Extrinsic Anisotropy of Two-Phase Newtonian Aggregates: Fabric Characterization and Parameterization

Rocks of the Earth's crust and mantle commonly consist of different minerals with contrasting mechanical properties. During progressive, high-temperature (ductile) deformation, these rocks develop extrinsic mechanical anisotropy linked to strain partitioning between different minerals, amount of accumulated strain, and bulk strain geometry. Extrinsic anisotropy plays an important role in a wide range of geodynamic processes up to the scale of mantle convection. However, the evolution of grain- and rock-scale fabrics causing this anisotropy cannot be directly simulated in large-scale numerical simulations. For two-phase aggregates-a good rheological approximation of most Earth's rocks-we propose a method to indirectly approximate the extrinsic viscous anisotropy by combining (a) 3D mechanical models of rock fabrics, and (b) analytical effective medium theories. Our results confirm that weak inclusions induce substantial weakening by forming a network of weak thin layers with limited lateral connectivity. Consequently, even when the inclusion phase is extremely weak, structural weakening is not larger than 30-60%, less than in previous estimates. On the other hand, the presence of strong inclusions does not have a profound impact on the effective strength of the aggregate, and lineated fabrics only develop at relatively low viscosity contrasts. When rigid inclusions become clogged, however, the aggregate viscosity can increase over the theoretical upper bound. We show that the modeled grain-scale fabrics can be parameterized as a function of the bulk deformation and material phase properties and combined with analytical solutions to approximate the anisotropic viscous tensor.