Analyses of Vehicle Trajectories when Leaving the Traveled Way on Curved, Superelevated Road Sections

Transcription

1 Analyses of Vehicle Trajectories when Leaving the Traveled Way on Curved, Superelevated Road Sections AUTHORS: Dhafer Marzougui, Associate Professor Center for Collision Safety and Analysis (CCSA) College of Science, George Mason University 4087 University Dr., Fairfax, VA USA Tel: (703) , Fax: (703) Kenneth S. Opiela, Transportation Consultant 7904 Larrick Court, Springfield, VA USA Tel: (703) and Cing-Dao (Steve) Kan, Professor Center for Collision Safety and Analysis (CCSA) College of Science, George Mason University 4087 University Dr., Fairfax, VA USA Tel: (703) , Fax: (703) Word Count: 216 (abstract) (text) + 16*250 (11 figures, 5 tables) = words [Note: Multiple tables were included to cover the range of conditions analyzed, but some could be cut to reduce the number of words.] 1

2 Analyses of Vehicle Trajectories when Leaving the Traveled Way on Curved, Superelevated Road Sections ABSTRACT The curvature and surface slope are known to affect vehicle dynamics and influence trajectories. On curved roadway sections, the vehicle can leave the road at a sharper angle and with superelevation the vehicle may have greater vertical force components. Consequently, impacts with roadside barriers could potentially result in a higher impact severity. The objective of this effort was to apply vehicle dynamics tools to assess the trajectories of vehicles leaving the traveled way on curved, superelevated roadway sections. The intent was to develop a better understanding of the influence of various roadway curvatures, superelevation, and shoulder or roadside designs on these trajectories to develop recommendations for effective barrier features and placement in these situations. The analyses considered two types of vehicles, six roadway curvature and superelevations rates, three impact angles, and three speeds. Data is presented comparing changes in roll, pitch, and yaw for vehicles on a roadway departure trajectory. Normalize trajectory plots were used to the potential effectiveness of three types of barrier relative to override and underride. Graphs indicating effective placement locations were generated for the three barrier types. Tabular summaries of the relative effectiveness measures are also provided. Efforts continue on this research to develop recommendation for the selection and placement of barriers on curved, superelevated roadway sections. 1. INTRODUCTION Highways are comprised of tangent and curved roadway sections for which there are well established design criteria. Curved roadway sections on higher sped roads are generally constructed with superelevation to compensate for the centripetal forces exerted on the vehicles and to make it easier for the driver to control the vehicle through the curved section. There are well developed guidelines for the design of curved superelevated roadway sections embodied in the AASHTO Policy for the Geometric Design of Highway (i.e., the Green Book) [1]. The same cannot be said for the design and installation of barriers for such sections of the road network. It is known that crashes occur proportionately more often on curves than tangent sections, but it is not clear whether the effects of the curvature and superelevation affect crash propensity. Barriers are often deployed on curved, supelevated roadway sections (CSRS) as a continuation of barriers on adjacent sections and/or to address situations created by the superelevated curve (i.e., the embankment needed to provide the superelevation slope). Guidance for the testing and deployment of barriers on CSRS is limited at best. The need exists for a better understanding of the behavior of vehicles that leave the traveled way in such situations and the performance requirements for barriers in proximity to the CSRS Background The curvature and surface slope are known to affect vehicle dynamics and influence vehicle trajectories, orientation, and speed. On curved sections, the vehicle is more likely to leave the road at a sharper angle and consequently impact the barrier with greater force that could potentially result in a higher impact severity. The superelevation can lead to a higher interface with the barrier which can increase vehicle instability, barrier climb, vehicle roll-over, or override. Further, the superelevation with a negative shoulder slope might cause the vehicle to impact the barrier at a different orientation (roll and pitch). Thus, an important starting point for analyses of barriers on curved, superelevated roadway sections is to understand the dynamics of vehicles as they leave the traveled way on CSRS. 2

