Micromechanical controls on the brittle-plastic transition in rocks

Abstract: The rheology of rocks transitions from a localized brittle behaviour to distributed plastic behaviour with increasing pressure and temperature. This brittle-plastic is empirically observed to occur when the material strength becomes lower than the confining stress, which is termed Goetze's criterion. Such a criterion works well for most silicates but is not universal for all materials. We aim to determine the microphysical controls and stress-strain behaviour of rocks in the brittle-plastic transition. We use a micro-mechanical approach due to Horii and Nemat-Nasser, and consider representative volume elements containing sliding wing-cracks and plastic zones. We find solutions for frictional slip, plastic deformation and crack opening at constant confining pressure, and obtain stress-strain evolution. We show that the brittle-plastic transition depends on the confining stress, fracture toughness and plastic yield stress but also critically on the friction coefficient on preexisting defects. Materials with low friction are expected to be more brittle, and experience transition to fully plastic flow at higher pressure than anticipated from Goetze's criterion. The overall success of Goetze's criterion for the brittle-plastic transition in rocks is likely arising from the low toughness, high strength, and medium friction coefficient character of most rock forming minerals.