Analysis of fuzzy-random reliability of slope stability

Because of the geological complexity and the inhomogeneous material the research on rock and soil engineering is very strong uncertain. According to the traditional reliability theory, the limit state function show the vicinal point very close to the zero would have two states: effective and failure states. It's unreasonable in the engineering: exactly there is a process from the effective state to failure state; the edge is fuzzy. So it's reasonable to consider the parameters as fuzzy-random case. And the value of destroy criterion to determine the state of engineering is also a process not a distinctly value. So it's reasonable to consider the parameters as fuzzy-random case. And the value of criterion to determine the state of engineering is also a process not a distinctly value. The fuzzy-random probability is carefully analyzed based on the traditional probability theory focused on slope stability. And the parameters are described as fuzzy set; the value of criterion is also defined as fuzzy set. The failure probability and the index of probability are also deduced with fuzzy set. From the results we can concluded that the method used in this paper is closer to the engineering practice. We also can know the index of probability would be a continued variable when consider the fuzzy character of the parameter and the criterion, It would be maximizing value when the restriction level up to 1, it's consistence with the engineering practice.