3 A considerable amount of effort has recently been devoted to analyzing the dynamic effects of vehicles on non-level terrain and the subsequent effects on their trajectories and interfaces with barriers. Vehicle dynamics analysis (VDA) has been shown to provide new insights on the effects of a vehicle s suspension system on trajectories in all three dimensions. Trajectory data in the vertical direction is, for example, directly related to the interface of the vehicle and the barrier. When the bounce of the suspension system causes a vehicle to exceed the height of the barrier, undesirable override conditions are likely to occur. The combined effect of the superelevation of the roadway, the slope of the shoulder, and the side slope of the roadside for a vehicle leaving the roadway in a curve can be explicitly analyzed using VDA tools. These tools readily allow the range of combinations of roadway, shoulder, and side slope design features to be analyzed for varying types of vehicles and their paths or trajectories determined. Guidelines for the testing and deployment of roadside safety barriers on sloped surfaces and curved sections are limited. For example, crash testing protocols for barriers have evolved to provide a practical worst case impact condition that is reproducible and comparable. Thus, barriers are tested under idealized impact conditions, with the tested barrier installed on a straight section having a flat approach terrain, and the impacting vehicle is freewheeling with minimum roll and pitch effects. These protocols have evolved to provide important assessments that allow determination of whether safety hardware is crashworthy. While crash testing protocols have evolved to include tests for a variety of angular impact conditions, one aspect that is not fully addressed is the crashworthiness of barriers installed on curved, superelevated roadway sections. A review of the literature revealed only a few older efforts to address the safety of designs or provide guidance for placement on CSRS. The need, therefore, exists to understand performance of longitudinal barriers along curved, superelevated roadway sections to develop effective barrier designs and appropriate placement guidelines for such locations. The need exists to systematically analyze a typical set of curved, superelevated roadway situations and the possible paths of errant vehicles to understand (1) the trajectories along the possible vehicle paths, (2) the associated vehicle-to-barrier interfaces for various barrier types and placement, and (3) the stability of the vehicle (i.e., functions of induced roll, pitch, and yaw effects) may affect the engagement with the barrier and its crashworthiness.). The VDA results provide a convenient means to understand trajectories and interface scenarios, as well as indicate those critical scenarios that warrant crash simulation analyses. The analysis of the overall motion of a vehicle can be very complex, especially at higher speeds. However, the vehicle motion is primarily governed by the forces and moments generated by the interaction of the tires and the ground. In most vehicle dynamics studies, only six degrees of freedom are studied: longitudinal, lateral, and vertical displacement and the roll, pitch, and yaw angles. Generally, the vehicle fixed coordinate system is associated with the center of gravity (CG) of the vehicle, but it is possible to generate metrics that allow the frontal interface region for each vehicle to be determined. These data allow one to evaluate potential barrier effectiveness given road departure speed and angle for the surface conditions associated with the roadway, shoulder, transition to the side slope, and the side slope. Such metrics are important to understanding the nature of the frontal region of the vehicle relative to the barrier Objective The objective of the efforts reported here was to apply vehicle dynamics tools to assess the trajectories of vehicles leaving the traveled way on curved, superelevated roadway sections. 3

4 The intent is to develop a better understanding of the influence of various roadway curvatures, superelevation, shoulder/roadside designs, and barrier features and placement on the dynamic response of vehicles and to assess the ultimate safety performance of barriers used in these situations. 2. RESEARCH APPROACH In this analysis, vehicle dynamics simulations were performed to assess vehicles trajectories as they crossed from the traveled way to the side-slope with varying shoulder widths for different roadway curvatures and superelevation. Simulations were conducted with varied vehicles, speeds, and departure angles. The following sections describe the VDA approach, the software tool used, and the factors considered in the analyses matrix. This section also describes the cases selected for analyses and the parameters describing them Vehicle Dynamics Analysis Applications The concept of using vehicle dynamics simulation software to analyze run-off-road vehicle behavior and motion is gaining popularity. McMillan in 1998 [2] conducted simulation studies to analyze driver response to roadway departure. This analysis was used to evaluate the ability of collision countermeasure systems to prevent run-off-road accidents. Similar analyses have been performed by Pape in 1996 and Hadden in 1997 [3, 4] where they extended the VDANL (Vehicle Dynamics Analysis, Non-Linear) model of the vehicle/driver to assess the effectiveness of the countermeasure system. Other studies have focused on the results of an off-road crash. Day and Garvey [5] used EDVSM (Engineering Dynamics Vehicle Simulation Model) to perform rollover simulations. They discussed the limitations of rollover simulation for on-road and off-road accident reconstruction. The use of simulation software for the analysis of off-road crashes has been very broad. Claar [6] concentrated on suspension modeling for improving off-road ride comfort whereas some studies have focused on friction influences in the case of water or snow on the road surface, as did Mancosu in 2002 [7]. There has been little research using vehicle dynamics simulation software to analyze and enhance the roadway design itself. In 2004, Sicking and Mak [8] presented a paper which suggested that efforts should focus on developing better vehicle and roadside safety hardware models. Also, they indicated that significant effort must be devoted toward improving the capability of computer simulations to model run-off-road crashes. The NCAC (National Crash Analysis Center) staff used the HVE simulation program to study the effect of edge drops for guardrail roadside barrier performance [9]. They used varied initial conditions and different vehicles to analyze the behavior of the vehicle encountering various edge drops. The NCAC used VDA to trace two critical points on impacts with W-beam guardrails to determine barrier effectiveness relative to vehicle underride or vaulting. Similarly, the NCAC made extensive use of VDA to analyze the effects of median configurations on the effectiveness of cable barrier placement [10, 11, 12]. Lastly, a study conducted at Pennsylvania State University [13] showed the utilization of commercially-available VDA software as a tool to analyze the effect of highway median width and slope on vehicle stability. Brennan and Hamblin used the CarSim programs to run thousands of simulations using different vehicles, median widths and slopes, steering conditions, and initial conditions to generate various metrics, including roll and lateral velocity. The resulting data were used to provide a preliminary assessment of tradeoffs in the size and slope of median profiles versus the types of accidents observed. 4

