Horizontal Curve Design Research Articles

Reliability Based Geometric Design of Horizontal Circular Curves

Geometric design of horizontal circular curve primarily involves with radius of the curve and stopping sight distance at the curve section. Minimum radius is decided based on lateral thrust exerted on the vehicles and the minimum stopping sight distance is provided to maintain the safety in longitudinal direction of vehicles. Available sight distance at site can be regulated by changing the radius and middle ordinate at the curve section. Both radius and sight distance depend on design speed. Speed of vehicles at any road section is a variable parameter and therefore, normally the 98th percentile speed is taken as the design speed. This work presents a probabilistic approach for evaluating stopping sight distance, considering the variability of all input parameters of sight distance. It is observed that the 98th percentile sight distance value is much lower than the sight distance corresponding to 98th percentile speed. The distribution of sight distance parameter is also studied and found to follow a lognormal distribution. Finally, the reliability based design charts are presented for both plain and hill regions, and considering the effect of lateral thrust.

Safety Evaluation and Adjustment of Superelevation Design Guides for Horizontal Curves Based on Reliability Analysis

In general, the use of superelevation and changes in a road’s transverse slope are typically based on the road’s design speed to provide safety and comfort for a vehicle driving on a horizontal curve. However, due to the difference between operating and design speeds, there has always been uncertainty in determining the margin of safety using superelevation. This paper discusses the assessment of the safety margins obtained from the application of superelevation in horizontal-curve design. The assessment uses geometric design guides and a reliability index to determine any uncertainties in the design parameters. In addition, adjusted design charts of superelevation values related to the radius of horizontal curves at various levels of probability of noncompliance are provided. The results show that the adjusted superelevation values are generally greater than those derived from current standards. The adjusted design charts can help designers select an appropriate superelevation value for a particular horizontal curve for highways that have geometric constraints. These adjusted charts may also aid designers in predicting the consequences and safety margins associated with the selection of superelevation alternatives required to approve geometric designs that involve violations of the standard requirements due to environmental constraints.

Safety Effects of Horizontal Curve Design on Motorcycle Crash Frequency on Rural, Two-Lane, Undivided Highways in Florida

The association between horizontal curve design (e.g., radius and type) on rural, two-lane, undivided highways and motorcycle crash frequency is not well documented in existing reports and publications. This study aimed to investigate the effects of design parameters and associated factors on the occurrence of motorcycle crashes with consideration of the issue of unobserved heterogeneity. A random-parameters negative binomial regression model was developed on the basis of data on 431 motorcycle crashes, which were collected on 2,179 horizontal curves along two-lane, undivided highways in Florida for 11 years (2005 to 2015). Four normally distributed random parameters (i.e., logarithm of curve radius, reverse curves, pavement condition, and rough pavement indicator) were identified to represent their heterogeneity caused by unobserved factors over time, space, individuals, or some combination thereof. The major conclusions are the following: ( a) an increase in curve radius, on average, significantly and near-logarithmically reduced motorcycle crash frequency on rural, two-lane, undivided highways (this effect was more significant when the curve radius was less than 2,000 ft); ( b) 74.8% of reverse curves tended to reduce motorcycle crash frequency on rural, two-lane, undivided highways (for the remaining 25.2%, the effect had an opposite effect; on average, the likelihood of motorcycle crashes on reverse curves decreased by 39%); ( c) the crash modification function (CMF) for curve radius on rural, two-lane, undivided highways was established, given the radius of 5,000 ft as the baseline, as a power formula, CMF = (radius/5,000)-0.208.

Modeling Safety Effects of Horizontal Curve Design on Injury Severity of Single-Motorcycle Crashes with Mixed-Effects Logistic Model

Horizontal curves have been of great interest to transportation researchers because of expected safety hazards for motorcyclists. The impacts of horizontal curve design on motorcycle crash injuries are not well documented in previous studies. The current study aimed to investigate and to quantify the effects of horizontal curve design and associated factors on the injury severity of single-motorcycle crashes with consideration of the issue of unobserved heterogeneity. A mixed-effects logistic model was developed on the basis of 2,168 single-motorcycle crashes, which were collected on 8,597 horizontal curves in Florida for a period of 11 years (2005 to 2015). Four normally distributed random parameters (moderate curves, reverse curves, older riders, and male riders) were identified. The modeling results showed that sharp curves (radius <1,500 ft) compared with flat curves (radius ≥4,000 ft) tended to increase significantly the probability of severe injury (fatal or incapacitating injury) by 7.7%. In total, 63.8% of single-motorcycle crashes occurring on reverse curves are more likely to result in severe injury, and the remaining 26.2% are less likely to result in severe injury. Motorcyclist safety compensation behaviors (psychologically feeling safe, and then riding aggressively, or vice versa) may result in counterintuitive effects (e.g., vegetation and paved medians, full-access-controlled roads, and pavement conditions) or random parameters (e.g., moderate curve and reverse curve). Other significant factors include lighting conditions (darkness and darkness with lights), weekends, speed or speeding, collision type, alcohol or drug impairment, rider age, and helmet use.

