Stochastic Finite Element Modeling of Heterogeneities in Massive Concrete and Reinforced Concrete Structures

The lifespan of a reinforced concrete (RC) structure can be greatly influenced by the spatial variability of its material characteristics which, in particular, explains the observed or measured reduction of the tensile strength at first crack when the volume under tension increases. This paper discusses the ability of accounting for the spatial variability of the tensile strength of concrete in RC structures using a stochastic finite element (SFE) method based on random field simulations. In this work, the generation of random fields on the concrete tensile strength aims at computing the force corresponding to the first crack occurrence, and the reduced tensile strength of the structure. The method can be applied in particular to large-sized structures, which show a pronounced size effect, for different types of loading. The method consists of, first, estimating the mean of the random field, using the analytical approach of the weakest link and localization method (WL2A). Then, the discretized random field is defined on a particular 2D or 3D grid, and it is finally projected on the finite element mesh of the studied structure. The study of the parameters that influence the prediction of the cumulative density functions (CDFs) of the rupture force or the tensile strength is highlighted using experimental series of concrete beams having different volumes and subjected to 4-point bending loading. Moreover, the SFE method is applied to a RC tie-beam under tensile loading, characterized by a weak stress gradient, which complicates the prediction of crack positions.