Physically consistent modeling of fracture energy in concrete using dimensionless analysis and Bayesian regression

Abstract

Fracture energy is a key parameter governing crack propagation and post-cracking behaviour in concrete; however, its reliable prediction remains challenging due to material heterogeneity, size effects, and experimental scatter. This work combines dimensional analysis and Bayesian inference to improve fracture energy prediction in both plain and steel fibre-reinforced concrete. For plain concrete, a physically admissible formulation is derived using the Buckingham Π theorem, ensuring dimensional consistency while capturing the influence of compressive strength, elastic modulus, maximum aggregate size, and water–cement ratio. For steel fibre-reinforced concrete, equivalent fracture energy is evaluated through an equivalent toughness parameter, and a Bayesian regression framework based on Hamiltonian Monte Carlo sampling is employed to quantify uncertainty associated with fibre-related mechanisms. The results provide physically interpretable parameter estimates with credible intervals, highlighting the limitations of deterministic approaches and the benefits of uncertainty-aware modelling. The proposed framework integrates physical consistency with statistical robustness, offering a transparent and adaptable approach for fracture energy assessment and uncertainty-informed design of cement-based materials.