The design of freeway entrances and exits requires managing the high operating speeds on the through lanes and the intense lane-change manoeuvres due to merging and diverging. Therefore, adequate lengths between these entrances and exits and provision of adequate speed-change lanes would help drivers execute such tasks safely. Most of the previous research has focused on analyzing operational conditions of the merge and diverge areas based on kinematic analysis of speeds and distances. However, little research has addressed the safety effects of merging and diverging and the interrelationship with geometric features. In this study, 26 interchanges were selected to quantify the effects of ramp terminal spacing and traffic volumes on safety performance through regression analysis. Negative binomial models were developed using 5 year collision data. Modelling attempts resulted in several statistically significant models relating traffic volumes and geometric features to collision frequency.
The potential usefulness of reliability analysis has recently been stressed in many engineering applications. Given the variability in the design parameters, a reliability-based probabilistic approach is well suited to replace the current deterministic highway design practice. However, progress in this regard is generally slow. In this study, the reliability analysis was used to estimate the probability of hazard (POH) that might result from insufficiency of sight distances. As an application, the available sight distance was checked against required stopping sight distance on an assumed road segment. Variation of the design parameters was addressed with Monte Carlo simulation using 100,000 sets of design parameters based on distributions available in the literature. A computer program was developed to use these sets of design parameters to calculate the profiles of available and required stopping sight distances in two- and three-dimensional projections as well as the profile of POH. The approach was applied to a horizontal curve overlapping with flat grade, crest curves, and sag curves in a cut section where the side slope would restrict the sightline. The analysis showed that the current deterministic approach yields very conservative estimates of available and required stopping sight distance, resulting in very low POH. The application example also showed the change of POH with the change of vertical alignment parameters.
A speed-change lane (SCL) is an auxiliary lane added to the traveled way for the acceleration and deceleration of vehicles entering or leaving a roadway. When the length of an acceleration SCL is adequate, drivers are able to accelerate comfortably from the speed at entrance to a speed appropriate to the road, find a gap in the traffic flow, and merge in a safe and secure manner. The length of an SCL is currently determined in terms of the ramp design speed, the freeway design speed, and the acceleration rate. Embedded in these values are assumptions for the operating speed at the entrance and merging points. This study examined a probabilistic approach instead of such a deterministic approach. The main benefit of a probabilistic approach is that traffic flow characteristics are assumed to be stochastic; therefore, the outcome of a probabilistic methodology is a distribution of drivers’ acceleration distance on the SCL. The reliability-based analysis enables designers to select a specific percentile value of this distribution as a design length that better matches a certain situation and avoids unnecessary extra construction costs. This paper presents analytical and simulation models for the application of the reliability approach, with all parameters based on recently collected field data. Even though the presented model should be superior to the deterministic model adopted in current design guides, additional enhancements are recommended for a full reliability-based, safety-explicit design model.
Sight distance is an important criterion in highway geometric design. Many design elements, such as horizontal and vertical curvatures and offsets to lateral obstructions, must be checked so that drivers have sufficient sight distance to operate safely. One of the obstacles that can restrict sight distance is the roadside or median concrete barriers that are frequently placed along the road edges for safety. There are common types and dimensions for such barriers, such as New Jersey, F-shape, and constant-slope concrete barriers. Such barriers may cause a significant reduction in the available sight distance on horizontal curves, especially in the lane closest to the barriers. However, there is a clear lack of a reliable, accurate tool to determine the available sight distance when the sight distance is restricted by road barriers in three-dimensional combined alignments. This paper uses a software package previously developed by the authors to examine closely the trends of available stopping sight distance and the effects of the overlapping vertical alignment. The results confirm previous findings that the available sight distance depends on the type of the vertical alignment and the curvature of crest or sag vertical curves overlapping on the horizontal curve. In addition, it is shown that the recommendations in current design guides could lead to barrier placement that compromises the available sight distance. Charts were prepared as an easy-to-use tool to estimate the available stopping sight distance on horizontal curves when overlapping with a specific vertical alignment.
In this paper, we obtained the expression for the noncommutative quadrupole potential and computed the second-order noncommutative quadrupole effect on the ground-state energy of the hydrogen atom. This computation was done using both the second-order perturbation theory and the exact computation using the Dalgarno–Lewis method. As a result, a sum rule was obtained and shown to be consistent with the quadrupole sum rule derived by Bell.
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