Description:

_Journal of Structural Geology 32 (2010) 330–341 Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com/locate/jsg Numerical modeling of crenulation cleavage development: A polymineralic approach Fe´lice M.J. Naus-Thijssen*, Scott E. Johnson, Peter O. Koons Department of Earth Sciences, University of Maine, 5790 Bryand Global Sciences Center, Orono, ME 04469, USA Article info Article history: Received 9 July 2009 Received in revised form 10 December 2009 Accepted 4 January 2010 Available online 14 January 2010 Keywords: Crenulation cleavage Finite element analysis Anisotropic elasticity Pressure solution OOF2 Abstract The finite element method was used to investigate how the elastic interactions of quartz and muscovite minerals affect grain-scale stress and strain distributions at different stages of crenulation cleavage development. The polymineralic structure comprises individual grains that were each assigned their own 3D stiffness tensor and orientation. Gradients in mean stress and volumetric strain within quartz grains develop between the limbs and hinges of microfolds at the earliest stages of crenulation development, with higher values in the microfold limbs. These gradients decrease with development of the crenulation cleavage, as the microfold limbs become phyllosilicate-rich (P) domains and the hinges become quartz- and feldspar-rich (QF) domains. Crystallographic orientations of the quartz grains have a relatively minor effect on the mean stress and volumetric strain distributions. Our findings are broadly consistent with both pressure solution and strain-driven dissolution models for crenulation cleavage development. However, because crenulation cleavage development typically involves metamorphic reactions, we favor a model in which dissolution is driven by those reactions, and mass transfer leading to development of the mineralogically segregated fabric is driven by pore fluid pressure gradients that follow gradients in volumetric strain. Local concentrations of stress and strain across mineral interfaces may identify sites of enhanced reaction. © 2010 Elsevier Ltd. All rights reserved. 1. Introduction Although crenulation cleavage is the most common type of cleavage in multiply-deformed, intermediate to high-grade metapelitic rocks (Williams et al., 2001), its formation and role in strain partitioning across a range of scales are incompletely understood. Crenulation cleavage is characterized by phyllosilicate-rich (P) domains, in which phyllosilicates define the overall cleavage, separated by quartz- and feldspar-rich (QF) domains (Fig. 1). Quartz grains in this fabric show little to no evidence for internal deformation or recrystallization (Vernon and Clarke, 2008 and references therein). The characteristic mineralogical differentiation is therefore thought to result from dissolution of quartz and feldspar in the P-domains and precipitation of the dissolved material in the QF-domains (e.g. Gray and Durney, 1979; Schoneveld, 1979; Mancktelow, 1994). Alternatively, some percentage of the dissolved material may be removed from the local system (e.g. Bell et al., 1986; Wright and Henderson, 1992). There are two dominant hypotheses for crenulation cleavage formation: pressure solution is * Corresponding author. Fax: +1 207 581 2202. E-mail address: felice.thijssen@umit.maine.edu (F.M.J. Naus-Thijssen). 0191-8141 $ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2010.01.004 most commonly invoked as the driving force for both dissolution and mass transfer from P-domains to QF-domains in both slaty cleavage (e.g. Sorby, 1863; Durney, 1972; Robin, 1979) and crenulation cleavage (e.g. Durney, 1972; Robin, 1979; Rutter, 1983). Pressure solution, sometimes referred to as dissolution or solution-precipitation creep or stress-induced dissolution and/or solution transfer, involves (1) the dissolution of material at grain boundaries that are subjected to a high normal stress, (2) diffusion of dissolved material down a chemical potential gradient induced by a gradient in normal stress, and (3) precipitation on open pore walls or within grain boundaries subjected to a lower normal stress. Strain-driven dissolution, where material moves from regions of high dislocation density to regions of low dislocation density, has been cited as an alternative to stress-induced dissolution (Bell et al., 1986; Vernon, 2004; Passchier and Trouw, 2005). The influence of folding in a single or multilayered materials on stress and strain distributions, and how these distributions can be coupled to mass transfer, has been investigated numerically by a number of workers (e.g. Durney, 1978; Stephansson, 1974; Hobbs et al., 2000; Zhang et al., 2000). In these studies, folding of homogeneous layers is considered. However, rocks typically contain two or more minerals with variable geometrical and crystallographic arrangements relative to one another. The elastic interactions of F.M.J. Naus-Thijssen et al. Journal of Structural Geology 32 (2010) 330–341 331 these individual minerals lead to marked heterogeneity in the spatial distributions of stress and strain during deformation (e.g. Tullis et al., 1991; Johnson et al., 2004). Thus, the question arises as to how this grain-scale spatial heterogeneity will influence the larger scale (e.g. microfold half-wavelength) stress and strain gradients, and therefore the driving forces responsible for mass transfer during crenulation cleavage development. In order to examine grain-scale elastic interactions, we use the finite element method to evaluate instantaneous models containing hundreds of individual quartz and muscovite grains. Each grain is assigned its own crystallographic orientation and material-specific 3D stiffness tensor. The microstructure models are subjected to an elastic shortening strain of 1%. To evaluate how the spatial distributions and intensities of mechanical quantities change with fabric evolution, we consider three different stages of crenulation cleavage development (based on stages 2, 3 and 4 of Bell and Rubenach, 1983). Below, we provide some background information on crenulation cleavage and its development. We then give background information and methodologies for our numerical experiments. Finally we discuss the results of our experiments and the implications for crenulation cleavage development. In summary, we find that mean stress and volumetric strain values in quartz grains vary systematically depending on domainal position within the crenulation cleavage microstructure. The resulting gradients between P- and QF-domains are consistent with a pressure solution mechanism of fabric formation, but they are also consistent with a formulation that emphasizes volumetric strains as opposed to stresses. The volumetric strain gradients are used as a proxy for how fluids will flow during fabric evolution, providing a quantitative basis for understanding mass transfer during crenulation cleavage development. 2. Background 2.1. General observations Crenulation cleavage has been observed and described since the mid-19th century (e.g. Sharpe, 1849; Sorby, 1857, 1880), but it was not until the second half of the 20th century that workers began to systematically investigate the variables that determine its morphology and microstructure (e.g. Cosgrove, 1976; Gray, 2.2. Previous modeling The evolution of macro-, meso- and micro-scale folds, including the distributions of stress and strain within them, has been explored by theoretical (e.g. Biot, 1957, 1961; Ramberg, 1963; Johnson and Fletcher, 1994), analog (e.g. Ramberg, 1963; Means and Rogers, 1964; Means and Williams, 1972; Etheridge, 1973; Abbassi and Mancktelow, 1992) and numerical (e.g. Dieterich and Carter, 1969; Stephansson, 1974; Zhang et al., 2000; Hobbs et al., 2000) models. In theoretical models, the formation of crenulation cleavage is divided into different stages. First, buckling instabilities are developed in an anisotropic medium, such as mineral fabrics or multilayered rocks. This is followed by the development of crenulation cleavage planes that are related to the microbuckles and are formed and further developed by a dissolution-precipitation process and mineral redistribution (e.g. Williams, 1972; Cosgrove, 1976; Gray and Durney, 1979). Bell and Rubenach (1983) proposed a six-stage model of crenulation cleavage development based on observations of both matrix and porphyroblast inclusion trails (Fig. 2). Stage 1 represents the initial homogeneous state. Figure 1. Photomicrograph of crenulation cleavage. Indicated are the P- (crenulation limbs) and QF- (crenulation hinges) domains and two generations of foliation, Sn and Sn+1. Sample from the Main Central thrust zone, Nepal Himalaya. Ключевые слова: e, r, o