Analytical and observational relations between landslide volume and surface area

Abstract

A remarkable field observation is that landslides of different sizes, from different locations around the globe and triggered by different mechanisms, all seem to follow a single relation, with their volume to surface area ratio following a power law of ∼1.4. This paper presents an analytical examination of the shape of landslides on the basis of limit equilibrium principles involving the exact mathematical solution of the failure mode. The obtained analytical relation between the volume and the surface area of a landslide agrees well with the function obtained from the field observations, and hence a mechanical basis is given to the previously poorly understood field observations. In addition, this paper presents a new graphical interpretation of the factor of safety associated with slope stability analysis and its relation to the probability of failure.