In search of appropriate repositories for radioactive waste from nuclear power plants, disused rock salt mines are considered. A safe inclusion of the radioactive material requires the salt mines to be closed hermetically, which is realized by the use of salt concrete for which a limited crack growth for long timescales has to be guaranteed. Since conventional concrete structures are designed for a lifetime of 30 to 50 years, new approaches are necessary to model the respective material properties under given mechanical loading conditions where the constitutive behavior is influenced by aging as well as by creep and relaxation processes on long time-scales.
The project “ProVerB” aims to develop material models for long time-scales using fractional calculus, i.e. derivatives of non-integer order with respect to time. Moreover, in contrast to existing approaches, the aging processes will be described by a time-dependent order of derivative. The resulting constitutive equations will be used in finite element simulations in order to calculate the deformation processes of concrete structures. A verification of the methodology is realized by comparison with experimental data from creep and relaxation tests with concrete samples.
The project “ProVerB” is conducted in cooperation with the Materials Testing Institute of the University of Stuttgart (MPA) and the engineering company GNS in Brunswick. It is supported by a subsidiary of the BGE, the federal company for radioactive waste disposal. Creep tests with salt concrete specimens, which are needed to validate material models, are carried out by the MPA. The GNS designs and implements efficient algorithms to integrate the models into a commercial engineering finite element software. The project is funded by the program “KMU-innovativ” of the German Federal Ministry of Education and Research (Grant No. 01IS17096).
Cooperation with Prof. Nowak
Finally, since the measurements are governed by a significant variance, the impact of the resulting uncertainties on the constitutive equations shall be examined. In contrast to elastomers or metals, the determination of the concrete’s creep behavior is characterized by a much higher variance. Aside from various external factors, this is mainly determined by the inhomogeneity of the material, with no two samples being the same. Thus, the identification of the material parameters also goes along with respective uncertainties, which in turn leads to ‘fuzzy‘ simulation results in calculations over long periods of time. The questions and problems that arise from this fact are investigated in the framework of a cooperation with Prof. Nowak (SimTech department). An article about the cooperation was published in the magazine "forschung leben" by the University of Stuttgart.
Hinze, M., Schmidt, A. and Leine, R.I.: "Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation", in Fractional Calculus and Applied Analysis, Vol. 22(5), pp. 1321-1350, 2019. PDF, Link
Hinze, M., Schmidt, A. and Leine, R.I.: "Numerical Simulation of Fractionally Damped Mechanical Systems Using Infinite State Representation", Proceedings of the 2019 International Conference on Fractional Calculus Theory and Applications, Bourges, France, 2019. PDF