5 2.2. Analyzing Vehicle Dynamics There is a well-developed body of knowledge about the physics of vehicles that has evolved with automotive industry. Detailed vehicle dynamics analysis has been packaged into commercially available software tools. The vehicle dynamics analyses in this effort were undertaken with the CarSim software [14]. CarSim is a non-linear vehicle simulation model capable of analyzing vehicle-roadway interaction and providing a detailed description of the vehicle s trajectory considering speed, weight, suspension system, surface features, and other factors. It is readily linked to development tools such as MATLAB to extend its functionality. It also allows batch inputs to reflect ranges of conditions that define performance enveloped Critical Vehicle Interface Analysis Approach Findings in this research effort from the literature review, the state DOT survey, reviews of design documents like the AASHTO Green Book, and discussions with the Project Panel led to the identification of factors believed to affect the safety performance of longitudinal barriers when placed on curved, superelevated roadway sections. These factors and specific parameters associated with them are indicated below. Barrier Type o Concrete barrier (height 32 in [813 mm]) NJ-shape concrete barrier o Strong post W-beam guardrail (height < 31 in [787 mm]) G4(1S) o Strong post W-beam guardrail (height 31 in [787 mm]) MGS Vehicle Type o 2270P pick-up truck 2007 Chevrolet Silverado model o 1100C small car 2010 Toyota Yaris model Curvature/Superelevation Combinations o 614 ft (187 m) / 12% o 2130 ft (649 m) / 12% o 758 ft (231 m) / 8% o 2670 ft (814 m) / 8% o 833 ft (254 m) / 6% o 3050 ft (930 m) / 6% Width and Slope o 4 ft (1.22 m), 8 ft (2.44 m), and 12 ft (3.66 m) widths o 0%, 3%, and 6% slopes (-2% added) Roadside Slope o 12H:1V (negative) relative to shoulder for all simulations Impact Conditions o Three impact angles: 20, 25, and 30 degrees o Three impact speeds: 57, 62, and 67 mph (90, 100, and 110 km/hr) Barrier Placement Relative to Road Section o Lateral position: at edge of shoulder, 4 ft (1.22 m) offset, and 8 ft (2.44 m) offset o Vertical orientation (normal to road and parallel to true vertical) VDA software was used to simulate vehicle behavior for the above range of conditions to obtain trajectories for each case. Aggregating the results across subsets of these parameters allowed the generation of maximum and minimum trajectory traces that provide a means for analyzing vehicleto-barrier interface for varying lateral placement. These results provide a basis for identifying critical scenarios for the finite element simulations, as well as providing insights useful to generating recommendations for improved practices. 5

6 2.4. Vehicles Considered The study focused primarily on two different types of vehicles typically found on US highways: a Chevrolet Silverado pick-up truck (2270 kg) and a Toyota Yaris sedan (1100 kg). These vehicles correspond to test vehicles defined in MASH. The specific weigh, size, frontal geometry, and suspension system characteristics of these vehicles were incorporated into the VDA. In these analyses two points were defined for each type of vehicle considered to represent the primary interface (engagement) region on the vehicle. These points are labeled 1 and 2 on Figure 1. The points are located at positions on the front of the vehicles that are believed to represent the engagement point that differentiates between tendencies to override or underride a barrier. Point 1 for the small vehicle is located at a height of 21 inches, while Pont 2 for the pick-up has a height of 25 inches. These point positions were defined by examining the frontal profile of the vehicle and reviewing full-scale crash tests conducted using similar vehicles. The traces of these points are critical in determining the interface with barriers for any vehicle trajectory. Point Point Figure 1 Vehicle models used in VDA analyses and critical interface points defined 2.5. Vehicle-to-Barrier Interface Regions Three barriers were selected for analysis and an interface region was defined such that if the two critical points (Point 1 and Point 2) are inside this region at the start of the impact, the barrier is considered likely to redirect the vehicle. If Point 1 (from the small car) falls below the interface region, an underride or significant snagging is likely to occur. Similarly, if Point 2 (from the pickup truck) is above the interface region, vehicle override is likely to occur. The interface regions are shown with a green shaded box in Figure 2 as the maximums and minimums. These regions are defined based on the geometry of the barrier and review of full-scale crash tests conducted on these barriers. For the concrete barrier, only the override condition is considered, so there is no minimum. It is important to note that these interface analyses accounted for the effects of vehicle orientation (changes in roll, pitch, and yaw angles) in computations to determine the positions of Points 1 and 2 relative to the vehicle center of gravity (CG). Further, variations in the designs of these barriers, such as the inclusion of rub rails, increased heights, or different shapes for the concrete barrier were not considered. 6