Sight distance restriction on highways’ horizontal curves: insights and sensitivity analysis

The study focuses on sight distance restrictions on horizontal curves in highway design. Barriers along open highways and walls on tunnels may restrict the available sight distance in the design of horizontal curves. The study aims to finalize a desirable horizontal radius by examining the equilibrium requirement of the centrifugal force vs. horizontal sight distance constraints. The study examines these restrictions for the conventional case when the stopping sight distance lies within the length of the horizontal curve (case 1) and when the stopping sight distance lies outside the length of the horizontal curve (case 2). Also included in this study is a sensitivity analysis when the stopping sight distance is longer than the length of horizontal curve (case 2), based on the ratio between them. For the conventional case (case 1) the minimum horizontal radius that is based on the equilibrium of centrifugal force, is too small for the requirements of stopping sight distance when there are obstructions along the road that intrude on the line of sight. Sensitivity analysis results for case 2 show that the gap between the available horizontal stopping sight distance (for the minimum horizontal radius) vs. the design (demanded) stopping sight distance values and between the minimum horizontal radius vs. the desirable radius can be totally resolved when the ratio between stopping sight distance and the length of horizontal curve equals to 4.5 (for horizontal sightline offset of 4.8 m, i.e. shoulder width of 3.0 m plus half lane width of 1.8 m). Practically, the resulted conditions of the ratio between stopping sight distance and the length of horizontal curve are not feasible in horizontal curve design especially when the horizontal sightline offset equals to 3.0 m. When the limitations of horizontal stopping sight distance are valid and the obstruction height is higher than the maximum, the highway engineer might consider a tradeoff by increasing the horizontal curve radius as well as adjusting the design to case 2.

Multi-mode reliability-based design of horizontal curves

Recently, reliability analysis has been advocated as an effective approach to account for uncertainty in the geometric design process and to evaluate the risk associated with a particular design. In this approach, a risk measure (e.g. probability of noncompliance) is calculated to represent the probability that a specific design would not meet standard requirements. The majority of previous applications of reliability analysis in geometric design focused on evaluating the probability of noncompliance for only one mode of noncompliance such as insufficient sight distance. However, in many design situations, more than one mode of noncompliance may be present (e.g. insufficient sight distance and vehicle skidding at horizontal curves). In these situations, utilizing a multi-mode reliability approach that considers more than one failure (noncompliance) mode is required. The main objective of this paper is to demonstrate the application of multi-mode (system) reliability analysis to the design of horizontal curves. The process is demonstrated by a case study of Sea-to-Sky Highway located between Vancouver and Whistler, in southern British Columbia, Canada. Two noncompliance modes were considered: insufficient sight distance and vehicle skidding. The results show the importance of accounting for several noncompliance modes in the reliability model. The system reliability concept could be used in future studies to calibrate the design of various design elements in order to achieve consistent safety levels based on all possible modes of noncompliance.

Use of Side Friction in Horizontal Curve Design: A Margin of Safety Assessment

Current engineering practice uses a point-mass model to design horizontal curves on highways and streets. In this model, a maximum side friction factor is used, in combination with the selected design speed and maximum rate of superelevation, to determine the minimum radius of the curve for an alignment. The limiting value for side friction used in design was established in the 1940s and was based on driver comfort thresholds. The lateral friction available at the tire–roadway interface is a measure of friction supply and is dependent on the pavement surface type and condition, vehicle operating speed and deceleration characteristics, vehicle lane position, and tire type. The drivers’ selection of individual operating speeds on a roadway results in a side friction demand when traversing a horizontal curve. The purpose of this paper is threefold. First, key side friction concepts in horizontal curve design are described. This description includes the definitions of and the fundamental principles associated with the application of side friction factors in horizontal curve design policy. Second, the paper provides an analysis of the margin of safety in horizontal curve design policy. This analysis considers various vehicle types, pavement surface types, and operating speed distributions, and makes comparisons between friction supply, demand, and design side friction factors. Third, the paper describes a framework for more effective consideration of the current vehicle fleet, range of pavement conditions, and vehicle speed distribution in horizontal curve design policy.

