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

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1 Superelevation Criteria for Sharp Horizontal Curves on Steep Grades Geometric design policy for horizontal curves is established by the American Association of State Highway and Transportation Officials (AASHTO) and published in A Policy on Geometric Design of Highways and Streets (referred to as the Green Book). Design criteria for horizontal curves are based on a mathematical model that represents the vehicle as a point mass. As a vehicle traverses a horizontal curve, it undergoes a centripetal acceleration that is balanced by a combination of superelevation and friction at the tire–pavement interface. Horizontal curves designed in accordance with AASHTO policy have been shown to provide a substantial margin of safety with respect to vehicle skidding and rollover for both pas- senger cars and trucks under normal conditions. However, the policy indicates that vehicles traveling on steep downgrades or upgrades may require some adjustment in superelevation rates, to maintain an adequate margin of safety, for grades steeper than 5%. The supereleva- tion adjustment is made by assuming a slightly higher design speed for horizontal curves on steep downgrades and, because vehicles slow down on an upgrade, adding superelevation in the curve. The recommendation to adjust the design speed and superelevation on steep grades has not been fully investigated. The purpose of this research was to develop superelevation criteria for sharp horizontal curves on steep grades. A series of field studies and vehicle dynamics simulations were undertaken to investigate the combination of horizontal curve and vertical grade design criteria. The field studies included collecting vehicle speed and lane-change maneuver data from 20 locations across the United States. Additionally, tire–pavement friction data were collected at eight locations, representative of pavement surface conditions on multi- lane, divided highways. Crash data were acquired for the data collection locations and statistical models of the predicted number of crashes were estimated as a function of traf- fic volume and margins of safety for skidding and rollover. The vehicle dynamics simula- tions used the AASHTO design criteria, in combination with the field-measured data, to investigate the margins of safety against skidding and rollover for several vehicle types on sharp horizontal curves with steep grades. The point-mass model was the simplest model considered, while more complex models such as the bicycle and multibody models were also considered which simulate vehicles accounting for multiple axles and multiple tires, respectively. The following vehicle types were considered in this research: • Passenger Vehicles: – E-class sedan (i.e., mid-class sedan) – E-class sport utility vehicle (i.e., mid-size SUV) – Full-size SUV S U M M A R Y

2• Trucks: – Single-unit truck – Tractor semi-trailer truck – Tractor semi-trailer/full-trailer truck (double) The vehicle maneuver scenarios studied in this research for vehicles on curves include the following: • Vehicle maintains constant speed equal to the design speed of the curve (no deceleration, i.e., 0 ft/s2) • Vehicle brakes at a deceleration rate that drivers typically use when entering a curve (-3 ft/s2) • Vehicle brakes on the curve at a deceleration rate equivalent to that assumed for stopping sight distance design criteria (-11.2 ft/s2) • Vehicle brakes on the curve at a deceleration rate greater than that assumed for stop- ping sight distance design criteria, equivalent to the deceleration used in an emergency braking maneuver (-15 ft/s2) Each of these vehicle maneuver scenarios was considered for a vehicle maintaining its lane position and also for a vehicle changing lanes while traversing the curve and decelerating, as described above. The vehicle maneuver scenarios were assessed, and it was concluded that the following scenarios occur so rarely that they do not represent a reasonable basis for design: • Deceleration at rates greater than -11.2 ft/s2 while traversing a curve (i.e., an emergency stop with deceleration greater than that assumed for stopping sight distance design criteria) • Deceleration at rates of -11.2 ft/s2 or greater (i.e., a controlled stop with deceleration greater than or equal to that assumed for stopping sight distance design criteria) while traversing a curve and simultaneously changing lanes on the curve Thus, modifications to current AASHTO Green Book horizontal curve–superelevation design policy should be based on the assumption that a vehicle should be able to maintain its desired trajectory within the same lane while undergoing deceleration equivalent to that considered for stopping sight distance design criteria (-11.2 ft/s2). For this research, a sharp horizontal curve is defined as a minimum-radius curve as deter- mined from the maximum rate of superelevation and maximum side friction factor for each design speed, in accordance with the design criteria in the AASHTO Green Book. The results obtained here should assure that, if a vehicle can brake on a minimum-radius curve without loss of control, then that same vehicle will be able to brake on larger-than-minimum-radius curves without loss of control. The following conclusions were drawn from the research effort: • The AASHTO Green Book maximum side friction factors (fmax) used in horizontal curve design are below friction supply curves for lateral (cornering) and longitudinal (braking) directions, for both passenger vehicles and trucks, as measured in the field for design speeds greater than 20 mph. Thus, current horizontal curve design policy appears to pro- vide reasonable lateral friction margins against skidding in most situations. However, the more complex vehicle dynamics models (i.e., the transient bicycle and multibody models) indicate that the point-mass model generally overestimates the margins of safety against skidding and rollover across all vehicle types.

