A Bayesian bootstrap-Copula coupled method for slope reliability analysis considering bivariate distribution of shear strength parameters

Estimation of the uncertainties of geotechnical parameters is a fundamental task in slope reliability analysis, and it becomes more challenging when only limited data on geotechnical parameters are available. In this study, a Bayesian bootstrap-Copula coupled method is proposed for slope reliability analysis based on limited geotechnical data. Specifically, the bivariate distribution of shear strength parameters ((cohesion (c) and friction angle (φ)) can be evaluated using the Bayesian bootstrap method and Copula theory, and then the slope reliability can be calculated using Monte Carlo simulation (MCS). Application to a homogeneous, undrained cohesive slope demonstrates the accuracy and effectiveness of the proposed approach. The results indicate that even when data are limited, the bivariate distribution of c and φ can be determined and the estimated statistics met the predefined ones well. Satisfying estimations of the mean ( \({\mu }_{FS}\) ${\mu }_{\mathit{FS}}$ ) and standard deviation ( \({\sigma }_{FS}\) ${\sigma }_{\mathit{FS}}$ ) of the factor of safety (FS) and failure probability (P_f) can be obtained. The representative sliding surface with the greatest likelihood is found to approximate the critical one based on the mean values of c and φ. Besides, when the available sample size of geotechnical data exceeds a threshold, stable estimations of the bivariate distribution of c and φ can be obtained, and the estimated \({\mu }_{FS}\) ${\mu }_{\mathit{FS}}$ is stable, while the values of \({\sigma }_{FS}\) ${\sigma }_{\mathit{FS}}$ and P_f synchronously vary within a small range. Applications of the proposed Bayesian bootstrap-Copula coupled method indicate that it can be used to estimate the bivariate distribution of correlated parameters and the reliability of various geotechnical problems based on limited data.