Modified Reliability Theory for Speed-Based Evaluation of Successive Geometric Elements

The current study proposes a modified reliability theory and methodology for the speed-based evaluation of successive geometric elements such as a long tangent followed by a curve. A formulation based on lower limit and upper limit speed adjustments, $S_L$ and $S_U$, respectively, between the successive geometric elements is developed for range-based reliability evaluation. To understand the sensitivity of reliability, graphical representations for the variations in reliability due to variations in speed difference distributions, ${\mu }_G$ and ${\sigma }_G$, are explained. It is observed that the reliability of highway geometric elements changes with variations in ${\mu }_G$ and ${\sigma }_G$. For fixed values of ${\sigma }_G$, $S_L$, and $S_U$, the reliability of highway geometric elements can increase or decrease with increases in ${\mu }_G$. However, for fixed values of ${\mu }_G$, $S_L$, and $S_U$, the reliability of highway geometric elements increases with decreases in ${\sigma }_G$. A typical example using this method has also been discussed in this paper to provide an idea on the practical application of the method. Analysis of the geometric effects on reliability values elucidates an inverse relationship between reliability ratio ($RR$) and deflection angle. Conversely, a direct relationship between radius and curve length was observed. The observed negative relationship of deflection angle and degree of curvature with $RR$ is in compliance with AASHTO’s recommendation of designing for smooth curve appearance. Design engineers can suitably use the proposed methodology for a targeted reliability(Re) and/or $RR$ value. These findings can help to generate a reliable design of successive geometric elements at the design stage and recommend suitable low-cost safety measures to mitigate the geometric design shortcomings in the operational stage of highways.