Consideration of the runouts and their subsequent retests into S-N curves modelling based on a three-parameter Weibull distribution

•The Weibull model allows to include the runouts and their subsequent retests into the modelling of the S-N curves.•Considering the runouts and their retests into the modelling of S-N allows to estimate the fatigue limit with certain probability.•The Weibull model allows to determine the damage accumulation of a runout.•A detailed procedure for modelling the S-N curves based in the Weibull distribution is proposed.

Considering the influence of runouts and their subsequent retests helps to determine the S-N curves which are used by engineers to estimate design stress levels with a high realiability. The Weibull model proposed by Castillo et al. is a unified statistical methodology to describe this phenomen. In this article, a procedure to model the S-N curves, subject to the constraints mentioned above is presented. Finally, two applications considering the experimental data of girders from an antique steel bridge built in 1895 and the experimental data of welded specimens made of steel S690QL are presented.