Reliability-Based Design of Horizontal Curves on Two-Lane Rural Highways

Current design guides adopt a deterministic approach to the design of horizontal curves; each factor included in the design is represented by the near-worst-case value. In the context of horizontal curve design, the design procedure is based only on the driver comfort criterion, and data correspond to experiments conducted in the 1930s. Furthermore, current horizontal curve design procedures lack a quantitative evaluation for safety. To overcome those shortcomings, a new design framework is proposed to design horizontal curves; a probabilistic approach is adopted and two criteria are considered: vehicle dynamic stability and driver comfort. Reliability analysis was used to provide a quantitative evaluation for the design in regard to the probability of failure, probability of noncompliance, and reliability index. Outputs of simulation runs in a vehicle dynamics model were used to estimate demand lateral friction and lateral acceleration depending on the geometric characteristics of horizontal curves. In addition, data of an instrumented vehicle experiment were used to develop driver-level models for the distribution of the curve speed and driver comfort threshold. The first-order reliability method was used to estimate the probability of failure, probability of noncompliance, and reliability index. The proposed design framework and developed models were applied in an example to design a horizontal curve for a specific design speed.

Разработка критериев устойчивости автопоезда при назначении элементов плана автомобильных дорог

In the design of horizontal curves, the speed is set by the criterion of sustainability train. To determine the reliability of calculation methods and the effectiveness of interventions, arranged in these areas conducted field observations of the modes of movement of vehicles on curves. As a result of of data research in the field conditions established that at application of of this approach to designing of of transient curves with the device Superelevation the calculated speed of movement of on the given sites approached to normative for the data of categories of roads.

Research on the horizontal curve's radius under coupling effects of uneven adhesion coefficient and crosswind

In order to study the effects of uneven adhesion coefficient and crosswind on alignment design indexes, a six-axle semi-trailer is selected as the typical vehicle model to investigate the effects of uneven adhesion coefficient caused by superelevation under the condition of rainfall on the truck's lateral stability, quantifying the crosswind using TruckSim. Based on the basic theory of vehicle dynamics, vehicle safety driving model is established. Also, the minimum radius is calculated with the consideration of uneven adhesion coefficient and crosswind. The results show that the effects of uneven adhesion coefficient and crosswind on the truck's lateral stability increase with the increasing of the truck's speed. Truck's lateral slide instability begins to appear when crosswind grade grows up to 9 or above. According to sensitive analysis, speed, rainfall, crosswind, and the interaction of the speed and rainfall have significant influences on the truck's lateral stability. The results quantify the effects of uneven adhesion coefficient and crosswind on truck's lateral stability. The advised index for horizontal curve design control is proposed, which provides a good reference for road safety design and safety protective measures. It can also provide theoretical basis and guidelines for highway safe operation in the windy and rainy areas.

Incorporating Vehicle Emissions Models into the Geometric Highway Design Process

This study used fuel consumption and emissions on horizontal curves to provide guidelines and tools for quantifying environmental impacts. The second-by-second speed profiles for various conditions were generated on the basis of speed prediction and polynomial models. The generated speed profiles were matched with the rates of fuel consumption and emissions from the most recently developed motor vehicle emission simulator. Then, fuel consumption and emissions per second were aggregated during a trip on the curves. The results demonstrated that the design vehicle with a speed of 70 km/h consumed 34% more fuel on the curve that was designed with a 50% reduced radius than the recommended minimum standard in the Green Book. For emissions—carbon monoxide, nitrogen oxides, hydrocarbons, and particulate matter of 2.5 microns or less—there were increases up to 91% on the curve. In the benefit–cost analysis with actual horizontal curves with a radius less than half the minimum standard, the curve design improvement with the recommended minimum standard contributed to reducing fuel consumption, emissions, travel time, and societal and health effects, as well as construction and operating costs, by shorter length of alignment. Thus, horizontal curve design with the recommended minimum standards can be environmentally and economically beneficial throughout the life of the highway. This research also shows that adverse environmental impacts from vehicle movements on highways can be controlled and reduced through environmentally conscious highway design.

