Safety Evaluation for Highway Geometric Design Based on Spatial Path Properties

Safety is an important aspect of road design. In highway geometric design, road engineers use a two-stage design method due to its convenience, but the available two-dimensional design tools on the market are believed to impose limitations. Horizontal and vertical alignment parameters are considered and determined at the designer’s discretion, potentially downplaying the three-dimensional characters of spatial curves. This study focuses on the three-dimensional characteristics of highway alignments and investigates a safety evaluation method to establish the relationship between crash rate and spatial curve properties. This will necessitate an analytical investigation into the effects of higher-order properties, such as curvature and torsion, on the geometry of spatial Cartesian curves. First, these combinations of horizontal and vertical alignments were categorized into six classifications, each with its own spatial expression in mathematical form. After manipulating the curvature and torsion of the spatial curve algebraically, the correlation between geometric design variables and crash rate was ultimately established. A few cases involving geometric design data and crash facts were utilized for verification. The results revealed a considerable positive correlation between curvature or torsion variance and crashes per million vehicles kilometers, as a slight difference between curvature and torsion could also be spotted. And curvature distribution is correlated with collision frequency more closely than torsion spatial variation.