A novel speed model for safety evaluation of freeway alignment in Euclidean 3D space

Objective: Operating speed is a critical indicator to evaluate consistency of road alignment and safety. Although extensive studies have been conducted on developing operating speed models, few researchers have considered the interactive influence of horizontal and vertical alignment in 3D space. The purpose of this study is to develop a speed model based on 3D alignment in Euclidean space rather than traditional horizontal and vertical alignment. Methods: According to the curve theory of differential geometry, a novel method to estimate operating speed is proposed in our study using 3D space curvature instead of traditional horizontal or vertical parameters to describe the spatial geometric properties for a freeway alignment. Speeds of 54 different alignment segments are observed to develop the speed model. Several observing sites of each segment are selected beforehand, and the speeds of more than 300 vehicles in each site are observed. Space curvature is used as an important index to estimate operating speed. Results: The findings of this study indicated that both horizontal alignment and vertical alignment contribute to space curvature. Space curvature mainly affects direction control operating performance. However, vehicles overcome the effects of gravity along the vertical alignment in the z direction. Results indicate that operating speed exponentially declines with space curvature and that quadratic parabola decline with vertical grade. Conclusions: It can be concluded that there is a clear correlation between velocity and spatial curvature, which is proved by variance analysis. The estimation results of the speed models are reliable as tested using a real engineering example. The study would provide a scientific basis for safety evaluation of freeway alignment.