约束随机场下的边坡可靠度随机有限元分析方法

Slope reliability analysis by random FEM under constraint random field

目前边坡可靠度中常用的简化分析方法,不考虑边坡土体的空间变异性,每次计算整个边坡都取用相同的强度参数,由离散点试样试验得到的土体参数统计特性只能反映点特性,而边坡的稳定性受滑面上平均抗剪强度特性控制,因此,需要考虑空间范围内的平均特性。描述空间变异性的随机场理论对变异性较高的土体,实际上高估了其空间变异性。把随机场理论和地质统计中的区域化变量理论结合起来,建立约束随机场,并在此基础上进行Monte-Carlo随机有限元分析。计算实例表明,在高变异性条件下约束随机场能有效降低完全随机场的模拟方差,得到更低的破坏概率。对比了随机有限元和简化法的计算结果表明,简化法在土体强度变异性很高时其结果并非偏于保守。另外也指出了可靠度分析中存在的边坡尺度效应和简化法的适用条件。

The simplified method for slope reliability analysis ignores the spatial variability and use same strength parameters during every computation. The probabilistic characterization of soil properties are obtained through discrete sample test; thus can only represent point variability. The stability of slopes is often controlled by the average shear strength within a zone of influence, hence the average properties in the slope domain should be accounted. The unconfined random field ignores the samples＇ location information and may lead to higher variability especially when the variability of soil is high. The constraint random field （CRF） is proposed and implemented utilizing random field theory and regionalized variable theory of geostatistics to ensure that the random field realizations match the parameters at the sample locations exactly; and slope reliability analysis is performed by Monte-Carlo random FEM （RFEM） and shear strength reduction technique. The computation results show that the CRF can significantly reduce variance of the random field simulation and get lower probability of failure when the soil variability is high. The comparison of RFEM and simplified method also shows that the simplified method will not always overestimate the probability of failure. The scale effect in slope reliability analysis is highlighted through RFEM; and the applicability of simplified method is discussed.