对滑坡、崩塌和不稳定斜坡等地质灾害规模参数幂律相依性进行定量研究,拓展了规模参数之间幂律相依性的研究范围。研究结果发现：① 地质灾害规模参数的幂律相依性不仅存在于体积与面积之间,而且存在于面积与长、面积与宽等参数之间;② 幂指数可以作为间接反映区域地质灾害或者不同类型地质灾害的宏观特征表征谱;③ 体积与面积关系式的幂指数分布为不稳定斜坡>滑坡>崩塌;面积与长关系式的幂指数分布为崩塌>滑坡>不稳定斜坡。面积与宽关系式的幂指数的分布为滑坡>崩塌>不稳定斜坡。

Landslides are significant natural hazards in many areas of the world.they often resulting in both human and material losses.A number of authors have argued that the power law is the symbol of self-organized critical state.Many empirical observations have shown that landslides caused by various triggers,including earthquakes,rainfall and rapid snowmelt,and are influenced by multiple factors,such as local and regional morphological and topography,soil and lithological setting,fractures and bedding planes and moisture content obey power law statistics.In this paper,we first collect information witch include volume,area,length,width,depth in a dababase of landslides,collapses and unstable slope. Based on the geological hazards, such as landslides, collapses and unstable slope, the power-law dependence was quantitative researched, explore the power law relationship between the scale parameter for the first time in domestic, and the research scope of scale parameter between power-law dependence was expanded.The results showed that: 1) Based on the detailed inventory,we model the empirical relationship adopting least square linear fit between area and volume was fitted to the empirical data which were log-transformed. We compare the new relationship to similar relationships in the literature and found that the exponent of power law about volume and area of geological disasters was between 0.88 and 1.95,this indicates that it has a similar trend under the log-log coordinate.The research prove that the power law correlation of geological disasters not only exist between volume and area scale parameters, it exists in the area between parameters such as length,area, and the width. 2) Estimating the volume of landslide,collapse and unstable slope in an area is an even more difficult and chanllenging task thal requires information on the surface and sub-surface geometry of slope.At present,we can adopting the empirical relationships to estimate the volume of landslides. Given landslide, collapse and slope instability parameters such as length, width, through the above a given formula can estimate the area and the volume. It was important to the geological hazard investigation and the understanding of the law; 3) Different power laws of geo-hazards depend on the different local geomorphological,topography and other conditions, the power exponent can also be used as a indirectly reflection of the regional geological disasters or macro features of different types of geological disasters; 4) The power exponent distribution between the volume and area were as follows: unstable slope>collapses>landslide; the area and length were as follows: collapse >landslide>unstable slope; the area and width showed the as follows: landslide>collapse> unstable slope. For the landslides and collapses, the power exponent distribution were as follows:the area and length> the area and width> the volume and area; And for unstable slope, the power exponent distribution were as follows: the volume and area >the area and length> the area and width.5) All these evidences suggested that the phenomenon of geological hazard seems disorderly and unsystematic, while it follows certain laws, which further show the unity and universality of our world. Researching power law has essential significance for us to improve the knowledge of geological disaster.