7 a - G4(1S) b MGS c - NJ Concrete Barrier Figure 2 Interface regions for the three barriers selected 2.6. Roadway Curve Conditions Various degrees of roadway curvatures were considered in the study to reflect the range of superelevation applications commonly found on highways. These range from tight curves used on ramps to gentle sweeping curves. Figure 3 provides examples of the range of curves considered in the simulation. A total of six roadway curve conditions with different curvatures and superelevations were used in the VDA analysis. These conditions were selected based on the Green Book design superelevation tables. The analyses incorporated three superelevations (6, 8, and 12%). For each superelevation, two curvatures were selected representing the minimum radii at the 50 mph (80 km/hr) and 80 mph (130 km/hr) design speeds. Figure 3 Typical Variations in Roadway Curvature 7

8 3. ANALYSIS OF VEHICLE TRAJECTORIES ON CSRS Figure 4 shows the typical path or trajectory (via sequential images) of a vehicle attempting to negotiate a curve before departing the roadway. A superelevated curve would have a cross section perpendicular to the centerline (as indicated by the black line and shown in Figure 5. In this case, the banking of the roadway surface is exaggerated. The shoulders reflect a negative slope relative to the roadway. The red line reflects to the typical path or horizontal trajectory of an errant vehicle leaving the road on a CSRS. It shows a rising surface reflecting a diagonal crossing of the superelevation followed by either negative, neutral, or positive slopes for the shoulder, and then a 12H:1V roadside slope. In the VDA analysis, the vehicle was run a distance of about 1000 ft (300 m) on this surface to be in a curve operation equilibrium state before it is directed off the road. Several predefined departure paths are input into the software to represent various departure angles. Repeated simulations of vehicles traversing such paths were simulated. These were varied to reflect exit angles of 20, 25, and 30 degrees for the vehicles traveling at 57, 62, and 67 mph (90, 100, and 110 km/h). Figure 4 VDA Generated Perspective of Vehicle Leaving the Road 8

9 Figure 5 Vertical Surface Cross Section for a Sharp, Superelevated Curve In this research, a number of different possible conditions for road departures were considered with the following underlying assumptions: The vehicles carry a single average male occupant. The roadside has a firm surface, making ploughing or furrowing into the surface by tires is negligible. Vehicles are tracking as they enter the roadside (i.e. vehicle initial speed is in same direction as its longitudinal axis). Velocity of the vehicle was kept constant during the simulation. There are no driver inputs (e.g., steering, braking) that affect the vehicle. The road friction was made identical in all runs using a friction coefficient of 0.9. The simulation software provided dynamics analysis results every thousandth of a second as the vehicle traversed the roadway, shoulder, and side slope. There is a smooth transition between the pavement and shoulder and shoulder and side slope. Where this is not the case, other effects will occur that will alter the stability of the vehicle Vehicle Dynamics Analysis for a Worst Case Departure Scenario The dynamic effects on a vehicle traversing a worst case path for a CSRS was undertaken to better understand the effects as reflected in changes in the vehicle s trajectory (i.e., x-, y-, and z- coordinates, and the roll, pitch and yaw rates). The effects were considered to be the greatest where the higher slopes and inflection changes took place. These analyses also consider that they occur as the vehicle is on a diagonal path, so the right front tire will incur the change before the left front tire and so on. Such changes imply that the changes at Points 1 and 2 located on the right front will be different for the left front. The VDA results reflect such differences as shown in Figures 6 and 7. Figure 6 shows the effect of vehicle type and supereleveation on the angles of the vehicle. The plots cover a duration of 12 seconds, but the critical period is between 4 and 7 seconds where the vehicle is reaching the shoulder, traversing it, and then encountering the side slope. Similar patterns are noted for the roll angle for both vehicles (1100C and 2270P) and for both the superelevated and non- superelevated cases. A negative roll begins when the tire encounters the shoulder slope, but it is countered as more of the vehicle gets on the shoulder. The roll effect 9

