The concept of event-size dependent exhaustion and its application to paraglacial rockslides

Abstract. Rockslides are a major hazard in mountainous regions. In formerly glaciated regions, the disposition mainly arises from oversteepened topography and decreases through time. However, little is known about this decrease and thus about the present-day hazard of huge, potentially catastrophic rockslides. This paper presents a new theoretical concept that combines the decrease in disposition with the power-law distribution of rockslide volumes found in several studies. The concept starts from a given initial set of potential events, which are randomly triggered through time at a probability that depends on event size. The developed theoretical framework is applied to paraglacial rockslides in the European Alps, where available data allow for constraining the parameters reasonably well. The results suggest that the probability of triggering increases roughly with the cube root of the volume. For small rockslides up to 1000 m³, an exponential decrease of the frequency with an e-folding time longer than 65,000 yr is predicted. In turn, the predicted e-folding time is shorter than 2000 yr for volumes of 10 km³, so that the occurrence of such huge rockslides is unlikely at present times. For the largest rockslide possible at present times, a median volume of 0.5 to 1 km³ is predicted. With a volume of 0.27 km³, the artificially triggered rockslide that hit the Vaiont reservoir in 1963, is thus not extraordinarily large. Concerning its frequency of occurrence, however, it can be considered a 700 to 1200-year event.