黄土滑坡发育特征参数的幂律相依性研究

Power law correlations between feature parameters of loess landslides

以天水市麦积区幅为例,利用最小二乘法的拟合方法,对黄土滑坡发育特征参数的幂律相依性进行了研究。结果表明:(1)滑坡-累积频率的幂律相依性不仅存在于滑坡面积-累积频率、体积-累积频率间,还存在于滑坡后缘距离分水岭高程与其发生的累积频率之间;(2)滑坡规模参数幂指数分布特征为面积与长度>面积与宽度>体积与面积;运动特征参数幂指数的分布特征为体积与最大垂直滑动距离>体积与最大水平滑动距离>面积与最大垂直滑动距离>面积与最大水平滑动距离;(3)滑坡的等效摩擦系数与滑坡面积、体积的幂函数相关性差,故而该经验关系式仅能代表趋势特征,不能作为定量分析的依据。

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 Gansn 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.