The volume-to-surface-area ratio constrains the rollover of the power law distribution for landslide size

The rollover observed in the landslide size distribution, i.e., the deviation from power law behavior for small landslides, has not been previously described by a widely accepted physical interpretation. In this paper, the volume-to-failure-surface-area ratio V/S is proposed as an essential constraining factor for the emergence of the rollover. We first demonstrate that, from a three-dimensional perspective, landslide failures require a minimum threshold V/S value for a given mechanical configuration. The heterogeneity of the slope properties presents each potential landslide with a probability that V/S will exceed the threshold value, and further, results in a decay of frequency but not a cutoff for small landslides in the landslide size distribution. Empirical data show that the variance of the landslide shape is one aspect of the heterogeneity that can cause the inverse power law distribution of the landslide volume to decrease for smaller sizes.