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Repositories in deep clay geological formations are considered one of the most promising solutions for a sustainable management of High Level radioactive Waste (HLW). The Swiss HLW disposal concept consists in horizontal tunnels excavated at high depth in strongly over consolidated clay (Opalinus Clay) where Granular Bentonite is chosen for enclosing steel canisters containing the waste. This paper presents the theoretical approach and the research activities aiming at investigating the behaviour of this material. An elasto-plastic constitutive model taking into account coupled processes of stress, capillary pressure, and temperature is used. In this framework, from an experimental point of view, an exhaustive characterization is necessary in order to calibrate required parameters and to validate the model. Laboratory tests designed for this purpose are described. Particular attention is paid in investigating the swelling behaviour, which is among the features that distinguish materials potentially usable in nuclear waste disposals. First results confirm indeed that the chosen bentonite shows a natural and remarkable swelling attitude.