Explosive fragmentation criteria and velocities for vesicular magma

We present a new criterion for primary fragmentation of natural rock samples in shock-tube experiments, and new formulae for the effective strength of natural rock samples, for the size of primary fragments, and for fragmentation velocities. These formulae and the fragmentation criterion are given in terms of the physical properties of the rock and in terms of experimental parameters. The formulae and criterion are derived from numerical solutions and asymptotic analytic solutions to a novel recently published mathematical model for the explosive fragmentation of vesicular magma in shock-tube experiments. This model is singularly successful in accounting for the length-scales observed in these experiments. The criterion and formulae provide good matches to data from shock-tube experiments on natural samples.