Development of Bayesian Approaches for Uncertainty Quantification in In Situ Stress Estimation

Knowledge of the in situ stress state is crucial for a wide range of rock mechanics applications, but stress estimation at different scales may be unreliable due to various sources of uncertainty. It is therefore critical to be able to probabilistically quantify uncertainty in stress estimation, as it both permits quantitative assessment of the reliability of stress estimations and facilitates application of the more rational probabilistic design in rock engineering. There is also a crucial need for logically incorporating stress information from other sources in order to obtain more reliable stress estimations. This thesis makes contributions of developing novel Bayesian approaches for probabilistic uncertainty quantification in stress estimation at the measurement and local scales and demonstrating how additional stress information can be incorporated for improved stress estimation. The work begins by discussing major sources of uncertainty in stress estimation and why Bayesian approaches are appropriate for uncertainty quantification. Following this, a principal contribution is made by proposing a statistical simulation approach that provides insights into the common question during local stress field estimation: how many stress measurements are required in order to obtain a reliable mean stress estimate? Then, a principal contribution is made by presenting a Bayesian multivariate model that can probabilistically quantify uncertainty in local stress field estimation; importantly this model allows rigorous quantification of uncertainty in principal stresses and formal incorporation of additional stress information through informative priors. Subsequently, a principal contribution is made by presenting a Bayesian regression model that can probabilistically quantify uncertainty in overcoring stress estimation. We demonstrate how this model can overcome two critical limitations of the classical approach to overcoring stress estimation. After this, a principal contribution is made by presenting a powerful Bayesian hierarchical regression model for analysis of multiple overcoring tests that can simultaneously quantify uncertainty in overcoring stress estimation and local stress field estimation. We show that this hierarchical model can give improved stress estimation for each individual overcoring test by borrowing information from the other tests and can account for uncertainties in these individual tests to give a more reasonable estimation of uncertainty in the mean stress.Ph.D