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135 CHAPTER 7. GUIDELINE DEVELOPMENT This chapter presents the development of the traversability guidelines using the results of the vehicle encroachment simulations. The first step in development of the guidelines was to assign a weightage to each simulation case based on the probability of occurrence of the encroachment conditions used in that case. For this purpose, the researchers developed probability distributions of the various encroachment parameters using crash or sales data. Once these probability distributions were developed, they were applied to the 43,000 simulation cases to obtain weighted outcomes of these simulations. The weighted simulation outcomes were then used to develop the traversability guidelines. The process of developing the probability distributions and the evaluation of the weighted simulation outcomes to arrive at the slope traversability guidelines is presented in this chapter. 7.1 PROBABILITY DISTRIBUTIONS To develop the traversability guidelines using the results of the simulations, the simulation outcomes were to be weighted according to the probability of occurrence of each encroachment condition. For this purpose, the researchers needed to develop probability distributions for the various encroachment variables using the real world data. These encroachment variables include the encroachment angle, encroachment speed, vehicle type, and the driver input type, which also incorporated whether the vehicle was tracking or not. For developing these probability distributions, the researchers used the NCHRP 17-22 crash database. This database was developed by performing detailed accident reconstructions of the crashes included in the database. It therefore contains information about the encroachment conditions for each of the crashes. The crash database was used for the developing probability distributions for the encroachment angle, encroachment speed, and driver input. For probability distribution of the vehicle types, the researchers used vehicle sales data for year 2016. 7.1.1 Encroachment Angle and Speed Probability Distributions Using the NCHRP 17-22 crash database, the researchers developed the probability distributions for encroachment angles and speeds. These are presented in Figure 7.1 and Figure 7.2, respectively. The reported crash encroachment angles and speeds were grouped into discrete ranges based on the values selected in the simulation matrix. Each range represented a specific discrete encroachment value used in the simulations. For example, in Figure 7.1, all the encroachment angles in the crash database between 0 and 7.5 degrees were grouped together and were represented by the 5-degree encroachment angle used in the simulations. Similarly, encroachment angles of 7.6 to 12.5 degrees were grouped together and are represented by the 10- degree encroachment angle used in the simulations. The probability of a given range of encroachment angles was determined by calculating the ratio of the number of crash cases in that range and the total number of crashes in the database. This same approach was used to determine the probabilities for the encroachment speeds presented in Figure 7.2.
136 Figure 7.1. Encroachment angle distribution for weighting simulation results. Figure 7.2. Encroachment speed distribution for weighting simulation results. 7.1.2 Driver Input Probability Distribution The five driver inputs used in the simulation analyses were a combination of three primary factors. These were, whether the driver applied steering, whether the driver applied braking, and whether the vehicle was tracking or non-tracking at the point of departure (see Figure 5.21 for the simulation driver input details). To determine the probability distribution of the driver inputs simulated, the researchers used the data from NCHRP Project 17-22 crash database. For each of the encroachments reported in the database, there is information available on whether the driver applied steering and/or braking. The database does not provide direct information on whether the vehicle was 0.17 0.25 0.21 0.14 0.10 0.13 0.00 0.05 0.10 0.15 0.20 0.25 0.30 5 10 15 20 25 30 & above Pr ob ab ili ty o f O cc ur re nc e Encroachment Angle (Degrees) Encroachment Angle Distribution 0.11 0.16 0.24 0.24 0.16 0.09 0.00 0.05 0.10 0.15 0.20 0.25 25 35 45 55 65 70 & above Pr ob ab ili ty o f O cc ur re nc e Encroachment Speed (mi/h) Encroachment Speed Distribution
137 tracking or non-tracking as it left the roadway. However, there is information available about the vehicleâs Departure Heading Angle and the Departure Angle, which was used to estimate if the vehicle was tracking or non-tracking at the time of departure from the roadway. The Departure Heading Angle defines the orientation of the vehicle. It is the angle between the roadway and the direction in which the vehicle is facing at the time the vehicle leaves the road. The Departure Angle however, is the angle between the vehicle CGâs trajectory and the roadway at the point of departure. In the tracking condition, the vehicle is facing in the direction that it is moving (see Figure 7.3, left). In other words, the vehicle is aligned with the path its CG is following, and therefore, the difference between the Departure Heading Angle and the Departure Angle is close to zero. On the other hand, if the difference between the two angles is large, it implies that the vehicle is not oriented in the direction that the vehicleâs CG is moving. This implies the vehicle is in a non-tracking mode (see Figure 7.3, right). Figure 7.3. Tracking and non-tracking conditions of the vehicle. To classify the encroachments in the NCHRP 17-22 database as tracking or non-tracking, the researchers determined the difference between the Departure Heading Angle and the Departure Angle for each encroachment. If the absolute difference was more than 15 degrees, the encroachment was classified non-tracking. Otherwise, it was classified as tracking. The 15- degree limit was considered a reasonable variation in the vehicleâs heading and departure angles, beyond which the wheels are most likely to be non-tracking due to a high side slip angle. Using this approach, the researchers determined the probabilities of tracking and non-tracking encroachments to be 0.59 and 0.41, respectively. Using the tracking and non-tracking encroachment probabilities, and the probabilities of the steer and brake application reported in the NCHRP 17-22 database, the researchers then determined the combined probability of each of the five driver inputs used in the simulation analyses. These probabilities are listed in Figure 7.4.
