Fragment size distributions in brittle deformed rocks

The production of breccias and cataclasites is commonly proposed to result in power-law or log-normal probability distributions for fragment (grain) size. We show that in both natural and experimental examples, the common best fit probability distributions for the complete distributions are members of the Generalised Gamma (GG), Extreme Value (GEV) and Pareto (GP) families; power-law and log-normal distributions are commonly, but not always, poor fits to the data. An hierarchical sequence, GG -> GEV -> GP, emerges as the sample mean of the fragment size decreases. The physical foundations (self-similar fragmentation, collisional fragmentation, shattering) for these distributions are discussed. Particularly important is the shattering continuous phase transition that results in the simultaneous development of both coarse fragments and ultra-fine particles (dust). This phase transition leads to Generalised Pareto fragment size distributions for the coarse fragments. Also included is a discussion of the relations between fragment size distribution, processes and deformation history in the context of monomineralic rocks. The overall reported size distributions are compatible with theoretical developments but the topic would benefit from observations and experiments conducted with the theories in mind.