Mechanical origin of power law scaling in fault zone rock

Abstract

A nearest neighbor fragmentation model, previously developed to explain observations of power law particle distributions in 3D with mass dimension D3 ≈ 2.6 (D2 ≈ 2.6 in 2D section) in low‐strain fault gouge and breccia, is extended to the case of large strains to explain recent observations of D3 ≈ 3.0 (D2 ≈ 2.0 in 2D section) in the highly strained cores of many exhumed fault zones. At low strains, the elimination of same‐sized nearest neighbors has been shown to produce a power law distribution which is characterized by a mass dimension near D3 ≈ 2.6. With increasing shear strain these isolated same‐size neighbors can collide, in which case one of them fractures. The probability of two same size neighbors colliding and fragmenting in a simple shear flow is a function of the size and density of the two particles. Only for a power law distribution with D3 = 3.0 is this collision probability independent of the size of the particles.