138 Driver Input Short Description Probability 1 No driver input. Tracking encroachment. 0.202 2 Panic steer to roadway. Tracking encroachment. 0.054 3 Panic steer to roadway and brakes. Tracking encroachment 0.417 4 Constant steer to roadway. Non-tracking encroachment 0.037 5 Constant steer to roadway and brakes. Non-tracking encroachment 0.290 Figure 7.4. Probability distribution for driver inputs used in the simulation analyses. 7.1.3 Vehicle Type Probability Distribution To determine the probability distribution of the vehicles used in the simulation analyses, the researchers used the automotive sales data for the United States for year 2016 (42). Each of the vehicles appearing in the sales data was classified into a specific vehicle category using Insurance Institute of Highway Safetyâs (IIHS) vehicle classification method specified by its Highway Loss Data Institute (HLDI) (43). According to these vehicle classification guidelines, a passenger sedan is classified based on its curb weight and the âshadowâ of the vehicle calculated by taking a product of its overall length and width. These classifications are shown in Figure 7.5. The two marks on the figure show the location of the two passenger cars used in this project â the Kia Rio 2006 (MASH 1100C) and the Ford Taurus 2001 sedan. Figure 7.5. Passenger car classification method by HLDI. To determine the vehicle probability distribution for the vehicles used in the simulation analyses, all passenger cars sold in 2016 were represented by the two of the simulated vehicles. The curb weights and shadows of all passenger cars sold in 2016 were calculated and classified according to the IIHS-HLDI classification. After that, the âMicro,â âMini,â and âSmallâ passenger cars were represented by the model of the Kia Rio 2001 (MASH 1100C small car).
139 The âMidsize,â âLarge,â and âVery Largeâ vehicles were represented by the model of the Ford Taurus 2001 mid-size sedan. All of the pickup trucks were represented by the pickup truck model of the 2007 Dodge RAM 1500 (MASH 2270P pickup) that was used in the simulations. Similarly, all of the sports utility vehicles (SUV) were represented by the Ford Explorer 2002 vehicle model. Minivans and crossovers were also lumped into the SUV category. Once all of the vehicles sold in 2016 were categorized as being represented by one of the four vehicles used in the simulations, a probability distribution for the simulation vehicle models was determined. This was done by calculating the ratio of the total number of sales of each vehicle type and the total number of vehicles sold. The vehicle probability distribution is presented in Figure 7.6. Figure 7.6. Probability distribution for vehicle types used in simulation. A summary of all of the probability distributions used in weighting the simulation outcomes in this project are presented in Figure 7.7.
140 SIMULATION VALUE RANGE PROBABILITY VEHICLE TYPE Small Car âMicro,â âMini,â and âSmallâ 0.1303 Midsize Sedan âMidsize,â âLarge,â and âVery Largeâ 0.2917 Sport Utility Vehicle All SUVs 0.4246 Pickup Truck All Pickups 0.1534 TOTAL 1 ENCROACHMENT SPEED (MPH) 25 <= 30 0.1149 35 30-40 0.1598 45 40-50 0.2368 55 50-60 0.2356 65 60-70 0.1609 75 >70 0.092 TOTAL 1 ENCROACHMENT ANGLE 5 <=7.5 0.1676 10 7.5 - 12.5 0.2463 15 12.5 â 17.5 0.2782 20 17.5 - 22.5 0.1417 25 22.5 - 27.5 0.1001 30 >27.5 0.1305 TOTAL 1 DRIVER INPUT 1 Tracking, No Steer or Brake 0.202 2 Tracking, Steer 0.054 3 Tracking, Steer and Brake 0.417 4 Non-Tracking, Steer 0.037 5 Non-Tracking, Steer and Brake 0.290 TOTAL 1 Figure 7.7. Probability distributions for weighting simulation results.
