Rock Strength and Texture Evolution During Deformation in the Earth's Ductile Lithosphere: A Two‐Phase Thermodynamics Model

Abstract

Building upon the two-phase and grain damage theory, we propose a new formulation allowing to track the evolution of phase mixing/segregation during ductile deformation of a two-phased aggregate. Our model is based on a set of variables characterizing a rock texture: the mean grain sizes and the phase proportion. During ductile deformation, activation of different micromechanical processes impacts the aggregate texture. Dislocation and diffusion creep are the two main deformation processes considered. We only account for the effect of Zener pinning in slowing down grain growth and allow for active grain-size reduction mechanisms in the diffusion creep domain. For this purpose, an equation is proposed to track the phase mixing evolution during ductile deformation. Numerical application using anorthite rheology shows that any grain reduction mechanisms that could be active in the diffusion creep regime requires a very high partition fraction in order to reach the grain size predicted by the feldspar piezometer. Application of this model to gabbroic composition, relevant for the ductile crust, demonstrates that the strong coupling between phases grain sizes and interface evolution results in steady-state grain sizes far below the field boundary. This effect is coeval with an important increase of mixing between the two phases. In addition, accounting for the phase mixing results in a drop of the global aggregate stress during deformation. This model allows for further comparison of mylonitized textures evolution with natural shear zones at the local and regional scales. Plain Language SummaryIn the Earth lower crust, the rocks deform by slow creep instead of breaking due to high temperature and pressure. Observations of natural material deformed in such conditions show that deformation concentrates on narrow-banded structures. At small scales (1 cm to 1 m), these shear bands generally present a very fine mean crystal size and a very good mixing of the minerals. These features are characteristic of deformed rocks, but their origins and consequences on geological structures at larger scales (1 m to 100 km) are yet to be fully understood. In this study we propose a physical model (a mathematical representation of reality) that allows to represent a rock consisting of two minerals, their mean crystal sizes and proportions and the quality of their mixing. This is based on parameters constrained experimentally for each pure mineral. Using this model, we are able to track the evolution of these rocks microscopical characteristic and their consequences on the rock strength during deformation. Eventually, the results allow us to refine our understanding of the implied processes by comparing the computed variables to measures performed on rock samples. The physical equations proposed could then be used to model the rock strength in geodynamical models at larger scales.