Hierarchical Bayesian modeling to quantify fracture limit uncertainty of high-burnup advanced fuel cladding tubes under loss-of-coolant accident conditions

For realizing a highly reliable fracture limit evaluation of fuel cladding tubes during loss-of-coolant accidents (LOCAs) in light-water reactors, we developed a method to quantify the fracture limit uncertainty of highburnup advanced fuel cladding tubes. This method employs a hierarchical Bayesian model that can quantify uncertainty even with limited experimental data. The hierarchical Bayesian model was an extended version of the fracture probability estimation model developed in our previous study. The fracture limit uncertainty was quantified as a probability using the amount of oxidation (Equivalent cladding reacted: ECR) and the initial hydrogen concentration (the hydrogen concentration in the fuel cladding tubes before the LOCA-simulated tests) as explanatory variables. We divided the regression coefficients of this model into a hierarchical structure with an overall average term common to all types of fuel cladding tubes and a term representing differences among various types of fuel cladding tubes. This hierarchical structure enabled us to quantify the fracture limit uncertainty through the effective use of prior knowledge and data, even for high-burnup advanced fuel cladding tubes with a small number of data points. The fracture limits representing a 5% fracture probability with 95% confidence of the high-burnup advanced fuel cladding tubes evaluated by the hierarchical Bayesian model were higher than 15% ECR for the initial hydrogen concentrations of up to 700-900 wtppm and restraint loads below 535 N. These fracture limits were comparable to the limit of the unirradiated Zircaloy-4 cladding tube, indicating that the burnup extension and use of the advanced fuel cladding tubes do not significantly lower the fracture limit of fuel cladding tubes. Further, we proposed a method to reduce the fracture limit uncertainty by using non-binary data, instead of the binary data, depending on the condition of the fuel cladding tube specimens after performing the LOCA-simulated test, thereby increasing the amount of information in the data.