The Energetics of Cataclasis Based on Breakage Mechanics GIANG D. NGUYEN and ITAI EINAV Abstract—We develop a constitutive model for rocks that are constituted from brittle particles, based on the theory of breakage mechanics. The model connects between the energetics and the micromechanics that drive the process of confined comminution. Given this ability, our model not only describes the entire stress-strain response of the material, but also connects this response to predicting the evolution of the grain size distribution. The latter fact enables us to quantify how the permeability reduces within cataclasite zones, in relation to aspects of grain crushing. Finally, our paper focuses on setting a framework for quantifying how the energy budget of earthquakes is expensed in relation to dissipation events in cataclasis. We specifically distinguish between the dissipation directly from the creation of new surface area, which causes further breakage dissipation from the redistribution of locked-in stored energy from surrounding particles, dissipations from friction and from the configurational reorganisation of particles. Key words: Cataclasis, fault gouge, breakage, permeability, energy balance, fracture energy. 1. Introduction The stability of fault gouges holds the key to understanding earthquake dynamics (e.g., MARONE et al., 1990;SCHOLZ, 1990; BEN-ZION and SAMMIS, 2003), and the associated release of energy (e.g., SLEEP and BLANPIED, 1992;RECHES and DEWERS, 2005). Fault gouges evolve in high pressure or even ultrahigh-pressure environments of cataclasis (e.g., MORROW et al., 1981;LUND and AUSTRHEIM, 2003), commonly because of the severe motion of the lithospheric plate boundaries. In fault gouges, cataclastic rocks undergo lifecycles of healing and granulation (MARONE et al., 1995;OLSEN et al., 1998;RENARD et al., 2000;TENTHOREY et al., 2003;HEILBRONNER and KEULEN, 2006;BEN-ZION, 2008). During the granulation stage the parent rocks initially disintegrate into the product of granular minerals, which may then be furthered crushed during the tectonic slip. The grain size distribution (gsd) is therefore an evolving property during the slip, which starts from a healed agglomerated rock mass and becomes attracted towards an ultimate grading that is often found (or conveniently assumed) to be fractal, complying both self- similarity and power-law scaling (SAMMIS et al., 1986;STEACY and SAMMIS, 1991; An and SAMMIS, 1994). Experiments show that this continuous shift of the gsd towards School of Civil Engineering J05, The University of Sydney, Sydney, NSW 2006, Australia. E-mail: i.einav@civil.usyd.edu.au Pure appl. geophys. 166 (2009) 1693–1724 Ó Birkha ¨user Verlag, Basel, 2009 0033–4553/09/101693–32 DOI 10.1007/s00024-009-0518-x Pure and Applied Geophysics