Stable deformation growth as a fatigue life indicator for concrete: Experimental and multiscale numerical insights

Ensuring structural safety and durability requires accurate fatigue life prediction. Currently, the S–N (Wöhler) curves are well-established for evaluating the fatigue life of concrete, yet the obtained results in experimental investigations regularly reveal notable scatter. Recent studies point toward an alternative fatigue life assessment approach, which is referred to as the Sparks-Menzies relation and provides a strain-based failure criterion based on a linear relationship between the logarithmic strain rate in the second fatigue phase and the logarithmic number of cycles to failure. While previous research primarily focuses on the compressive fatigue behavior observed through cylinder tests, this study additionally applies the Sparks-Menzies relation to assess tensile fatigue life using notched three-point bending tests (3PBT) and shear fatigue life using punch-through shear tests (PTST), while also considering a broad range of varied test parameters. The experimental analysis validates the Sparks–Menzies relation as a highly reliable approach for fatigue life assessment, yielding coefficients of determination between R 2 = 0.954 and 0.998, whereas the corresponding S–N regressions ranged from R 2 = 0.329 to 0.907 and, in some cases, no meaningful linear regression could be established due to the pronounced scatter. Furthermore, the predictive capability of the strain-based evaluation approach has the potential to enable the estimation of the remaining fatigue life of runout specimens. In addition to the experimental investigation, meso- and macro-scale numerical simulations are performed to examine whether the linear relationship underlying the Sparks–Menzies relation can also be reproduced by physically motivated fatigue models. The simulations are based on a recently proposed fatigue hypothesis, in which fatigue degradation in concrete is driven by the cumulative inelastic sliding within inter-aggregate regions. To this end, a microplane constitutive model and a lattice discrete model developed by the authors are employed. Both models successfully reproduce the experimentally observed linear correlation between the logarithmic strain rate in the secondary fatigue phase and the logarithmic number of cycles to failure, thereby providing independent numerical confirmation of the Sparks–Menzies relation and supporting the underlying fatigue mechanism.