The most important problem in the risk analysis of slope is how to predict an unstable slope. In this paper, a method of evaluation for the risk degree of slope failures is described by the application of Hayashi's quantification method III, which is a mathematical-statistical method in order to convert qualitative data into quantitative relations. The investigated area is Sakurajima volcano located in the center of Kagoshima Bay, southern Kyushu, Japan. Taking engineering aspects into consideration, the basic data relevant to slope stability were obtained on topographic and geotechnical conditions, land utilization and vegetation in a fixed unit area overlaied with the mesh of 250m square.8 items and 33 categories are chosen as the factors of characterizing the unit area. The collected data are categorical, that is, non-numerical and qualitative, data, which can be quantified by the use of a suitable computer program based on the theory of quantification. Numerical values given to each category for the quantification are elements of eigenvectors, which are obtained from vector equation, corresponding to eigenvalues which are obtained from characteristic matrix. According to the relative distance between a couple of categories which can be calculated by elements of eigenvectors, each category is grouped into five classes, which are given the score of risk degree estimated by the values from 0 to 4. The rank of risk level is determined from the total scores of risk degree and finally a classification map of risk level of slope is presented.The remarkable feature of this paper is that the score of risk degree for categorical data of slopes was determined theoretically by the grouping classification using a mathematical-statistical approach. Moreover, it is greatly interested to note that the informations of slope failures are not always required in applying the method III to the prediction of risk degree of slope.
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