AbstractLimit equilibrium methods (

AbstractLimit equilibrium methods (LEMs) and finite element methods (FEMs) of slope stability analysis can be used in computer-based probabilistic simulation approaches (e.g., direct Monte Carlo Simulation (MCS) and Subset Simulation (SS)) to evaluate the slope failure probability (Pf). For a given slope problem, the computational effort for the LEM is generally much less than that required for the FEM, but the FEM tends to give a more realistic prediction of slope failure mechanism and its associated factor of safety. To make use of the advantages of both the LEM (e.g., computationally more efficient) and FEM (e.g., theoretically more realistic and rigorous in terms of slope failure mechanisms), a new probabilistic simulation method is developed in the paper. The proposed approach combines both a simple LEM (i.e., Ordinary Method of Slices considering a limited number of potential slip surfaces) and FEM with the response conditioning method to efficiently calculate Pf of slope stability and to give an estimate of Pf consistent with that obtained from directly performing MCS and SS based on the FEM. It is illustrated through two soil slope examples. Results show that the proposed approach calculates the Pf properly at small probability levels (e.g., Pf < 0.001). More importantly, it significantly reduces the number of finite element analyses needed in the calculation, and therefore improves the computational efficiency at small probability levels that are of great interest in slope design practice. In addition, the proposed approach opens up the possibility that makes use of the information obtained using a simple model (e.g., LEM) to guide the reliability analysis based on a relatively sophisticated model (e.g., FEM).1. IntroductionDuring the past few decades, several probabilistic simulation methods have been developed to evaluate the reliability (or failure probability, Pf) of slope stability, such as direct Monte Carlo Simulation (direct MCS) (e.g., [1–4]), importance sampling (e.g., [5]), and Subset Simulation (SS) (e.g., [6–8]). These methods involve repeatedly evaluating the safety margin of slope stability using a prescribed deterministic analysis method during the simulation, such as limit equilibrium methods (LEMs) (e.g.,[1,5,6,9,10]) and finite element methods (FEMs) (e.g., [2,3,11,12])LEMs (e.g., Ordinary Method of Slices (OMS), simplified Bishop’s method, and Spencer’s method) are widely used in slope engineering practice [13]. Compared with FEMs, LEMs are conceptually simple and require much less computational effort for slope stability analysis, particularly when OMS that has an explicit performance function is applied. However, as pointed out by Griffiths and Lane [14] and Griffiths et al. [2], LEMs need to assume the shape (e.g., circular) and location of slope failure surfaces in the analysis, which are rarely known prior to the analysis, particularly when spatial variability of soil properties is explicitly considered. Inappropriate assumptions on slope failure surfaces in LEMs might lead to negligence of the actual critical slope failure mechanism and, subsequently, result in the estimate of Pf inconsistent with that obtained using more rigorous slope stability analysis methods (e.g., FEMs) in simulation-based reliability analysis. FEMs provide a rigorous and versatile tool for slope stability analysis and alleviate assumptions on slope failure surfaces required in LEMs (e.g., [14,15]). However, FEM-based probabilistic simulation methods (e.g., random finite element method (RFEM)) are sometimes criticized for a lack of computational efficiency and requiring intensive computational power (e.g., [16–18]), particularly at small probability levels (e.g., Pf < 0.001). Then, an interesting question arises that how to make use of advantages of both LEMs (e.g., computationally more efficient) and FEMs (e.g., theoretically more realistic and rigorous in terms of the failure mechanism) in reliability analysis of slope stability so as to efficiently obtain consistent reliability estimates. Such a possibility has not been explored in geotechnical literature.Note that it is not uncommon that there exist different deterministic analysis models/methods (e.g., LEMs and FEMs) for the same geotechnical problem (e.g., slope stability analysis). These methods can be applied in different design stages. For example, at the preliminary design stage, site information (e.g., soil properties) might be too limited to