Probabilistic estimation of variogram parameters of geotechnical properties with a trend based on Bayesian inference using Markov chain Monte Carlo simulation

ABSTRACT

When geotechnical properties show a trend with spatial coordinates, estimation of a variogram model is a challenging task. In the previous studies, the trend-removal method based on ordinary least-squares approach has been commonly used. However, the obtained variogram is biased because the residuals are assumed to be statistically independent. In this study, the ability of Bayesian inference using Markov chain Monte Carlo (MCMC) simulation to estimate the variogram of geotechnical properties with a trend is explored using cone penetration resistance (q_c) data of piezocone penetration tests (CPTU). The results show that the Bayesian inference method can estimate variogram parameters and the coefficients of trend function accurately. Based on the posterior variogram models, the predictive uncertainty and total uncertainty bounds are presented using kriging and sequential Gaussian simulation (SGS) methods. 96% validation points lie within the 95% confidence intervals of the total uncertainty based on 200 measurements of q_c at NS31. The median and mean SSD of the prediction are 0.34 and 0.87, which is closer to the SSD criterion than the trend-removal method. The model uncertainty of the variograms, the predictive and total uncertainty of prediction all decrease as the sampling density increases at NS31 and NS12.

KEYWORDS:

• Spatial variability
• trend
• variogram
• Bayesian inference
• Markov chain Monte Carlo simulation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work in this paper was supported by the Natural Science Foundation of China (Project No. 51679135, No. 51979158, No. 51639008 and No. 51422905 ) and the Program of Shanghai Academic Research Leader by Science and Technology Commission of Shanghai Municipality (Project No. 19XD1421900).