A Physics-Aided Framework for Proactive Assessment of Head-on Risk at Two-Lane Rural Horizontal Curves from Both Crash Potential and Severity Perspectives

Head-on crashes on horizontal curves (HC), particularly in constrained rural terrains, pose a significant risk caused by restricted visibility and limited maneuverability. Traditional crash-based evaluations fail to capture this risk proactively, especially in low- and middle-income countries, where crash data are often sparse and underreported. To address these challenges, this study proposes a novel macroscopic theoretical framework for assessing head-on crash risk at two-lane undivided HCs by integrating two critical components: crash potential and crash severity. The Mutual Area in Lateral Distribution (MALD) is adopted to quantify the potential of head-on crashes by analyzing the overlap between vehicle lateral position (LP) distributions traveling in opposite directions. For crash severity, the change in kinetic energy (ΔKE) during a partially inelastic collision is estimated using vehicle mass and speed data. These two dimensions are integrated into a unified indicator called the Head-on Crash Risk Index (HCRI), which combines crash potential and severity at the curve level. The methodology is applied to 12 HCs in northeastern India using video-based data collection of LPs and speeds. Sensitivity analyses reveal that HCRI increases with decreasing curve radius, increasing deflection angle, and heavier vehicle interactions. Furthermore, validation using reported crash data demonstrates a strong correlation (R 2 = 0.77) between HCRI and actual head-on crash occurrences, with blackspot locations exhibiting significantly higher HCRI values. The study highlights HCRI’s usefulness as a proactive, data-driven screening indicator for identifying comparatively high-risk curves at two-way two-lane undivided HCs.