Probabilistic analysis of the crack spacing in reinforced concrete members under tensile loads - numerical investigation of size effects

This paper describes a set of theoretical and practical aspects related to the modelling of cracking in axially reinforced concrete members subjected to pure tension accounting for size effects. In particular, the paper describes a new methodology to achieve a probabilistic description of the crack's spacing using a spatially correlated Weibull random field coupled to an energetic-statistical size effect law. Such aspects do not seem to be significantly covered in existing studies; although the mean and maximal crack spacing values are systematically of interest to control the cracking state in reinforced concrete structures. The proposed approach is validated based on a set of tests performed by Farra and Jacoud (1993). Finally, the stochastic model is used to define a meta-model of the mean and maximal crack spacing values. Such explicit formulations are intended for engineering applications and involve explicitly size effect parameters. In that sense, they are an evolution of the current regulatory formulae in the Eurocode or the Model Codes (where size effects are overlooked).