A Performance-Based Earthquake Fatality Modeling Framework Using Collapse Volume Ratios

Conventional earthquake fatality models are commonly implemented using a binary representation of building collapse, an assumption that overlooks severe failure modes and systematically underestimates fatalities. To address this limitation, this study advances the collapse volume ratio—a continuous metric quantifying the reduction of survivable space during collapse—into a probabilistic framework that directly links structural failure to fatality risk. Although previously introduced and quantified in limited studies, we extend its role from a primarily descriptive measure to an analytical component of performance-based earthquake engineering modeling. The framework is designed for versatility, allowing implementation with different levels of data availability, including site-specific collapse observations, collapse fragility functions, or complete-damage fragility functions. Its applicability is demonstrated by leveraging post earthquake data from reinforced concrete moment frame buildings affected by the 2023 Kahramanmaraş earthquakes and through case studies of mid-1970s non-ductile and post- 1997 ductile concrete space-frame archetypes in California. Results show that conventional approaches, constrained by binary collapse assumptions, may under predict fatalities by up to fortyfold at high shaking intensities. In contrast, the proposed framework reproduces observed fatality rates, estimating that under Maximum Considered Earthquake shaking, non-ductile buildings may experience fatality rates of 65%, compared to 11% for ductile buildings. These findings provide quantitative evidence of the life-safety benefits of modern seismic design and highlight the urgent need for retrofit policies addressing older, non-ductile construction.