Power law correlations between feature parameters of loess landslides

Loess landslides are significant natural hazards in the Loess Plateau. They often result in both human and material losses. In this paper, we first collect information including area, volume, length, width, depth and height in a database of loess landslides from the Maiji district of Tianshui in Gansu Province. The power-law dependence is quantitatively examined and the power law relationships among the feature parameters are explored. Based on the detailed inventory, we model the empirical relationships by adopting least square linear fit between the characteristic parameters for the empirical data which are log-transformed. The results show that (1) the power law correlation of the geological disasters not only exists between the cumulative frequency and area scale as well as volume parameters, it also exists in the area between the cumulative frequency and the height difference between loess landslide rear and watershed slopes. (2) For the scale parameters, the power exponent distribution are as follows: the area and length > the area and width > the volume and area. For the motion parameters, the power exponent distribution are as follows: the volume and maximum vertical sliding distance > the volume and maximum horizontal sliding distance > the area and maximum vertical sliding distance > the area and maximum horizontal sliding distance. (3) There is a bad correlation in the power exponent distribution between the sliding equivalent friction coefficient and the area as well as volume. Therefore, their empirical formula can only indicate the trends, and cannot be used as the basis for quantitative analyses.