An analysis of anisotropy of rocks containing shape fabrics of rigid inclusions

Abstract

This paper presents a theoretical basis for estimation of mechanical anisotropy in homogeneous rocks containing shape fabrics of rigid inclusions. The analysis is based on two types of viscous models: one containing linear fabrics of prolate (a > b = c) inclusions (cf. L-tectonite) and the other containing planar fabrics of oblate (a < b = c) inclusions (cf. S-tectonite). Models show contrasting bulk viscosities in stretching (normal viscosity) and shearing (shear viscosity) parallel to the fabric. The axial ratio R (= a/b) and the volume concentration (ρ_v) of rigid inclusions appear to be the principal parameters in determining the viscosity contrast. In anisotropic models with linear fabrics, normal viscosity (η_p) increases monotonically with increase in R, whereas shear viscosity (η_s) increases to a maximum, and then drops down to a near-stationary value. In anisotropic models with planar fabrics, the normal viscosity increases little with increasing flatness of inclusions, but the variation assumes a steep gradient when the latter is large. Shear viscosity, on the other hand, is relatively less sensitive to the shape of inclusions. The ratio of normal and shear viscosities, conventionally described as anisotropy factor δ, in both the models is always greater than 1, indicating that normal viscosity will be essentially greater than shear viscosity, irrespective of the axial ratio of inclusions forming the fabric. Models with a linear fabric show contrasting normal viscosities in pure shear flow along and across the linear fabric. The anisotropy is expressed by the ratio of longitudinal and transverse normal viscosities (anisotropic factor σ). It is revealed that the transverse viscosity is essentially less than the longitudinal viscosity, as observed in test models.