Geometric scale invariance, genesis, and self-organization of polygonal fracture networks in granitic rocks

Abstract

We documented polygonal fracture networks in the Tuolumne Intrusive Suite, Sierra Nevada Batholith by collecting data on the size, orientation, and length of fractures and fracture-bound polygons in nearly isotropic granitic rocks. Polygonal fracture networks are constrained to sheets of rock sub-parallel to the underlying rock, with the sheets bound above and below by fractures (i.e., free surfaces). Data indicate that most geometric characteristics of the polygonal fracture networks are scale-invariant; large (m-scale) networks exhibit the same geometry as small (cm-scale) networks. A linear correlation exists between sheet thickness and average polygon size. Polygons within the networks are anisotropic, with the degree of anisotropy correlated with the degree of sheet curvature. The preferred orientation of the polygons correlates with the inclination of the sheet, with long axes of polygons parallel to sheet strike. Based on geometry, we suggest that the polygonal fracture networks in granitic rocks observed in this study formed from temperature fluctuations that caused thermal expansion and contraction in the rock. Repeated cycles of expansion/contraction led to the initiation and propagation of fractures within the network. We propose that the observed fracture patterns are not a product of extrinsic conditions but rather a product of interactions between fractures, implying that the polygonal fracture networks are self-organizing systems.