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

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    • MATSUMURA Tarojiro
    • Graduate School of Science and Technology, Educational Division, Shizuoka University
    • KUWATANI Tatsu
    • Department of Solid Earth Geochemistry, Japan Agency for Marine–Earth Science and Technology


<p>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 (<i>p</i>) and the far–field differential stress (<i>σ</i><sub>0</sub>). 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 (<i>σ</i>) and <i>σ</i><sub>0</sub>. An intact grain becomes a microboudinaged grain when <i>σ</i> is higher than its fracture strength at a specific point within the grain. Here, we make calculations of <i>p</i> for all intact grains under increasing <i>σ</i><sub>0</sub> from 0 to 20 MPa. Our calculations show that the modeled and observed distributions of <i>p</i> and the aspect ratio have similar patterns for both intact and microboudinaged grains. The value of <i>p</i> increases with increasing <i>σ</i><sub>0</sub>, with 70% of the grains being microboudinaged when <i>σ</i><sub>0</sub> = 20 MPa. These results suggest that our model is capable of reproducing observed data for microboudinaged columnar grains and that the relationship between <i>p</i> and <i>σ</i><sub>0</sub> 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.</p>


  • Journal of Mineralogical and Petrological Sciences

    Journal of Mineralogical and Petrological Sciences 112(1), 25-30, 2017

    Japan Association of Mineralogical Sciences


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