Quantifying uncertainty of in situ horizontal stress and geotechnical parameters using a Bayesian inference approach for pressuremeter tests

Understanding in situ horizontal stress is crucial for various applications in deep ground, including oil drilling, hydraulic fracturing, and nuclear waste repository design. The pressuremeter has gained increasing attention as a tool for characterizing in situ stress fields and engineering properties of soil and rock. However, quantifying the uncertainties associated with in situ horizontal stress and geotechnical parameters remains a challenging task. In this study, we propose a Bayesian inference approach formulated by an objective function that calculates the logarithm of the probability density function using observed and predicted data to address this problem. This approach integrates the analytical solution and the finite-difference numerical model into the Bayesian model. The Bayesian inference approach consists of two phases: (1) using the maximum a posteriori method for point estimation, and (2) employing Markov chain Monte Carlo sampling to obtain parameter statistics from posterior distributions. Compared to frequentist statistical methods, the Bayesian inference approach provides a natural way to incorporate prior knowledge, update our beliefs by conditioning on the observed data, and facilitate exploratory analysis of Bayesian models with various diagnostic tools. This provides a robust and adaptable framework for addressing uncertainty in the study of in situ stress fields and geotechnical parameters using the pressuremeter.