10 becomes constant once the vehicle gets on the side slope. The variation between the sets of curves reflects the roll effect induced by the superelevation. Figure Yaw angle plot in Figure 6 shows the greatest amount of deviation, but it must be noted that the scale reflects small changes in pitch. The inflection points occur when the shoulder and the side slope is reached for either vehicle. The effect on the pick-up is greatest for the pick-up without superelevation. For the yaw, the dynamics of both vehicles is similar for all cases as the vehicle traverses the shoulder and the reaches the side slope. The pick-up shows more change in yaw on the side slope than the small vehicle due to its longer wheelbase. Figure 7 shows the effect of vehicle type and superelevation on the X, Y and Z position of the vehicle CG. As would be expected, there is little difference in the X- and Y- values for the horizontal trajectory. The Z-value while appearing different, only reflect the difference in height associated with the superelevation. These metrics show that for this worst case that the vehicle is relatively stable as it traverses the shoulder and initial part of the side slope. It also suggests that the VDA tool is reflecting the variations in surface conditions. This indicates that there is not likely to be a lot of extraneous variance in the consolidated interface results. Other conditions related to these assumptions could be modeled, but they were not at this stage. A- Roll Angle B- Pitch Angles C- Yaw Angle Figure 6 Comparisons of Roll, Pitch, and Yaw Angles on Sharp Curve with Negative & Side Slopes. A- X Position B- Y Position C- Z Position Figure 7 Comparison of X, Y, and Z Position on Sharp Curve with Negative & Side Slopes. 10

11 4. VEHICLE DYNAMICS ANALYSIS RESULTS The VDA software was used to generate trajectories for each of the vehicles at the selected exit angles and speeds for each road departure condition. The vertical trajectories or trace paths of Point 1 for the 1100C vehicle (brown) and Point 2 for the 2270P vehicle (blue) negotiating a curve and departing onto the roadside of a given configuration are shown in Figure 8 by line color and type (Note the various vehicle weights, speeds, and exit angles in the legend). These trace paths would be visualized by standing on the roadside downstream from the point a vehicle leaves the roadway and observing the change in elevation of Point 1 or 2. Multiple curves reflect variations in departure speed and angle for each of the vehicles (as noted in the legend). The differences in basic vehicle heights are reflected by the relative positions of the two sets of curves. There is a consistency in the heights with the road profile shown by the black line at the base of the graph. Dynamic effects of the sprung mass cause the curves to vary for the changes in cross section conditions. A similar graph was generated for each set of the conditions in the analysis matrix. Figure 8 Sample plot of non-normalized vehicle trajectory Figure 9 shows an example of the typical results in a normalized representation of the vertical trajectory. In the normalized view the variations in trajectory are indicated relative to a horizontal plane as opposed to the actual cross section surface. The lower pane shows the path profile or cross section as a reference for the vehicle dynamics traces. The normalized view provides a convenient means to analyze and compare vehicle dynamics effects for different conditions simultaneously. The normalized version is also useful to translate the vertical trajectories to a common plane to allow the aggregation of groups of results to define limits. Figure 10 depicts a primary use of the normalized graphs of the trajectory data. All trajectory traces for a given set or subset of conditions were plotted from which maximum and minimum limit curves can be derived. In this case, the red line represents the maximum trajectory height limit across the entire path. Similarly, the green line indicates the minimum trajectory height. These limits indicate requirements for any barrier system in that roadside configuration for any lateral positions beyond the shoulder. This approach can be used to determine the potential effectiveness for varying barrier systems across all possible lateral positions for a given roadside configurations. 11

12 Figure 9 Sample plot of normalized vehicle trajectories Maximum limit curve Minimum limit curve Figure 10 Example use of normalized view to show limiting conditions Figure 11 shows more specific examples of how the plot of maximums and minimums can be applied. For a given superelevated curve and roadside configuration (e.g., 614 ft [187 m] radius curvature and 12% superelevation) the limits can be plotted along with the interface area provided by a specific barrier. These interface areas are represented by the blue and green lines that reflect the maximum and minimum vertical position of the vehicle critical points as it leaves the roadway and moves onto the roadside. For the barrier to be effective, it must have a good interface with the 12

