The relationship between the proportion of microboudinaged columnar grains and far–field differential stress: A numerical model for analyzing paleodifferential stress

Abstract

Microboudin paleopiezometry is an intensive endeavor that involves measurement of several hundred grains per sample to produce reliable estimations of far–field differential stress. This procedure is particularly time–consuming when conducting stress analysis for a large number of samples within a metamorphic belt. To improve and expedite the stress estimation procedure, we propose a numerical model that uses grain–shape data to calculate the relationship between the proportion of microboudinaged columnar grains (p) and the far–field differential stress (σ₀). Our model combines the weakest link theory and the shear–lag model. The weakest link theory is used to derive the fracture strength of grains, whereas the shear–lag model is used to determine the relationship between the differential stress within a grain (σ) and σ₀. An intact grain becomes a microboudinaged grain when σ is higher than its fracture strength at a specific point within the grain. Here, we make calculations of p for all intact grains under increasing σ₀ from 0 to 20 MPa. Our calculations show that the modeled and observed distributions of p and the aspect ratio have similar patterns for both intact and microboudinaged grains. The value of p increases with increasing σ₀, with 70% of the grains being microboudinaged when σ₀ = 20 MPa. These results suggest that our model is capable of reproducing observed data for microboudinaged columnar grains and that the relationship between p and σ₀ can be used to estimate the magnitude of differential stress without the need to measure grain–size data for several hundred grains with a wide range of aspect ratios.