A probabilistic framework for assessing seismic functionality loss and recovery in buildings using a spatially explicit functionality metric

Current frameworks for assessing the seismic resilience of earthquake-damaged buildings typically represent functionality loss and recovery using binary or discrete operational states, as well as fault-tree approaches. These representations cannot capture the heterogeneous spatial distribution of damage within a building and lack a continuous, physically interpretable variable linking damage, repair actions, and operability. This study proposes a probabilistic methodology to evaluate earthquake-induced functionality loss and recovery using a spatially explicit performance metric. Functionality loss is defined as the percentage of non-usable floor area derived from tributary repair areas associated with damage to structural elements, non-structural components, and building contents. Recovery is modeled as a repair scheduling problem using the Program Evaluation and Review Technique (PERT), incorporating crew allocation, repair prioritization, and impeding factors. The methodology is implemented within the PEER performance-based earthquake engineering framework, transforming functionality assessment from a post-processing indicator into an explicit performance variable. Bootstrap resampling is used to construct vulnerability and fragility functions for functionality loss, recovery time, and associated workforce demand, allowing seismic resilience to be expressed as the joint exceedance domain of functionality loss and recovery time conditioned on seismic intensity. Application to a seven-story reinforced concrete office building in Mexico City under seven seismic hazard levels shows a transition from minor functionality losses with rapid recovery to complete functionality loss with recovery times of hundreds of days, even without structural collapse. Damage to non-structural components and building contents governs functionality loss, and the joint exceedance probability of functionality loss and recovery time emerges as a key indicator of seismic functional performance. These results indicate that, although modern seismic design provisions improve life-safety performance, they do not explicitly address functional consequences. Incorporating acceptable functionality loss and recovery time as performance objectives would complement traditional parameters such as interstory drift limits. The proposed methodology provides a quantitative basis for resilience-oriented seismic design and future evaluation of downtime-related consequences.