Probabilistic approach to rock fall hazard assessment: potential of historical data analysis

Abstract

Abstract. We study the rock fall volume distribution for three rock fall inventories and we fit the observed data by a power-law distribution, which has recently been proposed to describe landslide and rock fall volume distributions, and is also observed for many other natural phenomena, such as volcanic eruptions or earthquakes. We use these statistical distributions of past events to estimate rock fall occurrence rates on the studied areas. It is an alternative to deterministic approaches, which have not proved successful in predicting individual rock falls. The first one concerns calcareous cliffs around Grenoble, French Alps, from 1935 to 1995. The second data set is gathered during the 1912-1992 time window in Yosemite Valley, USA, in granite cliffs. The third one covers the 1954-1976 period in the Arly gorges, French Alps, with metamorphic and sedimentary rocks.For the three data sets, we find a good agreement between the observed volume distributions and a fit by a power-law distribution for volumes larger than 50 m 3 , or 20 m 3 for the Arly gorges. We obtain similar values of the b exponent close to 0.45 for the 3 data sets. In agreement with previous studies, this suggests, that the b value is not dependant on the geological settings. Regarding the rate of rock fall activity, determined as the number of rock fall events with volume larger than 1 m 3 per year, we find a large variability from one site to the other. The rock fall activity, as part of a local erosion rate, is thus spatially dependent.We discuss the implications of these observations for the rock fall hazard evaluation. First, assuming that the volume distributions are temporally stable, a complete rock fall inventory allows for the prediction of recurrence rates for future events of a given volume in the range of the observed historical data. Second, assuming that the observed volume distribution follows a power-law distribution without cutoff at small or large scales, we can extrapolate these predictions to events smaller or larger than those reported in the data sets. Finally, we discuss the possible biases induced by the Correspondence to: C. Dussauge-Peisser (carine.dussauge@ujf-grenoble.fr) poor quality of the rock fall inventories, and the sensibility of the extrapolated predictions to variations in the parameters of the power law.

Optimising 4-D surface change detection: an approach for capturing rockfall magnitude–frequency

“…Wolman and Miller (1960) proposed that the frequency of events that denude the Earth's surface is log-normally distributed, and that their geomorphic effectiveness (the product of magnitude and frequency) is greatest for the frequent, moderately sized events. This concept has been widely applied to study both the geomorphic efficacy of rivers (Wolman and Gerson, 1978;Hooke, 1980;Nash, 1994;Gintz et al, 1996) and the characteristics of landslides (Hovius et al, 1997(Hovius et al, , 2000Dussauge-Peisser et al, 2002;Turcotte et al, 2002;Dussauge et al, 2003;Malamud et al, 2004;Guthrie and Evans, 2007;Li et al, 2016) using inverse power-law distributions or similar.…”

Landslides, sandpiles, and self-organized criticality

“…Therefore, the relative importance of large landslides is lower than it is in the example of earth- Power-law exponents of the cumulative size distributions of some natural hazards (upper part) and results of the most widespread self-organized critical models (lower part). The tickmarks refer to the studies on landslides mentioned in the text, the rockfall data analyzed and reviewed by Dussauge-Peisser et al (2002), the four forest-fire data sets analyzed by Malamud et al (1998), and 38 earthquake catalogs from various geographic regions (Frohlich and Davis, 1993, quakes and much lower than in the example of forest fires. Geology, climate, type of landslides, and triggering mechanisms seem to be good candidates to account for the observed variations in the power-law exponents.…”

“…slides in the strict sense or flows) have been investigated in several studies. Dussauge-Peisser et al (2002) compiled data on the sizes of rockfalls from various sources, obtaining power-law distributions for the rockfall volume with exponents between 0.4 and 1.0. Although these values show a strong variability, a relationship to the geological setting was not found.…”

Modeling and managing uncertainties in rock-fall hazards

“…This includes (a) the analysis of historical datasets (Hungr et al 1999, Dussauge-Peisser 2002, (b) empirical models which describe rock-fall exposure as a function of different indicators (observable parameters), such as topography and geology (Budetta 2004, Baillifard et al 2004, (c) phenomenological (mechanical) models (Duzgun et al 2003, Jimenez-Rodriguez et al 2006, and (d) expert opinion (Schubert et al 2005). All these methods are useful in a particular context.…”

“…For these reasons, rock-fall modeling is associated with large uncertainties, which have been considered in the past. It has been realized that the stochastic nature of rockfall can only be captured by describing the release of rock mass in terms of probabilities or frequencies, typically using a power-law to describe the relation between frequency and rock volume (Hovius 1997, Hungr et al 1999, Dussauge-Peisser et al 2002. However, the uncertainty associated with this model is not generally quantified.…”