Controls on strain localization in a two-dimensional elastoplastic layer: Insights into size-frequency scaling of extensional fault populations

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B11, 2529, doi:10.1029/2001JB001712, 2003

Controls on strain localization in a two-dimensional elastoplastic layer: Insights into size-frequency scaling of extensional fault populations Kathryn M. Hardacre and Patience A. Cowie Department of GeoSciences, University of Edinburgh, Edinburgh, UK Received 13 December 2001; revised 7 April 2003; accepted 1 July 2003; published 18 November 2003.

[1] We use a two-dimensional (2-D) finite element code to investigate how mechanical

properties and boundary conditions influence progressive strain localization during extension of a 2-D elastoplastic layer. The deforming medium is modeled using a strain softening Von Mises rheology, with a Gaussian heterogeneity in yield strength distributed randomly in space. Specifically, we examine the effects of changing (1) the thickness of the deforming layer, (2) the basal boundary condition, (3) the range of strengths in the deforming layer, (4) the strength loss on failure, and (5) the total accommodated strain. Discrete zones of plastic shear strain are observed to nucleate and grow progressively during each experiment. In order to quantify and thus discriminate between the deformation patterns produced under differing conditions, we calculate the size-frequency distributions of the shear band populations. Size is defined as the total plastic strain represented by each discrete structure. A wide range of size-frequency distributions is observed, including both power law and exponential as well as distributions that show breaks in scaling with a transition from power law (at small sizes) to exponential (at large sizes). We show that these variations in population statistics are directly reflecting a change in strain localization in space and time caused by changing model parameters. Furthermore, by making an analogy between the model shear bands and tectonic faults, we provide insights into key features of fault size-frequency distributions that have been measured in continental and oceanic extensional settings and also observed in analogue INDEX TERMS: 8015 Structural Geology: Local crustal structure; 8020 Structural experiments. Geology: Mechanics; 8010 Structural Geology: Fractures and faults; 8109 Tectonophysics: Continental tectonics—extensional (0905); 8159 Tectonophysics: Rheology—crust and lithosphere; KEYWORDS: faulting, localization, scaling, extension, modeling Citation: Hardacre, K. M., and P. A. Cowie, Controls on strain localization in a two-dimensional elastoplastic layer: Insights into size-frequency scaling of extensional fault populations, J. Geophys. Res., 108(B11), 2529, doi:10.1029/2001JB001712, 2003.

1. Introduction [2] Observations show that the response of the crust to imposed plate boundary forces is to deform in an inhomogeneous fashion. In the lower crust, where the rheology is strongly temperature-dependent, heterogeneity is most obvious at the grain scale and at a larger scale the deformation can appear relatively homogeneous. However, at shallow depths (