Viscous anisotropy of two-phase composites, and applications to rocks and structures

Abstract

Anisotropy of viscosity in rocks has a significant effect on the development of geological structures, as demonstrated in several theoretical and analogue model studies. This paper develops the results of a self-consistent mechanics approach to modelling the bulk viscous properties of two-phase composites, to reveal the strength of the viscous anisotropy. Anisotropy factor, δ, is defined as the ratio of normal to shear viscosity, μ N/ μ S. The value of δ is determined for different types of composites of two viscous phases with varying viscosity ratio ( m=5, 10, 100), ranging from bilaminates to those with elliptical shape fabrics given by axial ratio, R. Bilaminates with equal layer thickness are the most highly anisotropic systems, where δ simply depends on m. These results are applied to rocks, modelled as two-phase composites of competent and incompetent lithologies, with the aim of quantifying the viscous anisotropy that is associated with natural rock deformation and the formation of geological structures. It is deduced that m=5 or 10 is an appropriate maximum viscosity contrast for many metasedimentary rocks (e.g. psammite/pelite composites), but that m=100 might be effectively reached in limestone/marl pairs, or in rocks containing surfaces of slip or zones of recrystallisation or grain-boundary sliding. These m values give rise to maximum δ values of 3, 5.5 and 25.5, respectively. An anisotropy factor of δ≫25 is effectively a composite of a rigid and a viscous phase, and may only be achieved in solid–melt mixtures. Anisotropic rocks, whether layered or containing a strong shape fabric, will develop folds more easily than isotropic rocks. Characteristic structures are similar folds, chevron folds, kink bands and shear bands. Geometric features of folds, especially fold angularity, may provide methods of quantifying the viscous anisotropy of rocks and composites.