Structural robustness quantification through the characterization of disproportionate collapse compared to the initial local failure

Modern design codes recommend ensuring an appropriate level of robustness to prevent disproportionate collapse under an exceptional event. This concept directly refers to the capacity of limiting progressive collapse after an unexpected initial local failure. Assessing a structure in terms of robustness results in a complex issue as it not only requires information on the structural response in a large non-linearity domain, but also as it introduces a high level of uncertainty due to the concept of exceptional initial action. This study proposes a strategy to assess structural robustness using collapse propagation and energy-based indicators. A case study on a demonstrative steel frame building is presented. The first step consists in the definition of the possible scenarios leading to the loss of one or several structural element(s), such as columns. For each scenario, the structural response, including collapse propagation and alternative equilibrium is investigated using a fast computational modelling coupling the yield design theory and a non-linear finite element analysis. Initial to final damage ratios of the structural system and needed energy for initial failure are computed to quantify the robustness of the structure through this scenario-based analysis. A Pareto front analysis of the scenarios is then conducted by solving bi-objective problems that aim to maximize the collapse propagation and minimize the required demand of the initial local failure scenarios. The scenario-based and Pareto front analyses are applied to compare different structural design configurations of a case study used for illustration purpose. Results clearly show how the two levels of analysis give complementary results that allow (i) quantifying and comparing robustness performance of the structure and (ii) identifying critical scenarios.