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

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 degrees 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.