Statistical analysis of rockfall volume distributions: Implications for rockfall dynamics

Abstract

We analyze the volume distribution of natural rockfalls on different geological settings (i.e., calcareous cliffs in the French Alps, Grenoble area, and granite Yosemite cliffs, California Sierra) and different volume ranges (i.e., regional and worldwide catalogs). Contrary to previous studies that included several types of landslides, we restrict our analysis to rockfall sources which originated on subvertical cliffs. For the three data sets, we find that the rockfall volumes follow a power law distribution with a similar exponent value, within error bars. This power law distribution was also proposed for rockfall volumes that occurred along road cuts. All these results argue for a recurrent power law distribution of rockfall volumes on subvertical cliffs, for a large range of rockfall sizes (102–1010 m3), regardless of the geological settings and of the preexisting geometry of fracture patterns that are drastically different on the three studied areas. The power law distribution for rockfall volumes could emerge from two types of processes. First, the observed power law distribution of rockfall volumes is similar to the one reported for both fragmentation experiments and fragmentation models. This argues for the geometry of rock mass fragment sizes to possibly control the rockfall volumes. This way neither cascade nor avalanche processes would influence the rockfall volume distribution. Second, without any requirement of scale‐invariant quenched heterogeneity patterns, the rock mass dynamics can arise from avalanche processes driven by fluctuations of the rock mass properties, e.g., cohesion or friction angle. This model may also explain the power law distribution reported for landslides involving unconsolidated materials. We find that the exponent values of rockfall volume on subvertical cliffs, 0.5 ± 0.2, is significantly smaller than the 1.2 ± 0.3 value reported for mixed landslide types. This change of exponents can be driven by the material strength, which controls the in situ topographic slope values, as simulated in numerical models of landslides [Densmore et al., 1998; Champel et al., 2002].

Integrating rockfall risk assessment and countermeasure design by 3D modelling techniques

“…N j ) was evaluated using magnitude-cumulative frequency (MCF) curves according to Hungr et al (1999) and Dussauge et al (2003). The reach probability P (T |L ) ij was derived from the results of 3D numerical modelling.…”

“…For landslides, different magnitude-frequency relationships both in terms of area and volume have been used (Stark and Hovius, 2001;Guzzetti et al, 2002;Malamud et al, 2004). As to rockfalls, several authors (Hungr et al, 1999;Dussauge et al, 2003;Malamud et al, 2004) demonstrated that the magnitude-cumulative frequency (MCF) distribution of events in given volume classes j can be described by a power law in the form:…”

“…The parameters of MCF curves themselves have no universal significance, although the exponent b has been found to vary in a quite narrow range, i.e. −0.7<b<−0.4 (Hungr et al, 1999;Dussauge et al, 2003), and should be based on complete local rockfall inventories. Since a site-specific event catalogue for the Fiumelatte area is lacking, a value of b=−0.41 was derived from the literature (i.e.…”

“…Since a site-specific event catalogue for the Fiumelatte area is lacking, a value of b=−0.41 was derived from the literature (i.e. value for carbonate rocks proposed by Dussauge et al, 2003). A conservative estimate of N 0 =10 was derived from available historical and geomorphological information for the entire 800 m long cliff span.…”

A Review of Studies Dealing with Tree Rings and Rockfall Activity: The Role of Dendrogeomorphology in Natural Hazard Research

“…Data on past rockfall activity is commonly gathered from historical archives (e.g., Hantz et al, 2003;Barnikel, 2004, Guzzetti andTonelli, 2004) and further investigated with frequency-volume statistics (DussaugePeisser et al, 2002;Dussauge et al, 2003) or frequency densities (Malamud et al, 2004).…”