^{1}, Francesco Di Maio

^{2}and Enrico Zio

^{3,4,5}

^{1}Politecnico di Milano, Italy. Aalto University, Finland.

^{2}Energy Department, Politecnico di Milano, Italy.

^{3}Energy Department, Politecnico di Milano, Italy.

^{4}MINES ParisTech/PSL Universit Paris, Centre de Recherche sur les Risques et les Crises (CRC), Sophia Antipolis, France.

^{5}Eminent Scholar, Department of Nuclear Engineering, Kyung Hee University, South Korea.

Bayesian networks can be used for the risk assessment of nuclear waste repositories by (i) modeling the causal relations among the set of Features, Events and Processes (FEPs), such as water flows and chemical concentrations, and (ii) calculating the probability that a safety threshold, e.g., on the radionuclide discharge to the environment, is violated. An important outcome of the safety assessment is also the identification of critical paths (i.e., particular combinations of FEP states) leading to such violations. To address this problem, we propose a recursive unsupervised procedure, based on spectral clustering and fuzzy-c-means, for generating mutually exclusive collectively exhaustive clusters of paths covering the possible system states. Then, the probability of each path conditioned on the violation of the safety threshold is evaluated to identify the most critical paths. The procedure is applied to an illustrative deep geological repository.