A million years – that's the period of time that underground radioactive waste repositories are supposed to be safe for according to the German Repository Site Selection Act (StandAG). Those areas in Germany that may be used as nuclear waste repositories were made public in the autumn of 2020: there are 90 locations, including salt mines, clay layers or granite, that are suitable in principle from a geological perspective. The first radioactive waste containers are to be deposited starting in 2050, but how can these storage sites really be hermetically sealed over such a long period of time
When even the most suitable geological formations, in which the underground repositories will one day be placed, contain cavities. The idea based on current state of technology is to use concrete closure systems – so-called dams and plugs – to seal them off once the nuclear waste has been deposited. However concrete is a new material that has only been around since the 19th century; nobody knows if it is really suitable for sealing mineshafts or how it will behave throughout a million years. Will the concrete remain stable? And what impact will geological effects and other influences have?
To answer these questions, the University of Stuttgart’s Institute for Nonlinear Mechanics (INM), Materials Testing Institute and the Gesellschaft für Numerische Simulation (GNS mbH) have joined forces in the collaborative ProVerB research project. "Predictive tools for the mechanical behavior of concrete over long periods of time for the safety analysis of closure systems for nuclear waste repositories” (ProVerB) research project. This project, which has been approved by the German Federal Ministry of Education and Research (BMBF), is receiving close collaboration from the German Federal Company for Radioactive Waste Disposal (BGE).
Generally speaking, this branch of science is not well known.Dr. André Schmidt
The core competencies of the applicants include conceptual, mathematical and numerical material modelling with a focus on models with so-called "fractional coefficients" for viscoelastic materials. "Generally speaking, this branch of science is not well known," as project leader Dr. André Schmidt from the INM explains: "Using fractional coefficients to describe long-term deformation behavior opens up new function classes that are particularly well suited to long-term modeling."
Traditional methods of estimation do not work
The currently expected service life for conventional concrete structures is 30 to 50 years. Empirical criteria and, where appropriate, regular inspections are used for verification purposes. "However," as Prof. Kai Diethelm explains, "traditional approaches cannot be applied to the temporal scale that needs to be taken into account to estimate the long-term safety of nuclear waste repositories. new methods need to be developed." In addition to his work for the GNS, Diethelm holds the professorship for mathematics and applied computer science at the University of Applied Sciences Würzburg-Schweinfurt, which is also participating in the project.
The researchers are developing a simulation technique based on the finite element method within the context of the ProVerB project, which will then be able to be used to simulate any scenario providing that the behavior of the material in question can be measured, described, and numerically mapped. Certain clearly defined assumptions have to be made to demonstrate the long-term safety required by law. “One first has to consider non reinforced concrete,” says Schmidt explaining the scenario established for the prediction: "so not reinforced with steel, in a static mineshaft, i.e., assumed to be invariable over time. Under these conditions, we study the behavior of the sealing structure over long periods of time."
This is where the question arises as to the certainty with which statements can be made about whether the nuclear repository will remain sealed or not. Schmidt puts it more precisely: "the broader question is what knowledge would one need to rule out failure with a reasonable degree of certainty under the given assumptions?"
To answer this question, the project partners also called on the expertise of a team led by Prof. Wolfgang Nowak Director of the Institute for Modelling Hydraulic and Environmental Systems (IWS) and Head of Research at the Simulation Technology (SimTech) Cluster of Excellence who also holds the Chair of Stochastic Simulation and Hydrosystem Safety Studies. Nowak specializes in data-integrated simulation, uncertainty and reliability analyses, and optimized experimentation design. Uncertainty analyses are required for the prediction of the complex long-term behavior of concrete.
To date, simulation models have been used in the evaluation of long-term experiments lasting up to three years, but this approach is far too uncertain for predictions of periods of thousands of years. "This is why we record the tiniest uncertainties when analyzing the experiments to enable us to quantify the remaining uncertainties within the prediction mode in an extremely precise manner," Nowak explains. The question then focuses on the size of these uncertainties: what level of certainty (i.e., probabilities converging 100 percent) could be achieved by tripling or quadrupling the safety factor? And could long-term experiments of five to ten years reduce the uncertainties and the associated risks?
"The good thing is that most simulations are one- or two-dimensional," Nowak explains: "this provides optimal conditions for the calculations, simulations and uncertainty analyses, because the individual calculations can be carried out extremely rapidly in just milliseconds to a few seconds, at least for the very simple cases." This enables the researchers to use elaborate methods that would otherwise not be feasible because they would require months, if not years, of computing time. Normally, a model reduction always has to be made for tasks such as this. "But in this case,” Nowak explains “we can bring out the big guns, in other words statistical methods that require millions of simulation runs, and with no upstream model reduction, which means that we can use rapid models to test out all the things we're researching in SimTech and other projects for slower, larger simulations."
The end goal of this interdisciplinary project is to have a flexibly applicable simulation tool combined with a methodology for measuring uncertainties for use in long-term analyses and from which recommendations could be derived for such things as the duration of long-term experiments to exclude any potential failure of the closure system with a sufficient degree of certainty.
Editors: Sabine Sämisch/Andrea Mayer-Grenu
Prof. Wolfgang Nowak, Institute for Modelling Hydraulic and Environmental Systems (IWS)
phone: +49 711 685 60113