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113 This chapter presents the development of the traversability guidelines using the results of the vehicle encroachment simulations. The first step in the 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 prob- ability 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 prob- ability distributions and evaluating 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 encroach- ment 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 driver input type, which also incorporated whether the vehicle was tracking or not. For developing these probability distributions, the researchers used the NCHRP Report 665 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 the vehicle sales data for 2016. 7.1.1 Encroachment Angle and Speed Probability Distributions Using the NCHRP Report 665 crash database, the researchers developed the probability distributions for encroachment angles and speeds. These are presented in Figures 7.1 and 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 C H A P T E R 7 Guideline Development
114 Guidelines for Traversability of Roadside Slopes 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. 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 data from the NCHRP Report 665 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 tracking or non-tracking as it left the roadway. However, there is information available about the vehicleâs departure heading angle and departure angle, which was used to estimate if the vehicle was track- ing 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. 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 il it y of O cc ur re nc e Encroachment Angle (degrees) Encroachment Angle Distribution Figure 7.1. Encroachment angle distribution for weighting simulation results. 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 il it y of O cc ur re nc e Encroachment Speed (mi/h) Encroachment Speed Distribution Figure 7.2. Encroachment speed distribution for weighting simulation results.
Guideline Development 115 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 7.3a). 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 that the vehicle is in a non-tracking mode (see Figure 7.3b). To classify the encroachments in the NCHRP Report 665 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 encroach- ment was classified as 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 encroach- ments 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 Report 665 database, the researchers deter- mined the combined probability of each of the five driver inputs used in the simulation analyses. These probabilities are listed in Figure 7.4. (a) (b) Figure 7.3. Vehicle (a) tracking and (b) non-tracking conditions. 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.
116 Guidelines for Traversability of Roadside Slopes 7.1.3 Vehicle Type Probability Distribution To determine the probability distribution of the vehicles used in the simulation analyses, researchers used the automotive sales data for the United States for 2016 (42). Each of the vehicles appearing in the sales data was classified into a specific vehicle category using Insurance Institute of Highway Safetyâs vehicle classification method specified by the Highway Loss Data Institute (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 arrows in the figure show the location of the two passenger cars used in this projectâKia Rio 2006 (MASH 1100C) and the Ford Taurus 2001 sedan. 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 simulated vehicles. The curb weights and shadows of all passenger cars sold in 2016 were calculated and classified according to the Insurance Institute of Highway Safetyâs vehicle classification method specified by the Highway Loss Data Institute. After that, the micro, mini, and small passenger cars were represented by the model of the Kia Rio 2001 (MASH 1100C small car). The midsize, large, and very large vehicles were represented by the model of the Ford Taurus 2001 midsize sedan. All of the pickup trucks were represented by the pickup truck model of the 2007 Dodge Ram 1500 (MASH 2270P pickup truck) that was used in the simulations. Similarly, all SUVs 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. A summary of all of the probability distributions used in weighting the simulation outcomes in this project is presented in Figure 7.7. Figure 7.5. Passenger car classification method by Highway Loss Data Institute.
Guideline Development 117 42.46% 15.34% 29.17% 13.03% SUVPickup TruckMidsize SedanSmall Car 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% Figure 7.6. Probability distribution for vehicle types used in simulation. SIMULATION VALUE RANGE PROBABILITY VEHICLE TYPE Small Car Micro, Mini, and Small 0.1303 Midsize Sedan Midsize, Large, and Very Large 0.2917 Sport-Utility Vehicle All SUVs 0.4246 Pickup Truck All Pickup Trucks 0.1534 TOTAL 1 ENCROACHMENT SPEED (MPH) 25 <30 0.1149 35 30â40 0.1598 45 40â50 0.2368 55 50â60 0.2356 65 60â70 0.1609 75 >70 0.092 TOTAL 1 ENCROACHMENT ANGLE 5 <7.5 0.1676 10 7.5â12.5 0.2463 15 12.5â17.5 0.2782 20 17.5â22.5 0.1417 25 22.5â27.5 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.
118 Guidelines for Traversability of Roadside Slopes 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 prob- ability of rollover for a specific terrain, 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) encroach- ment 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 simula- tion matrix, 2-, 6-, and 8-ft wide shoulders were selected. Figure 7.8 shows the influence of the shoulder widths on the probability of rollover as functions 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 of 16, 32, and 105 ft, the 6- and 8-ft shoulder widths have similar rollover probabilities, whereas the 2-ft shoulder has a higher rollover probability. Using this information, the researchers considered developing guidelines for two shoulder width types instead of three. These were defined as a 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.
