A Bayesian regression analysis of in situ stress using overcoring data

Abstract

Characterising the state of in situ stress at a target depth is crucial for all underground engineering projects. Consequently, on critical projects such as nuclear waste repositories extensive campaigns are implemented with the goal of estimating the in situ stress state. These campaigns often comprise both direct measurement and indirect estimation methods, but the data obtained across a project volume may exhibit significant variability. This poses significant challenges in both quantifying the variability and uncertainty of in situ stress, and determining the stress state to be used for design purposes. It is often assumed that the state of in situ stress increases linearly with depth, and thus linear regression of principal stress magnitude against depth are often found in the literature. As such methods not honouring the tensorial nature of stress are, strictly, incorrect. To show how this limitation may be overcome, here we present a Bayesian regression analysis of in situ stress with depth that uses the Cartesian stress tensor. The analysis is performed using over 100 overcoring data obtained at the SKB Forsmark site in Sweden. A comparison between the customary and Bayesian approaches is presented, which shows the superiority of the tensorial technique.