基于非线性随机有限元的堤坝边坡可靠度分析

Analysis of Embankment Slope Safety Based on Nonlinear Stochastic Finite Element Method

针对边坡稳定性分析中土体力学参数存在空间变异性的问题,提出了计算堤坝边坡安全系数分布的随机有限元方法,以及求解边坡可靠度的蒙特卡罗(MC)强度折减联合法与MC直接法。以各向同性二维边坡为例,首先抽样得到相应的材料特性随机场,随后求得边坡位移、应力及塑性区;然后在对随机场进行NMC次抽样的基础上采用以下方法得到边坡的失效概率并对可靠度指标进行求解分析:(1)联合法(M1),通过强度折减法得到各样本条件下的折减系数及其分布;(2)MC直接法(M2),利用黏塑性方法直接求解并判断边坡的失稳情况,对所有样本条件下的失稳情况进行统计。结果表明:考虑材料特性随机场的边坡稳定分析,通过边坡安全系数的均值、方差、分布及可靠度指标对边坡安全进行综合评价,能够得到可靠的边坡稳定分析结果。

Aiming at the issue of spatial variability of soil mechanical parameters in slope stability analysis,this paper proposed a stochastic finite element method for calculating the distribution of FS(factor of safety)of embankment slopes,and Monte Carlo(MC)strength reduc⁃tion combined method and MC direct method were proposed to calculate the reliability of slope.Taking isotropic two-dimensional slope as an example,firstly,sampling to get the corresponding random field of material properties,and then the slope displacement,stress and plasticity zone results were calculated;then on the basis of NMC times sampling of random field,the failure probability of the slope was obtained and the reliability index was solved and analyzed by the following methods of a)combined method(M1):the strength reduction method was used to get the reduction coefficient of each sample and its distribution;b)MC direct method(M2):using viscoplastic method to solve directly to judge the instability of slopes,and the instability cases under all sample conditions were counted.The results show that the slope stability analysis considering the material properties random field,the mean,variance,distribution of FS and reliability indexes are integrated to eval⁃uate the slope safety,which can get the real and reliable slope stability analysis results.