A three-dimensional coupled plastic–damage–subcritical-damage–creep–shrinkage model for long-term performance of concrete structures under sustained loading

Concrete members under sustained service loading can develop stiffness loss and delayed cracking below their short-term strength. This paper presents a three-dimensional creep-analysis method that couples a CDPM1-type bi-scalar plastic-damage framework with subcritical damage growth (SCG), creep, and shrinkage. Tensile and compressive damage evolve through an energy-release-rate law and a stress-activated SCG branch, creep follows a Dirichlet-series kernel fitted to AS 3600, and shrinkage is imposed as a stress-free strain; the model is implemented in Abaqus as an implicit UMAT with effective-stress return mapping, crack-band regularisation, and a consistent tangent. It is assessed against sustained flexural tests on general-purpose (GP) and GGBFS concretes: within the 280 day window GP mid-span deflections are predicted with RMSE of 0.086–0.098 mm and a maximum MAPE of 6.22%, and the same fixed SCG parameters are consistent with the slower GGBFS response, although the GGBFS data alone do not discriminate the SCG term. For the GP beams, disabling SCG shows linear creep alone cannot capture the decelerating long-term branch. The model is then applied, without recalibration, to the independent Gilbert–Nejadi benchmark — two further beams at two load levels analysed over a 300-day sustained-load window on a different section — whose measured deflections it reproduces to within about 0.3–0.6 mm. For the independent benchmark beams the SCG contribution is amplified markedly once shrinkage is active: with shrinkage disabled the subcritical increment collapses from +1.13/+0.33 mm to +0.07/+0.10 mm, as shrinkage-induced tensile stress enlarges the cracked region in which the subcritical kinetics operate. The framework thus predicts long-term serviceability deterioration under sustained flexure across the tested and benchmarked configurations.