The paper is devoted to the use of mathematical modelling for analysis of the thermo-mechanical (T-M) phenomena, which are relevant for the assessment of underground repositories of the spent nuclear fuel. Particularly, two model problems are analysed concerning the Swedish KBS3 concept and its realization in Aspo prototype repository and a concept of underground interim storage Skalka in the Czech Republic. We shall discuss the formulation, numerical methods, computer implementation and describe some computed results and computing experience. The Aspo prototype repository model serves as an example of large-scale 3D modelling with the time scale 50 years and space discretization with about 2.5 and 7.5 million of degrees of freedom for the temperatures and displacements, respectively. The Skalka model shows modelling with the presence of more complicated heat transfer mechanisms.
The problem of storage of the spent nuclear fuel (SNF) is extremely important for both the environment protection and further development of the nuclear energy utilization. The deposition of the nuclear waste (NW) in underground repositories is one of possible final solutions, which is most realistic with respect to the nowadays technology. The design of a safe underground deposition of the SNF from nuclear power stations requires careful study of the repository construction, reliability of the protecting barriers between SNF and the environment and study of all kinds of risks related to the behaviour of the whole repository system. For the assessment of the repository performance, it is fundamental to be able to do large-scale computer simulations of various coupled processes as heat transfer, mechanical behaviour, water and gas flow and chemical processes in rocks and water solutions. Generally, we speak about T-H-M-C processes and their modelling. These processes are coupled, but only some of the couplings are crucial for a reliable mathematical modelling, see Figure 1.
In this paper, we restrict to modelling of T-M processes with a one-directional coupling via thermal expansion term in the constitutive relations.
(Figure in full paper)
Generally, there are many different concepts of SNF repositories, which were developed in Sweden, Germany, Belgium, US etc. for NW deposition in granite rocks, salt, clay etc. We select two concepts - Swedish KBS-3V and Czech interim repository Skalka - as examples of projects interesting from the point of view of NW storage in the Czech Republic (cf. Brewitz 2004). Note that from the point of view of modelling, the different concepts share many similar aspects (Stephansson 1996,2001) and e.g. modelling of the heat loading for Skalka repository is similar to modelling of an early stage (no backfill) in the US Yucca Mountain project.
The Aspo Prototype Repository is an internationally recognised project located at the Aspo Hard Rock Laboratory in Sweden. It represents a full scale experiment following the KBS-3 concept and investigating the performance of engineered barriers and the surrounding rock (Svemar & Pusch 2000).