141 7.2 EVALUATION OF WEIGHTED SIMULATION RESULTS Using the probability distributions developed for various encroachment parameters, the researchers weighted the outcome of each simulation and determined the combined probability of rollover for a specific roadside terrain. This process enabled the researchers to expose various trends, which were then used to develop the slope traversability guidelines. To understand the process of weighting the simulations and determining the combined probability of rollover for a specific terrain, it should be noted that 60 unique terrains were simulated in this project. This number can be calculated by multiplying the various roadside design parameters incorporated in the simulation matrix as below. 3 shoulder widths Ã 5 foreslopes Ã 4 foreslope widths = 60 terrains For each of these terrains, 720 encroachment cases were simulated. This number can be calculated from the simulation matrix as follows. 4 vehicle types Ã 6 encroachment angles Ã 6 encroachment speeds Ã 5 driver inputs = 720 cases This resulted in a total of 43,200 simulations (720 cases Ã 60 terrains) performed in the project. As described previously, for each of the 720 simulations performed on a specific terrain, the outcome was recorded as whether the encroachment resulted in a rollover, the vehicle returning to road, the vehicle reaching the bottom of the ditch, etc. For each simulation case, the outcome was weighted using the probability distributions of the four (4) encroachment parameters involved (i.e. vehicle type, encroachment speed, encroachment angle, and driver input). By combining the outcome probabilities of all 720 cases for a given terrain, the researchers determined the combined probability of rollover for a specific terrain. This process was repeated for all 60 terrains to determine the combined probability of rollover for each terrain. The researchers then looked at the effects of different terrain features on the combined rollover probability, independent of the encroachment conditions. By evaluating the various trends, the researchers then prepared the slope traversability guidelines. Some of the key trends noted are presented next. 7.2.1 Shoulder Width The researchers looked at the effect of shoulder width on rollover probability. In the simulation matrix, a 2 ft, 6 ft, and an 8 ft wide shoulder were selected. Figure 7.8 shows the influence of the shoulder width on the probability of rollover as function of the foreslope. Figure 7.8a shows that for a foreslope width of 8 ft, the change in shoulder width has minimal effect on the rollover probability. Hence all three lines on the plot are tightly banded together. However, Figures 7.8b to 7.8d show that for higher foreslope widths (16 ft, 32 ft, and 105 ft), the 6 ft and 8 ft shoulder widths have similar rollover probability, whereas the 2ft shoulder has higher rollover probability. Using this information, the researchers considered developing the guidelines for two shoulder width types instead of three. These were defined as a
142 narrow shoulder and a full shoulder. A shoulder up to 4 ft wide was considered as a narrow shoulder and was represented in the guidelines using the rollover probability of a 2 ft wide shoulder. Similarly, a shoulder wider than 4 ft was considered as a full shoulder and was represented in the guidelines using the rollover probability of the 8 ft wide shoulder. 7.2.2 Foreslope Width Figure 7.9 shows the influence of the foreslope width on the probability of rollover. It can be seen that the probability of rollover increases significantly when foreslope width is increased from 8 ft to 16 ft, except for the 1V:10H foreslope, for which the rollover probability remains at approximately 10% for all foreslope widths. The jump in rollover probability from 8 ft to 16 ft seems to be related to the opportunity the vehicle has to interact with the sloped terrain. With an 8 ft wide foreslope, in most cases, the vehicle coming off the roadway does not have enough interaction with the sloped terrain to cause a significant destabilization effect. This results in a lower rollover probability for the 8 ft wide foreslope. Increasing the foreslope width further to 32 ft results in decrease in rollover probability, except for flatter slopes, which remain at nearly the same rollover probability as the 16 ft foreslope width. This trend highlights the destabilizing effect of the ditch bottom on the stability of the vehicle. Sudden change in the terrainâs slope as the vehicle goes from a steep foreslope to the flat ditch bottom results in a destabilizing effect. In some cases, the effect of this slope change is more detrimental to vehicle stability than traversing on the foreslope itself. This is why it can be seen that for steeper slopes (1V:2H and 1V:3H), the rollover probability generally decreases with increasing foreslope width. On the other hand, for flatter slopes (1V:6H and 1V:10H) this destabilizing effect is not as pronounced since the slope difference between the foreslope and the ditch bottom is not that significant. The influence of foreslope width on rollover probability, as described above, can have significant effect on the rollover probability, especially for the steeper slopes. Thus foreslope width was retained as one of the design parameters to be used in the slope traversability guidelines. 7.2.3 Foreslope Figure 7.10 shows the influence of the foreslope on the probability of rollover for various foreslope widths. Figure 7.10a and 7.10b show rollover probabilities for the narrow shoulder (4 ft wide or less) and the full shoulder (wider than 4 ft). It can be seen that on a relatively flat 1V:10H slope, the rollover probability for all foreslope widths is fairly close (11%-13%). As the foreslope increases, the rollover probability increases. Trends in Figure 7.10 also show a significant jump in rollover probability when foreslope is increased from 1V:3H to 1V:2H. For the 16-ft and 32-ft foreslope width, the rollover probability of a 1V:2H slope is 40% and 43.5%, respectively. Due to such high rollover probabilities, the researchers are recommending to exclude 1V:2H foreslope as a design option.