3 • There is no concern of a passenger vehicle rolling over while traveling at the design speed on a sharp horizontal curve with a steep downgrade, when designed according to current AASHTO Green Book policy. • Based upon a review of the literature, the lowest rollover thresholds for tanker trucks (i.e., liquid-cargo tank trucks) are in the range of 0.28 to 0.30. Because carriers are discouraged from hauling half-filled tanks, because completely filled and empty tanks produce rigid- load behaviors that are generally more predictable and the rollover thresholds are closer to 0.56 than 0.30, and because crash data show that few crashes involve vehicles with rollover thresholds less than 0.35, horizontal curve design and superelevation criteria should not be based upon tanker trucks with rollover thresholds of 0.28 to 0.30. Rather horizontal curve design and superelevation criteria should be based upon more typical loading and truck configurations. For vehicles considered in the simulation modeling in this study, the minimum rollover threshold was 0.56. • On downgrades, the lowest margins of safety against skidding and rollover generally occur at design speeds of 40 mph and lower for all vehicle types. This appears to be the result of higher side friction factors used in design for horizontal curves with lower design speeds. • Steep vertical downgrade–sharp horizontal curve combinations that necessitate braking to maintain a constant speed (and maintain lane position) from the approach tangent through a horizontal curve for a passenger car sedan have large margins of safety against skidding (>0.33) for design speeds ranging from 25 to 85 mph (see Figure 87). Similarly, positive margins of safety against skidding (≥0.23) for passenger cars that decelerate at a rate of -3 ft/s2 (similar to rates measured in the field for the present study and reported by Bonneson [2000b]) or at a rate of -11.2 ft/s2 (stopping sight distance deceleration) exist for all design speed–downgrade combinations considered in the present study. Decelera- tion rates of -15 ft/s2 (emergency braking) produce negative margins of safety for many design speeds for vertical downgrade–sharp horizontal curve combinations when the pas- senger car sedan enters the horizontal curve. However, the latter scenario does not seem likely to occur with sufficient frequency to constitute a reasonable basis for design. • Steep vertical downgrade–sharp horizontal curve combinations that necessitate braking to maintain a constant speed (and maintain lane position) from the approach tangent through a horizontal curve for a mid-size SUV have large margins of safety against skid- ding (>0.34) for design speeds ranging from 25 to 85 mph (see Figure 88). Similarly, margins of safety against skidding for a mid-size SUV that decelerates at a rate of -3 ft/s2 exceed 0.3 for all design speeds for vertical downgrade–sharp horizontal curve combi- nations considered in the present study. When mid-size SUVs must decelerate at a rate of -11.2 ft/s2 (stopping sight distance braking), positive margins of safety (>0.15) were produced for all design speeds for vertical downgrade–sharp horizontal curve combi- nations considered in the present study. Deceleration rates of -15 ft/s2 (emergency braking) produce negative margins of safety for most designs considered in the present study. However, the latter scenario does not seem likely to occur with sufficient frequency to constitute a reasonable basis for design. • The margins of safety against skidding for a full-size SUV were similar to those reported for the mid-size SUV (see Figures 88 and 89). • Steep vertical downgrade–sharp horizontal curve combinations that necessitate brak- ing for a single-unit truck to maintain a constant speed (and maintain lane position) from the approach tangent through a horizontal curve have large margins of safety against skidding (>0.25) for design speeds ranging from 25 to 85 mph (see Figure 90). Similarly, margins of safety against skidding for the single-unit truck that decelerates at a rate of -3 ft/s2 exceed 0.10 for all design speeds for vertical downgrade–sharp hori- zontal curve combinations considered in the present study. Based upon the steady-state

