PROGRESS IN MICROBOUDIN METHOD FOR PALAEO-STRESS ANALYSIS OF METAMORPHIC TECTONITES: APPLICATION OF MATHEMATICALLY REFINED EXPRESSION

Abstract

The microboudin method for palaeo-stress analysis is mathematically refined by incorporating the recently proposed shear-lag model, which describes the relationship between stress distribution along a fibre embedded within an elastic matrix and the far-field differential stress applied to the matrix. The refined probability density function of fractured fibres (G) with respect to the aspect ratio of the fibre (r) and the stress parameter (λ) is given byG(r, λ)=1-exp-m-1mrλmEfEqm1-1-EqEf1cosh(Ar)mwhere Eq and Ef are the elastic constants of the matrix and fibre, m is the Weibull modulus of the fibre material, and A is a constant. The stress parameter λ is defined as λ=σ0/S*, where σ0 is the far-field differential stress applied to the matrix and S* is the modal fracture strength of the fibre material at r=1. This method is applied to tourmaline and piemontite boudins in quartzose rocks from six areas, and it is revealed that the probability density function adequately models the proportion of boudinaged tourmaline and piemontite grains. The value of λ is determined for each sample, allowing σ0 to be determined by this method when S* is known.