Mechanical Interpretation of Shrinkage Restraint in UHPC–NSC Overlays

Shrinkage restraint in an ultra-high-performance concrete (UHPC) overlay is commonly quantified by comparing restrained and free-shrinkage strains. However, a local restraint index may not represent the mean axial response of the overlay. This study examines the mechanical interpretation of the degree of restraint (Kr) in bonded UHPC–normal-strength concrete (NSC) overlays using strain measurements in both layers. Five UHPC mixtures were monitored for 56 days at three longitudinal locations. A self-equilibrated two-layer model was used to establish a model-based restraint ceiling, Kr,max, while apparent axial forces inferred independently from UHPC and NSC strains were compared for mechanical consistency. Kr,max ranged from 0.702 to 0.714. At the end of monitoring, the apparent-force ratios at midspan were 17.06 and 16.75 for 650-SFB10 and 650-SFB15, respectively, whereas the maximum for 650-SFB20 occurred at x = 900 mm (23.70). These imbalances indicate that local strains did not consistently represent mean axial strains. From approximately 14 days onward, x = 900 mm exhibited the highest Kᵣ in all five specimens. The elastic-equivalent tensile-demand ratio ranged from 1.15 to 3.06, although no visible cracking was observed. These results indicate that Kr is best interpreted as a local, position- and time-dependent response index rather than a unique measure of section-level restraint.