13 large and small vehicles at any given lateral position. The graphs show the limits for the G4(1S) and MGS barriers as yellow lines across the graph for various positions where it can be placed. If the maximum and minimum limits fall with the yellow lines then the barrier will have a good interface. Where the blue line goes above the top yellow line there is the opportunity for an override to occur. Where the green line falls below the lowest yellow line, the possibility of an under-ride exists. The lower portion of Figure 16 shows the profile or cross section of the road related to the upper graph. Effective placement areas are shown in this pane. The red hatched area defines the lateral positions where the specific barrier has an interface area above the maximum lower height limit (green curve) and/or below the minimum height limit (blue curve). Effective lateral placement occurs where both criteria are met are shaded green. The differences in the effectiveness of the G4(1S) and MGS barriers (by virtue of their design differences) is reflected when the effectiveness areas are compared. The Limits as a function of vehicle dynamics for the given configuration remain the same, but the yellow barrier isobars are different. Plots of this type for all different curve and roadside configurations selected were generated and are presented at the end of this document. Thus, effective lateral placement options can be studied and inferences for crash simulation analyses derived. Tables 1 and 2 summarize the effectiveness results for the analyses of two barriers for a common curvature and superelevation condition. Deciphering the content of 82 graphs can be daunting, but they are presented so that the vehicle dynamics for specific cases can be analyzed. The following observations were noted overall from these graphs: Each graph represents the aggregate of 36 VDA runs to reflect the effects of each of the 82 roadway curvature, superelevation, shoulder, and roadside slope configurations for three speeds, three exit angles for the two vehicles. These are normalized dimensions for the heights of Points 1 and 2 and the critical barrier heights meaning that a horizontal plane represents the common reference surface. There are points of inflection in the maximum and minimum traces in each graph induced by the changing of the profile from the roadway to the shoulder and later to the roadside slope. The maximum and minimum traces are not uniform as they are associated with vehicles of different weights and size. Weight influences basic dynamic response. The graphs run out more than 35 feet beyond the edge of traveled way. This might be useful in considering clear zone options for curved, superelevated roadway sections where 12H:1V roadside slopes are possible. The yellow lines are isobars indicating the critical heights for the specific barrier at any lateral placement position from the edge of the travel way. The degree of change in point height or bounce is a function of the degree of change from one surface to the next (e.g., traveled way to shoulder). The bounce effect is lower for the gentler curves (i.e., longer radius) when all other conditions are the same. The bounce effects vary with the width of the shoulder. The effectiveness is a function of the barrier s critical heights for any trace condition. The relationships cited can be more explicitly depicted by comparing graphs for a selected factor (e.g., curvature, superelevation) to others where the parameters are the same. More insights are provided by looking at tabular summaries of the interfaces for specific barrier placement conditions. 13

14 Figure 11 Barrier interface & effectiveness analyses for a given curve and roadside profile 14

15 Table 1 Profile Comparisons Curvature 614 ft, G4(1S) Barrier. Case Parameters Profile Diagram Case - 1 Curvature: 614 ft Superelevation: 12 % Width/Slope: 4 ft/ 0 % Case 2 Curvature: 614 ft Superelevation: 12 % Width/Slope: 4 ft /3 % Case 3 Curvature: 614 ft Superelevation: 12 % Width/Slope: 4 ft / 6% Case 4 Curvature: 614 ft Superelevation: 8 % Width/Slope: 8 ft / 0% Case 5 Curvature: 614 ft Superelevation: 8 % Width/Slope: 8 ft / 3% Case 6 Curvature: 614 ft Superelevation: 8 % Width/Slope: 8 ft / 6% Case 7 Curvature: 614 ft Superelevation: 6 % Width/Slope: 12 ft / 0 % Case 8 Curvature: 614 ft Superelevation: 6 % Width/Slope: 12 ft / 3 % Case 9 Curvature: 614 ft Superelevation: 6 % Width/Slope: 12 ft / 6% 15

16 Table 2 Profile Comparisons Curvature 3050 ft. New Jersey-shaped Concrete Barrier Case Parameters Profile Diagram Case 1 Curvature: 3050 ft Superelevation: 12 % Width/Slope: 4 ft/ 0 % Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 Curvature: 3050 ft Superelevation: 12 % Width/Slope: 4 ft /3 % Curvature: 3050 ft Superelevation: 12 % Width/Slope: 8 ft / 6% Curvature: 3050 ft Superelevation: 8 % Widthlope: 8 ft / 0% Curvature: 3050 ft Superelevation: 8 % Width/Slope: 8 ft / 3% Curvature: 3050 ft Superelevation: 8 % Width/Slope: 8 ft / 6% Curvature: 3050 ft Superelevation: 6 % Width/Slope: 12 ft / 0% Curvature: 3050 ft Superelevation: 6 % Width/Slope: 12 ft / 6% Curvature: 3050 ft Superelevation: 6 % Width/Slope: % 5. TABULAR SUMMARIES OF INTERFACE ANALYSES The VDA results were used to determine the maximum and minimum heights for all combinations of curvature, superelevation, and shoulder width and slope for the three barrier lateral placement conditions (i.e. L1, L2, L3) for each of the three barrier systems selected. The maximum and minimum heights are tabulated in Tables 1 through 3. Each cell represents the barrier height for the specific conditions. If the value is red, then it implies that the height is outside the limits (e.g., too high or too low). These tables as well as the interface plots, shown at the end of this document, 16

