A fragmentation criterion for highly viscous bubbly magmas estimated from shock tube experiments

When a highly viscous bubbly magma is sufficiently decompressed, layer-by-layer fracturing propagates through the magma at a certain speed (fragmentation speed). On the basis of a recent shock tube theory by Koyaguchi and Mitani [Koyaguchi, T., Mitani, N. K., 2005. A theoretical model for fragmentation of viscous bubbly magmas in shock tubes. Journal of Geophysical Research 110 (B10), B10202. doi:10.1029/2004JB003513.], gas overpressures at the fragmentation surface are estimated from experimental data on fragmentation speed in shock tube experiments for natural volcanic rocks with various porosities. The results show that gas overpressure at the fragmentation surface increases as initial sample pressure increases and sample porosity decreases. We propose a new fragmentation criterion to explain the relationship between the gas overpressure at the fragmentation surface, the initial pressure and the porosity. Our criterion is based on the idea that total fragmentation of highly viscous bubbly magmas occurs when the tensile stress at the midpoint between bubbles exceeds a critical value. We obtain satisfactory agreement between our simulation and experiment when we assume that the critical value is inversely proportional to the square root of bubble wall thickness. This fragmentation criterion suggests that long micro-cracks or equivalent flaws (e.g., irregular-shaped bubbles) that reach the midpoints between bubbles are a dominant factor to determine the bulk strength of the bubbly magma.