Failure criteria for porous dome rocks and lavas: a study of Mt. Unzen, Japan

Abstract. The strength and macroscopic deformation mode (brittle vs. ductile) of rocks is generally related to the porosity and pressure conditions, with occasional considerations of strain rate. At high temperature, molten rocks abide by Maxwell's viscoelasticity and their deformation mode is generally defined by strain rate or reciprocally by comparing the relaxation timescale of the material (for a given condition) to the observation timescale – a dimensionless ratio known as the Deborah (De) number. Volcanic materials are extremely heterogeneous, with variable concentrations of crystals, glass–melt, and vesicles (of different sizes), and a complete description of the conditions leading to flow or rupture as a function of temperature, stress and strain rate (or timescale of observation) eludes us. Here, we examined the conditions which lead to the macroscopic failure of variably vesicular (0.09–0.35), crystal-rich (∼ 75 vol %), pristine and altered dome rocks (at ambient temperature) and lavas (at 900 °C) from Mt. Unzen volcano, Japan. We found that the strength of the dome rocks decreases with porosity and is commonly independent of strain rate; when comparing pristine and altered rocks, we found that the precipitation of secondary mineral phases in the original pore space caused minor strengthening. The strength of the lavas (at 900 °C) also decreases with porosity. Importantly, the results demonstrate that these dome rocks are weaker at ambient temperatures than when heated and deformed at 900 °C (for a given strain rate resulting in brittle behaviour). Thermal stressing (by heating and cooling a rock up to 900 °C at a rate of 4 °C min⁻¹, before testing its strength at ambient temperature) was found not to affect the strength of rocks.

In the magmatic state (900 °C), the rheology of the dome lavas is strongly strain rate dependent. Under conditions of low experimental strain rate (≤ 10⁻⁴ s⁻¹), ductile deformation dominated (i.e. the material sustained substantial, pervasive deformation) and displayed a non-Newtonian shear thinning behaviour. In this regime, the apparent viscosities of the dome lavas were found to be essentially equivalent, independent of vesicularity, likely due to the lack of pore pressurisation and efficient pore collapse during shear. At high experimental strain rates ( ≥ 10⁻⁴ s⁻¹) the lavas displayed an increasingly brittle response (i.e. deformation resulted in failure along localised faults); we observed an increase in strength and a decrease in strain to failure as a function of strain rate. To constrain the conditions leading to failure of the lavas, we analysed and compared the critical Deborah number at failure (De_c) of these lavas to that of pure melt (De_melt = 10⁻³–10⁻²; Webb and Dingwell, 1990). We found that the presence of crystals decreases De_c to between 6.6×10⁻⁴ and 1×10⁻⁴. The vesicularity (φ), which dictates the strength of lavas, further controls De_c following a linear trend. We discuss the implications of these findings for the case of magma ascent and lava dome structural stability.