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Distribution of frequency-size of geological disaster base on principle of maximum entropy in loess plateau
QIU Hai-jun ,CUI Peng ,CAO Ming-ming ,LIU Wen ,GAO Yu ,WANG Yan-min,
. 2014, 35 (12 ):
3541-3549.
This study investigates the principles of frequency-size of geological disaster in loess hilly region. Baota district in Yan’an city in Shaanxi province is chosen as the typical geological disaster region in loess plateau. The database of geological disaster in Baota district is built through 3S technology, field survey and remote sensing interpretation. In the view of the holism and in the base of scale distribution analysis and maximum entropy principle, the theory that the parameters of frequency-size such as the length, width and thickness of collapse, landslide and unstable slope accorded with negative exponential distribution is come up for the first time using mathematical statistic method. As a result, a simple and effective formula about frequency- size distribution is put forward. At the end, the formula is verified by the example of Baota district. (1) The results mainly show that the geological disaster of Baota district is mainly middle-scale landslide and collapse; however, large-scale disaster plays important role in the control of total area and volume of collapse. (2) Then this study defines the grade index of volume size for researching size distribution of geological disaster. The results show that the size grade index of landslide, collapse and unstable slope is mainly in (5.5, 6], (4, 4.5] and (5, 5.5], respectively. (3) The frequency-size distribution of collapse, landslide, and the length, width and thickness of unstable slope accord with the exponential relation; furthermore, the curve would not have rollover effect. (4) One of simple methods to solve the frequency-size distribution is to get the square root of area and cube root of volume. The results show that they present negative exponential distribution with a good fitting effect (R2>0.9, P<0.05). Thus the formula plays important role in the prediction of the occurrence frequency of landslide in any size.
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