Integrated statistical-analytical framework quantifying bond behaviour of FRP‑reinforced concrete structures

Air-entrained concrete (AEC) is widely used to enhance the durability of reinforced concrete (RC) structures, particularly under freeze-thaw exposure. This study investigates the combined effects of air entrainment and Fibre Reinforced Polymer (FRP) reinforcement on bond behaviour in concrete. An integrated analytical-statistical approach is proposed that combines analytical bond modelling with multifactor statistical evaluation. The bond response is evaluated through bond stress-slip relationships, forming the basis for structural modelling. The analysis is based on an experimental programme comprising 224 pull-out tests. Analytical calibration was performed using the experimental programme, whereas the multifactor statistical analysis considered a nominal subset of 136 GFRP and BFRP specimens with diameters of 6‐12 mm. The study calibrates the parameters of the CMR and the ascending branch of the modified BPE (mBPE) models. Multifactor ANOVA with bootstrap resampling is employed to quantify the effects of air entrainment, concrete strength (approximately 35 and 75 MPa), bar diameter (6‐12 mm) and surface characteristics. The results indicate that air entrainment has a statistically significant but comparatively small effect on bond strength, while concrete strength and FRP surface characteristics have substantially larger effects within the investigated dataset. A significant interaction between FRP surface configuration and diameter is also observed. The results demonstrate that bond behaviour is governed by interaction effects rather than single variables, providing a basis for improved modelling of FRP‑reinforced concrete systems.