State-Dependent Framework for Cascading Hazard Risk Analysis

Cascading hazards challenge conventional performance assessment because the effects of a subsequent hazard depend on the residual state left by the primary event. Conventional single-hazard or independently combined multihazard assessments may misrepresent cascading hazard risk, as they often treat hazards as isolated or additive events and neglect the residual system state created by the primary hazard. This study develops a state-dependent framework for cascading hazard risk analysis within a performance-based engineering context. The proposed framework propagates primary-hazard effects through three connected components: vulnerability amplification, consequence amplification, and residual exposure updating. Vulnerability amplification is represented by a reduction in the median capacity of secondary-hazard fragility functions due to residual damage caused by the primary hazard. Consequence amplification is represented by increased casualty rates and repair-cost ratios under degraded post-event conditions. Residual exposure is updated to evaluate cumulative consequences on the remaining population and asset value and to avoid double-counting. A numerical illustration is conducted for a coastal school building subjected to an earthquake–tsunami sequence. Results show that, relative to an uncoupled assessment, the coupled analysis increases predicted total casualties and direct economic losses by approximately 54.93% and 31.67%, respectively. These findings demonstrate that residual damage and degraded post-event conditions can materially alter cascading hazard consequences. The proposed framework can support risk-informed mitigation, emergency planning, and performance-based design decisions for infrastructure exposed to cascading hazards.