考虑隶属函数特性的边坡模糊可靠性分析

Fuzzy reliability analysis of slopes considering characteristics of membership function

针对边坡工程岩土参数所具有的随机性、模糊性与区间性,根据隶属函数分布特征与截集技术提出岩土参数隶属函数截集取值方案,构建隶属函数不同分布形式的表征方法及其取值界限确定方法,建立基于截集技术与模糊点估计法的边坡模糊可靠性分析方法。通过两个典型算例不同工况计算结果的系统分析获得了岩土参数隶属函数分布形式、截集取值方案与取值界限对边坡模糊可靠度的影响规律。岩土参数样本数据量较少时可优先采用取值界限为±2.5σ的三角形分布与正态分布,对数正态与拟正态分布次之,而Beta（4,3）与Beta（4,4）分布将使模糊可靠度计算结果偏大。界限截集水平对计算结果影响程度显著,三角形、拟正态与Beta（4,3）分布的截集区间可取[0,1.0],正态与对数正态分布的截集区间可取[0.05,0.95],并选取隶属函数界限值与0.1间隔的截集水平值进行计算。获得了考虑隶属函数特性的边坡模糊可靠性分析方法,其将使边坡模糊可靠度计算结果更具合理性。

With regard to the randomness, fuzziness and interval characteristics of geotechnical parameters of slope engineering, the scheme to select the cut set values of geotechnical parameters is proposed based on the distribution features of membership function and the cut set technique. The methods for expression of membership functions with different distribution forms and the determining methods for their boundary values are also proposed. Then the fuzzy reliability analysis method for slopes is established based on the cut set technique and the fuzzy point estimation method. The fuzzy reliability indexes of two typical slope examples are calculated under different conditions. The influence rules of distribution forms of membership function, selecting schemes of cut set values and boundary values of geotechnical parameters are analyzed according to the calculated results. The normal distribution and triangular distribution with ±2.5 times the standard deviation as the boundary values can be firstly used if the data size is not enough. The lognormal distribution and approximate normal distribution can be used secondly. The Beta（4, 3） distribution and Beta（4, 4） distribution will make the calculated results larger. The influences of boundary of cut set levels on the results can not be ignored. The cut set intervals for triangle, approximate normal and Beta（4, 3） distributions can be [0, 1.0]. And it can be [0.05, 0.95] for the normal and lognormal distributions. Both the boundary and cut set levels with 0.1 interval should be used to calculate the fuzzy reliability indexes. The fuzzy reliability analysis method for slopes considering characteristics of membership function can make the calculated much more reasonable.