A multilevel calculation scheme for risk-based robustness quantification of reinforced concrete frames

•A multi-level scheme is proposed to calculate the reliability of damaged RC frames.•The structure is subdivided in two parts to reduce the computational effort.•Non-linear FEM is used to include membrane action of the RC elements.•The multi-level scheme is combined with LHS to perform reliability calculations.•Risk-based robustness quantification using results of the reliability calculations. Structural robustness has become an important research topic in the engineering community since several large failures in the past decades led to the public awareness and indicated the importance to consider structural robustness during the structural design. So far most research has been focusing on structural measures to improve structural robustness and on theoretical methods to quantify structural robustness. However with respect to the analysis of concrete frames, there are only a limited number of examples which try to quantify the achieved robustness level for the available structural measures, such as the development of alternate load paths by membrane action. In this paper both advanced calculation methods and quantification approaches for robustness are combined by a computational efficient calculation scheme which considers different levels of structural idealisation. The developed approach is able to quantify the reliability and structural robustness of planar reinforced concrete frames in an objective way while using a conditional risk-based robustness index and taking into account the developed membrane action. As an illustration the developed calculation scheme is applied and discussed for two alternative designs of a regular office building. The results show the importance of the uncertainty on membrane action effects on the structure in case of an unforeseeable event leading to a notional column removal.