Abedulgader Baktheer
Mies-van-der-Rohe-Str. 1
Hall G, Room 104
52074 Aachen

Tel.: +49 (0) 241 80-28569
Fax: +49 (0) 241 80-22055

Motivation and objectives

Reinforced concrete and pre-stressed concrete will become increasingly important in the future for the construction of towers and grounding of on- and offshore wind turbines. Wind turbines are structures exposed to cyclic loads with a very high number of load cycles (N>107). Reinforced concrete and pre-stressed concrete construction possess many advantages with respect to the costs of production and maintenance compared to steel construction. Prefabrication and improved transportability of precast concrete components enable the efficient realization of wind turbines with capacities of up to 2 MW and hub heights of more than 100 m [1].

Due to the advanced development as well as to ensure an economic and reliable construction, it is necessary to revise the existing design concept. Furthermore, there are only insufficient basic findings on the fatigue behavior of concrete and the damage mechanisms taking place in concrete under fatigue loading [2].

Due to the large number of required investigations, several research institutes are involved in the collaborative research project WinConFat. In addition to seven university institutes, the "Bundesanstalt für Materialforschung und -prüfung", the "Deutsche Beton- und Bautechnik-Verein" and the "Deutsche Ausschuss für Stahlbeton" are also involved. The IMB is responsible for two work packages.


Variable amplitudes and loading sequence-effects

The main objective of the work package "Variable amplitudes and loading sequence-effects" is on the one hand the verification of existing models for the estimation of the fatigue behavior and on the other the further development of modelling approaches able to detect the elementary damage effects under cyclic loading. Because of the high experimental effort and non-linear relationships, further development and improvement of the existing models are required, particularly for the reproduction of sequence effects. For this purpose, a combined experimental and numerical methodology is implemented, as illustrated in Figure (1). Based on this, a systematic characterization of concrete formulations in terms of compressive threshold stress will be possible in the future with significantly less effort.

As part of the experimental investigations, tests are conducted with concrete cylinders. For the different experiments four load scenarios (LS1 - LS4) were compiled to analyze different stages of load, from static to cyclic to fatigue tests.

On the basis of the conducted experiments the model approaches are calibrated, further developed and subsequently validated. Finally an engineering model can be derived that is able to realistically predict the concrete fatigue behavior under variable amplitudes and sequence-effects.


Figure 1: Combined numerical and experimental method

Different modeling approaches will be used to simulate the fatigue behavior of concrete cylinder specimens under compressive loading. The first approach is based on the concept of "equal damage for equal work" (Pfanner, 2003) [3]. Here the fatigue behavior is considered as a function of the number of cycles. The second approach is based on fatigue damage driven by an equivalent tensile strain measure modeling the specimen behavior cycle by cycle (Alliche, 2004) [4]. Furthermore, an innovative fatigue microplane model based on a cumulative measure of shear strains will be developed. In Figure (2a), the dissipative mechanisms of the microplane fatigue model are illustrated. An elementary study of the model behavior under monotonic and cyclic loading is depicted in Figure (2b).


Figure 2: Microplane fatigue model: a) dissipative mechanisms; b) Elementary study of the model behavior.


Bond behavior under Very-high-cycle fatigue

Bond standards between reinforcement and concrete were not developed for the very-high-cycle-fatigue range (N> 107). Therefore the use of reinforced concrete in carrying structures exposed to a very high number of load cycles (e.g. wind turbines) is restricted. The objective of the work package "Very-high-cycle bond fatigue behavior" is to develop design proposals and construction rules to ensure the bond between reinforcement and concrete even at a very high number of load cycles.

Experimental investigation of composite resistance are performed by using beam-end tests. Based on low amplitudes with a high number of load cycles, the influence of load level on the bond-slip behavior shall be analyzed. Subsequently, the differential equation of bond-slip can be solved by the bond-slip behavior observed in the experiments.

The load-bearing effect of compression rods differs from tension rods primarily in an additional force transfer over the end bearing (Figure 3, right). The proportion of the stress in the bars transferred by end bearing and concrete compression struts is between 20 % und 40 %. Overlapping connections of bars can lead to a degradation of the concrete as a result of tensile stresses. In order to investigate the influence of end bearing, a modified beam-end test is used to ensure a prevention of the end bearing.

