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 m³ , or 20 m³ 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 m³ 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 poor quality of the rock fall inventories, and the sensibility of the extrapolated predictions to variations in the parameters of the power law.

International audienceThis study reviews seismograms from 10 rock-fall events recorded between 1992 and 2001 by the permanent seismological network Sismalp in the French Alps. A new seismic-magnitude scale was defined that allowed us to compare and classify ground-motion vibrations generated by these Alpine rock falls. Each rock fall has also been characterized by its ground-motion duration t30 at an epicentral distance of 30 km. No relation was found between rock-fall parameters (fall height, runout distance, volume, potential energy) and rock-fall seismic magnitudes derived from seismogram amplitudes. On the other hand, the signal duration t30 shows a rough correlation with the potential energy and the runout distance, highlighting the control of the propagation phase on the signal length. The signal analysis suggests the existence of at least two distinct seismic sources: one corresponding to the initial rupture associated with an elastic rebound during the detachment and the other one generated by the rock impact on the slope. Although the fall phenomenon includes other complex processes (fragmentation of the block, interaction with topography, plastic deformation during and after impact) 2D finite-element simulations of these two seismic sources are able to retrieve the main seismogram characteristics

The influence of meteorological conditions on rockfall occurrence has been often highlighted, but knowledge of it is still not sufficient due to the lack of exhaustive and precise rockfall databases. In this study, rockfalls have been detected in a limestone cliff by annual terrestrial laser scanning, and dated by photographic survey over a period of 2.5 years. A near-continuous survey (one photo every 10 min) with a wide-angle lens has made it possible to date 214 rockfalls larger than 0.1 m³, and a monthly survey with a telephoto lens has dated 854 rockfalls larger than 0.01 m³. Analysis of the two databases shows that the rockfall frequency can be multiplied by a factor as high as 7 during freeze–thaw episodes and 26 when the mean rainfall intensity (since the beginning of the rainfall episode) is higher than 5 mm h⁻¹. Based on these results, a three-level scale has been proposed for predicting the temporal variations of rockfall frequency. The more precise database and freeze–thaw episode definition make it possible to distinguish different phases in freeze–thaw episodes: negative temperature cooling periods, negative temperature warming periods and thawing periods. It appears that rockfalls occur more frequently during warming and thawing periods than during cooling periods. It can be inferred that rockfalls are caused by thermal ice dilatation rather than by dilatation due to the phase transition. But they may occur only when the ice melts, because the cohesion of the ice–rock interface can be sufficient to hold the rock compartment which has been cut.

A new method (HGP for Historical, Geomechanical and Probabilistic) is proposed to estimate the failure probability of potentially unstable rock masses in a homogenous area, as a function of time. Analysis of a rock falls inventory yields the mean number of rock falls which may be expected in the area for the given time period and a given volume range. According to their geomechanical features, the potentially unstable rock masses are distributed in classes corresponding to different failure probabilities. The expected number of rock falls can be expressed as a function of these unknown probabilities. Assuming that only the ratio between these probabilities can be estimated, combining the historical and geomechanical analysis allows estimating the order of magnitude of the different failure probabilities. The method gives a quantitative significance to the evaluations which are usually attributed to potentially unstable rock masses. Rock-fall hazard can then be compared with other natural hazards, such as floods or earthquakes. The method is applied to a case study of calcareous cliffs in the area of Grenoble, France.