In March 2017, the German Bundestag passed a law concerning the selection of a site for a repository for high-level radioactive waste. This has now been followed up by a report, published late September, on potential locations for a repository in Germany. The law itself calls for a repository that will provide protection against the effects of the waste for a period of one million years. The current approach is to place the waste in underground tunnels, which are then sealed using concrete.
With the search for a repository site now very much back on the agenda, the timing of a joint project by the Institute for Nonlinear Mechanics (INM) and SimTech couldn’t be better. How does concrete behave in nuclear repositories, particularly when it is stored for such a long time? Good question! But what if you can’t answer that question by yourself? You bring in additional expertise to help. And that’s just what the project team has done.
The main question being explored on the project is how concrete behaves in nuclear repositories. In other words, is it possible to ensure an acceptable level of safety when radioactive waste is stored in concrete-sealed underground facilities? There are numerous uncertainties involved, especially if the aim is to make predictions for an extremely long period, such as one million years. Why? Because concrete is quite a new material, which only came into existence in the 19th century and is now completely different to back then. So nobody really knows how concrete behaves over such a long period of time. Does it remain stable? Does it disintegrate or gradually begin to swell? And what about the impact of earthquakes, general geological effects and other factors?
Nowadays, conventional concrete structures are designed to last 30 to 50 years. To verify the lifetime, empirical criteria are used, backed up, if necessary, by periodic inspection. However, traditional methods cannot be applied to the time frames that need to be investigated when assessing the long-term safety of repositories. Consequently, new approaches need to be developed. In addition, scenarios and conditions need to be clearly defined in order to make predictions for such a long period. The project is therefore working on the development of a simulation technique based on the finite element method. This will make it possible to simulate the long-term behavior of concrete – at least to the extent of our knowledge of the material and our ability to record and map its behavior and express it in numerical terms. The scenario defined for the prediction involves observing non-steel-reinforced concrete in a static underground facility (i.e. a facility that is assumed not to alter over time). This is the framework within which the project is investigating how the sealing structure will behave over long periods of time. The pressing question here is with what certainties or uncertainties is it possible to say whether or not the repository will leak? Or, to go a step further, what would we have to know to be able to rule out a failure with sufficient certainty under the assumed conditions?
Now the material modeling and computation phases that followed the two to three years of long-term experiments at the Materials Testing Institute at the University of Stuttgart have been completed, it’s time for Wolfgang Nowak and his team to provide their input. The Department of Stochastic Simulation and Safety Research for Hydrosystems (LS3) at the Institute for Modelling Hydraulic and Environmental Systems offers expertise in data-integrated simulation, uncertainty and reliability analysis and optimal experimental design. As such, it complements the expertise in conceptual, mathematical and numerical materials modeling at the Institute for Nonlinear Mechanics (INM), which is headed by Remco Leine. In particular, the INM is specialized in models with “fractional derivatives” for viscoelastic long-term deformation of concrete. The research project is being managed by André Schmidt (who co-proposed it) along with Matthias Hinze.
“Working with Wolfgang Nowak and his team is a real stroke of luck for us. The comments the reviewers made with regard to uncertainties meant we had to bring appropriate expertise on board. I’m deeply impressed by how well our collaboration with the SimTech team has worked and their dedication and passion, just as I am by the results we’ve achieved so far. I’m also convinced everyone involved can learn a great deal from this interdisciplinary cooperation and expand their horizons in the process,” says Schmidt.
So the goal is to produce an uncertainty analysis for concrete in nuclear repositories and to be able to predict the long-term behavior of concrete. Long-term experiments lasting two to three years are conducted and evaluated using simulation models to investigate the material’s complex behavior. However, long-term experiments of this type are not a reliable means of predicting behavior over a period of a thousand (or several thousand) years. As a result, a precise record of any uncertainties is kept when the experiments are evaluated so that any uncertainties remaining in the predictive model can be clearly identified. The next question to tackle is how strong the uncertainties are. What level of reliability (probability of almost 100%) can be achieved using a safety factor* of 3 or 5? And could long-term experiments with a duration of five to ten years reduce the uncertainties and thus the risks?
“The nice thing is that most of the simulations are in 1D or 2D. That’s ideal for the computations/simulations/uncertainty analyses because the individual calculations are very quick, i.e. milliseconds to just a few seconds. That’s true of the simplest cases at least. It means we can actually apply complex methods that would otherwise be rejected due to extremely long computation periods (i.e. months or years). Normally, a reduction of the model is required before an uncertainty or reliability analysis can be performed or an experiment optimized. But in this case we can really go to town and use fast models to just try out everything we’re researching simultaneously in SimTech and on other projects for (considerably) slower models in order to achieve the same results,” says Wolfgang Nowak, explaining the benefits of the approach.
We will keep you updated about the results of the project.
* A safety factor is always included when designing structures, machinery or other technical equipment. For instance, if a bridge is planned to be able to carry 20t and a safety factor of 3 is applied, the load-bearing capacity is assumed to be 60t and the bridge is planned in such a way that the failure load is 60t. This ensures sufficient leeway before the bridge fails when, for instance, a heavy goods vehicle weighing 25t crosses the bridge or the material only has a load-bearing capacity of 80% due to ageing.