Progressive deformation in anisotropic rocks

Abstract

Field observations show that the majority of crustal rocks possess a penetrative foliation defined by either compositional layering, preferred orientations of crystals, or both. Ductile deformation involving planar anisotropy of viscosity can be characterized by an anisotropy factor δ = q N / r/ s , the ratio of the bulk viscosities in pure and simple shear, respectively. This ratio of the normal and shear viscosities may be determined analytically if the anisotropy is resolvable in a multilayer sequence with individual laminae of isotropic viscosity. In that case, the resistance to normal compression will be largely controlled by the competent layers, whereas the resistance to shear is controlled by the soft layers. More specifically, the viscosities of the individual laminae add up like resistances in series and in parallel in the expressions for the normal and shear viscosities, respectively. The reorientation of the bulk stress within an anisotropic multilayer is systematically investigated for a range of anisotropy factors. The mode of progressive deformation is controlled only by the anisotropy factor and the orientation of the principal deviatoric stress. The rate of deformation can be scaled if the bulk normal viscosity and the magnitude of the principal deviatoric stress are also known. The results are illustrated in a series of nomograms showing the spectrum of strain and rotation histories possible in rock volumes deforming with planar anisotropy. It appears that with increasing anisotropy factor the deformation spectrum will narrow on simple shear, irrespective of the orientation of the background or bulk deviatoric stress axes. Plane strain and isochoric conditions are assumed throughout the analysis.