Microphysics of brittle-plastic transition and origin of Goetze’s criterion

The rheology of rocks transitions from a localized brittle behaviour to a distributed plastic behaviour as the pressure and temperature increase with depth in the crust. Goetze's criterion defines this brittle-plastic transition as the depth at which the material strength becomes lower than the effective confining stress. However, such a criterion is not universal and seems material-dependent. In this work, we use a micromechanical model based on grain-scale frictional sliding cracks that can extend either as tensile “wing” cracks or as planar plastic zones (dislocation array), and we analyse the micro-mechanical controls of the brittle-plastic transition in rocks. We assume a constant confining stress loading condition consistent with most laboratory rock deformation tests and derive the corresponding stress-strain evolution. Our results indicate that apart from the confining stress and the ratio of fracture toughness and shear yield strength, the friction coefficient and frictional cohesion also play a significant role in the brittle-plastic transition. Low friction coefficients tend to promote a more brittle behaviour which is consistent with observations in talc and phyllosilicates. Moreover, we show that the presence of pore fluids may also extend the brittle regime. Our microphysical analysis shows that the overall success of Goetze’s criterion in rocks likely arises from the fact that most rocks share similar toughness, shear yield stress, and friction coefficient.