Guideline Development 119 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 the foreslope width is increased from 8 to 16 ft, except for the 1V:10H foreslope, for which the rollover probability remains at approximately 10 percent for all foreslope widths. The jump in rollover probability from 8 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 a decrease in rollover probability, except for flatter slopes, which remain at nearly the same rollover probability as the 16 ft fore- slope width. This trend highlights the destabilizing effect of the ditch bottom on the stability of the vehicle. A 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. (a) (b) (c) (d) Figure 7.8. Influence of shoulder widths on the rollover probability for (a) 8-ft, (b) 16-ft, (c) 32-ft, and (d) 105-ft foreslope widths.
120 Guidelines for Traversability of Roadside Slopes (a) (b) (c) Foreslope Foreslope Width (ft) R ol lo ve r Pr ob ab ili ty Foreslope Width (ft) R ol lo ve r Pr ob ab ili ty Foreslope Width (ft) R ol lo ve r Pr ob ab ili ty Figure 7.9. Influence of foreslopes on the rollover probability for (a) 2-ft, (b) 6-ft, and (c) 8-ft shoulders.
Guideline Development 121 The influence of foreslope width on rollover probability can have a significant effect on the rollover probability, especially for steeper slopes. Therefore, 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. Figures 7.10a and 7.10b show rollover probabilities for a narrow shoulder (4 ft or less than 4 ft wide) and a full shoulder (more than 4 ft wide). It can be seen that on a relatively flat 1V:10H slope, the rollover probability for all foreslope widths is fairly close (11 to 13 percent). As the foreslope increases, the rollover probability increases. Trends in Figure 7.10 also show a significant jump in rollover probability when the foreslope is increased from 1V:3H to 1V:2H. For the 16- and 32-ft foreslope width, the rollover probability of a 1V:2H slope is 40 and 43.5 percent, respectively. Due to such high rollover probabilities, the researchers are recommending to exclude the 1V:2H foreslope as a design option. 7.2.4 Generalized Traversability The current slope traversability guidelines define various roadside slopes as recoverable, âtraversable or non-recoverable, and critical. The researchers used the results of the simulation to determine the overall probability of various outcomes for vehicles encroaching on slopes (i.e., rollover, recoverable, and traversable or non-recoverable). 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, Foreslope (degrees) R ol lo ve r Pr ob ab ili ty (a) Figure 7.10. Influence of foreslopes on the rollover probability for (a) a narrow shoulder (4 ft or less than 4 ft wide) and (b) a full shoulder (more than 4 ft wide). (continued on next page)
122 Guidelines for Traversability of Roadside Slopes Figure 7.11. Probability of outcome for vehicles encroaching on slopes. Foreslope (degrees) R ol lo ve r Pr ob ab ili ty (b) Figure 7.10. (Continued).
Guideline Development 123 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. 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 percent if the width of the foreslope changes from 8 to 16 ft. Similarly, comparing the rollover probability of a 16 ft wide 1V:3H foreslope shows that the rollover probability jumps from 22 percent for an 8-ft shoulder (Figure 7.9c) to 27 percent for a 2-ft shoulder (Figure 7.9a). Because of such variations in 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 shoulder width. 7.3 Traversability Guidelines Figure 7.12 presents the proposed guidelines for roadside slope traversability in terms of the 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. Because of very high rollover probabilities associated with the 1V:2H foreslope, the researchers have not recom- mended it as a design option. If a user agency would like to have this slope included, the pro- posed 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 vehicles 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 user agency may use them. Chapter 8 can be used to incorporate these guidelines into other documents with minimal editing if needed.
124 Guidelines for Traversability of Roadside Slopes Figure 7.12. Slope traversability guidelines showing the rollover probability for (a) a narrow shoulder (4 ft or less than 4 ft wide) and (b) a full shoulder (more than 4 ft wide). (a) (b)
Guideline Development 125 (a) (b) Figure 7.13. Slope traversability guidelines showing the probability of vehicle return to roadway for (a) a narrow shoulder (4 ft or less than 4 ft wide) and (b) a full shoulder (more than 4 ft wide).