Multi-scale progressive collapse in hierarchical RC frames via fracture mechanics

This paper addresses the problem of structural collapse by establishing a novel analogy between the ductile-to-brittle transition observed in materials and the progressive failure mechanisms in framed structural systems. This study builds upon existing literature, which often considers fragility indices, stress intensification factors in the presence of cracks, and energy-based failure criteria at the material scale, extending these concepts to analyse the behaviour of full-scale structures under progressively increasing vertical loads. The work focuses on reinforced concrete frames with varying levels of structural hierarchy, specifically 2 × 2, 5 × 5, and 11 × 11 configurations, to explore how hierarchical organisation influences the onset and propagation of damage. The investigation evaluates the ductile-to-brittle transition using a dual-scale approach, combining geometric and energetic perspectives. At the macroscopic level, geometric criteria serve as indicators of structural fragility, identifying points at which load redistribution becomes insufficient and localised damage begins to propagate towards global instability. At the microscale, energetic criteria derived from classical fracture mechanics, including the concept of a critical fracture length based on material properties such as tensile strength, elastic modulus, and fracture energy, provide a physically grounded measure of the structure’s ability to dissipate energy before catastrophic failure occurs.