The relationship between the proportion of microboudinaged columnar grains and far-field differential stress

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.