边坡模糊可靠性分析隶属函数取值界限研究

Study of boundaries of membership function values for slope fuzzy reliability analysis

针对岩土参数取值所具有的随机性、模糊性与区间性特征，建议采用隶属函数表征参数取值，分别构造了岩土参数三角形分布、正态分布与拟正态分布隶属函数，并建立了采用隶属函数取值界限表示的不同截集水平岩土参数区间值确定方法，提出分别采用均值加减2．5倍标准差与3倍标准差确定岩土参数三角形分布与拟正态分布隶属函数取值界限，进而以此为基础采用模糊点估计分析方法对工程算例进行分析，结果表明，在截集水平个数为11时，模糊点估计方法所得边坡稳定模糊可靠性指标与蒙特卡洛法所得随机概率可靠性指标精度相当，截集水平个数为9时，评价结果偏安全，建议在工程分析时，截集水平取0．1～0．9问的9个，该方法计算过程直接简单，计算代价低，更具工程实用性。

In light of the randomness, fuzziness and interval feature of values of geotechnical parameters, the triangular distribution functions, normal distribution functions and quasi-normal distribution membership functions are separately proposed to express the distribution of the parameter values. The methods to determine the distribution functions of geotechnical parameters and their interval values with different cut-levels are presented. And the interval values can be expressed by the boundary values of the membership functions. The boundary values of triangular distribution functions and quasi-normal distribution functions are suggested to be determined with their average values and standard deviations. The upper or lower limit of triangular distribution function boundary value can be got by the average value plus or minus two point five times standard deviation. And the upper or lower limit of quasi-normal distribution function boundary value can be got by the average value plus or minus three times standard deviation. Then the fuzzy point estimate method is proposed to analyze the fuzzy reliability of slope engineering. The results show that the slope fuzzy reliability index determined by eleven cut-levels are approximately equal to the probabilistic reliability index got by the Monte Carlo method. The number of cut-levels is proposed to be nine. And the cut-levels can be selected from 0.1 to 0.9. The fuzzy point estimate method with the determined boundary values of different distribution functions can be used to evaluate the slope fuzzy reliability; this method is simple and practical.