A mathematical framework to quantify physical damages from concurrent and consecutive hazards

When two or more natural hazards occur in the same location simultaneously or within a short time frame, the physical integrity of assets and infrastructures can be compromised, and the resulting damage can be higher than the simple sum of the damages generated by individual hazards occurring in isolation. Current literature highlights the lack of comprehensive frameworks to quantify the damages caused by multiple hazards. Complexity in formalizing quantitative aspects and understanding feedback loops between hazard, exposure, and vulnerability emphasizes this gap. 

This research presents a comprehensive mathematical framework for quantitatively assessing multi-hazard physical damage on exposed assets, such as buildings or critical infrastructures, over time. The proposed framework covers both the damages generated by concurrent hazards (i.e., hazards that impact the same assets simultaneously), as well as by consecutive hazards (i.e., the second hazard impacting the asset while it is still undergoing recovery from the damages caused by the first hazard). In case of concurrent hazards, the proposed framework models the increased damage resulting from the combined impacts. In the case of consecutive events, the proposed formalization considers the effect of cumulative damages, the reduction in the exposure value, the modification of vulnerability in the time in between hazards, and the recovery dynamics. 

The framework is applied to a real-world case study in Puerto Rico, including the impacts from the concurrent wind and flood generated by the passage of Hurricane Maria, as well as the impacts caused by the consecutive seismic sequence of 2019-2020. The application to the Puerto Rico case study well highlights the potentialities and limitations of the proposed approach, specifically regarding data availability.

By offering a generalized formalization to perform quantitative multi-hazard impact assessments across a diverse array of natural hazards and incorporating amplification phenomena and recovery dynamics, the framework provides scientists and decision-makers with a thorough and enhanced comprehension of the impacts resulting from concurrent and consecutive events. This deeper understanding serves as valuable input for conducting comprehensive multi-hazard risk assessments and implementing effective disaster risk reduction strategies.