Abstract: In the geotechnical engineering reliability analysis and design, it is very difficult to accurately select the random field parameters and the correlation function, and to accurately describe the spatial variability of soil parameters. Based on Bayesian theory, this paper presents a method to quantify the spatial variability of effective internal friction angle of sand. A proper correlation function using prior knowledge and cone penetration test (CPT) data are used to determine the random field parameters and the correlation function of the effective internal friction angle of sand by the method. This method takes reasonable account of the uncertainty of the empirical regression equation between the effective internal friction angle and the cone resistance. Markov chain Monte Carlo simulation (MCMCS) method is applied in this paper to generate random samples following the posterior distribution. The MCMCS samples are used to calculate the posterior distribution by a Gaussian Copula-based method. Then, the plausibility of a candidate correlation function is obtained and the most probable correlation function is selected. Finally, the proposed approaches are illustrated and validated by using real-life CPT data obtained from NGES at Texas A&M University. It is shown that the proposed approaches can, correctly and reasonably, determine the random field parameters and correlation function of sand effective friction angle by using the indirect CPT data. It is possible to accurately describe the spatial variability of sand effective friction angle. The correlation function of effective friction angle at the sand site of NGES at Texas A&M University is second-order Markov correlation function.

Key words: spatial variability, effective friction angle, cone penetration test, Bayesian theory, Markov Chain Monte Carlo Simulation, Gaussian Copula