4and transient bicycle models for a vehicle, when single-unit trucks must decelerate at a rate of -11.2 ft/s2 (stopping sight distance braking) or a rate equivalent to emergency braking (-15 ft/s2), significant negative margins of safety against skidding result across all design speed–downgrade combinations considered in the present study. However, based on multibody model analyses for deceleration rates of -11.2 ft/s2 and -15 ft/s2 by a single-unit truck on a curve, the single-unit truck is able to maintain control on the curve when equipped with an anti-lock brake system (ABS). • Steep vertical downgrade–sharp horizontal curve combinations that necessitate braking for a tractor semi-trailer to maintain a constant speed (and maintain lane position) from the approach tangent through a horizontal curve have large margins of safety against skid- ding (>0.28) for design speeds ranging from 25 to 85 mph (see Figure 91). Similarly, mar- gins of safety against skidding for a tractor semi-trailer that decelerates at a rate of -3 ft/s2 exceed 0.26 for all design speeds for vertical downgrade–sharp horizontal curve combi- nations considered in the present study, and when a tractor semi-trailer must decelerate at a rate of -11.2 ft/s2, the margins of safety exceed 0.11. For emergency braking (-15 ft/s2), a tractor semi-trailer will experience negative lateral friction margins at low design speeds (e.g., 35 mph or less). The margins of safety against skidding were slightly higher for the tractor semi-trailer/full-trailer truck when compared to the tractor semi-trailer. The emer- gency braking scenario does not seem likely to occur frequently enough to constitute a reasonable basis for design. • When maintaining a vehicle operating speed at or near the design speed on a horizontal curve, grade and maximum superelevation rate (emax) appear to have little effect on the margins of safety against skidding and rollover for all vehicle types. • Eck and French (2002) suggest that high superelevation rates (e.g., between 8% and 16%) make horizontal curves on steep downgrades more forgiving. The vehicle dynamics simulations in the present study suggest that maximum rates of superelevation should not exceed 12% on downgrades because the superelevation transition occurring on the approach tangent can begin to reduce the margins of safety against skidding prior to curve entry. On curves designed with emax greater than 12%, the margin of safety against skid- ding by a vehicle may be smaller in the superelevation transition area than on the curve proper. Thus, the results of this research do not support the recommendation by Eck and French that emax values up to 16% should be considered in some cases. On upgrades of 4% and greater, emax should be limited to 9% for minimum-radius curves with design speeds of 55 mph and higher, to avoid the possibility of wheel-lift events. Alternatively, emax values up to 12% could be used for minimum-radius curves if it can be verified that the available sight distance is such that deceleration at -11.2 ft/s2 is unlikely to be required. • When vehicles change lanes in a horizontal curve, the margins of safety against skid- ding decrease considerably for all vehicle types considered in the present study. When lane changing occurs during a stopping sight distance or emergency braking maneuver, all vehicles exhibit negative margins of safety against skidding, as shown in Figures 132 through 143. For those situations (i.e., combinations of horizontal curvature, grade, and vehicle maneuvers) in which the transient bicycle model predicted skidding (i.e., nega- tive lateral friction margins), the multibody model showed that if a vehicle has ABS, and the driver properly responds to minor lateral skidding, then the vehicle can maintain its intended path. In cases where the driver does not correct the steering input in response to a lateral shift, and the vehicle is not equipped with ABS, the transient bicycle model showed the lateral skidding of passenger sedan vehicles with negative margins of safety is small (i.e., less than 1.5 ft in lateral direction) across all combinations of vertical down- grade, design speed, deceleration rate, and lane-change maneuvers. A mid-size SUV, full- size SUV, and single-unit truck without ABS all exhibit large lateral shifts when the margin

5 of safety against skidding is negative in certain conditions, most notably situations when more aggressive braking is needed such as deceleration rates similar to those used to develop stopping sight distance or emergency braking design criteria (-11.2 or -15 ft/s2). The case of a tractor semi-trailer without ABS need not be considered because all tractor semi-trailers are mandated to have ABS. [Note: Federal Motor Vehicle Safety Standard No. 121 mandates ABS on all new airbraked vehicles with gross vehicle weight ratings of 10,000 lb or greater. ABS is required on tractors manufactured on or after March 1, 1997, and airbraked semi-trailers and single-unit trucks manufactured on or after March 1, 1998 (Allen, 2010).] • Based on current AASHTO Green Book horizontal curve–superelevation design policy, a vehicle that performs an emergency braking maneuver (-15 ft/s2 deceleration) on a steep downgrade–horizontal curve combination will likely skid off the roadway in many cases if the vehicle is not equipped with ABS. • The method used in the current AASHTO Green Book policy to distribute superelevation and side friction on tangent–curve transitions is adequate and produces positive margins of safety against skidding and rollover for all vehicle types on horizontal curves designed using maximum superelevation