143 7.2.4 Generalized Traversability The current slope traversability guidelines define various roadside slopes as ârecoverable,â âtraversable, non-recoverable,â and âcritical.â The researchers used the results of the simulation to determine the overall probability of various outcomes for vehicles encroaching on slopes (i.e. ârollover, ârecoverable,â and âtraversable, non-recoverableâ). These probabilities are shown in Figure 7.11 for different roadside slopes. Some of the trends observed with the unweighted simulation outcomes are again observed for the weighted simulation results in the figure. For example, the probability of rollover increases with steeper slopes. Similarly, as the slope increases, the probability of a recoverable encroachment decreases. While these trends are logical, it can be seen that for each foreslope type, there is a significant probability of any of the three outcomes. Assigning one particular outcome type to a specific foreslope leaves a ditch designer unaware of the true hazard of the slope. This becomes more obvious when rollover probabilities are evaluated in conjunction with other roadside slope parameters such as the shoulder and foreslope widths. So for instance, comparing the rollover probability of a 1V:3H foreslope with a 2-ft shoulder (Figure 7.9a), the rollover probability jumps from 17% to 27.5% if the width of the foreslope changes from 8 ft to 16 ft. Similarly, comparing rollover probability of a 16 ft wide 1V:3H foreslope shows that the rollover probability jumps from 22% for an 8-ft shoulder (Figure 7.9c) to 27% for a 2-ft shoulder (Figure 7.9a). Due to such variations in the rollover probabilities, it was considered more suitable for the final guideline to be defined in terms of rollover probability as a function of the foreslope, foreslope width, and the shoulder width. 7.3 TRAVERSABILITY GUIDELINES Figure 7.12 presents the proposed guidelines for roadside slope traversability in terms of probability of vehicle rollover on slopes. These plots are the same as those shown in Figure 7.10 with the exception that the 1V:2H foreslope option has been removed. Due to very high rollover probabilities associated with the 1V:2H foreslope, the researchers have not recommended it as a design option. If a user agency would like to have this slope included, the proposed guidelines will take the form of the plots in Figure 7.10. In addition to the rollover probability, it may be beneficial to know the probability of a vehicle returning to the roadway if it encroaches on a certain slope configuration. Similar to the vehicle rollover probability plots, the researchers developed plots for the probability of vehicle returning to the roadway. These are presented in Figure 7.13 and are also recommended for inclusion in the traversability guidelines. These guidelines are presented again in the next chapter, along with an example of how a ditch designer or a user agency may use them. The following chapter can be used to incorporate these guidelines into other documents with minimal editing if needed.
(a) (b) (c) (d) Figure 7.8. Influence of shoulder width on rollover probability for various foreslopes.
145 (a) (b) (c) Figure 7.9. Influence of foreslope width on rollover probability.
146 (a) (b) Figure 7.10. Influence of foreslope on rollover probability.
147 Figure 7.11. Probability of various outcomes for vehicle encroaching on slopes
148 (a) (b) Figure 7.12. Slope traversability guidelines showing vehicle rollover probability.
149 (a) (b) Figure 7.13. Slope traversability guidelines showing probability of vehicle return to roadway.