Probability density contour-based slope reliability analysis involving implicit limit state functions

A practical probability density contour-based reliability method (CBRM) for slope stability analysis involving an implicit limit state function in the original physical space is proposed. First, the vine copula theory for modelling the joint probability distribution of soil variables is introduced. Next, the existing CBRM is reviewed. Then, a discrete grid model is incorporated into the CBRM to deal with a complex slope reliability problem with an implicit limit state function. Finally, four slope examples are presented to illustrate and demonstrate the proposed CBRM. The results indicate that the proposed method exhibits good accuracy in solving the reliability index for a typical slope reliability problem. They also show that the C-vine and D-vine copulas for characterising various dependence structures among the cohesion, friction angle, natural soil unit weight, and saturated soil unit weight influence the reliability index value. As the proposed contour-based method operates in the original physical space, it can be applied to obtain the reliability index and the design points for various slope stability problems produced by these copulas. The proposed method yields reliability index estimates for four typical slope cases that are in close agreement with results from the vine copula-based simulation method, but with significantly fewer evaluations. Such a method can be used as an alternative to the traditional sampling method.