How to conceptualize the connotation of “resilience – risk” for critical infrastructures? An exploratory theoretical framework

Critical infrastructures (CIs) play an important role in urban economic development and the maintenance of social stability. In recent years, with the increase in natural and man-made risk events affecting CI operations, CI risk management is facing severe challenges and gradually transitioning to CI resilience management. However, the connotation of "resilience - risk" for CIs is still not clearly conceptualized. To address this problem, an exploratory theoretical framework is constructed, including three stages of system resilience identification, resilience impact analysis and connotation element extraction. Subsequently, based on the constructed framework, probability, consequence, and resilience-based scenario that align with the resilience characteristics and impact analysis results are extracted as connotation elements to define a triplet spatial-temporal evolution function of "resilience - risk". This study can provide a theoretical reference for better understanding the relationship between CI resilience and CI risk.