Bayesian updating of geotechnical parameters with polynomial chaos Kriging model and Gibbs sampling

Abstract

Due to the complex nature of site conditions and the influence of deposition conditions, aging, environmental exposure, and characterization techniques, the calibration of geotechnical parameters is significantly uncertain. The present study introduces a Bayesian updating method for geotechnical parameters to address the issues of parameter uncertainty and incomplete parameter information. Developed by combining a high-fidelity Polynomial Chaos Kriging (PC-Kriging) model with the Gibbs sampling method, this approach uses Least Angle Regression (LAR) to construct the Polynomial Chaos Expansion (PCE) coefficients, incorporating PCE as the trend function in the Kriging method to build the PC-Kriging model. The proposed method can avoid the computational challenges involved in Bayesian inference using dense numerical models, effectively reducing computational costs while obtaining the posterior distribution and statistical information of the model. This study primarily applies the proposed PC-Kriging-Gibbs (PCK-Gibbs) method to geotechnical engineering issues. The method is validated on two critical dynamic soil problems: Horizontal-to-vertical spectral ratio (HVSR) inversion and equivalent linearization in site response analysis. Meanwhile, the Kriging method and PCE were also used to verify the feasibility and computational efficiency of the proposed method. The posterior distribution samples of the model parameters obtained show good consistency between the sample means and actual values, significantly reducing the uncertainty of shear wave velocity. Compared to Bayesian inference analysis using only the Gibbs method, the proposed method dramatically decreases computation time while maintaining satisfactory results, providing a powerful computational tool for parameter updating in geotechnical engineering.