Reliability Approach to Horizontal Curve Design

AASHTO's Policy on Geometric Design of Highways and Streets contains geometric design criteria for horizontal curves for new and major reconstruction. These criteria are based on design side friction factors that were established in the 1940s. The objective of this research was to establish a probabilistic approach to the design of horizontal curves and compare the results with current design criteria. Reliability analysis commonly is used in structural engineering and recently has been used in stopping sight distance research for transportation design. In this research, design variables were considered random instead of deterministic to incorporate variations that occurred in the field (e.g., driver heterogeneity or differences in tire performance characteristics) into the analysis. The effects of wet pavements and tire characteristics for passenger cars and heavy trucks were considered. The superelevation rate was considered as a design input, and minimum radii for a target reliability index were presented for combinations of input mean speeds and superelevation rates. All other design inputs were considered random variables (e.g., available pavement friction), along with their appropriate distributions, in the reliability analysis. The results show that a target reliability index of 3.0 is appropriate for use in the probabilistic design of horizontal curves. Furthermore, when only skidding failure is considered, the design criteria for passenger cars can reasonably accommodate heavy trucks. The recommendations for future research consider probabilistic methods and more complex models of horizontal curve forces.

Superelevation Design for Sharp Horizontal Curves on Steep Grades

The objective of this study was to develop superelevation criteria for sharp horizontal curves on steep grades. Field studies were undertaken and vehicle dynamics simulations (point mass, bicycle, and multibody) were performed to investigate combinations of horizontal curve and vertical grade design criteria. The vehicle dynamics simulations used AASHTO design criteria and field-measured data to investigate the safety margins against skidding and rollover for several vehicle types on sharp horizontal curves with steep grades. Research results indicated that for a simple horizontal curve, the maximum rate of super elevation should not exceed 12% on a downgrade. A spiral curve transition is recommended if the maximum superelevation rate is greater than 12%. On upgrades of 4% and greater, the maximum superelevation rate should be limited to 9% for minimum-radius curves under certain conditions. The superelevation attained at the point of curve entry should be checked and compared with a lateral friction margin condition so that the lateral friction margin on curve entry is not less than the margin within the curve. On multilane highways, the “Stay in Lane” sign should be installed in advance of sharp horizontal curves on steep downgrades.

Stopping Sight Distance and Horizontal Sight Line Offsets at Horizontal Curves

Criteria for the design of horizontal curves implicitly rely on design speed to produce safe and efficient designs, particularly for horizontal sight line offsets and stopping sight distances. Current design guidance provides a method for calculating minimum horizontal sight line offsets that is accurate and valid only when both driver and object are within the limits of the curve. Other methods are available to estimate minimum horizontal sight line offsets when the driver, object, or both are not within the curve limits. However, design guidance recommends using the calculated value for offsets as a conservative estimate near the ends of curves. In this study, speed prediction models and reliability theory were used to estimate the probability that drivers would not have enough sight distance to see, react to, and stop before reaching an object in the roadway if horizontal sight line offset criteria were applied when the driver or object was outside the limits of a horizontal curve. Six scenarios at the curve approach and inside the curve were analyzed. Reliability estimates (based on minimum horizontal sight line offsets from current minimum design criteria) and stopping sight distance distributions (based on individual driver characteristics) indicated that the probability of drivers not having enough stopping sight distance was much greater on the approach to than inside the horizontal curves. For improvement of design consistency, the use of calculated horizontal sight line offsets beyond the limits of the curve (approach and departure tangents) is suggested to provide extra sight distance to drivers near the curve.

Review of Fundamentals of Road Design by Wolfgang KühnWIT Press, Billerica, MA; 2013; ISBN 978-1-84564-097-2; 327 pp.; $312.

Review of <i>Fundamentals of Road Design</i> by Wolfgang KühnWIT Press, Billerica, MA; 2013; ISBN 978-1-84564-097-2; 327 pp.; $312.

Reliability Analysis of Vehicle Stability on Combined Horizontal and Vertical Alignments: Driving Safety Perspective

A driver/vehicle/road closed loop dynamic simulation model considering three-dimensional (3D) alignment was established using Matlab/Simulink for reliability analysis of vehicle stability on the combined horizontal and vertical curve. Pavement friction and vehicle operating speed were considered as the random variables. The point-mass-model based performance function considering the failure model of skidding, vehicle dynamic simulation-based performance function considering the failure model of skidding, and vehicle dynamic simulation-based performance function considering the failure model of rollover were presented, respectively, according to crash types of vehicle occurring on the curve road. Monte Carlo sampling was used to solve reliability. Followed by a parametric study, the results show that the probability of skidding calculated by the vehicle dynamic simulation is larger than that by point-mass model; and the probability of failure decreases with increasing superelevation, while rises with increasing road slope. It indicates that the current horizontal curve design oversimplifies vehicle model, ignores vehicle transient responses, and separates the horizontal and vertical alignments, which could be adverse for vehicles navigating the curved road.

