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Mathematical Problems in Engineering
Volume 2016, Article ID 6141838, 11 pages
Research Article

Copula-Based Slope Reliability Analysis Using the Failure Domain Defined by the -Line

1Key Laboratory of Geomechanics and Embankment Engineering, Ministry of Education, Hohai University, 1 Xikang Road, Nanjing 210098, China
2Key Laboratory of Geological Hazards on Three Gorges Reservoir Area, Ministry of Education, China Three Gorges University, 8 Daxue Road, Yichang 443002, China

Received 15 June 2016; Revised 21 August 2016; Accepted 29 August 2016

Academic Editor: Renata Archetti

Copyright © 2016 Xiaoliang Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The estimation of the cross-correlation of shear strength parameters (i.e., cohesion and internal friction angle) and the subsequent determination of the probability of failure have long been challenges in slope reliability analysis. Here, a copula-based approach is proposed to calculate the probability of failure by integrating the copula-based joint probability density function (PDF) on the slope failure domain delimited with the -line. Here, copulas are used to construct the joint PDF of shear strength parameters with specific marginal distributions and correlation structure. In the paper a failure (limit state) function approach is applied to investigate a system characterized by a homogeneous slope. The results show that the values obtained by using the failure function approach are similar to those calculated by means of conventional methods, such as the first-order reliability method (FORM) and Monte Carlo simulations (MC). In addition, an entropy weight (EW) copula is proposed to address the discrepancies of the results calculated by different copulas to avoid over- or underestimating the slope reliability.