不排水抗剪强度非平稳随机场模拟及边坡可靠度分析

边坡可靠度分析中通常假定采用平稳或准平稳随机场表征土体参数的空间变异性，然而大量现场试验数据表明，土体参数如不排水抗剪强度沿土体埋深常呈现明显的非平稳分布特征，即其均值和标准差均随埋深发生变化，因此亟需发展土体参数非平稳随机场模型及其模拟方法。针对目前不能有效单独模拟土体参数趋势分量和随机波动分量的不确定性，提出了一种有效的不排水抗剪强度参数非平稳随机场模型，并给出了土体参数二维非平稳随机场模拟方法计算流程，同时将新提出的模型与现有非平稳随机场模型及平稳随机场模型进行了系统比较。最后通过不排水饱和黏土边坡算例验证了提出模型的有效性，并揭示了不排水抗剪强度非平稳分布特征对边坡可靠度的影响规律。结果表明：提出模型能够有效地单独模拟土体参数趋势分量和随机波动分量的不确定性，考虑土体参数均值和标准差随埋深增加而增大的特性，可为表征土体参数非平稳分布特征提供了一条有效的途径。此外，与采用非平稳随机场模拟土体参数空间变异性相比，采用常用的平稳随机场模型会低估边坡失效概率，从而造成偏危险的边坡工程设计方案。

Slope reliability analysis by simulation of non-stationary random field of undrained shear strength

Spatial variabilities of soil properties are usually modeled by stationary or weakly stationary random fields in slope reliability analysis. However, abundant in-situ data demonstrates that the means and standard deviations of soil properties such as undrained shear strength change with the soil depth. Thus, it is important to develop non-stationary random field models and approaches to model spatial variations of soil properties. To tackle the uncertainties of the trend component and fluctuation of component in existing models, this paper proposes an effective non-stationary random field model of undrained shear strength. The approach for modeling the two-dimensional non-stationary random fields of soil properties is also presented. Thereafter, the effectiveness of the proposed model is illustrated by comparisons with the existing non-stationary random field models and stationary random field models of soil properties systematically. A clay slope under undrained conditions is investigated to explore the effect of the non-stationary distribution characteristics of undrained shear strength along the depth on the slope reliability. The results indicate that the proposed model can simulate the uncertainties of the trend component and fluctuating component separately. Both the means and standard deviations of soil properties increase with the depth. It provides an effective means for characterizing the non-stationary distribution characteristics of soil properties. Compared with the slope reliability analysis results underlying the non-stationary random fields, it will lead to an underestimation of the probability of failure and dangerous slope engineering designs when the commonly-used stationary random fields are utilized to model the spatial variability of soil properties.