考虑参数空间变异性的边坡系统可靠度分析

System Reliability Analysis of Slopes Considering Spatial Variability of Soil Properties

在考虑土体参数空间变异性基础上,提出了基于多重随机响应面法的边坡系统可靠度分析方法,同时建议了一种新的代表性滑动面搜索方法.采用Karhunen-Loève展开方法离散二维相关非高斯随机场,通过Hermite随机多项式展开近似代表性滑动面安全系数与土体参数间的非线性隐式函数关系,在此基础上采用直接蒙特卡洛模拟计算边坡系统失效概率.研究了所提方法在考虑参数空间变异性的边坡系统可靠度分析中的应用.结果表明,提出的基于多重随机响应面法的系统可靠度分析方法为考虑参数空间变异性的边坡系统可靠度问题提供了一条有效的分析途径.提出的代表性滑动面确定方法具有较高的计算精度和效率,无需单独计算滑动面安全系数间的相关性,而且能够有效地计算低概率水平的边坡系统可靠度.边坡系统失效概率随着抗剪强度参数变异性和垂直相关距离的增大而增加、随着抗剪强度参数间负相关性的增加而减小.此外,忽略土体参数空间变异性会明显高估边坡系统失效概率.

The paper aims to propose an effective method for evaluating the system reliability of soil slopes based on the multiple stochastic response surface method considering the spatial variability of soil properties. A new approach for also suggested The Karhunen-Lo^ve expansion identifying the representative slip surfaces is method is employed to discretize the two- dimensional cross-correlated non-Gaussian random fields of soil properties. The factor of safety of each representative slip surface is explicitly expressed as function of input uncertain parameters using the I-Iermite polynomial chaos expansion. The direct Monte-Carlo simulation is then employed to calculate the system probability of slope failure based on these representative slip surfaces. Two examples of system reliability analysis of slopes with a consideration of spatially varying soil properties are finally presented to demonstrate the validity and capability of the proposed method. The results indicate that the proposed method can provide an effective tool for evaluating the system reliability of slopes considering the spatial variability of soil properties. The proposed approach for determining representative slip surfaces can not only avoid tedious procedures of calculating the correlations between the factors of safety of any two potential slip surfaces, but also effectively evaluate system reliability of slopes at relatively small probability levels. The system probability of slope failure increases with increasing the variability and vertical autocorrelation distance, while decreases as the negative correlation of shear strength parameters becomes strong. In addition, it will lead to overestimating the system probability of slope failure if the spatial variability of soil properties is ignored.