A criterion for the fragmentation of bubbly magma based on brittle failure theory

The fragmentation of bubbly magma is a defining point in a volcanic eruption—before fragmentation the magma flows relatively slowly, during fragmentation the bubbles break up to release compressed gas and, afterwards, the eruption becomes a violent gas flow carrying suspended magma particles. Seemingly benign lava flows or domes can suddenly fragment into deadly pyroclastic flows1,2,3. Several criteria have been proposed to define the point of magma fragmentation or foam stability4,5,6,7. The criterion of Papale7 is based on melt relaxation theory and equates magma strain rate with the rate of increase of flow velocity with distance. It ignores, however, the role of bubble pressure in causing fragmentation. Two empirical approaches4,5 consider the role of high bubble pressure in causing fragmentation but do not address the underlying physics of magma fragmentation. Here I develop a fragmentation criterion for bubbly magma based on brittle failure theory and apply it to the fragmentation of lava domes and flows. On the basis of this theory, a bubbly magma will fragment when the tensile stress at the inner walls of bubbles exceeds the tensile strength of the magma. The fragmentation conditions depend strongly on initial water content, with calculated vesicularity and final water levels coinciding reasonably well with those in observed pumices. This suggests that the proposed criterion captures the essence of the fragmentation process in bubbly magma.