Numerical Analysis of Size Effects on the Stabilized Cracking Stage in RC Members

The control of random cracking in reinforced concrete members is of crucial interest to assess their serviceability and durability. From a regulatory point of view, such control within the design phase is ensured using a set of guidelines (definition of the reinforcement ratio, limitation of the crack width, limitation of the deflection, etc.). One can find corresponding formulae in the Eurocode2 (Design of concrete structures—Part 1-1: General rules and rules for buildings, [1]), Code Models (fib Model Code for concrete structures, [2]) or others. On the one hand, those regulatory formulations do not provide accurate results for all concrete types as the used experimental results for fitting show a large discrepancy. On the other hand, and mostly, they do not account for size effects observed on the tensile strength of concrete. This contribution aims at analyzing size effects on the cracks’ distribution in axially reinforced concrete members subjected to pure tension. For the most part, the paper presents an alternative approach (to existing regulatory formulae) based on the use of spatially correlated Weibull random field coupled to an energetic-statistical size effect law. The main interest is geared towards the estimation of the mean and maximal spacing values once the stabilized cracking stage is reached. The method is validated based on the set of tests performed by Farra and Jacoud (Rapport des essais de tirants sous déformation imposée de courte durée. Projet: Influence du béton et de l’armature sur la fissuration des structures en béton. Publication N°140. IBAP. Ecole Polytechnique Fédérale de Lausanne, [3]). The obtained results show a logarithmic decrease of the mean and maximal spacing values with the effective size of the ties which should be considered for future regulatory formulations.