各向异性随机场下的边坡模糊随机可靠度分析

土性参数具有很大的空间变异性,且在水平方向和垂直方向上差异显著。基于随机变量模型的传统边坡模糊随机可靠度分析方法并未对此进行考虑。提出一种能合理考虑土性参数空间变异性的边坡模糊随机可靠度分析方法。首先,视黏聚力和内摩擦角的均值为正态模糊数,对其取不同的λ截集水平并在各截集水平上进行参数组合。其次,利用各向异性随机场模拟土性参数的空间变异性,将有限元法和Monte–Carlo模拟相结合,计算各参数组合对应的可靠度指标。再通过数学方法得到边坡在各截集水平上的可靠度指标。最后,运用加权平均法计算边坡的模糊随机可靠度指标。算例分析表明:与水平方向的空间变异性相比,垂直方向的空间变异性对边坡模糊随机可靠度的影响更为显著;不考虑土性参数的空间变异性在一般情况下会低估边坡的模糊随机可靠度指标,但在抗剪强度参数变异性较大时,反而可能会高估边坡的模糊随机可靠度指标;此外,黏聚力与内摩擦角之间的相关性对边坡失效概率的影响趋势基本不受土性参数空间变异性的干扰。

Fuzzy-random reliability analysis of slope stability in anisotropic random fields

Spatial variability is the essential characteristic of the soil properties, which performs remarkable difference between the horizontal and vertical directions. In order to improve the traditional fuzzy-random reliability analysis methods which cannot deal with the spatial variability, a new method for slope fuzzy-random reliability analysis with reasonable consideration of the spatial variability is proposed. Firstly, the mean values of cohesion and friction angle are described by the normal fuzzy numbers and then randomly combined via cut set theory at different levels. Secondly, the corresponding reliability index of each parameter combination is calculated by the cooperation of finite element method and Monte-Carlo simulation under the anisotropic random fields of soil properties. And then, the total reliability index at each cut set level is obatined through a mathematical method. Finally, the fuzzy-random reliability index of the slope is achieved by the weighted average method. The illustration results show that the vertical-direction spatial variability has a more significant influence on fuzzy-random reliability of the slope, and ignoring the sptial variability of soil properties may also underestimate the probability of failure when the cohesion and the friction angle have great coefficients of variations. Moreover, the effect tendency of the correlation between the cohesion and the friction angle to failure probability is insensitive to the spatial variation of soil properties.