Developing safety performance functions incorporating reliability-based risk measures

Current geometric design guides provide deterministic standards where the safety margin of the design output is generally unknown and there is little knowledge of the safety implications of deviating from these standards. Several studies have advocated probabilistic geometric design where reliability analysis can be used to account for the uncertainty in the design parameters and to provide a risk measure of the implication of deviation from design standards. However, there is currently no link between measures of design reliability and the quantification of safety using collision frequency. The analysis presented in this paper attempts to bridge this gap by incorporating a reliability-based quantitative risk measure such as the probability of non-compliance (Pnc) in safety performance functions (SPFs). Establishing this link will allow admitting reliability-based design into traditional benefit–cost analysis and should lead to a wider application of the reliability technique in road design. The present application is concerned with the design of horizontal curves, where the limit state function is defined in terms of the available (supply) and stopping (demand) sight distances. A comprehensive collision and geometric design database of two-lane rural highways is used to investigate the effect of the probability of non-compliance on safety. The reliability analysis was carried out using the First Order Reliability Method (FORM). Two Negative Binomial (NB) SPFs were developed to compare models with and without the reliability-based risk measures. It was found that models incorporating the Pnc provided a better fit to the data set than the traditional (without risk) NB SPFs for total, injury and fatality (I+F) and property damage only (PDO) collisions.

Assessment of the design of reverse horizontal curves to accommodate heavy vehicles based on simulation

Current geometric design policies use passenger cars as design vehicles, while truck operational and dynamic characteristics are not included or not addressed consistently. Furthermore, critical geometric design parameters such as horizontal curves radii are determined without consideration of the effect of vertical alignment. The objective of this work is to investigate whether critical sections such as reverse horizontal curves with spiral curves, can accommodate typical heavy vehicles with safety. The analysis was focused on rural and suburban two-lane roads with undivided pavement that produce the largest accident rates. By means of road - driver - simulation system developed in TruckSim, the vehicle dynamic response to inputs from the immediate environment is analyzed, while same kind of outputs that might be measured with physical tests involving instrumented vehicles are calculated and plotted. Results indicated that horizontal curves minimum radii that are implemented according to several design criteria, can not be used in conjunction with the allowed interval of grades, and that the table of minimum radii must comprehend a limitation for the applicable grade. Otherwise, exclusively speed limits depending on the geometry or larger radii must be used in order to adequately accommodate heavy vehicles.

Comfort thresholds for horizontal curve design

A key to better geometric design of highways is designing horizontal curves conforming to driver behaviour. The values of side friction factors in the point mass formula, used for the design of the minimum radius of a horizontal curve, are based on the upper threshold of driver comfort. In the current guidelines, these driver comfort levels were established in research work carried out back in the 1930s. Recently, it was found that faster drivers tend to accept higher comfort thresholds to maintain their speed and minimize speed reduction between curve and tangent. An experiment was designed at Carleton University to collect newer data on driver behaviour including speed and lateral acceleration. The results confirmed the need to revise the values of side friction demand especially for sharp curves. In addition, a model was developed to determine the side friction factor to be used in design or in consistency evaluation of horizontal curves on rural roads and ramps.

Friction Reliability Criteria Applied to Horizontal Curve Design of Low-Volume Roads

Design of road horizontal curves usually considers geometric characteristics and surface pavement condition by means of friction, superelevation, and speed equations in a deterministic point of view: a unique radius and superelevation are selected, considering a uniform behavior of drivers and pavement surface condition. However, empirical evidence shows that operating speed usually exceeds design speed when design speed is lower than 100 km/h. This means that the aggregated friction demand exceeds the design friction. The friction threshold and variability are not considered in design at the present time. Therefore, the designer does not know the remaining friction available and cannot estimate the margin of safety provided by the design. This problem is important in low-volume roads (LVRs) because the design speed usually considered is lower than 100 km/h. In this paper a methodology to design horizontal curves for LVRs is proposed, considering the variability of skid resistance, pavement texture, driver behavior, and geometric design elements. Critical speed is obtained for two conditions: consistency between design and operational conditions and consistency between friction thresholds considered for the pavement surface and operational condition. For this purpose, a reliability index is estimated by using the Hasofer–Lind method. Results show that a more realistic design is obtained when an aggregated friction demand based on driver behavior is considered. A good design is obtained when design speed ranges around 60 km/h and the standard deviation of curve radius is lower than 20% of the mean radius.