Distributing Superelevation to Maximize Highway Design Consistency

Several methods for distributing highway superelevation (e) and side friction (f ) have been presented by the American Association of State Highway and Transportation Officials (AASHTO). Based on a subjective analysis, AASHTO has recommended the curvilinear distribution method. This paper presents an objective method that distributes superelevation using mathematical optimization. A safety margin is defined as the difference between the maximum limiting speed (corresponding to $f_{\max })$ and the design speed. The objective function of the model minimizes the overall variation of the safety margin along the highway (aggregate analysis) or the individual variations of the safety margin between adjacent curves (disaggregate analysis). Both objectives maximize highway design consistency. The model includes constraints related to the maximum side friction, minimum and maximum superelevations, centripetal ratio, and safety margin. The e and f distributions can be discrete values with no specific mathematical shape or follow a general quadratic curve with a parameter determined by the optimization model. Application of the model was illustrated using two examples, and the results show that the design consistency obtained by the model is considerably better than that obtained by the AASHTO methods.