Objective: In today's increasingly interconnected world, risks—whether natural, technological, economic, or social—rarely exist in isolation. Instead, they often intertwine, which increases their impacts and complicates mitigation efforts. Such complex intertwining of risks poses significant challenges to emergency decision-making and public safety management. To address this issue, this study examines the mechanisms underlying risk intertwining to establish a scientific foundation for optimizing emergency response strategies. By enhancing the understanding of how risks interwine, this study seeks to improve the risk prevention, mitigation, and resilience-building for multifaceted crises. Methods: This study adopts a research methodology that combines qualitative and quantitative analysis. Through qualitative analysis, we examine (1) intertwining characteristics, analyzing interaction patterns between different risks; (2) root causes, investigating the fundamental driving mechanism of risk intertwining; and (3) forms of manifestation, identifying observable risk intertwining patterns, such as synchronous occurrence, secondary triggering, or latent correlations. Through quantitative analysis, we calculate (1) the time span, quantifying the duration of risk intertwining to assess its persistence and long-term impacts, and (2) the coupling intensity—computing the degree of interdependence between risks to establish quantifiable indicators of intertwining strength. This integrated approach enables a comprehensive investigation of both the qualitative and quantitative dimensions of risk intertwining. Results: This study investigates the intrinsic mechanisms of risk intertwining. By deconstructing the inherent patterns of risk intertwining, this study transcends the limitations of traditional descriptive analysis and reveals fundamental mechanism governing risk intertwining phenomena. An analytical framework is developed to assess real-time public safety risk intertwining utilizing open-source information such as news reports, social media data, and government bulletins for real-time monitoring and risk correlation assessment. A public safety risk intertwining model is proposed and empirically validated through case studies and testing using real-world data, demonstrating its practical applicability in real-life scenarios. The model's effectiveness is confirmed across multiple verification dimensions. Conclusions: This study proposes an open-source intelligence-based model that analyzes the intertwining mechanisms of public safety risks by integrating risk perception, identification, and mechanism exploration capabilities to evaluate complex risk composites. This study systematically elucidates the characteristics and underlying causes of risk intertwining while establishing a comprehensive evaluation index system to assess the degree of intertwining between different risk themes. Using 23 years of open-source data from websites, such as X, as a case study, the model's effectiveness in applications related to public safety and emergency management has been empirically validated. The study finds that (1) the proposed mixed methods model effectively reveals complex intertwining mechanisms, particularly in the public safety domain, where risks are high and information is abundant; (2) the risk perception model enables the prediction and generation of multiple risk topics through the contextual analysis of vast open-source information to promptly identify emerging risks and facilitates effective preventive measures; and (3) building on traditional qualitative descriptions, the risk intertwining model achieves a mathematical representation of risk intertwining by calculating the similarity between different risk topics. The model quantitatively assesses the evolving trends of risk intertwining over time, providing auxiliary decision-making support for preventing and mitigating public safety risks.