Correlation Analysis of Operational Safety Risks in Inter-Basin Water Transfer Projects Based on ISM-Copula

Inter-basin water transfer projects (IBWTPs) play a pivotal role in alleviating the spatiotemporal imbalances of water resources. However, their operation is exposed to multiple, highly interdependent safety risks that can significantly undermine system stability and water supply reliability. Existing studies predominantly focus on isolated risk factors or rely heavily on subjective data, which limits their ability to capture the complex interrelationships among risks and reveal their underlying propagation mechanisms. To address these limitations, this study proposes a novel risk correlation analysis framework that integrates Interpretive Structural Modeling (ISM) with copula functions. ISM is first employed as a preprocessing tool to structure expert knowledge and develop an initial risk correlation framework. It is then used to hierarchically organize the complex interrelationships among risks. Subsequently, copula functions are utilized to model nonlinear dependencies and tail behaviors among risk variables. This enables a quantitative assessment of correlation strengths and facilitates the construction of a risk topological network. An empirical case study is conducted based on the Middle Route of the South-to-North Water Diversion Project. The results reveal 13 significant correlations among six second-level risk categories. Natural risks (e.g., floods and geological hazards) are identified as the primary driving factors. They exhibit a strong positive correlation (0.6155) with engineering risks and serve as the most critical nodes for proactive risk prevention and control. Engineering risks function as central intermediary hubs in the risk transmission process, whereas water quality and economic risks are characterized as terminal endpoints. Furthermore, three principal risk propagation pathways are identified: (1) natural risks → engineering risks → economic risks; (2) natural risks → operational scheduling risks → social risks; and (3) engineering risks → water quality risks → economic risks. The resulting risk topological network demonstrates significant small-world properties, indicating highly efficient risk transmission within the system. Ultimately, this study provides a robust quantitative approach for analyzing risk interactions in complex engineering systems and enriches the theoretical framework of engineering risk management. It also identifies critical nodes and key transmission pathways for risk prevention and control in IBWTPs, thereby offering significant practical implications for operational safety.