Application of Bayesian Inference to the Inspection of Bentonite Layer in Radioactive Waste Disposal Facilities: Method to Evaluate the Uncertainty of Macroscopic Permeability Coefficient

In this paper, we propose a method to quantify the uncertainty of the macroscopic permeability coefficient (permeability coefficient of a bentonite layer as a whole), an inspection indicator of the low permeability of bentonite layers in radioactive waste disposal facilities, based on a Bayesian inference method. The Bayesian inference method makes it possible to evaluate the probability that the estimated macroscopic permeability coefficient of the bentonite layer after construction will satisfy a criterion of the macroscopic permeability coefficient by expressing statistical values such as the mean and standard deviation as a probability distribution. This explicitly explains the conservatism contained in the estimated macroscopic permeability coefficient. Furthermore, by utilizing the proposed method, we reasonably determine the sample size for the microscopic permeability coefficient (permeability coefficient obtained from laboratory permeability tests using undisturbed samples collected locally from the bentonite layer) required for inspecting the bentonite layer. This method can potentially provide a more fully underpinned justification for sampling plans and inspection results on a statistical basis, compared with classical frequentist statistical methods such as the maximum likelihood estimation method.