A Bayesian Approach for Uncertainty Quantification in Overcoring Stress Estimation

Abstract

In civil and mining engineering, three-dimensional in situ stress states are commonly measured using overcoring (OC) techniques. With these techniques, stresses are usually estimated by classical least-squares regression analysis of measured OC data. However, the estimated stresses are uncertain and may even be unreliable, due to factors such as rock heterogeneity, measurement errors and inadequacy of the regression model. Quantifying such uncertainty is crucial, as doing so both permits quantitative assessment of the reliability of the measured stress state and facilitates application of probabilistic design approaches in rock engineering such as reliability-based design. The classical approach to OC stress estimation suffers various limitations in this respect, particularly the failure in quantifying uncertainty in estimates of principal stresses, and the inability to improve stress estimation by incorporating stress information from other sources (say, stress states measured at nearby locations and orientation of the major principal stress as determined from observations of borehole breakouts). To overcome these limitations, this paper proposes a novel Bayesian approach to OC data analysis that probabilistically quantifies uncertainty in stress estimations and permits formal incorporation of additional stress information in forms of prior distributions. It also discusses the challenges faced in developing the informative prior distributions that are required to allow incorporation of additional stress information.