A consistent engineering model will be developed in close cooperation with the project partner by combining the results of beam-end tests under tensile and compressive stress.



Figure 3: Beam-End-Test setup; test setup without end bearing (left) and with end bearing (right)


In the framework of this research project, a bond fatigue model has been developed. This model is a thermodynamically consistent bond-interface pressure-sensitive damage model with cumulative sliding strain measure as a fundamental source of fatigue damage. The modeling approach provides a clear physical interpretation of the dissipative mechanisms governing the propagation of fatigue damage within the concrete-steel interface so that it is possible to reproduce both the monotonic and the cyclic behavior of the bond with a consistent set of material parameters. Figure (4) presents the model behavior of a single material point.

The model has been applied for simulation of the degradation process in the bond between concrete and reinforcement under pullout fatigue loading and validated with tests published in the literature by  [5] (Figure 5).  This model will be used further to simulate the bond fatigue behavior in the Beam-End-Test specimen.



Figure 4: Bond fatigue model: a) bond slip response for monotonic and cyclic loading; b) corresponding damage evolution


Figure 5: Simulation of pull-out fatigue - comparison with (Rehm and Eligehausen 1979) test program: a) test setup; b) displacement vs. pull-out force curve for monotonic and cyclic loading; c) fatigue creep curve for different load levels; d)  Wöhler curve



The investigations presented in this paper are supported by the Federal Ministry for Economic Affairs and Energy (BMWi 0324016C). We would like to sincerely thank the funding agency for its support.

Funding agency: Federal Ministry for Economic Affairs and Energy, 11.2016 -10.2019

Project team: Abedulgader Baktheer, Benjamin Camps, Homam Spartali




  1. Hansen, M.; Göhlmann, J.; Grünberg, J.: Bemessungsmodell für die Ermüdungsbeanspruchung bei schwingungsanfälligen turmartigen Bauwerken aus Stahlbeton und Spannbeton – Abschlussbericht, Fraunhofer IRB-Verlag Stuttgart, Vol. 3228, 2010.
  2. Hegger, J.; Roggendorf, T.; Goralski, C.; Roeser, W.: Emüdungsverhalten von Beton unter zyklischer Beanspruchung aus dem Betrieb von Windkraftanlagen, Abschlussbericht, Fraunhofer IRB-Verlag Stuttgart,Vol. 3305, 2014.
  3. Pfanner, D: Zur Degradation von Stahlbetonbauteilen unter Ermüdungsbeanspruchung. Dissertation, Technisch-wissenschaftliche Mitteilungen, Institut für Konstruktiven Ingenieurbau Ruhr-Universität Bochum, VDI-Verlag, Düsseldorf, 2003
  4. Alliche, A.: Damage model for fatigue loading of concrete. In: International Journal of Fatigue (26), 9/2004, pp. 915-921. ISSN: 01421123.
  5. Rehm, G.; Eligehausen, R.: Bond of Ribbed Bars Under High Cycle Repeated Loads. In: ACI Journal 76-15, 2/1979, pp. 297-309
  6. Baktheer, A., Aguilar, M., Chudoba, R.: Microplane fatigue model MS1 for plain concrete under compression with damage evolution driven by cumulative inelastic shear strain. International Journal of Plasticity, 143 (2021).
  7. Baktheer, A., Chudoba, R.: Experimental and theoretical evidence for the load sequence effect in the compressive fatigue behavior of concrete. Materials and Structures, 54, 82 (2021).
  8. Baktheer, A., Spartali, H., Hegger, J., Chudoba, R.: High-cycle fatigue of bond in reinforced high-strength concrete under push-in loading characterized using the modified beam-end test. Cement and Concrete Composites, 118 (2021).
  9. Baktheer, A., Spartali, H., Chudoba, R., Hegger, J.: Concrete splitting and tip-bearing effect in the bond of anchored bars tested under fatigue loading in the push-in mode: An experimental investigation. Materials and Structures, 55, 101 (2022).