Statistical analysis of rockfall volume distributions: Implications for rockfall dynamics

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]. INDEX TERMS: 5104 Physical Properties of Rocks: Fracture and flow; 1815 Hydrology: Erosion and sedimentation; 8122 Tectonophysics: Dynamics, gravity and tectonics;