Driving risk evolution and characteristics on foggy bridges considering the emergency: an approach based on field theory

Driving safety on foggy bridges poses unique challenges. Using field theory, this study quantifies fog-induced driving risk through driving simulation experiments on the ordinary road, ordinary bridge, and foggy bridges, which include car-following and braking processes. We optimise risk field models considering roads, vehicles, and drivers, with K-means clustering used to identify critical risk patterns. The results indicate that: (1) Bridge exacerbates speed heterogeneity and impair drivers’ cognition. Fog degrades the driving physiology–psychology state and skill. (2) Car-following risk escalates with reduced following distance and increased speed difference (especially sensitive to following distance). Foggy bridge presents the highest car-following risk, particularly at narrow speed difference (2–3 m/s) and short following distance (