Collision prediction models for three-dimensional (3D) alignments of two-lane rural highways are lacking in the literature. This paper presents such models using vehicle collision data on 5,760 km (3,600 miles) of two-lane rural highways in the Washington State collected during 2002-2005. Five statistical models were developed for different combinations of 3D alignment to establish the relationships between the collision frequency and the relevant variables. The alignment combinations are: (1) horizontal curves combined with crest vertical curves, (2) horizontal curves combined with sag vertical curves, (3) horizontal curves combined with multiple vertical curves, (4) horizontal curves combined with grades less than 5%, and (5) horizontal curves combined with grades greater than 5%. For each combination, four different statistical techniques were explored: Poisson, negative binomial, zero-inflated Poisson, and zero-inflated negative binomial. For validation, two models were selected and estimated using the first three years of collision data and validated with the last-year data. The results show that the most significant predictors for collisions on horizontal curves on 3D alignments are the degree of curvature, roadway width (lanes plus shoulders), access density, product of grade value and grade length, road section length, and average annual daily traffic.
Collision prediction models for horizontal tangents are presented in a companion paper. The results of this study should be useful in evaluating road safety on 3D alignments and optimizing their design based on substantive safety approaches.