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.

中文翻译：

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多晶材料 3D 裂纹网络各向同性渗流开始的实验验证，对渗流理论对地壳岩石的适用性的启示

渗流理论经常被提出作为理解裂隙岩石中的流动和运输的框架，但渗流理论对自然系统的适用性仍然不确定。由于难以在晶体材料中系统地创建 3D 裂纹网络，因此对渗透理论预测的实验验证具有挑战性。使用冰作为岩石模型，我们通过实验测试了渗流理论的预测，即对于足够大的样本，即使裂缝网络是各向异性的，渗流的开始也是各向同性的。与理论一致，通过实验我们发现，在足够高的应变率下由单轴加载引起的强各向异性裂纹网络中，在样品中，渗透的开始几乎是各向同性的，其中样品的尺寸比最大裂缝的长度大一个数量级。尽管近 90% 的诱导裂纹定向在施加压缩方向的约 10° 内，但渗透的开始是各向同性的。相似性分析表明，对于典型的地温和地质应变率，与渗流理论预测一致的裂缝网络仅可能出现在非俯冲花岗岩板片的上部几十公里内和辉长岩俯冲板片的数百公里深处。 .