Thermal design criteria computation using various statistical approaches – Application to a SFR fuel element

•The thermal design criteria of fuel melting margin is assessed for an SFR fuel element.•Uncertainties are considered for the vast majority of parameters.•Analytical method, Monte-Carlo simulations and FORM/SORM reliability methods are used.•A coupling between GERMINAL and LICOS is used.•Fuel geometrical defects are taken into account using a 3D thermomechanical model. In the framework of the Generation IV research and development project, in which the French Commission of Alternative and Atomic Energies (CEA) is involved, a main objective for the design of Sodium-cooled Fast Reactor (SFR) is to meet the safety criteria. Design margins must be defined with the utmost accuracy. The design criterion considered here is the fuel melting margin in nominal operation conditions, which is given by the melting probability. Oxide fuel temperature and melting temperature are calculated with CEA dedicated fuel codes from the PLEIADES platform. A computation scheme coupling GERMINAL for entire fuel pin with a preliminary 3D thermomechanical modeling using LICOS for taking into account geometrical defects is developed. Results could be dependent on parameters like manufacturing processes, irradiation conditions and fuel behavior laws. The main goal of this paper is to quantify the uncertainties associated to these parameters in the melting margin evaluation and to quantify their influences and their sensitivities in order to improve the determination of the melting margin. After describing uncertain parameters by an appropriate distribution, uncertainty propagation is done using the URANIE platform, which is also used to create metamodels, a multi-linear regression and an artificial neural network. The result of sensitivity analysis shows that the melting margin is depending on the linear heat rate first, stoichiometry and initial gap after. Geometrical defects as the fuel pellet off-centering within the clad, which need a 3D thermomechanical model, has as well a non-negligible effect. Finally, melting probability obtained with Monte-Carlo simulations is compared to an analytical method and to FORM/SORM reliability methods.