Theoretical Investigation on New Analyzing Procedure of Anelastic Strain Recovery Method for Stress Measurements based on Bayesian Statistical Modeling

Abstract

One of the problems of in-situ stress measurements is that they cannot determine the uncertainty of the results. In this study, we propose a new analyzing procedure of anelastic strain recovery (ASR) method, one of the in-situ stress measurements, enabling us to conduct uncertainty quantification (UQ) based on Bayesian statistical modeling (BSM). This research consists of two stages. In the first stage, reported in this paper, we construct a new procedure and apply it to simulated ASR data to investigate its characteristics. In the second stage, we will examine its applicability using real ASR data. The new procedure consists of the following three steps: i) measuring the ASR of a rock core sample with strain gauges, ii) applying a probability model based on BSM to the measured ASR data and simulating the probability densities of the elements of an in-situ stress tensor and other parameters, iii) regarding the probability densities as the results of in-situ stress measurements with uncertainty. This paper shows the results obtained by the new procedure applied to simulated ASR data. The results show that the uncertainties of some parameters reduce by giving the elastic moduli. On the other hand, the rates of decrease in the uncertainties vary for each parameter. To reveal the cause of these differences, we introduce a new evaluation item of Sobol’ indices, one of the global sensitivity analyses, and make quantitative discussion.