01555399

Component

The objective of this paper is to develop a mathematical methodology that allows the design of the three-dimensional alignment of a road directly in space, while complying with current design policies. The presented methodology overcomes the conventional approach of studying the three-dimensional road configuration separately and sequentially in its horizontal and vertical alignment. Initially, the methodology foresees in a first stage approximation of the centerline of the road as a three-dimensional B-spline curve. This temporary road curve is modified to account for the engineering boundary design values of the curve s curvature and of the longitudinal slope of the specific road category. As far as the road surface is concerned, it is initially realized as a ruled surface whose directrix is the road centerline (three-dimensional B-spline curve). The rulings of the ruled surface are defined in such a way to be perpendicular to the road centerline. Moreover, the rulings are subjected to a rotation around the road centerline with respect to the horizontal vectors in order to comply with the conventional definition of the superelevation rate of the road pavement. Finally, the road surface is approached as a three-dimensional B-spline surface. The computational part of this approach is attained by expressing the functions in code through the programming language offered by the software Mathematica, whereas the whole process is demonstrated as a case study.

This paper was sponsored by TRB committee AFB10 Geometric Design.

01550057

15-1251

English

18p

2015

Transportation Research Board 94th Annual Meeting

Digital/other

Figures; References

Alignment; Curvature; Geometric design; Mathematical models; Methodology; Splines

Design; Highways; I20: Design and Planning of Transport Infrastructure

Transportation Research Board Annual Meeting 2015 Paper #15-1251

TRIS, TRB, ATRI

Dec 30 2014 12:29PM