A two-step damage model for analysis of recycled aggregate concrete beam on foundation: Displacement-based approach

This study presents a damage-inclusive analytical framework for the static bending analysis of recycled aggregate concrete (RAC) beams resting on elastic foundations. The principal contribution is not the rederivation of the previously published two-step RAC constitutive model itself, but its integration into new displacement-based beam-foundation formulations that enable a structural-level assessment of damage-informed stiffness degradation under different foundation idealizations. Three RAC homogenization schemes, namely the Voigt (parallel), Reuss (series), and generalized self-consistent models, are combined with Kerr-type, Winkler–Pasternak, and Winkler foundations within the Euler–Bernoulli beam framework. The governing differential equations, boundary conditions, and closed-form analytical solutions are derived assuming small deformations and linear, homogeneous, isotropic effective behavior. Parametric studies are then conducted to evaluate the effects of constituent volume fractions, foundation parameters, and foundation model type on beam deflection. The results show that increasing the recycled concrete aggregate content increases beam deflection, whereas increasing the natural coarse aggregate and cement paste contents reduces it. Increasing the shear-layer stiffness and subgrade stiffness decreases beam deflection, while the generalized self-consistent model consistently predicts responses between the Voigt and Reuss bounds. For the parameter range considered, the Kerr-type foundation yields the largest deflections among the three foundation idealizations. The proposed framework provides a useful analytical benchmark for serviceability-oriented assessment and preliminary design of RAC members supported by deformable media, such as ground beams, strip/slab-on-ground elements, sleepers, and pavement-related substructures.