[SY-K2] Symposium K-2

[SY-K2] Predictability of catastrophic failure in porous media

Invited

^○Ian Main¹, Ferenc Kun², Jeremie Vasseur³, Andrew Bell¹ (1.University of Edinburgh, UK, 2.University of Debrecen, Hungary, 3.Ludwig Maximilian University, Munich, Germany)

Recent discrete element models for the processes leading up to material failure provide a very close match to experiment in the case of high porosity, highly disordered materials. On approach to catastrophic, system-sized failure the number of micro-cracks and their associated acoustic emissions (AE) increase at a rate marked by a smooth inverse power law, defining a failure time at the singularity in AE rate. This behaviour is reminiscent of a second-order phase transition. At the same time the deformation becomes progressively more localised on an incipient optimally oriented fault plane, and the scaling exponent b for the frequency-magnitude distribution of the acoustic emissions decreases to a minimum near the failure time. On the other hand, a simple elastic fracture mechanics for an ideal ordered, uniform solid with a single pre-existing crack provides no warning of incipient failure. In between these limits there are clear precursors, but failure occurs suddenly, and earlier than predicted by the inverse power-law model, more reminiscent of a first-order phase transition. We develop a mean field model for a population of cracks emanating from pores in an otherwise uniform medium to explain this systematic error in the predicted failure time. The correction depends non-linearly on the porosity, specifically the distance between pores in the starting model, and tends to zero in the limiting case of high-porosity materials. It provides a good match to aggregate data obtained from experiments on a range of materials, both natural and synthetic. We show the behaviour scales very well to a range of data from earthquakes prior to volcanic eruptions, including quasi-periodic ‘drumbeat’ long-period earthquake signals preceding a recent large vulcanian explosion at Tungurahua volcano, Ecuador. Unfortunately, such signals are not yet detectable prior to large earthquakes above a null hypothesis of conventional epidemic-type earthquake triggering models.