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_Journal of Structural Geology 32 (2010) 1742–1753_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com/locate/jsg Simulating brittle fault evolution from networks of pre-existing joints within crystalline rock Heather Moir a,*, Rebecca J. Lunn a, Zoe K. Shipton b, James D. Kirkpatrickb a Department of Civil Engineering, University of Strathclyde, Glasgow, Scotland, UK b Department of Geographical and Earth Sciences, University of Glasgow, Glasgow, Scotland, UK Article info Article history: Received 9 February 2009 Received in revised form 17 August 2009 Accepted 20 August 2009 Available online 23 September 2009 Keywords: Numerical modelling Fault-zone evolution Abstract Many faults grow by linkage of smaller structures, and damage zones around faults may arise as a result of this linkage process. In this paper we present the first numerical simulations of the temporal and spatial evolution of fault linkage structures from more than 20 pre-existing joints, the initial positions of which are based on field observation. We show how the constantly evolving geometry and local stress field within this network of joints contribute to the fracture pattern. Markedly different fault-zone trace geometries are predicted when the joints are at different angles to the maximum compressive far-field stress ranging from evolving smooth linear structures to complex ‘stepped’ fault-zone trace geometries. We show that evolution of the complex fault-zone geometry is governed by: (1) the strong local variations in the stress field due to complex interactions between neighbouring joints; and (2) the orientation of the initial joint pattern with respect to the far-field stress. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Several authors have proposed that faults evolve under imposed stress by the linkage of pre-existing structures (Segall and Pollard, 1983; Martel, 1990; Bergbauer and Martel, 1999; Pachell et al., 2003). The pre-existing structures from which faults nucleate are commonly open or mineral-filled joints that are weaker than the surrounding rock (Segall and Pollard, 1983; Bergbauer and Martel, 1999; Pachell and Evans, 2002). When pre-existing features experience compressive loading, stress concentrations (both tensile and shear) develop around the tip of the feature. Shearing of these preexisting features often results in the formation of secondary fractures at (or near) the tip of the feature. These secondary fractures have different names including: tail cracks fractures (Cruikshank and Aydin, 1994; Willemse et al., 1997), splay fractures (Pachell and Evans, 2002; Myers and Aydin, 2004), horsetail fractures (Granier, 1985; Kim et al., 2004) and wing cracks (Crider and Peacock, 2004). In this paper all fractures (tension or shear) associated with faulting at (or near) the tip of a pre-existing feature are termed wing cracks. Conceptual models of fault evolution through the development of wing cracks (Martel, 1990; Martel and Boger, 1998) are supported by field observations of wing crack evolution from single joints or faults (Kattenhorn and Marshall, 2006; Joussineau et al., 2007) and * Corresponding author at: Department of Civil Engineering, University of Strathclyde, 16 Richmond Street, Glasgow G1 1XQ, Scotland, UK. E-mail address: heather.moir@strath.ac.uk (H. Moir). 0191-8141 $ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2009.08.016 In this paper, we focus on fault-zone development in crystalline rocks. Natural exposures of fault-zone traces within crystalline rocks can have many geometries, from smooth, approximately planar features (Fig. 1a) where faults appear to develop along strike, to complex stepped structures (Fig. 1b) where adjacent faults are linked at stepovers, or a combination of both (Fig. 1c). Key questions are: what governs the geometry of the evolving fault-zones? How are fractures within the fault-zone linked? A series of numerical models simulating fault growth, support these conceptual models for fault-zone evolution. These models have simulated the evolution of wing cracks from the tips of preexisting structures (Shen and Stephansson, 1993; Burgmann et al., 1994; Kattenhorn et al., 2000; Willson et al., 2007) or the linkage of pairs of faults with extensional and contractional geometries (Du and Aydin, 1995; Bremaecker and Ferris, 2004; Lunn et al., 2008). These simple, two-dimensional (2D) models have enabled prediction of the orientation of linkage fractures and their mode of failure, for a single fracture or pair of fractures in an ideal homogeneous medium. However, these simulations, derived from one or two fractures, are not sufficient to understand the range of complex geometries observed in the field (Fig. 1). Within this paper we H. Moir et al. Journal of Structural Geology 32 (2010) 1742–1753 1743 Fig. 1. Field examples of mapped sections from fault-zones. (a) A segment of the outcrop map from NE of Neves lake in the Italian Alps showing a section of fault-zone with smooth planar features (Pennacchioni and Mancktelow, 2007). (b) A segment of the outcrop map from the Waterfall region in the Sierra Nevada, California (Martel, 1990). (c) Map of fractures in an exposure of the Lake Edison granodiorite in the Bear Creek region in the Sierra Nevada, California, UTM coordinates are: 0333075 4136569. extend current knowledge by simulating fault-zone evolution in granite from a network of more than 20 joints. We show that evolution of the resulting fault-zone geometry is governed by: (1) the strong local variations in the stress field due to complex interactions between neighbouring joints; and (2) the orientation of the initial joint pattern with respect to the far-field stress. 