Modeling the failure of magmatic foams with application to Stromboli volcano, Italy

The failure of magmatic foams has been implicated as a fundamental process in eruptions occurring at open-conduit, basaltic volcanoes. In order to investigate the failure of magmatic foams we applied the fiber bundle model using global load sharing. The strengths of the fibers for the model were taken from bubble wall widths measured in four computer-simulated foams of low-porosity and from one very low-porosity and two high-porosity foams produced in the laboratory by heating hydrated basaltic glasses to 1200°C. The relative strength of an individual fiber in the model was calculated from the square of a bubble wall's average width and absolute strengths of the foams were calculated based upon the correlation of the strength of one modeled foam with experimental data. The fiber bundle model is shown to successfully reproduce measured tensile strengths of porous volcanic rocks studied by other researchers and confirms previous findings of the primary importance of foam porosity, as well as the secondary importance of structural details that affect the number and size of bubble walls and permeability. Because of the success of the fiber bundle model in reproducing experimental foam failure, its results are compared to infrasonic measurements associated with bubbles at Stromboli (Italy) and demonstrate that within uncertainty the power-law exponents of the infrasonic energies and of the fiber bundle model energies are in agreement; both show a crossover from an exponent of 5/2 associated with the bursting of small bubbles in the infrasonic measurements to an exponent of 3/2 for normal Strombolian eruptions associated with infrasonic signals from meter-scale bubbles. The infrasonic signals for major explosions and a paroxysmal eruption at Stromboli fall near the extrapolation of the power law defined by the low-amplitude, bubble bursting events and are interpreted to reflect the bursting of multitudes of small bubbles, rather than a few large bubbles. The measurement of small-amplitude infrasonic events at Stromboli appears useful in predicting the recurrence interval of paroxysmal eruptions at this volcano and may also provide a tool that uses common, small-amplitude infrasonic events to constrain the frequency of larger eruptions at other volcanoes.