distinguish how the early frictional properties of the fault influence the development of a damage zone. Although slip-weakening distance is a proxy for fault surface roughness, it does not reflect changes in fault planarity. Because our model is not constrained by a pre-existing mesh along which fractures have to form, these numerically generated fracture patterns can be compared with field-based measurements of macroscopic fractures._ _Pre-existing damage may affect the slip distribution as well. The formation of fractures alters the properties of the fault zone that effect rupture propagation and subsequent failures, such as: reducing stiffness of the host rock, absorbing energy through the creation of new surfaces, and, once the rock becomes highly fractured, providing additional material to crush into gouge. Rupture branching may result from activation of shear fractures off the main fault (Rice et al., 2005). Manighetti et al. (2004) suggested that slip profiles along a fault are modulated by pre-existing damage. We investigate the second episode of slip by inserting the damage patterns from the initial models in our study and re-slipping the fault._ _In addition to the fracture analysis, we investigate the effect of damage zone generation, as well as frictional variability on the fault system and the propagating rupture, by assessing the mechanical work budget. Work budget analyses examine the balance between the external work done on the system (stemming from stress and displacement at the boundaries) and the work consumed within the system by different deformational processes (e.g., Mitra and Boyer, 1986; Kanamori and Heaton, 2000; Cooke and Murphy, 2004; Abercrombie and Rice, 2005; Chester et al., 2005; Del Castello and Cooke, 2007; Ismat, 2008). Examining how elements of the work budget change as off-fault fractures grow provides insights into the tradeoffs among the deformational processes. Additionally, we can assess how development of damage zones changes the mechanical efficiency of faults on a systemic level._ _2. Methods_ _2.1. Numerical method_ _Numerical models based upon continuum mechanics have been used to model various geologic processes such as earthquake triggering (e.g., Stein, 1999) and fault interaction (e.g., Willemse et al., 1996; Maerten et al., 1999; Savage and Cooke, 2004; Marshall et al., 2008). Mechanical models are based upon the three governing equations of continuum mechanics, i.e. the equilibrium, compatibility and constitutive equations (Crouc'_ Ключевые слова: energy budget, total, pre-existing damage, joint formed, slip-weakening distance, shear, off-fault damage, shear stress, roughness, wong, strain, reach, modeled fault, smoother fault, decrease, seismic work, dynamic, process, mm, tensile, rupture, cluster, pre-existing, shipton, normal stress, sammis, tensile quadrant, earthquakes, study, cowie, slip-weakening, dalguer, stress fault, internal, andrews, small, falling, total work, smooth fault, weakening, cm, ohnaka, increase, off-fault fracture, external, propagation energy, analysis, work term, gradient, rispoli, scholz, position, fault zone, friction, doi, off-fault, pattern, geology, frictional work, function, work component, journal geophysical, damage zone, rougher fault, slip weakening, rst episode, static friction, fault slip, sagy, seismic, dieterich, modeled, journal, coef?cient, area, host rock, fault damage, dynamic friction, journal structural, normal displacement, fracturing, boundary, change, form, term, nature doi, rock, work, savage cooke, tensile strength, continuum mechanic, slip prole, slip gradient, greater, deformation, york, structural geology, nature, normal, radiated, wfric, element, fault, internal work, boundary condition, rupture reached, geophysical, work budget, slip-weakening length, slip, center patch, energy, fractures, broberg, drop, surface energy, savage, propagation, account, okubo schultz, faulkner, frictional strength, earthquake, patch, zone, small fault, displacement, slipweakening distance, slip distribution, rupture reach, compressive quadrant, distance, frictional resistance, wseis, shear fracture, martel, critical slip, model, damage, seismological society, weakening distance, smooth, crack, stress, event, external boundary, damage pattern, strike faults, surface, failure, journal structural geology, iteration, length, slip increase, rice, episode, slip distance, fracture pattern, stein, frictional, fracture, strength, slip episode, density, rupture propagation, model result, element length, geological society, condition, produce, generation, cluster form, mechanical efciency, yamashita, ha, budget, slip weakening distance, result, methods, seismic energy, stress drop, fracture propagation, rupture propagates, slip-weakening friction, range, tectonic fault, structural, chester, quadrant, friction coefcient, cooke, wilson, slip event, rough fault, primary fault, frictional variability, critical, fault interaction, external work, mechanical