29-25 Progressive Strain Modeling using an Excel Spreadsheet: Comparisons to Real-World and Digital Clast Deformation

Session: Undergraduate Research, Part II (Posters)

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Abstract:

Strain analysis via Rf-phi techniques conducted on sedimentary and metamorphic rocks from the southeastern U.S. and Sangre de Cristo Mountains (New Mexico) reveals a pattern of increasing calculated bulk strain (Rs) with increasing grain size. In a follow up study, digital deformation of an image of an undeformed conglomerate showed the same results, with populations of larger clasts (e.g., granules, pebbles) “deforming” more quickly than populations of smaller clasts (e.g., sand). Analysis of undeformed and relatively undeformed conglomerates from the Gulf Coastal Plain (Tuscaloosa Formation), the southern Appalachian Foreland (Attala Chert), and Sangre de Cristo Mountains (Flechado Formation) showed that grain size dependent clast orientation and aspect ratio explains this apparent “partitioning” of strain between smaller and larger clasts. Because larger clasts in sedimentary rocks have both higher initial aspect ratios and are more likely to be preferentially aligned in both bedding parallel and bedding perpendicular planes, initial Rf and phi anisotropy in populations of larger clasts results in higher calculated Rs values following deformation – even under the same stress field and P-T conditions. Here, we demonstrate that this apparent grain size dependent partitioning can be mathematically modeled using an Excel spreadsheet and modified equations for an ellipse. In this mathematical model, we “deformed” a series of elliptical clasts from an initial “undeformed” state (Rs = 1) to an Rs value of 4. Using large datasets (n>1000), we mathematically deformed three different populations of grains: isotropic with respect to Rf and phi, anisotropic with respect to Rf, and anisotropic with respect to phi. We demonstrate that models in which grain orientation and aspect ratio is independent of grain size, calculated Rs is uniform for populations of small vs. large clasts across each deformation step. For populations in which aspect ratio and orientation were anisotropic with respect to grain size, modeled deformation showed the same systematic apparent grain size dependent strain partitioning as our digitally deformed rock image and rocks deformed in natural environment. We show that grain size in deformed sedimentary rocks (e.g., conglomerate, meta-conglomerate) plays a significant role in calculations of Rs during typical Rf-phi studies. Those studies that do not consider grain size as a mitigating factor in Rs calculations may present misleading results.

Geological Society of America Abstracts with Programs. Vol. 58, No. 1, 2026

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