2. Methodology We use the computer code Modelling Of Permeability Evolution in the Damage Zone surrounding faults (MOPEDZ) (Willson et al., 2007) to simulate spatial and temporal evolution of complex patterns of linking fractures. MOPEDZ was developed using the commercially available finite-element software COMSOL which is called from within the MATLAB code. The COMSOL finite-element routines assume plane strain during the simulations. MOPEDZ is a 2D finite-element model which solves Navier’s equation in a series of ‘quasi’ steady-states and uses a combined Mohr Coulomb and tensile failure criteria. Elements within the finite-element mesh are either intact host rock or fractured host rock. Elements which contain fractures (including the initial joints) are represented by lower effective material values (10_ of the host) for Young’s modulus, Poisson’s ratio and material strength, in a similar approach to Tang (1997). Representing the accumulation of damage within each element by altering that element’s material properties is consistent with other damage mechanics models (Jing, 2003). The initial configuration for all MOPEDZ simulations is similar to that illustrated in Fig. 2 with the host rock (granodiorite) having the 1744 H. Moir et al. Journal of Structural Geology 32 (2010) 1742–1753 Fig. 2. Typical initial setup showing the orientation of s1 and s3 (simulated far-field stress). Gray area is host rock, black is host rock containing joints (n.b. the pixellated nature of the pre-existing joints is a product of the model). The model boundaries (red) are under displacement control, following the initial failure only the top and bottom boundaries are displaced. To avoid consideration of structures generated at the boundary in the large simulations, only the central window (within the blue box) was presented in the results. For all small simulations no window was taken and all results within the red model boundaries are presented. The number of mesh elements varies from 6400 to 136,500 depending on the size of the simulation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) simulations presented in this paper vary from 6400 to 136,500; the size of each cell is approximately 13 mm2. As an element fails (in either shear or tension) its material properties are altered. Although the first failures are triggered by displacement of the boundaries, the alteration of the material properties of those failed cells causes a change in both the direction and magnitude of s1Local and s3Local (Lunn et al., 2008). This alteration of the local stress may be sufficient to trigger additional failures without any further displacement of the model boundaries. These subsequent failures can be adjacent to previous failures, i.e. representing the lengthening of a macroscopic fracture, or they can occur in locations that are disconnected from any previous failure, or they may be further fracturing of the same element or any combination of these. MOPEDZ iteratively reduces the values of the material properties as elements are predicted to fail; this reflects increasing damage to the host rock (host rock elements containing pre-existing joints start with the lowest values, 10_ of host rock). Each element can fail up to a maximum of six times (resulting in a reduction of strength, Young’s modulus and Poisson’s ratio) in a geometric sequence (Willson et al., 2007) until they reach the lowest value permitted (equivalent to those elements containing the initial joints). properties listed in Table 1 and any elements containing pre-existing joints havi Ключевые слова: spatial temporal, relative position, evolving, evolution, lunn, mesh, geophysical, martel, steve martel, rst failure, fault-zone development, damage, aydin, linkage fracture, moir, smooth, secondary fracture, simulation joint, numerical, mopedz gures, small simulation, linking, overlapping joint, pair, fault-zone geometry, slipped joint, stress eld, far-?eld, wa, numerical model, predicted evolution, journal structural, model domain, initial joint, plot, ?eld, stress ?eld, university, structure, element, damaged element, elsevier, sierra, fault, neighbouring joint, wing crack, wing, peacock, compressional quadrant, angle, eld data, small fault, failure, moir journal, contractional, crystalline rock, simulation consisting, existing, initial length, compressive, kattenhorn, original joint, model, complex, development, pattern, ?nite-element, initial condition, commonly observed, position, fault zone, strain tensor, under-lapping joint, reactivated joint, pre-existing joint, predicted, fracture, pollard, geometry, rock mechanics, predicted structure, outcrop map, displacement, simulation, sierra nevada, fault-zone evolution, journal structural geology, slip, journal, joint, link, property, location, mopedz, trace, linkage, small, temporal, nite-element mesh, segall pollard, crack, strain evolution, held constant, pre-existing, boundary, original, nite-element model, network, extensional orientation, surface plot, avoid consideration, linkage structure, simulated, initial orientation, number, locations, isolated pair, joint pattern, complex interaction, gure legend, zone, local stress, structural geology, sandstone journal, small number, left lateral, result, aplite dyke, strain, extensional geometry, stress, mopedz simulation, segall, single fracture, journal geophysical, shipton, neighbouring, waterfall region, damage plot, material property, joint separation, structural, fault-zone, length, rock, secondary fracturing, magnitude, mechanics, initial, strike, extensional, temporal evolution, stress elds, large simulation, nal simulation, strike-slip fault, eld observation, martel pachell, eld, overlapping, geology, jing, contractional geometry, host rock, develop, feature, far-?eld stress, growth, temporal variation, high angle, martin, strain predicted, pachell, spatial, youngs modulus, joint length, previous failure, host, under-lapping, bulletin, observation, nal structure, local, tang, location orientation, nevada, evans, larger mesh, orientation, pixelated nature, shear