不完备概率信息条件下边坡可靠度分析方法

不完备概率信息条件下边坡可靠度估计是一个富有挑战性的问题。基于Copula函数提出了不完备概率信息条件下边坡可靠度分析方法。首先，简要介绍了基于Copula函数的岩土体抗剪强度参数联合概率分布函数构造方法。其次，定义了边坡稳定分析的名义安全系数，提出了边坡失效概率波动范围分析方法。最后以无限边坡稳定可靠度问题为例证明了所提方法的有效性。结果表明：不完备概率信息条件下边坡失效概率是不唯一的。抗剪强度参数间Copula函数类型对边坡失效概率具有明显的影响，这种影响直接导致了不完备概率信息条件下边坡失效概率的波动范围较大。边坡失效概率波动范围随名义安全系数的增大或失效概率的减小而增大。所提3种方法能够有效地缩小边坡失效概率的波动范围，提高了边坡失效概率的估计精度，从而为不完备概率信息条件下边坡可靠度分析提供了一条有效的途径。

Reliability analysis of slopes with incomplete probability information

Reliability analysis of slopes with incomplete probability information is a challenging problem. This paper aims to propose Copula-based methods for the reliability analysis of slopes with incomplete probability information. First, the method for constructing the joint probability distribution of shear strength parameters using Copulas is briefly introduced. Thereafter, the concept of nominal factor of safety for slope stability analysis is defined. The dispersion of probability of slope failure is derived. Finally, an example of reliability analysis for an infinite slope is presented to demonstrate the capability and validity of the proposed methods. The results indicate that the probability of slope failure can not be determined uniquely based on the incomplete probability information of shear strength parameters. The probabilities of slope failure produced by different Copulas can differ considerably. Such differences directly lead to large dispersion of probability of slope failure. The dispersion of probability of slope failure increases with increasing nominal factor of slope safety, and it increases with decreasing probability of slope failure. The proposed three Copula-based methods can narrow the dispersion of probability of slope failure effectively, which can improve the reliability estimation of slopes efficiently. These methods provide an effective tool for the reliability analysis of slope failure with incomplete probability information.