基于Copula函数的抗剪强度参数间相关性模拟及边坡可靠度分析

为了研究表征抗剪强度参数间相关性的Copula函数对边坡可靠度的影响规律，简要介绍了Copula函数的基本定义，收集了水利水电工程中4组岩基抗剪强度参数试验数据，采用AIC准则识别出表征抗剪强度参数间相关结构最优的Copula函数。提出了无限边坡失效概率计算的直接积分方法，以无限边坡可靠度问题为例系统地研究了Copula函数的类型对边坡可靠度的影响规律。结果表明：表征抗剪强度参数间相关性的Copula函数类型对边坡可靠度具有重要的影响，不同Copula函数计算的边坡失效概率具有明显的差别，这种差别随边坡安全系数的增加（或失效概率的减小）而增加、随抗剪强度参数间负相关性的增强而增大、随变异系数的减小而增大。常用的Gaussian Copula函数并不是表征抗剪强度参数间相关结构最优的Copula函数，Gaussian Copula函数构造抗剪强度参数的联合概率分布函数将会明显低估边坡的失效概率，不能为了计算简便而盲目采用Gaussian Copula函数表征抗剪强度参数间相关性。

Modeling dependence between shear strength parameters using Copulas and its effect on slope reliability

The influence of Copulas for modeling dependence between shear strength parameters on slope reliability is investigated. Firstly, four data sets of shear strength parameters in hydropower projects are collected. Then, the Akaike information criterion is adopted for identifying the best-fit Copula underlying the collected shear strength parameters. The formulae for probability of failure of an infinite slope using the direct integration are derived. Finally, an example of reliability analysis for the infinite slope is presented to demonstrate the influence of Copulas on the probability of slope failure. The results indicate that the Copulas have a significant influence on the probability of slope failure. The probabilities of slope failure produced by different Copulas may differ considerably. Such difference increases with increasing slope factor of safety (or decreasing probability of slope failure), increasing negative dependence between cohesion and internal friction angle and decreasing coefficient of variation of shear strength parameters. In addition, the Gaussian Copula is not the best-fit one for modeling the dependence structure underlying the shear strength parameters. If the Gaussian Copula is adopted, the probability of slope failure will be underestimated significantly. It is emphasized that the Gaussian Copula should not be adopted out of expedience without proper validation to model the dependence between the shear strength parameters.