Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Abstract

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P f <0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called "Subset Simulation (SS)" to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.

Three-dimensional slope reliability and risk assessment using auxiliary random finite element method

“…In slope reliability analysis and risk assessment, the probability of slope failure, P f , is defined as the probability that the safety factor of slope stability, FS, is smaller than a given threshold fs (e.g., fs = 1), namely P f = P(FS < fs), and the slope failure risk, R, can be defined as the product of P f and the average failure consequence C [17,31]. The computational efficiency and accuracy of P f and R depend on the deterministic analysis model of slope stability, such as the FE models with coarse and fine FE meshes (referred as coarse and fine FE models, respectively).…”

“…The original RFEM, also referred as MCS-based RFEM, incorporates the spatial variability of soil properties into slope reliability analysis using finite-element (FE) analysis and MCS. There are several successful applications of RFEM in reliability analysis of 3-D slope (e.g., [14][15][16]36]) and slope risk assessment (e.g., [17,31]). RFEM is a rigorous approach since the FE analysis of slope stability can automatically locate the critical slip surface without assumptions on the shape and location.…”

Investigating the Influence of Conditional Simulation on Small-Probability Failure Events Using Subset Simulation

“…Details on subset simulation and its application to slope stability analysis can be found in Au and Beck (2001), Li et al (2016a) and Eijnden and Hicks (2016).…”

“…This method was applied in slope stability analysis within the framework of the random finite element method (RFEM) by Li et al (2016a). Modifications were proposed to improve the efficiency of the method, based on computationally less expensive surrogate models (Li et al 2016b, Xiao et al 2016 or indicative relations (Huang et al 2016).…”

Efficient reliability updating of slope stability by reweighting failure samples generated by Monte Carlo simulation

“…Slope reliability has been investigated extensively in the literature due to unavoidable uncertainties in geotechnical engineering (e.g., [10,15,14,22,30,45,19,20,17,23,21,[36][37][38]24,25,27]). For slope reliability analysis, the uncertainties in geotechnical parameters involved in slope reliability analysis are often represented by a vector of random variables, x.…”