Physically-based collapse failure criteria in progressive collapse analyses of random-parameter multi-story RC structures subjected to column removal scenarios

The definition and determination of dynamic collapse limit states for design and safety assessment of civil structures is still an open problem in the context of progressive collapse, in particular for structural reliability and robustness quantifications. Hence, this paper summarizes, compares, and evaluates three kinds of collapse failure criteria in literature for reinforced concrete (RC) multi-story frames subjected to column removal scenarios, including the displacement-based criterion, the resistance-based criterion, and the energy-based criterion. Totally, 48 deterministic cases and 480 stochastic cases for six different planar RC frames subjected to 48 different column removal scenarios are studied in the progressive collapse analyses to evaluate the effectiveness and performance of the three kinds of criteria. In the stochastic analyses, the depth of the concrete cover and the key material mechanical properties for both concrete and reinforcing steel are chosen as random inputs, where the uncertainties are observed to have great influence on the collapse limit states. The results demonstrate that the different structural designs and the uncertainties in structural parameters will lead to different collapse limit states, which are strongly linked with the specific failure modes or paths during the progressive collapse. The code-compliant seismic design can significantly improve the deformation capacity of the RC frames and allow sufficient development of load redistributions. In such cases, the empirical collapse failure criteria including both the deformation-based and the resistance-based criteria adopting an empirically prescribe deterministic threshold may fail to accurately determine the collapse limit states. None of them can be adaptive to different structures with different failure modes or paths, either too conservative or too much overestimating the performance. Conversely, the energy-based criterion adopting a physical approach rather than an empirical constant threshold is a physically-based and problem adaptive approach, which can be adaptive to different structures with different failure modes or paths according to the specific computational results. Hence, the energy-based criterion shows the best performance for determining the collapse limit states and is less affected by the different failure modes or paths.