Estimating mountainous freeway crash rate: Application of a spatial model with three-dimensional (3D) alignment parameters.

The road alignment is a three-dimensional (3D) curve in nature. In this study, we quantitatively examine the effect of 3D road alignment on traffic safety on mountainous freeways. Geometric parameters of 3D curvature and torsion in mathematics are derived to characterize the 3D road curve. Based on the coordination of different horizontal and vertical elements, 3D road alignment is divided into twelve types of combined alignment. For each alignment combination, the 3D curvature and torsion are calculated according to the differential geometry theory. Regarding crash statistical modeling, the Bayesian spatial Tobit (BST) model is developed to accommodate possible spatial correlation of traffic crashes among adjacent freeway segments. The Bayesian Tobit (BT) model is also built for comparison. A 118-km mountainous freeway associated road geometric features, traffic volume with three years of crash data is used as a case study. The result from the model comparison shows the BST model outperforms the BT model in terms of goodness-of-fit. Parameter estimation result for the BST model shows that the differences of average 3D curvature (and torsion) between adjacent segments have statistically significant effects on the crash rate of the segment, indicating it is necessary to consider three-dimensional alignment parameters in estimating mountainous freeway crash rate. Moreover, by comparing the predicted crash rate calculated by the BST model and the observed crash rate, the result shows the proposed BST model can provide a reliable prediction for freeway crash rates of different combined alignments. This study provides new insight on the effect of road geometric design on traffic safety but also deepens our understanding of spatial correlations in freeway crash modeling.