Mathematical sustainability assessment framework of earthquake-induced steel building population

The ability to estimate the probability a building population under seismic events will be sustainable is timely, useful in appropriately allocating earthquake mitigation funds earmarked for repair, rehabilitation, and replacement. A building population is considered sustainable if actual cost incurred is less than a target cost at a given ground motion intensity level such as a certain level of spectral accelerations. The purpose of this study is to construct a mathematical framework coupled with Gompertz and power functions to determine the probability of sustainability of building population subjected to seismic events as a function of target repair-cost ratios. The framework accounts for the exceedence probability of certain earthquake occurrence in 50 years and the fragility data created by joint response surface metamodels (RSMs) and Monte Carlo Simulation (MCS). The fragility data for a population of L-shaped Steel Moment-Frame (LSMF) buildings located in the Central United States and the probability of spectral acceleration exceedence for the target region are used for this study. The probability of sustainability of the LSMF buildings built from pre-1970, between 1970 and 1990, and post-1990 are determined through the developed framework. The mathematical and graphical relationship between the probability of sustainability of the building population under a broad range of spectral accelerations and its target repair-cost ratio are determined. Key findings show that the buildings built in the post-1990 are more sustainable than those built from the pre-1970.