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 in the frequency with an e-folding time longer than 65 000 years is predicted. In turn, the predicted e-folding time is shorter than 2000 years for volumes of 10 km3, so the occurrence of such huge rockslides is unlikely at the present time. For the largest rockslide possible at the present time, 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.