Mechanical origin of power law scaling in fault zone rock

A nearest neighbor fragmentation model, previously developed to explain observations of power law particle distributions in 3D with mass dimension D(3) approximate to 2.6 (D(2) approximate to 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 D(3) approximate to 3.0 (D(2) approximate to 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 D(3) approximate to 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 D(3) = 3.0 is this collision probability independent of the size of the particles.