17 are used to provide the basis for determining those cases or types of cases that need to be analyzed with crash simulation. Analyzing the content of tables with 324 cells may not be any less daunting, but it is useful to note that the maximum and minimum heights in each of the cells in the same for each of the tables because the VDA interface results are generic to any type of barrier at a given lateral position. A difference in each of the tables is that the cell values are red for those cases where on of the three barriers does not provide a good interface for the conditions. Looking across all the values in the table it can be seen that the critical heights range from just under 19 inches to almost 30 inches. Looking at the results in each of the tables offers the insights noted below: Table 3 provides a summary for three placement options for the New Jersry-shaped Concrete Barrier. It can be noted that: o Since the concrete barrier has a 0 minimum interface height this barrier works all Min cases for all the curvature, superelevation, shoulder, and placement conditions. [This can be noted by observing that there are no red values in any of the Min rows.] o Similarly it can be noted that this barrier provides a good interface for all L1 placements by noting no red values in any of the columns labeled L1. o It might be inferred that the L3 placement option worked better for the gentler curves than sharp because there are fewer red values in columns labeled L3. o It can be noted that the highest maximum height value is inches, which suggests that the use of a concrete barrier with a critical interface height of 30 inches would provide good interface for all of the conditions considered here. Table 4 provides a summary for three placement options for the G4(1S) W-beam Guardrail Barrier. It can be noted that: o The G4(1S) barrier appears to meet the minimum interface requirements for all cases as there are no red values for any of the min rows. o There are only a few cases where the maximum requirement is met as indicated by the non-red values. These, interestingly, all occur for L1 placement and 0% shoulder slope cases. o Many of the red values are just slightly higher than the 25.5 inch maximum interface height requirement suggesting that a slightly higher version of the barrier might be warranted for these conditions. Table 5 provides a summary for three placement options for the MGS W-Beam Guardrail Barrier. It can be noted that: o The greater height of the MGS barrier accounts for more good maximum interface indications across a range of conditions [For example, all rows for 8 foot shoulder width meet the maximum requirement]. But there is not a corresponding meeting of the minimum requirements across any of the rows. A barrier must address both. o The MGS barrier meets both maximum and minimum for L1 and L2 placements for all shoulder conditions for the gentle radius curves. [There are two cases where the values are less than 0.20 inches off.] o Many of the red values are just slightly higher than the inch maximum and 21.0 inch minimum interface height requirements suggesting that a slightly modified version of the barrier might be practical for these conditions. These and other insights demonstrate the value of the VDA results. 17

18 6. SUMMARY AND CONCLUSIONS In this effort, trajectories for vehicles departing from curved, superelevated road sections were determined using vehicle dynamics analysis tools. VDA tools allowed the entry of data for specific vehicles that reflected differences in size, weight, suspension features, and other factors as well as the conditions of the cross-sectional surface for various conditions under which a vehicle can leave the roadway (i.e., speed, angle). The trace plots generated as the vehicle traverses the various cross sections reflected the effects of the suspension and provided useful insights into effects on the vehicle s interface area relative to the surface. The latter aspect is a critical metric for determining the most effective lateral placement of the barrier. The results from this analysis provide useful insights for identifying critical cases to be investigated using finite element simulations, as well as making recommendations for guidance on selecting and placing barriers on curved, superelevated roadway sections. The VDA results provide some useful insights about the potential effectiveness of different types of barrier on curved, superelevated roadway sections. Some possible recommendations suggested from the VDA results include: Barriers offering increased height and depth of their capture area should be used. This is more important for sharper curves and the higher levels of superelevation. Clear zones beyond the shoulder may be an option where sufficient run out area is available. This analysis only considered nearly level 12H:1V roadside slope conditions. It is important to remember that this analyses focuses strictly on the vehicle-to-barrier interface. This is a necessary condition, but not sufficient to assure that barrier will meet crashworthiness requirements. This is where further analyses using FE models and crash simulation becomes useful. Relative to selecting specific cases for crash simulation, there are not clear choices. The differences in barriers necessitates that crash simulations be conducted for each of them. For each barrier type, the following crash simulations should be considered: The most common acceptable interface scenario. The most divergent case for comparison of crashworthiness metrics and considerations of options for varying the design. Based upon the results of these crash simulations, decisions can be made on the value of additional simulations. For example simulations with: Impacts at shallower impact angles. Selected cases where poor interface might suggest a propensity to cause rollovers. Variations in the orientation of the barrier to true vertical. SUTs to understand higher interface and vehicle weight impacts. The benefits of these additional simulations will be weighed in the context of providing needed insights or support for the recommendations that are to be developed. These will be discussed with the panel. REFERENCES 1. Green Book 2. McMillan, N.J., Pape, D.B., Hadden, J.A., Narendran, V.K., Everson, J.H. Statistics-Based Simulation Methodology for Evaluating Collision Countermeasure Systems Performance. in IEEE Conference on Intelligent Transportation Systems Pape, D.B.; Narendran, V. K.; Koenig, M.J.; Hadden, J.A. and Everson, J.H.; (1996). Dynamic Vehicle Simulation to Evaluate Countermeasure Systems for Run-Off-Road Crashes. SAE,

