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.

Landslide Scaling: A Review

“…Parameterized cellular automata models that include one or more variables that affect shear stress in the surface materials, such as precipitation, soil properties, and topography, come closer to replicating the size‐frequency scaling exponents observed for larger event sizes of natural landslides (Avolio et al, ; Clerici & Perego, ; D'Ambrosio et al, ; Di Gregorio et al, ; Segre & Deangeli, ;). Mechanical models also replicate the observed power scaling, including a rolloff and cutoff (Jeandet et al, ).…”

“…Stark and Guzzetti () propose that the power function distribution observed for larger landslides is controlled by the relatively strong cohesion of bedrock while the scaling of small, shallow failures is the result of the low cohesion of soil and regolith. A mechanical model of Jeandet et al () for bedrock landslides produces a rollover that is due to the contribution of cohesion to slope instability, similar to mechanisms proposed by Stark and Guzzetti () and Frattini and Crosta ().…”

“…Jeandet et al's () model produces power scaling of landslide depth and area, with a rollover for small landslides due to the contribution of cohesion to slope instability, as proposed earlier by Stark and Guzzetti () and Frattini and Crosta (). The model also captures the scaling behavior of a cutoff at large events sizes caused by the topographic criterion combined with the finite size of hillslopes (Jeandet et al, ).…”

“…Jeandet et al () propose a mechanical model for bedrock landslides which assumes the rocks and soil behave as Mohr‐Coulomb materials, and failure occurs when shear stress on rupture surfaces exceeds resisting shear strength of the material, which is controlled by the frictional angle and cohesion. They model landslides as a planar failure and include the criterion that the rupture plane must intersect the topographic surface in the downslope direction; this results in shallower planes having a higher rupture probability than deeper planes (Jeandet et al, ). Jeandet et al's () model produces power scaling of landslide depth and area, with a rollover for small landslides due to the contribution of cohesion to slope instability, as proposed earlier by Stark and Guzzetti () and Frattini and Crosta ().…”

“…They model landslides as a planar failure and include the criterion that the rupture plane must intersect the topographic surface in the downslope direction; this results in shallower planes having a higher rupture probability than deeper planes (Jeandet et al, ). Jeandet et al's () model produces power scaling of landslide depth and area, with a rollover for small landslides due to the contribution of cohesion to slope instability, as proposed earlier by Stark and Guzzetti () and Frattini and Crosta (). The model also captures the scaling behavior of a cutoff at large events sizes caused by the topographic criterion combined with the finite size of hillslopes (Jeandet et al, ).…”