Soil Slope Reliability Assessment through Bayesian Updating: A Comparative Study Using RLEM, RFDM, and RFEM

Abstract This study aims to establish an objective analytical framework for determining the number of boreholes that are essential for addressing soil slope design challenges in diverse geological/geotechnical settings. This study utilizes the covariance matrix decomposition method and a two-directional one-dimensional Markovian covariance function to create a two-dimensional random field. A Monte Carlo simulation is used to assess the statistical response based on the generated random fields. A random limit equilibrium method (RLEM) code in MATLAB (version R2023a) is developed using circular slip surfaces equipped with a chaotic particle swarm optimization technique for the reliability analysis of soil slopes. Additionally, the strength reduction method based on the finite difference/finite-element (FE) techniques is adopted to compare the reliability analysis results, such as the probability of failure (Pf). A new programming strategy is adopted to simulate the spatial variability in the FE soil slope model and calculate the factor of safety using a gradient of the maximum slope displacement. Bayesian updating is applied to adjust the conditional probabilities of decision variables and the component reliability. The strategic deployment of boreholes at the toe, middle, and top of the slope results in a significant reduction in the estimated Pf according to the RLEM, the random finite difference method (RFDM), and random FEM (RFEM) analyses. However, employing subsequent boreholes does not proportionally decrease the Pf. The influence of the horizontal autocorrelation distance (ACD) on the Pf is explored, showing that as the horizontal ACD increases from 10 to 20 m, the estimated Pf for the three boreholes decreases to 19% and 13% in the RFEM and RLEM, respectively. This reduction becomes less pronounced, dropping to 4% and 1.3%, respectively, when the ACD increases to 30 m.