Reliability-Based Safety Evaluation of Headlight Sight Distance Applied to Road Sag Curve Standards

Sight distance is key to ensure safe road geometric design under all circumstances. Road design standards propose models simulating nighttime driving that contemplate the features of vehicle frontlighting systems to address the design of sag curves. These models are based on a deterministic approach, which is known to present a number of drawbacks. It neglects the stochastic nature of the variables involved and, therefore, no information is available about the safety margin of the design output. As opposed to design based on deterministic methods, probabilistic methods overcome these inconveniences providing a solid approach to broach the analysis of sag curves. This research study applied a probabilistic approach to evaluate the risk level (probability of noncompliance, Pnc) associated to sag curve designs, and assessed the effect of the variables involved in headlight sight distance (HSD) on the Pnc. The required stopping sight distance was considered not to be met when it exceeded the HSD. A total of 71,334 case studies were generated by combining the range of values of the variables involved in the HSD as per the Spanish geometric design standard. The risk level associated to each case was calculated by means of a Monte Carlo simulation. The results showed that variables modeling headlight features significantly affect the risk level. Moreover, the risk associated to design outputs that are considered equivalent by the standard varies significantly. Therefore, the use reliability theory in the development of standards and design guides is recommended.