考虑自相关函数影响的边坡可靠度分析

自相关函数是表征岩土体参数空间变异性的重要参数,不同自相关函数对边坡可靠度影响程度还缺乏定量地评价。给出了基于乔列斯基分解中点法的相关非高斯随机场模拟步骤,统计了抗剪强度参数自相关长度的取值范围。在考虑土体抗剪强度参数间互相关性、变异性、黏聚力和内摩擦角取不同波动范围的基础上,以摩擦/黏性土坡可靠度问题为例研究了常用的5种自相关函数对边坡可靠度的影响。结果表明：基于乔列斯基分解中点法的相关非高斯随机场模拟计算过程简便,容易编程实现,可模拟任意几何形状的随机场分布,具有较高的计算精度和效率。在参数负相关性和垂直波动范围较大、变异性较小时,不同自相关函数得到的边坡可靠度结果差别较明显。当黏聚力和内摩擦角的垂直波动范围不同时,不同自相关函数对边坡可靠度的影响非常显著。高斯型、二阶自回归型和指数余弦型自相关函数产生的随机场分布光滑度和连续性较好,较为符合实际情况,它们能够有效地描述土体参数的空间自相关性。由这三种自相关函数计算得到的边坡可靠度结果偏小。基于指数型自相关函数的随机场分布波动性较大,连续性较差,计算的边坡可靠度偏大。

Slope reliability analysis considering effect of autocorrelation functions

The autocorrelation function (ACF) is a prerequisite for properly characterizing the spatial variability of soil properties. The effect of different types of ACFs on the slope reliability has not been qualitatively evaluated. A procedure for simulating correlated non-Gaussian random fields based on the Cholesky decomposition technique with midpoint discretization is proposed. The typical ranges of autocorrelation length of shear strength parameters of soils are summarized. An example of reliability analysis of frictional/cohesive soil slope is then presented to investigate the effect of five common types of ACFs for the geostatistical analysis on the slope reliability. The influence of cross-correlation, variability of soil properties and different scales of fluctuation of the cohesion and friction angle are taken into account, respectively. The results indicate that the proposed method is computationally simple and easily implementable for simulating the correlated non-Gaussian random fields with any geometry, and it can effectively evaluate the slope reliability with a sufficient accuracy. The differences in the slope reliability underlying five types of ACFs are more obvious when the negative cross-correlation and vertical scales of fluctuation become stronger, and the variability of soil properties becomes smaller, respectively. These differences become very significant when the cohesion and friction angle take different vertical scales of fluctuation. Additionally, the target random fields are very smooth and the slope reliability is underestimated underlying the square exponential, second-order autoregressive or cosine exponential ACFs, and they may account for the spatially correlated soil properties more realistically. In contrast, the target random field is a roughly varying field and the slope reliability is overestimated underlying the exponential ACF.