Analytical method of incorporating failure probability to predict the fatigue life of ultra-high-performance concrete (UHPC)

This study predicted the fatigue life (N) of UHPC incorporated with different volume fractions ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math> = 0.0%, 0.5%, 1.0%, 1.5% and 2.0%) of steel fiber under flexural cyclic loading at various stress levels (S). The Weibull distribution, a two-parameter model, was utilized to estimate the distribution of fatigue life in UHPC. Subsequently, three methods were employed to calculate the parameters: the graphical method, the method of moments, and the method of maximum likelihood. The averaged values of these parameters were then obtained to enhance the accuracy of the estimation. The results are presented in the form of S-N diagrams, which depict the quantitative relationship between stress (S) and fatigue life (N). This relationship was determined using the Wohler equation, the modified Wohler equation, and the power equation. By employing these equations, the flexural fatigue strength of UHPC can be accurately predicted. Subsequently, the fatigue failure probability (P f ) was incorporated to enhance the reliability of the S-N quantitative relation. The fatigue testing results were presented in the form of S-N-P f curves, which comprehensively reflect the relationship between stress, fatigue life, and failure probability. Furthermore, the mathematical relation of the S-N-P f curves was derived to predict the fatigue life of UHPC with a given failure probability, providing a more comprehensive and accurate assessment of its fatigue behavior.