Modeling the impact of sand encroachment on driving safety in freeway curves: An improved safety field theory approach

Understanding how drivers respond to complex geometric and surface perturbations is crucial for modeling risk dynamics in transportation systems. This study presents a field-based theoretical framework grounded in principles of statistical physics to quantify driver risk in freeway curves with sand encroachment. A 3D simulation environment was constructed to emulate curved road segments with varying levels of lateral surface occupation, capturing interactions between human driving behavior, vehicle motion, and road geometry. An improved safety field model was developed by integrating vehicle kinematics, spatial constraints, and behavioral response profiles, incorporating both longitudinal and lateral risk potentials into a unified field representation. Empirical data from a controlled driving experiment with fifty participants were used to estimate spatiotemporal risk potentials under two perturbation scenarios. Results reveal distinct driver response patterns and nonlinear risk field distributions. When sand encroached one-third of the outside lane, 72.73 % of drivers adopted a braking-only strategy, generating an M-shaped energy profile aligned with increased deceleration and centerline adherence. In contrast, under the more severe encroachment scenario, 81.82 % combined braking with steering, leading to an inverted V-shaped risk potential associated with more abrupt trajectory shifts. These distributions reflect emergent transitions in control strategy, modulated by spatial constraints and perceived risk. The proposed model captures key aspects of energy field deformation, trajectory adaptation, and control feedback within the driver–vehicle–environment system, providing a physics-informed foundation for generalizing risk field behaviors under varying perturbations. These insights also offer guidance for designing safer road infrastructure and developing proactive driving assistance strategies.