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

Abstract

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, P nc ) associated to sag curve designs, and assessed the effect of the variables involved in headlight sight distance (HSD) on the P nc . 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.

Driver glare exposure with different vehicle frontlighting systems

“…In recent studies, the impact of the headlight beam features on headlight sight distance under such approaches was quantified (De Santos-Berbel et al, 2016). Moreover, variations of the vertical spread angle have been found to potentially produce a significantly different impact on safety (Andrade-Cataño et al, 2020).…”

Reliability Analysis of Intersection Sight Distance at Roundabouts

“…where µ denotes the mean of the indicated random variable. Case 2: Substituting t' and v e ' from Equations ( 14) and ( 15) and d cir and t cir from Equations ( 11) and ( 12) into Equation ( 16), then substituting D 1 into Equation (27), the first derivatives of SM 1 with respect to v c , a, t c , and r can be derived as…”

“…Case 3: Substituting t and d cir from Equations ( 5) and (11) into Equation ( 17), then substituting D 1 into Equation (27), the first derivatives of SM 1 with respect to v e , v c , a, t c , and r can be derived as…”

“…The more advanced first-order method (FORM) has been used by several authors, including Osama et al [20], Richl and Sayed [21], De Santos-Berbe et al [22], and Llorca et al [23]. In addition, some researchers have used Monte Carlo (MC) simulation, such as El-Khoury and Hobeika [24] who studied passing sight distance (PSD) on two-lane highways; Sarhan and Hassan [25], who studied sight distance on three-dimensional highway alignments; Wood and Donnell [26], who studied sight distance on horizontal curves; and Andrade-Catano et al [27], who studies headlight sight distance on sag vertical curves. MC simulation has also been used in some studies to verify the assumptions of the analytical reliability methods [17].…”

Reliability-based analysis of horizontal curve design by evaluating the impact of vehicle automation on roadway departure crashes and safety performance

“…They compared the accuracy and reliability of various estimation methods and provided recommendations for selecting the most appropriate method in different roadway design situations. In their study, Andrade-Cataño et al [ 32 ] applied a probabilistic approach to evaluate the risk level associated with sag curve designs and assessed the effect of variables involved in headlight sight distance (HSD) on the probability of noncompliance. The results showed that variables modelling headlight features significantly affect the risk level and that the risk associated with design outputs considered equivalent by the standard varies significantly.…”