Testing Stress Percolation as a Model for Stress Transmission in Rocks

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This project will test stress percolation hypothesis and its utility for working with geologic materials. Both scientists and engineers have assumed that when a rock is loaded by either tectonic forces or within the context of engineering projects, the load is borne evenly throughout the rock. The PI has developed an alternative hypothesis that the stresses produced by external loads on a rock are distributed throughout the rock according to a pattern that resembles the pattern created by water flowing through otherwise dry sand. If the hypothesis proves correct, then stress distribution in rocks will join a large class of phenomena that exhibit 'percolation' behavior, including the patterns of stress distribution observed in granular materials. Thus one implication of the hypothesis is that there is a single unifying physical model for deformation of all earth materials. The value in understanding the stress distribution in rocks is that it will allow us to create better models of rock deformation and better predict the mechanical behavior of rocks, which has implications for deepening our understanding of a variety of Earth processes as well engineering applications. The existence of stress percolation and a refined understanding of how it operates in rocks has tremendous implications for many disciplines beyond geophysics. Researchers in materials science, metallurgy, and shock physics, all struggle with the so called 'polycrystalline problem' - like rocks, many solid materials are composed of aggregates of crystalline grains with a variety of properties. Understanding the response to loading of many of these materials has presented challenges similar to those experienced by those working on rock deformation. Thus, this research will contribute to a better understanding of mechanical problems in all of these disciplines. Using finite element (FEM) simulations of a polycrystalline material the PI has recently shown that local variations in stress and strain participate in large-scale patterns, likely caused by stress percolation. The patterns are a function of the heterogeneity and statistical distribution of elastic and plastic properties across the population of mechanical components (grains and grain boundaries) in the material. Greater degrees of heterogeneity lead to more intense stress concentrations across a less dense pattern. Lower degrees of elastic heterogeneity lead to a denser pattern of stress transmission that carries smaller modulations. Paralleling the development of shear bands in granular materials, the stress patterns lead directly to shear localization. The proposed project will compare the stress and strain heterogeneity observed in experimentally deformed mono-phase rocks with the stress and strain heterogeneity observed in FE models tuned to simulate these rocks. Specifically, the variation in the orientation of local stress tensor as predicted by FE models will be compared with microstructures that are sensitive to the compression direction such as twins and kinkbands and the distribution of the magnitude of the local compressive stress predicted by the FE models will be compared with local compressive stress distributions derived from synchrotron x-ray diffraction data from in-situ deformation experiments. Model design elements to be examined include the shapes of grains, grain boundary and grain interior rheology, as well as model size and aspect ratio. The impact of using 2D vs 3D models will also be examined. Additional direct comparisons will be made between the pattern of variation in microstrains observed on the surface of experimentally deformed polycrystalline slabs and the results from FE models built to match EBSD maps of the slab surfaces. These comparisons between models and experimental data will provide a test of the stress percolation hypothesis and provide a foundation for further investigations of stress percolation.