Development of Bayesian Probabilistic Methods and Application for Estimation of Engineering Properties of Soil

Abstract

The estimation of geotechnical properties is an important step in solving geotechnical engineering problems. It is well recognized that variabilities and uncertainties are inevitable during the estimation of geotechnical properties. In recent years, probability and statistics have been increasingly used to characterize these uncertainties. Moreover, several probability-based analysis methods and design codes have been developed that require probabilistic estimations of geotechnical properties. These estimations require large amounts of observation data, but the data available from site investigations are often limited. To address this problem, a Bayesian equivalent sample method was recently developed. However, its detailed formulations vary for various geotechnical properties and most geotechnical practitioners who do not have an extensive background in probability, statistics, and simulation algorithms face mathematical hurdle in applying it. It also remains a difficult task to characterize the cross-correlation between geotechnical properties due to limited observation data. In addition, the estimation of spatially varying geotechnical properties at unobserved locations is a difficult task, because of the sparse observation data usually available in practice. Furthermore, the development of empirical curves to estimate dynamic properties of soil has become a challenging task due to the mismatch between new test results and numerous pre-existing curves that are available for use. This study aims to address these challenges associated with the estimation of geotechnical properties through the development of Bayesian approaches and software for the probabilistic characterization of geotechnical properties and probabilistic site response analysis.

A Bayesian approach is developed to probabilistically characterize the cross-correlation between two correlated geotechnical properties. The approach uses a Bayesian framework to integrate site observation data with prior knowledge. When only a limited number of data regarding two correlated geotechnical properties (e.g., effective cohesion, c', and effective friction angle, ϕ' of soil) is available from a site, the Bayesian framework is integrated with Markov chain Monte Carlo (MCMC) simulation to generate a large number of sample pairs of the properties whose cross-correlation is of interest. The approach is illustrated and validated with several sets of real observation data. The approach is shown to provide proper probabilistic characterization of the cross-correlation between two geotechnical properties.

Furthermore, a Bayesian approach is developed in this study to construct and compare normalized modulus reduction curves for dynamic properties of soil. The approach starts with the identification of model parameters through a Bayesian framework that also evaluates parameter and model uncertainties. Next, the approach selects the most appropriate model among available candidate models based on the evaluated model parameters and uncertainties. Subsequently, the Bayesian framework is integrated with MCMC simulation to generate a large sequence of parameter samples, which are used to construct the best fitted normalized modulus reduction curve and its confidence interval. This approach is illustrated with real life observation data, and is found to perform satisfactorily well.

A user-friendly software is also developed to remove the mathematical hurdle involved in obtaining probabilistic estimations of geotechnical properties for geotechnical practitioners. The software implements the Bayesian equivalent sample method, which probabilistically integrates limited observation data with prior knowledge and uses MCMC simulation to transform the integrated knowledge into a large number of equivalent samples of geotechnical properties of interest. It provides a convenient toolkit to obtain reasonable probabilistic estimations of geotechnical properties from limited data. The software is demonstrated and validated through examples of soil and rock property characterizations.

Finally, a comparative study is conducted among interpolation methods to address the challenge of estimating geotechnical properties at unobserved locations when only sparse data is available. Using simulated and real-life data, the comparative study evaluates the performance and suitability of the interpolation methods for sparse geotechnical data.

Date of Award	8 Aug 2017
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Yu WANG (Supervisor)