考虑空间变异性条件下的边坡稳定可靠度高效敏感性分析

Efficient reliability sensitivity analysis for slope stability in spatially variable soils

在有限数据条件下,可靠度敏感性分析是研究各种不确定性因素对边坡失稳概率影响规律的重要途径。基于直接蒙特卡洛模拟和概率密度加权分析方法提出了一种高效边坡稳定可靠度敏感性分析方法。所提出的方法通过随机场表征岩土体参数的空间变异性,并采用局部平均理论建立岩土体参数的缩维概率密度函数,用于概率密度加权分析中高效、准确地计算不同敏感性分析方案对应的边坡失稳概率。最后,通过一个工程案例——詹姆斯湾堤坝说明了所提出方法的有效性和准确性。结果表明:在敏感性分析过程中,所提出的方法只需要执行一次直接蒙特卡洛模拟,避免了针对不同敏感性分析方案重新产生随机样本和执行边坡稳定分析,节约了大量的计算时间和计算资源,显著提高了基于蒙特卡洛模拟的敏感性分析计算效率;在概率密度加权分析中采用岩土体参数的缩维概率密度函数能够准确地计算边坡失稳概率,避免了有偏估计,使概率密度加权分析方法适用于考虑空间变异性条件下的边坡稳定可靠度敏感性分析问题。

Reliability sensitivity analysis provides a rational vehicle to shed light on effects of different uncertain parameters on slope failure probability when only a limited number of data is available. This paper develops an efficient reliability sensitivity analysis method for slope stability. The proposed approach combines direct Monte Carlo simulation（DMCS） and probability density reweighting method（PDRM） to, efficiently and accurately, calculate slope failure probabilities for different cases considered in sensitivity analysis. In the proposed approach, random field theory is used to model geotechnical spatial variability. Local spatial averaging technique is applied to constructing the joint probability density function of geotechnical parameters with relatively low dimensions, which is directly used in PDRM. Finally, the proposed approach is illustrated using a design scenario of James Bay Dyke. Results show that： only one run of DMCS is needed in the proposed approach, avoiding repeated generation of random samples and performing slope stability analysis. This saves a large amount of computational efforts, and significantly improves computational efficiency for DMCS-based reliability sensitivity analysis. Using joint probability density function of geotechnical parameters derived from local spatial averaging in PDRM gives proper estimates of slope failure probability and avoids biased estimates, making PDRM feasible in reliability sensitivity analysis of slope stability in spatially variable soils.