A theoretical model of the explosive fragmentation of vesicular magma

Recent experimental work has shown that, when a vertical column of rock under large pressure is suddenly depressurized, the column can 'explode' in a structured and repeatable way. The observations show that a sequence of horizontal fractures forms from the top down, and the resulting blocks are lifted off and ejected. The blocks can suffer secondary internal fractures. This experiment provides a framework for understanding the way in which catastrophic explosion can occur, and is motivated by the corresponding phenomenon of magmatic explosion during Vulcanian eruptions. We build a theoretical model to describe these results, and show that it is capable of describing both the primary sequence of fracturing and the secondary intrablock fracturing. The model allows us to suggest a practical criterion for when such explosions occur: firstly, the initial confining pressure must exceed the yield stress of the rock, and, secondly, the diffusion of the gas by porous flow must be sufficiently slow that a large excess pore pressure is built up. This will be the case if the rock permeability is small enough.