19 4. Hadden, J.A.; Everson, J.H.; Pape, D.B.; Varendran, V.K.; (1997). Modelling and Analysis of Driver/Vehicle Dynamics with Run-Off-Road Crash Avoidance System. ISATA 97SAF Day, T.D and J. Travis Garvey (2000). Applications and Limitations of 3-Dimensional Vehicle Rollover Simulation. SAE Claar, P.W., Buchele, W.F., Sheth, P.N., Off-Road Vehicle Ride: Review of Concepts and Design Evaluation with Computer Simulation. SAE , Mancosu, F., Vehicle-Road-Tyre Interaction in Potential Dangerous Situations: Results of VERT Project. SAE , Sicking, D.L. and Mak, K.K., Improving Roadside Safety by Computer Simulation. Committee on Roadside Safety Features A2A04, Marzougui, D., Kan, C.D.; and Opiela, K.S.; (2007). Effects of Drop-off on W-Beam Guardrail Performance. The George Washington University. 10. Marzougui, D., Kan, C.D.; and Opiela, K.S.; Evaluation of the Influences of Cable Barrier Design and Placement on Vehicle to Barrier Interface, NCAC Document 2008-W-001, The National Crash Analysis Center, The George Washington University, October Marzougui, D., Kan, C.D.; and Opiela, K.S.; Using Vehicle Dynamics Simulation as a Tool for Analyzing Cable Barrier Effectiveness Report 2010-W-006 prepared for FHWA by the National Crash Analysis Center, George Washington University, August Marzougui, D., Kan, C.D.; and Opiela, K.S.; Analyzing the Effects of Cable Barriers Behind Curbs Using Computer Simulation Report 2009-W-008 prepared for FHWA by the National Crash Analysis Center, George Washington University, November Sean N. Brennan and Bridget C. Hamblin (2007). Utilization of Vehicle Dynamic Simulations as Predictors of Highway Safety. ASME International Mechanical Engineering Congress and Exposition, IMECE CarSim, Mechanical Simulation Corporation, AASHTO, Roadside Design Guide, published by the American Associations of State Highway & Transportation Officials, Washington, DC, Ross, Jr., H.E., Bligh, R.P.; Liu, J.; Evaluating the Benefits of Slope Rounding, A report prepared for the Minnesota DOT by the Texas Transportation Institute, College Station, TX, June

20 4 ft Width 8 ft Width 12 ft Width Table 3 Summary table for NJ concrete barrier installed in all curved, superelevated road configurations 0% Slope 3% Slope 6% Slope -2% Slope 0% Slope 3% Slope 6% Slope -2% Slope 0% Slope 3% Slope 6% Slope -2% Slope Barrier Placement Rad.: 614ft (187m) Rad.: 2130ft (649m) Rad.: 758ft (231m) Rad.: 2670ft (814m) Rad.: 833ft (254m) Rad.: 3050ft (930m) Sup. Elev.: 12% Sup. Elev.: 12% Sup. Elev.: 8% Sup. Elev.: 8% Sup. Elev.: 6% Sup. Elev.: 6% L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) a L1 Barrier placed at edge of shoulder a L2 Barrier placed 4 ft (1.22 m) from edge of shoulder a L3 Barrier placed 8 ft (2.44 m) from edge of shoulder 20

21 4 ft Width 8 ft Width 12 ft Width Table 4 Summary table for MGS W-beam barrier installed in curved, superelevated road configurations 0% Slope 3% Slope 6% Slope -2% Slope 0% Slope 3% Slope 6% Slope -2% Slope 0% Slope 3% Slope 6% Slope -2% Slope Barrier Placement Rad.: 614ft (187m) Rad.: 2130ft (649m) Rad.: 758ft (231m) Rad.: 2670ft (814m) Rad.: 833ft (254m) Rad.: 3050ft (930m) Sup. Elev.: 12% Sup. Elev.: 12% Sup. Elev.: 8% Sup. Elev.: 8% Sup. Elev.: 6% Sup. Elev.: 6% L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) a L1 Barrier placed at edge of shoulder a L2 Barrier placed 4 ft (1.22 m) from edge of shoulder a L3 Barrier placed 8 ft (2.44 m) from edge of shoulder 21

22 4 ft Width 8 ft Width 12 ft Width Table 5 Summary table for G4(1S) W-beam barrier installed in curved, superelevated road configurations 0% Slope 3% Slope 6% Slope -2% Slope 0% Slope 3% Slope 6% Slope -2% Slope 0% Slope 3% Slope 6% Slope -2% Slope Barrier Placement Rad.: 614ft (187m) Rad.: 2130ft (649m) Rad.: 758ft (231m) Rad.: 2670ft (814m) Rad.: 833ft (254m) Rad.: 3050ft (930m) Sup. Elev.: 12% Sup. Elev.: 12% Sup. Elev.: 8% Sup. Elev.: 8% Sup. Elev.: 6% Sup. Elev.: 6% L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c L1 a L2 b L3 c Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) Min (in) Max (in) a L1 Barrier placed at edge of shoulder a L2 Barrier placed 4 ft (1.22 m) from edge of shoulder a L3 Barrier placed 8 ft (2.44 m) from edge of shoulder 22