Effect of nano-SiO₂ on the fracture properties determined by the Hillerborg method and the flexural capacity of reinforced concrete beams

This study investigates the effect of nano-SiO₂ (NS) on the load-bearing capacity of reinforced concrete beams using experimental testing, fracture mechanics, and finite element analysis. Portland cement was replaced with 0%, 1%, 3%, and 5% NS at water-to-cement ratios of 0.35 and 0.45. Experimental evaluation based on Hillerborg’s fracture model revealed that the mixture containing 3% nano-SiO₂ exhibited the greatest enhancement in fracture properties, with total fracture energy ( G F ) increasing by 8.03% and 4.27% at water-to-cement ratios of 0.35 and 0.45, respectively.These parameters were used to evaluate the flexural capacity of geometrically similar tension-controlled beams using ACI 318-19, the Carpinteri, and Bosco and Carpinteri methods, and Abaqus simulations. While all methods provided similar predictions for smaller beams, differences became more pronounced with increasing beam size, with ACI 318-19 generally predicting higher capacities than the fracture mechanics-based and numerical approaches. The results highlight the importance of size effects and demonstrate the suitability of fracture mechanics-based methods for assessing the behavior of large reinforced concrete beams.