Dynamic Risk Transmission in Public–Private Partnership Projects: A Causality-Informed Network Framework

Interdependent factors in complex engineering systems propagate and amplify through directed influence networks rather than evolving independently. This study proposes a causality-informed dynamic transmission framework and applies it to risk propagation in Public–Private Partnership (PPP) infrastructure projects. Directed inter-factor influences are quantified using the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method to construct a directed influence structure. Each factor’s endogenous evolution is modeled by a logistic trajectory (slow accumulation–rapid escalation–gradual saturation), while an external-transfer component separates internal dynamics from transmission-induced increments. A five-dimension, 21-factor PPP risk system is developed from the literature and failure cases. Here, “causality-informed” denotes expert-elicited directional assumptions, not formal counterfactual causal identification. The results show that transfer-driven increments concentrate mainly in technical/engineering and economic dimensions, whereas political/legal risks exhibit smaller increments; such increments are most evident for preparation-related and all-stage factors and cluster around the rapid-rise interval. We further propose the Risk Transmission Initiation Index (RTII) to identify likely upstream initiators with cascade-triggering potential, enabling prevention-oriented risk control in coupled engineering systems.