A continuum damage modeling of quasi-static fatigue strength of plain concrete

► Flexural fatigue damage of concrete. ► Gauge function with power and bi-power laws. ► Wöhler curves computed and compared with experimental results. ► The model is also used for compressive fatigue damage. ► Full algorithmic details for a finite element implementation. A three-dimensional phenomenological model is developed to describe the fatigue behavior of concrete. The approach is based on the framework of continuum damage mechanics where the fatigue model is derived by means of Marigo’s formulation where the yield concept is replaced by a loading–unloading irreversibility concept allowing to account for damage accumulation even for loading levels below the yield surface. Specifically, a static damage model is proposed and deeply investigated. Its extension to the fatigue range is proposed through two different functions of the power-law-type. While the first one only needs one additional parameter, the second one needs three additional parameters. In all cases, these latters need to be identified by means of fatigue tests through Wöhler curves. In this paper, flexural fatigue tests have been performed on a concrete the formulation of which is close to the one used for urban railway slabs. A set of numerical examples is presented. It shows good agreements with the present experimental results together with some data found in the literature.