Bayesian framework for evaluating spatial distribution of soil liquefaction based on CPT data

The change in density of saturated soil and the critical state reached during shear failure are key to understanding soil liquefaction behaviour, and the state parameter ($\psi$), which is based on the framework of critical state soil mechanics considering the influences of sandy soil compactness and confining stress effects, has significant advantages for soil liquefaction analysis. While assessing the spatial distribution of site's liquefaction potential usually involves the establishment of semi-empirical or stochastic models (e.g., random fields) of $\psi$, whose inherent spatial variability and various uncertainties are unavoidable. In this study, an in-situ $\psi$-based Bayesian updating (ISP-BU) approach was proposed for evaluating the spatial distribution of soil liquefaction potential. It consists of (i) the ISP-BU framework for sequential updating of semi-empirical models and data information obtained from field tests, including site-specific prior knowledge and cone penetration test (CPT) data; (ii) 2D random field interpretation and evaluation of the spatial distribution of liquefaction potential based on sparse in-situ $\psi$ data; and (iii) simultaneously incorporating the spatial variability, uncertainties, and measurement errors in a reasonable and quantifiable manner into the probabilistic characterization of the spatial distribution of liquefaction potential. This study uses real-life CPT measurement data for illustration and validation. The results show that the proposed method is a universal modelling framework and can be widely applied in areas with soil liquefaction potential according to the requirements of different risk projects.