title: A theoretical explanation of grain size distributions in explosive rock fragmentation.
abstract: We have measured grain size distributions of the results of laboratory decompression explosions of volcanic rock. The resulting distributions can be approximately represented by gamma distributions of weight per cent as a function of [Formula: see text], wheredis the grain size in millimetres measured by sieving, with a superimposed long tail associated with the production of fines. We provide a description of the observations based on sequential fragmentation theory, which we develop for the particular case of 'self-similar' fragmentation kernels, and we show that the corresponding evolution equation for the distribution can be explicitly solved, yielding the long-time lognormal distribution associated with Kolmogorov's fragmentation theory. Particular features of the experimental data, notably time evolution, advection, truncation and fines production, are described and predicted within the constraints of a generalized, 'reductive' fragmentation model, and it is shown that the gamma distribution of coarse particles is a natural consequence of an assumed uniform fragmentation kernel. We further show that an explicit model for fines production during fracturing can lead to a second gamma distribution, and that the sum of the two provides a good fit to the observed data.
authors.affiliation: MACSI, University of Limerick, Limerick, Republic of Ireland; OCIAM, University of Oxford, Oxford, UK.
authors.forename: A C
authors.identifier: 0000-0002-2062-6372
authors.initials: AC
authors.lastname: Fowler
authors.affiliation: Earth and Environmental Sciences , LMU München, München, Germany.
authors.forename: Bettina
authors.initials: B
authors.lastname: Scheu
keywords: grain size distribution; rock fragmentation; sequential fragmentation theory