Bayesian probabilistic characterization of the shear-wave velocity combining the cone penetration test and standard penetration test

The shear-wave velocity VS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{S}$$\end{document} a crucial parameter for determining small-strain soil stiffness characteristics and site classification. However, directly measuring VS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{S}$$\end{document} in the field can be challenging, and requires specific equipment. As a result, researchers have conducted numerous studies on VS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{S}$$\end{document} correlation, and extensive research has demonstrated that the results from cone penetration test (CPT) and standard penetration test (SPT) data are strongly related to the shear-wave velocity. Due to the uncertainty of the transformation model, the accuracy of the VS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{S}$$\end{document} derived from the empirical equations are unsatisfactory. The purpose of the present paper is to propose a Bayesian framework for determining the probabilistic characteristics of VS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{S}$$\end{document} while considering the transformation uncertainty. The Bayesian framework considers both the in-situ test data (SPT, CPT) and prior information, and the results show that the framework considering two in-situ tests accurately predicts the shear-wave velocity. There are several advantages of using the Bayesian method described in this study: (1) The Bayesian framework incorporates both the inherent uncertainty of the shear-wave velocity and the transformation uncertainty. (2) Prior information and field data can be combined to improve the accuracy of predictions. (3) In the framework, the statistical characteristics of VS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{S}$$\end{document} can be ascertained from small samples of field test data.