ABSTRACT
Ensuring the long-term performance and safety of reinforced concrete (RC) structures depends on the ability to understand their evolving condition and the ability to assess their situation. Within Structural Health Monitoring (SHM), this requires physically meaningful indicators that capture a structure’s inherent ductile or brittle tendencies. This study revisits a validated Integrated Fracture-Based Model (IFBM) and establishes it as a foundation for damage quantification and performance assessment. The IFBM analytically describes lightly reinforced concrete beam behaviour across two key stages: crack propagation with tensile softening and crack rotation with compression softening, through a closed-form solution satisfying equilibrium, compatibility, and constitutive relationships, including bond-slip and post-cracking stress distribution. A dimensionless Ductility Number (DN) is formulated from dimensional analysis of the IFBM, integrating material, geometric, and interface parameters such as reinforcement ratio, concrete strength, elastic moduli, bond stress, and critical crack opening. The DN characterises the stability of cracking, where higher values indicate ductile, bond-controlled failures and lower values correspond to brittle, reinforcement-fracture modes. Validation against Digital Image Correlation experiments confirmed strong correlation between DN and observed failure mechanisms. The DN thus quantifies a structure’s intrinsic ductility potential, enabling SHM systems to interpret sensor data within a mechanical context. As a mechanics-based indicator, it provides a baseline for condition tracking, risk assessment, and early detection of performance deviations in reinforced concrete structures.
