A combined 2-D/1-D magma ascent model of explosive volcanic eruptions

SUMMARY Explosive eruptions involve the fragmentation of magma that changes the flow regime from laminar to turbulent within the volcanic conduit during ascent. If the gas volume fraction is high, magma fragments and the eruption style is explosive, but if not, the magma flows effusively out of the vent. Gas escape processes depend on how the magma can rupture, and recent experimental studies measured rupture stress thresholds of the order of a few megapascals. It is thus critical to model the gas content and state of stress evolution in the flowing magma within the conduit. We present a new self-consistent model of an explosive eruption from the magma chamber to the surface, based on a critical gas volume fraction. Our model allows to explore irregular geometries below the fragmentation level (2-D). We first compare our model with classical 1-D models of explosive eruptions and find that in the case of straight conduits and fragmented flows, 1-D models are accurate enough to model the gas pressure and vertical velocity distribution in the conduit. However, in the case of an irregular conduit shape at depth, 2-D models are necessary. Despite a certain conduit radius visible at the surface, very different stress fields within the flow could be present depending upon the position and shape of any conduit irregularities. Stresses of the order of more than 1 MPa can be attained in some locations. High tensile stresses are located at the centre of the conduit, while high shear stresses are located at the conduit walls leading to several potential rupture locations. Due to the interplay between the velocity field and decompression rate, similar conduit radius visible at the surface might also lead to very different fragmentation depths with a difference of more than 1500 m between an enlarged conduit shape at some depth and a straight conduit. At depth, different conduit sizes might lead to the same order of magnitude for the mass flux, depending on the conduit geometry.