The method for risk analysis of slope failure of the earth dam based on grey-stochastic risk

The concepts of grey probability, grey probability distribution, grey probability density, grey expectation and grey variance are defined based on the theory of probability and grey system approach. The method of grey-stochastic risk for risk analysis of slope failure of the earth dam is established. In this method, the uncertainty of slope failure risk of the earth dam is attributed to grey uncertainty of system, the variables of performance function of the dam slope system are treated with grey probability distributions and the hazard of slope failure is quantified with grey-stochastic risk. The grey-stochastic risk can be transformed into ordinary stochastic risk and computed using advanced first-order second-moment method. An example of application is given.