Robustness quantification of reinforced concrete structures subjected to progressive collapse via the probability density evolution method

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Robustness is the most comprehensive and acceptable index that describes the ability of structures to withstand progressive collapse induced by accidental extreme events such as impact, explosion and terrorist attacks. As found in the literature, several approaches have been proposed to quantify the robustness of a structure, e.g., approaches based on deterministic structural performance, failure probabilities (or the collapse reliabilities), and collapse risks. In this paper, the reliability-based approach is adopted to quantify the structural robustness of reinforced concrete (RC) structures subjected to progressive collapse since it is a trade-off between comprehensiveness and operability. An efficient calculation framework is developed based on the probability density evolution method (PDEM). Emphasis is placed on two aspects, i.e., the progressive collapse behavior modeling and the evaluation of the structural reliability. The static nonlinear pushdown method is employed to represent the progressive collapse capacity of the structures, and the force-based frame element is used to generate the finite element model. Then, the PDEM incorporated with the equivalent extreme value event is used to capture the reliability indices before and after progressive collapse. With the reliability indices, the robustness index can be easily computed. The developed framework is applied to two prototype RC frames designed in accordance with the Chinese design code. The reliability and robustness indices of the frames under different initial local damage scenarios (namely, removal of columns in typical pushdown method) are obtained, and the influences of the position of the initial damage scenarios on the robustness are also discussed.