A Practical Formulation for Seismic Damage Accumulation on Multiple Mainshock‐Aftershock Sequences Based on Disaggregation of the Mainshock Hazard

ABSTRACT Earthquakes often occur in clusters (foreshocks, mainshocks, and aftershocks) and can lead to cumulative structural damage. Many studies have extended traditional performance‐based earthquake engineering (PBEE) to account for damage accumulation in multiple mainshock‐aftershock (MS‐AS) sequences using Markov chain processes and state‐dependent fragilities. However, existing MS‐AS risk analysis methods often intertwine seismic hazard assessment with structural risk analysis, requiring analysts to process detailed seismological and structural data. In addition, the use of logic‐tree structures to represent epistemic uncertainties makes current methods computationally expensive, particularly for large logic‐tree models. This study introduces a practical MS‐AS risk assessment method that accounts for epistemic uncertainties without requiring explicit handling of full logic‐tree structures within the structural risk analysis workflow. The method relies on four hazard outputs: total hazard curves, hazard disaggregation data, the expected number of aftershocks and the conditional distribution of aftershock intensity measures for each disaggregation bin. Using these inputs, the proposed method practically decouples the work of seismic hazard analysis from the structural risk assessment. Moreover, the method has the potential to reduce computational effort by avoiding explicit repetition over MS logic‐tree branches. The method is demonstrated through an MS‐AS risk analysis of 4‐ and 8‐story steel special moment frame (SMRF) buildings at two primary sites affected by 3D fault surfaces using a 32‐branch logic‐tree. Benchmark transition matrices and the assessed time‐variant risks obtained using current methods are compared with those from the proposed approach. Results from the illustrative case study show that with sufficiently fine disaggregation, errors remain below 5%.