This study proposes a framework for incorporating time-dependent fragility into large-scale risk assessment models, focusing on incremental building expansion as a significant driver of changes in vulnerability. In rapidly urbanizing areas in developing countries, the pay-as-you-go process of informal building construction and staged expansion is the de facto pattern of growth. While there is a common understanding that such expansions increase the earthquake vulnerability of buildings, this study proposes a framework to model and quantify this increase. Vulnerability curves are developed through incremental dynamic structural analysis for common building expansion typologies. Building expansions are modeled as Markov chain processes and used to simulate stochastic expansion sequences over a building's lifetime. The model is then used to simulate a hypothetical neighborhood in the Kathmandu valley area to understand neighborhood-level risk over time. The study provides a new methodology to analyze changing seismic risk over time, driven by any building modification that impacts the building's vulnerability (incremental expansion, deterioration, retrofit, etc.).

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