Superelevation Criteria for Sharp Horizontal Curves on Steep Grades (2014)

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7 S E C T I O N 1 1.1 Background Geometric design policy for horizontal curves is set by the American Association of State Highway and Transportation Officials (AASHTO) in A Policy on Geometric Design of High- ways and Streets, commonly known as the Green Book, and by the design manuals of individual highway agencies. These criteria are based on the physics of the interaction between vehicles and the roadway, as well as consideration of vehicle stability and driver behavior. As a vehicle traverses a horizontal curve, it undergoes centripetal acceleration equal to the square of the vehicle speed divided by the radius of the vehicle’s curved path. This acceleration is balanced by a combination of superelevation and friction between the pavement and tires on the vehicle. Horizontal curves designed in accordance with Green Book criteria, even minimum-radius curves, have been shown to provide a substantial margin of safety with respect to both vehicle skidding and rollover under normal circumstances for both passenger vehicles and trucks (Harwood et al., 1989; Harwood and Mason, 1994; Harwood et al., 2003). Geometric design criteria for horizontal curves are based on a simple mathematical model that represents the vehicle as a point mass. Research (MacAdam et al., 1985) has shown that the vertical loads on tires, in particular on trucks, and the side friction that can be supplied between the tires and pavement surface when traversing a horizontal curve vary dynamically and can be represented by a more sophisticated model than the point-mass model. Braking and tractive forces associated with vehicle maneuvering on grades also lead to variations between tires in vertical load and side friction supply. These variations in tire loads and vertical forces may lead to skidding or rollover at lateral accelerations less than those suggested by the point-mass model. Finally, the simple point-mass model assumes that the vehicle is on a planar surface. However, the combination of a superelevated curve and a steep grade cre- ates a road surface that is clearly not planar. The variation in the side friction factor values and tire loads suggested by the point-mass model in the AASHTO Green Book is expected to increase for horizontal curves on steep grades, but this phenomenon has not been thoroughly inves- tigated. NCHRP Report 439 (Bonneson, 2000b) included a preliminary investigation of this issue, based on a two-wheel “bicycle” model to represent a vehicle in a more complex form than the point-mass model. The Green Book has implemented the results from NCHRP Report 439 for horizontal curves on grades with the following policy statement: On long or fairly steep grades, drivers tend to travel faster in the downgrade than in the upgrade direction. Additionally, research has shown that the side friction demand is greater on both down- grades (due to braking forces) and steep upgrades (due to the tractive forces). Some adjustment in superelevation rates should be considered for grades steeper than 5%. This adjustment is particularly important on facilities with high truck volumes and on low-speed facilities with intermediate curves using high levels of side friction demand. In the case of a divided highway with each roadway indepen- dently superelevated, or on a one-way ramp, such an adjustment can be readily made. In the simplest practical form, values from Tables 3-8 to 3-12, presented in Section 3.3.5, can be used directly by assuming a slightly higher design speed for the downgrade. Since vehicles tend to slow on steep upgrades, the superelevation adjustment can be made by not reducing the design speed for the upgrade. The appropriate variation in speed depends on the particular conditions, especially the rate and length of grade and the magnitude of the curve radius compared to other curves on the approach highway section. On two-lane and multilane undivided roadways, the adjust- ment for grade can be made by assuming a slightly higher design speed for the downgrade and applying it to the whole traveled way (both upgrade and downgrade sides). The added superelevation for the upgrade can help counter the loss of available side friction due to tractive forces. On long upgrades, the additional super- elevation may cause negative side friction for slow-moving vehicles (such as large trucks). This effect is mitigated by the slow speed of the vehicle, allowing time to counter steer, and the increased experience and training for truck drivers. (AASHTO, 2011) Introduction

