Bayesian partial pooling to reduce uncertainty in overcoring rock stress estimation

Abstract

The state of in situ stress is a crucial parameter in subsurface engineering, especially for critical projects like nuclear waste repository. As one of the two ISRM suggested methods, the overcoring (OC) method is widely used to estimate the full stress tensors in rocks by independent regression analysis of the data from each OC test. However, such customary independent analysis of individual OC tests, known as no pooling, is liable to yield unreliable test-specific stress estimates due to various uncertainty sources involved in the OC method. To address this problem, a practical and no-cost solution is considered by incorporating into OC data analysis additional information implied within adjacent OC tests, which are usually available in OC measurement campaigns. Hence, this paper presents a Bayesian partial pooling (hierarchical) model for combined analysis of adjacent OC tests. We performed five case studies using OC test data made at a nuclear waste repository research site of Sweden. The results demonstrate that partial pooling of adjacent OC tests indeed allows borrowing of information across adjacent tests, and yields improved stress tensor estimates with reduced uncertainties simultaneously for all individual tests than they are independently analysed as no pooling, particularly for those unreliable no pooling stress estimates. A further model comparison shows that the partial pooling model also gives better predictive performance, and thus confirms that the information borrowed across adjacent OC tests is relevant and effective.

Keywords

• Overcoring stress measurement
• Uncertainty reduction
• Partial pooling
• Bayesian hierarchical model
• Nuclear waste repository