Quantification of statistical uncertainties of unconfined compressive strength of rock using Bayesian learning method

Abstract

ABSTRACT Due to the sparse data in geotechnical site investigation, statistical characteristics of geo-material properties generally have more or less uncertainties, such as the unconfined compressive strength (UCS) of rock. Based on a site investigation report in Bukit Timah Granite (BTG) formation in Singapore, this paper presented a set of database about UCS from four sites in BTG formation. Subsequently, Bayesian method was applied to quantitatively evaluate the uncertainties of statistical characteristics including the mean, variance, and scale of fluctuation (SOF) of UCS of BTG rocks making use of the available test data. To overcome the limitation of complex analytical solutions, Markov Chain Monte Carlo (MCMC) algorithm is adopted to perform the sampling procedure to obtain the equivalent samples, namely Bayesian-based MCMC method. The results show that the proposed method can be effectively used to quantify the statistical uncertainties and the statistical uncertainties of these three statistical characteristics of BTG rocks are significant. Besides, it is found that the evaluated uncertainties of statistical characteristics to some extent rely on the selection of basic parameters (overall basic parameters or basic parameters of each site) as well as the autocorrelation function (ACF) classes.