Experimental Verification of the Isotropic Onset of Percolation in 3D Crack Networks in Polycrystalline Materials With Implications for the Applicability of Percolation Theory to Crustal Rocks. Issue 12 (10th December 2021)

• Record Type: Journal Article
• Authors: Renshaw, Carl E.; Murdza, Andrii; Schulson, Erland M.
• Is Part Of: Journal of geophysical research. Volume 126:Issue 12(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-12-10
• Subjects: Geomagnetism -- Periodicals; Geochemistry -- Periodicals; Geophysics -- Periodicals; Earth sciences -- Periodicals; 551.1
• DOI: 10.1029/2021JB023092
• Languages: English
• ISSNs: 2169-9313

Abstract

Abstract: Percolation theory is often proposed as a framework for understanding flow and transport through fractured rock, yet the applicability of percolation theory to natural systems remains uncertain. Experimental verification of the predictions of percolation theory are challenging because of the difficulty in systematically creating 3D crack networks in crystalline materials. Using ice as a model for rock, we experimentally test the prediction of percolation theory that for a sufficiently large sample, the onset of percolation is isotropic even when the crack network is anisotropic. Consistent with theory, experimentally we find that in strongly anisotropic crack networks induced by uniaxial loading at a sufficiently high strain rate, the onset of percolation is nearly isotropic in samples where the dimension of the sample is about an order of magnitude greater than the length of the largest crack. The onset of percolation is isotropic even though nearly 90% of the induced cracks are oriented within about 10° of the direction of applied compression. A similitude analysis indicates that for typical geotherms and geologic strain rates, crack networks consistent with the predictions of percolation theory are only possible within the upper several tens of km of a nonsubducting granite slab and to depths of several hundreds of km in subducting slabs of gabbro. Plain Language Summary: Percolation theory is often proposed as a framework for understanding how cracks in rock interconnect, yet the applicability of this theory to fractured rock is uncertain as it assumes the geometry of the cracks is random, an assumption that may not be valid for fractured rock. Here, we use ice as a model material for rock and create crack networks in the ice by compressing it in one direction. When created using a sufficiently high strain rate, the resulting crack network is strongly anisotropic, with more than 90% of the cracks oriented within about 10° of the direction of compression. Yet despite this strong anisotropy, and consistent with the predictions of percolation theory, we find that when crack growth is sufficient to create a pathway in one direction, connected pathways are simultaneously created in all directions, at least in samples where the size of sample is 10 times or more larger than the longest crack in the network. Extrapolating results to crustal rocks, we find that the predictions of percolation theory may only apply to crack networks above a critical crustal depth. Key Points: Using ice as a model for rock we created 3D crack networks where more than 90% of the cracks were aligned along the same direction Despite this strong anisotropy, the onset of percolation was isotopic in samples larger than 10 times the longest crack in the network A similitude analysis with typical geotherms and strain rates indicates percolation theory may not apply below a critical crustal depth