3D modeling-based area-volume power-law relationships for incipient rotational slides

Abstract

The relationship between landslide area and volume has been shown to obey to a power law with a scaling exponent α varying from 1.1 to 1.6. This paper presents a three-dimensional upper bound method of limit analysis to evaluate the scaling exponent for the power-law relationship between source area and source volume of incipient rotational failure in soils. Based on an ensemble of data from calculated 20,000 theoretical homogenous slopes, the relations between landslide area and volume are calculated on a statistical basis and two fitting forms are systemically analyzed. Form 1, which gives the area-volume relations directly, shows an excellent agreement with field observations, with the scaling exponent α equal to 1.40. Form 2, considering the soil materials, is more suitable for the analysis of landslides affecting artificial homogeneous slopes. Three kinds of failure surface geometries, i.e., deep, intermediate, and face failure are discussed. The parametric study illustrates that the failure surface geometry affects the scaling exponent within a limit range. Further, the proposed method reveals that if the hillslope inclination, internal friction angle, and hillslope relative width are determined, the geometry of the landslide shows self-similar behavior, otherwise, the behavior is self-affine.