Tools for the prediction of the mechanical behaviour of concrete over long time spans for the safety analysis of locking systems for final repository sites
[Photo: Max Kovalenko]

Creep test with concrete specimens
Creep test with concrete specimens

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.

Micrograph of a salt concrete specimen
Micrograph of a salt concrete specimen

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).

Kooperation mit Prof. Nowak

Basierend auf den entwickelten Materialgesetzen soll abschließend der Einfluss der Unsicherheiten untersucht werden, die sich aus der Streuung der Messergebnisse ergeben. Anders als bei Elastomeren oder metallischen Werkstoffen ist die Bestimmung des Kriechverhaltens von Beton von einer deutlich höheren Varianz gekennzeichnet. Diese lässt sich durch verschiedene äußere Einflussfaktoren erklären, wird aber ganz wesentlich durch die Inhomogenität des Materials bestimmt, durch die kein Probekörper dem anderen gleicht. Damit können auch die Materialparameter nur mit einer entsprechenden Unsicherheit identifiziert werden, wodurch wiederum Simulationsrechnungen über lange Zeiträume zu „unscharfen“ Ergebnissen führen. Den sich daraus ergebenden Fragestellungen wird im Rahmen einer Kooperation mit Prof. Nowak (SimTech) nachgegangen. Über die Zusammenarbeit ist ein Artikel in der Zeitschrift "forschung leben" der Universität Stuttgart erschienen.

Journal articles

  1. Hinze, M., Schmidt, A., & Leine, R. I. (2021). Finite element formulation of fractional constitutive laws using the reformulated infinite state representation. Fractal Fractional, 5(132), Article 132.
  2. Hinze, M., Schmidt, A., & Leine, R. I. (2020). The direct method of Lyapunov for nonlinear dynamical systems with fractional damping. Nonlinear Dynamics, 102, 2017--2037.
  3. Hinze, M., Schmidt, A., & Leine, R. I. (2020). Lyapunov stability of a fractionally damped oscillator with linear (anti-)damping. International Journal of Nonlinear Science and Numerical Simulation, 21(5), Article 5.
  4. Hinze, M., Schmidt, A., & Leine, R. I. (2019). Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation. Fractional Calculus and Applied Analysis, 22(5), Article 5.


  1. Hinze, M., Schmidt, A., & Leine, R. I. (2019). Numerical simulation of fractionally damped mechanical systems using infinite state representation. Proceedings of the 2019 International Conference on Fractional Calculus Theory and Applications (ICFCTA 2019).
  2. Hinze, M., Schmidt, A., & Leine, R. I. (2018). Mechanical representation and stability of dynamical systems containing fractional springpot elements. Proceedings of the ASME 2018 International Design Engineering Technical Conferences (IDETC2018), DETC2018-85146, Article DETC2018-85146.


This image shows Remco I. Leine

Remco I. Leine

Prof. Dr. ir. habil.

Director of the Institute for Nonlinear Mechanics

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