and minimum curve radii. However, the superelevation attained at the point of curve entry should be checked and compared to a lateral friction margin condition to ensure that the lateral friction margin on the curve entry is not less than the margin within the curve. • AASHTO policy uses superelevation to balance the effects of sharper curvature. This bal- ance may be imperfect when axle-to-axle differences are considered. The balancing effect is slightly more conservative with higher superelevation rates, often resulting in lower lateral friction margins occurring for lower superelevations (e.g., 0% superelevation). However, differences in lateral friction margins between different superelevations are very small. • The crash analysis performed in the present study showed that the predicted number of single-vehicle run-off-road and single-vehicle rollover crashes decreases as the margins of safety against skidding and rollover increase for both passenger vehicles and trucks. The recommended design guidance developed based on the research conducted in the present study is as follows: • Figures 30 and 32 of this report show passenger vehicle and truck tire measurements of skidding wet-tire friction in the lateral (cornering) and longitudinal (braking) directions. It is recommended that the lateral friction curves (two standard deviations below mean) be integrated into AASHTO Green Book Figures 3-4 and 3-5, which show the maximum side friction factors used in horizontal curve design for high-speed and low-speed streets and highways (respectively). Incorporating these curves into Figures 3-4 and 3-5 of the Green Book would be informative to designers. The modified figures would, for the first time, illustrate friction measurements that take into consideration the effects of corner- ing. For a conservative design policy, horizontal curve–superelevation design policy rec- ommendations should be based upon the 2nd percentile (i.e., mean friction minus two standard deviations) of the friction supply provided at the tire–pavement interface. • For a simple horizontal curve, the maximum rate of superelevation should not exceed 12% on a downgrade. If considering a maximum superelevation rate greater than 12%, a spiral curve transition is recommended to increase the margins of safety against skid- ding between the approach tangent and horizontal curve. On upgrades of 4% or more, the maximum superelevation rate should be limited to 9% for minimum-radius curves with design speeds of 55 mph and higher, to avoid the possibility of wheel-lift events. Alternatively, if it can be verified that the available sight distance is such that deceleration

6at -11.2 ft/s2 is unlikely to be required on upgrades of 4% or more (i.e., the available sight distance is greater than minimum stopping sight distance design values), emax values up to 12% may be used for minimum-radius curves. • For sharp horizontal curves (or near minimum-radius curves) on downgrades of 4% or more, the “Stay in Lane” sign (R4-9) should be installed in advance of the curve on multi- lane highways. Consideration may also be given to using solid white lane line markings to supplement the R4-9 sign. • Sharp horizontal curves (or near minimum-radius curves) on downgrades of 4% or more should not be designed for low design speeds (i.e., 30 mph or less). In the event that such situations cannot be avoided, warning signs to reduce speeds well in advance of the start of the horizontal curve should be used. • The following condition should be used to check that the superelevation achieved at the point of curvature (PC) of a simple horizontal curve (i.e., with no spiral transition curves) is less than the threshold value computed based on the given design speed–curve radius combination: 100 1 1 tangent 2e p V gR < + × where: e = superelevation at PC of horizontal curve, ptangent = proportion of the maximum superelevation that is attained at the PC of horizon- tal curve, V = design speed (ft/s), g = gravitational constant (32.2 ft/s2), and R = radius of horizontal curve (ft). If the condition presented above is met, the superelevation transition may be placed as indicated in Green Book Table 3-18. If the condition presented above is not met, designers should reduce the proportion of the maximum superelevation attained at the PC of the horizontal curve, or introduce a spiral transition curve between the approach tangent and simple horizontal curve. Based on an analysis completed for the present study, the condi- tion above is satisfied for maximum-superelevation–minimum-radius curves for all design speeds. However, the condition above may be violated when using greater than minimum horizontal curve radii. In such cases, it is important to check the superelevation condition above, and if the condition is not met, it is recommended that a lower proportion of the superelevation runoff (e.g., 70%) be introduced prior to horizontal curve entry.