Multiscale Modelling of Reinforced Concrete Structures

Abstract: Concrete cracks at relatively low tensile stresses; cracks open up for ingress of harmful substances, negatively affecting the durability of reinforced concrete structures. Crack widths are thus limited in the design codes, and accurate predictions are needed, especially for large reinforced concrete structures such as bridges or nuclear reactor containment buildings. On the one hand, cracking of concrete, constitutive behaviour of steel, and the bond between them must be accounted for in order to properly describe crack growth. On the other hand, explicitly resolving these features in large structures could prove computationally intractable. This thesis concerns multiscale modelling of reinforced concrete structures. More specifically, different two-scale models, based on Variationally Consistent Homogenisation (VCH), are developed. In these models, the response of a Representative Volume Element (RVE) is upscaled to a few popular structural models: a homogenised solid in plane stress, the effective Euler-Bernoulli beam and the effective Kirchhoff-Love plate. The effective response of the RVE is defined through a boundary value problem, for which different types of boundary conditions are developed and discussed. Furthermore, in order to allow for reinforcement slip transfer across the large-scale elements, a novel macroscopic reinforcement slip field is introduced. The developed two-scale models are used to analyse reinforced concrete deep beams subjected to membrane loads, reinforced concrete beams subjected to uniaxial tension and bending, and reinforced concrete panels subjected to combinations of membrane and bending loads. The results show that the general structural behaviour is reflected well by the multiscale models compared to single-scale analyses. By enriching the model with a macroscopic reinforcement slip field prescribed at the boundary of the RVE, the crack width predictions given by the two-scale models are improved and localisation of effective strain is observed at the large-scale. However, the results were dependent on the large-scale mesh and RVE sizes. In order to improve the objectivity of the model, a novel boundary condition type, prescribing the effective slip in the volume of the RVE, was developed. The macroscopic reinforcement slip became no longer RVE-size dependent, and the maximum crack width predictions were more consistent and showed a smaller variance for different large-scale meshes and sizes of RVEs. In conclusion, the developed two-scale models allow for the analysis of a wide range of reinforced concrete structures, and show potential in saving computational time in comparison to single-scale analyses.