8The approach suggested in the Green Book of adjusting the design speed to determine the appropriate superelevation for curves located on steep grades is a suitable approach given the current state of research knowledge. Additional knowledge is needed, however, to make such guidance more quantitative for specific combinations of curvature and grade. 1.2 Research Objective and Scope The objective of this research was to develop superelevation criteria for sharp horizontal curves on steep grades. The basic elements of horizontal curve design, in addition to super- elevation, include the radius of curvature, curve length, side friction factor, and superelevation transition. These basic ele- ments of horizontal curve design, in addition to supereleva- tion, were considered in this research. This research was based on quantitative analyses. Data for the quantitative analyses were based on theoretical consider- ations and simulation, supported by actual field data collected at horizontal curves on steep grades. This research investigated operational and vehicle dynam- ics data for horizontal curves on grades of 4% and greater. The research documented in NCHRP Report 439 and incorporated in the 2011 Green Book indicates that an adjustment in super- elevation rates should be considered for grades steeper than 5%. Rather than assuming the current superelevation criteria are sufficient for grades of 5% and below, this research inves- tigated the impact on superelevation of grades as low as 4%. By considering grades of 4% and greater, this research more clearly and explicitly defined the boundary at which super- elevation rates on grades should be adjusted. The results of this research are applicable for urban and rural high-speed facilities including freeways, multilane divided and undivided highways, and two-lane roads; turning roadways (particularly ramps); and low-speed facilities. Both passenger vehicles and trucks were considered in developing the super- elevation criteria. This research focused on superelevation crite- ria for sharp horizontal curves on steep downgrades; however, because undivided facilities must also be considered, upgrades were studied as well. This research does not address issues related to pavement/ shoulder cross-slope breaks on horizontal curves. 1.3 Overview of Research Methodology In Phase I of the research, the research team summarized the literature related to superelevation criteria for sharp curves on steep grades. Topics covered in the review included horizontal curve design, the effects of heavy truck character- istics on horizontal curve design, the relationship between safety and horizontal curve design, driver comfort studies on horizontal curves, friction studies on horizontal curves, an overview of vehicle dynamics simulation modeling, and a summary of current horizontal curve design practice used across a range of state transportation agencies in the United States. The research team also identified critical parameters to be considered during field data collection and vehicle dynam- ics simulation modeling. In Phase II the research team conducted speed studies, an instrumented vehicle study, and friction testing at sites in the eastern and western parts of the United States. Data col- lection sites were identified through a review of geometric design data and crash data when available. Vehicle dynamics simulation models were used to model vehicle dynamics at the actual field data collection sites and a range of hypothetical horizontal and vertical geometries. The field data were used to validate the vehicle dynamics simulation models. The simu- lation models used in this research ranged in complexity from the point-mass model (least complex) to the bicycle model to multibody models (most complex). The vehicle dynamics simulation models were used to identify combinations of hori- zontal curves and grades where skidding and/or vehicle rollover may be of concern for either passenger vehicles and/or trucks. A crash analysis was also conducted to investigate the relation- ship between lateral friction and rollover margins and crashes. Based upon the results of the simulation models and the crash analysis, recommended design criteria for super elevation on sharp curves on steep grades were developed. 1.4 Key Terms The following list provides key terms used throughout this report and their definitions: Centripetal Acceleration (ar): an object that moves in a cir- cular path (i.e., horizontal curve) with a constant speed follows a path that is tangent to the curve. Because the velocity vector undergoes a change in direction, the object (i.e., vehicle) undergoes an acceleration perpendicular to the path and toward the center of the horizontal curve. The centripetal acceleration is equal to the square of the vehicle speed divided by the radius of the circular path. Lateral Acceleration: a term used by highway engineers that is equivalent to centripetal acceleration for the purposes of horizontal curve design. Radius of Curve (R): describes a horizontal curve with a con- stant radius. Minimum Radius of Curve (Rmin): minimum radius of hori- zontal curve, which is a function of the maximum rate of superelevation and the maximum demand side friction used in horizontal curve design. Side Friction Supply (ftire-pavement): friction available between the pavement surface and vehicle tires to prevent skidding

