Annual Acceptable Collapse Probability and CMR of Viscous-Damped Structures Considering Seismic Hazard and Total Uncertainty

Seismic collapse can cause catastrophic losses, and acceptable annual collapse probability with its CMR target is a core metric in performance-based design. Existing ATC-63-based CMR research mainly addresses non-damped systems and often uses a single lumped dispersion, obscuring damper-reliability contributions and hindering alignment with CECS 392 limits. This study proposes a unified, code-consistent decision framework for acceptable annual collapse probability and CMR that jointly accounts for seismic hazard and damper-related uncertainty. The total collapse dispersion is decomposed as σtotal,damp2=σbase2 + σdamper2, where σbase represents background dispersion independent of dampers and σdamper captures incremental uncertainty induced by degradation and partial failure. A code-designed viscous-damped RC frame is evaluated under three scenarios (nominal damping, 20% damping-coefficient reduction, and 7% random damper failures). Using the same 14 records and SaT1,5% as the intensity measure, multi-stripe IDA and Probit-based lognormal fragility fitting yield median collapse intensities Sc≈2.18−2.24 g, with only ~2–3% reduction under mild degradation/failure. A random-effects variance decomposition identifies σdamper ≈ 0, indicating a limited marginal contribution of damper-related uncertainty within the degradation range considered in this study. Closed-form relationships between annual collapse rate, Sc, and σtotal,damp are then derived under a power-law hazard model and inverted to generate acceptable-risk intervals and CMR target curves/matrices. Results show that higher design intensity and larger σtotal,damp demand substantially higher CMR, highlighting potential risk underestimation when relying solely on nominal CMR. The framework enables explicit identification of damper-related uncertainty from limited collapse data and provides a practical workflow for collapse-prevention design and post-assessment under explicitly defined scenario conditions, with a clear pathway for extension to broader scenario spaces.