Failure criteria for porous dome rocks and lavas: a study of Mt.
Unzen, Japan
Authors: Coats Rebecca , Kendrick Jackie E. , Wallace Paul A. , Miwa Takahiro , Hornby Adrian J. , Ashworth James D. , Matsushima Takeshi , Lavallée Yan 
Published: March 2018

Abstract. The strength and 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 to Maxwell’s viscoelasticity and their deformation mode (brittle vs ductile) 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 failure for variably vesicular (9–35 %), crystal-rich (~ 75 %), 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 alteration 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 low strain rate conditions (≤ 10−4 s−1) the lavas behaved ductilly (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 independent of vesicularity, likely due to efficient pore collapse during shear. At high 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 (Dec, the ratio between the relaxation time and the experimental observation time) of these lavas to that of pure melt (Demelt=10−3–10−2; Webb &amp; Dingwell, 1990). We found that the presence of crystals decreases Dec to 2.11×10−4. The vesicularity (φ), which dictates the strength of lavas, further controls Dec following −5.1×10−4φ+2.11×10−4. We discuss the implications of these findings for the case of magma ascent and lava dome structural stability.