Coulomb Mechanics and Relief Constraints Explain Landslide Size Distribution

Abstract

Despite the idea that topography could control landslide size scaling law, the contribution of landscape geometry to landslide size distribution remains elusive. We define a simple mechanical model accounting for the complexity and variability of natural hillslopes to infer the landslide depth probability density function (PDF) in a given landscape and upscale it to landslide area PDF. This model is based on both a Mohr-Coulomb stability analysis, accounting for cohesion and friction, and a criterion of intersection between rupture planes and the topographic surface. It can reproduce the distribution of observed landslide areas triggered by several past events. We found the ranges of effective cohesion (10–35 kPa) and friction (20–45°) consistent with previous estimates of large-scale rock strength. Using synthetic topographies, we found that the finite geometry of hillslopes (length, steepness, and concavity) exerts a first-order control on the PDF of landslide areas, especially for large landslides.