Abstract：The landslip of rock slope with the influence of blasting vibration often results in serious disasters，frequently with heavy losses of life and damage to property. It is generally difficult to precisely analyze rock slope stability due to the vast number of unknown variables，such as slope type，height and angle of slope，physical properties of rock mass，and so on. The prediction of failure of rock slope is an important problem of rock mechanics in the engineering excavation activities，especially the open-pit mine in mountainous areas. It is difficult to determine the rational slope angle of rock slope because of the complexity of the problem. Recently，fuzzy theory has been applied to predict the landslip and failure of rock slope. The landslip of rock slope can be regarded as a fuzzy event. The landslip will take place at a fuzzy probability，and so the theory of fuzzy measures can be applied to predict the landslip and failure of rock slope. By using statistical analysis，the initial damage of the rock slope in mountainous areas is found to be of normal distribution. Based on the results of statistical analysis of a large amount of measured data in slope engineering，the fundamental fuzzy model of failure of rock slope is established by using the theory of fuzzy mathematics. The formulas of two-dimensional problems are derived and applied to the prediction of slope failure due to surface mining. The fuzzy measure models are adopted for determination of rational slope angle considering the influence of the blasting vibration on open-pit mine in mountainous areas. The fuzzy failure probability and dynamic responses of the rock slope are calculated. Numerical results are compared with those obtained from independent field tests. The agreement of the theoretical results with the field measurement shows that the presented model is satisfactory and the formulas obtained are valid，and thus can be effectively used for prediction of slope failure and determination of the rational slope angle of rock slope.
