Simplified collapse fragility assessment utilizing a geometric mean spectral acceleration based intensity measure for PDelta vulnerable, cyclic deteriorating frame structures

The assessment of collapse-induced earthquake casualties requires the collapse fragility of a building, which is a relationship that defines the probability of structural collapse with respect to the ground motion intensity. The prediction of this quantity for regular, Moment Resisting Frame (MRF) structures vulnerable to the PDelta effect and cyclic deterioration based on a simplified assessment methodology is the main objective of this dissertation. In the first step the parameter range in terms of fundamental structural properties is revealed, where global sidesway collapse is in general governed by PDelta only, and where cyclic deterioration in combination with PDelta has a significant impact on the sidesway collapse capacity. Additionally, an “optimal” Intensity Measure (IM) that results in a low inherent Record-To-Record (RTR) depended variability of collapse capacity of the considered types of structures is identified, composed of the geometric mean of spectral pseudo accelerations in a certain period range.

The simplified collapse assessment methodology is based on an equivalent Single-Degree- Of-Freedom (equivalent SDOF) system. Since a previously developed equivalent SDOF model incorporates only the PDelta effect, nonlinear quasi-static cyclic tests in combination with subsequent optimization analyzes are used to identify cyclic deterioration parameters for the equivalent SDOF systems in terms of empirical relations. For these equivalent SDOF models the collapse fragility is obtained from series of Incremental Dynamic Analyses (IDAs) and compared to the “reference” values of the corresponding Multi-Degree-Of- Freedom (MDOF) systems. In an effort to reveal the parameter range of the applicability of the equivalent SDOF model the outcomes of the simplified collapse fragility assessment with respect to the underlying IM is evaluated, and in further consequence an “optimal” IM for the simplified assessment of the “equivalent” collapse fragility is defined. Based on these outcomes, a simplified methodology for the quick and accurate assessment of the sidesway collapse fragility of regular, MRF structures is presented. The proposed methodology relies on an empirically derived, analytical description of the collapse fragility of the equivalent SDOF systems as a function of characteristic structural properties and does not require time-demanding nonlinear dynamic analyses on the frame structure. The accuracy is tested by comparison of the predicted values with the actual collapse fragilities of the corresponding MDOF system. For instance, the relative error of the approximation of the median collapse capacity is for a certain class of structures less than 20 %, and for 75 percent of those structures less than 10 %.