Eur. Phys. J. Plus (2014) 129: 89
https://doi.org/10.1140/epjp/i2014-14089-y

Regular Article

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

¹ State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China
² Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada

^* e-mail: lanhx@igsnrr.ac.cn

Received: 9 February 2014
Revised: 22 March 2014
Accepted: 3 April 2014
Published online: 21 May 2014

Abstract

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.