9 on a horizontal curve, also referred to as the coefficient of friction. The maximum side friction supply is utilized when a vehicle is at the point of impending skid. Side Friction Factor ( f ): the unbalanced portion of lateral acceleration or the portion of lateral acceleration that is not balanced by superelevation. The side friction factor represents demand side friction and is also referred to as net lateral acceleration in the point-mass model. Rollover Threshold (frollover): the maximum lateral acceleration that a vehicle can experience without overturning. Maximum Side Friction (fmax): the maximum side friction demand set forth in the AASHTO Green Book for use in horizontal curve design. The maximum side friction is based on driver comfort levels (i.e., tolerance for lateral acceleration) and is also referred to as the limiting side fric- tion factor. Sharp Horizontal Curve: a minimum-radius curve as deter- mined from the maximum rate of superelevation and maxi- mum side friction factor for each design speed, in accordance with the design criteria in the AASHTO Green Book. Lateral Friction Margin: the difference between the avail- able tire–pavement friction and the friction demand of the vehicle as it tracks the curve [i.e., side friction supply (ftire-pavement) − side friction factor (f )]. This friction margin represents the additional lateral acceleration that a vehicle could undergo without skidding. A positive margin indicates a vehicle can undergo additional lateral acceleration without skidding, while a negative margin indicates the vehicle tires will skid given the level of friction supplied between the tire and pavement for the condition in question. Rollover Margin: defined in two ways in the present study. One rollover margin is based on lateral acceleration, which represents the difference between the current lateral accel- eration and the maximum lateral acceleration that a vehi- cle can experience without overturning. Rollover margin is also defined by the proximity of the load-transfer ratio to an absolute value of unity, e.g., how close an axle is to expe- riencing wheel lift. In both cases, a value of zero indicates the onset of wheel lift. Steep Grade: in the present study, a vertical grade of at least 4%. Point-Mass Model: a vehicle cornering model, where the vehicle is assumed to be a single object whose overall size does not influence its behavior. Maximum Rate of Superelevation (emax): the maximum banking or cross slope of the roadway cross section within a horizontal curve; this value ranges from 4% to 12%, depending on climatic conditions, area type, terrain, and the frequency of very slow-moving vehicles in the traffic stream. Trucks: a range of vehicle types that include single-unit, trac- tor semi-trailer, and tractor semi-trailer/full-trailer trucks. Design Speed (VDS): selected speed used to determine the various geometric design features of the roadway. Operating Speed: the speed at which drivers are observed operating their vehicles during free-flow conditions. The most common measure of operating speed is the 85th per- centile of the free-flow speed distribution. Bicycle Model: a vehicle dynamics model that treats each axle of a vehicle as a single tire located at the midline of the axle. Multibody Model: a vehicle dynamics model that treats each tire of a vehicle as a separate kinematic body. Transient Vehicle Behavior: when a driver changes the steer- ing input on a vehicle (e.g., during transition from an approach tangent to a horizontal curve), the vehicle will enter the curve with motions that are initially unsteady (i.e., the spin of the vehicle, the yaw rate, will not at first match that of the curve) but settle out to a constant turn- ing path on the curve. The behavior of the vehicle in this time period is called its “transient response.” Steady-State Vehicle Behavior: at the conclusion of the period of transient response resulting from a steering input change, the yaw rate of the vehicle will become constant, which is referred to as “steady-state response.” 1.5 Outline of Report This report documents the entire research effort. The remain- der of this report is organized as follows. Section 2 summarizes the literature related to superelevation criteria for sharp curves on steep grades and presents current design policy. Section 3 describes the field studies conducted as part of this research and presents the results. Section 4 presents the analytical and simu- lation modeling work performed to investigate superelevation criteria for sharp horizontal curves on steep grades. Section 5 summarizes a crash analysis that investigated the relationship between crashes and lateral friction margins and rollover mar- gins. Section 6 presents the final conclusions and recommenda- tions of the research, including recommended design guidance and the need for future research. The remainder of the report consists of a list of references and three appendixes. Appen- dix A provides the nomenclature of the various symbols used throughout this report along with their definitions. Appendix B shows the vehicle input parameters used in the simulation modeling, and Appendix C presents changes proposed for con- sideration in future editions of the Green Book and Manual on Uniform Traffic Control Devices (MUTCD), based on the find- ings and conclusions of this research.