Size effects in the analysis of reinforced concrete structures

Abstract

The mechanical properties of engineering materials are routinely determined by testing. In practice, the dimensions of structural elements are often much larger than those of the samples that, for technical or economic reasons, can be subjected to laboratory testing. Consequently, testing is usually conducted on reduced scale models or material samples. At the same time, available theories of material behavior that predict size or strain rate effects are receiving increasing attention in the technical literature. However, finite element models or similar representations, used for engineering predictions of the strength or loading capacity of large structures, rarely consider the influence of scale. The so-called discrete element method (DEM), in which a solid is replaced by a three-dimensional lattice of one-dimensional elements linking lumped nodal masses, has been extensively used to determine the dynamic response of concrete structures subjected to loads that produce fracture and fragmentation. In this paper, it is shown how the two major causes of size effects, namely the non-homogeneous character of the materials and the occurrence of fracture, can be incorporated in the analysis, in order to improve the prediction capability of the method. The latter is validated by numerically analyzing geometrically similar reinforced concrete beams, tested to rupture by Leonhart and Walter (1965). Those tests were later reproduced by Ramallo et al. (1993). Both the non-homogeneous character of concrete and steel were taken into account in the DEM, by assuming that the initial modulus and specific fracture energy are random fields in three-dimensional space. The constitutive criteria for the lattice elements, employed earlier by the authors to account for the energy dissipated by fracture, is adopted in the paper, with improvements in the consideration of the cross-correlation between relevant variables. As additional evidence of the reliability of the approach, the discrete numerical model was also used to numerically simulate experimental results due to Vliet et al. (2000), aimed at quantifying the influence of sample size on the tensile strength of concrete.