**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

**Suggested Citation:**"CHAPTER 5. BENEFIT-COST ANALYSIS METHODS." National Academies of Sciences, Engineering, and Medicine. 2021.

*Guidelines for Cost-Effective Safety Treatments of Roadside Ditches*. Washington, DC: The National Academies Press. doi: 10.17226/26127.

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78 CHAPTER 5. BENEFIT-COST ANALYSIS METHODS INTRODUCTION The scope of the project was to develop guidelines for the design and treatment of roadside ditches that âconsider, at a minimum, risk factors, cost-effectiveness, feasibility, road geometry, and traffic.â Here, risk factors are interpreted as those variables that are associated with an increased probability (or risk) of resulting in more severe occupant injuries when an errant vehicle traverses a ditch. For example, the encroachment speed and angle of an errant vehicle are viewed as risk factors because a high-speed and high-angle encroachment has a high probability of resulting in a severe crash. Several risk factors are considered in this study, including vehicle type, encroachment speed, encroachment angle, driver control input (i.e., braking and steering), vehicle tracking status at the POD, and the driverâs subsequent vehicle maneuvering behaviors after the encroachment has occurred. Based on the results from the literature review, survey of current practice, and analysis of existing data, a particular BCA method was researched and subsequently devised to meet the project requirement in a systematic way. The BCA methodology is described in this chapter. Motorist safety is a primary factor that influences the selection of various ditch design parameters, including ditch shape, slope, width, and lining. However, there are a number of other factors that can strongly influence the design of roadside ditches, including hydrologic and hydraulic requirements, environmental impact, roadside development (agricultural, residential, or commercial property), geotechnical factors (soil and rock conditions), and erosion control and management (e.g., the need to meet the flow capacity required to convey runoff of a 10-year design storm and the maximum flow velocity allowed for a given choice of lining). Moreover, terrain and project ROW limitations can dictate or restrict the choice of ditch geometry. The selection of a cut or a fill ditch section, for example, is often dictated by terrain features and to some extent by soil stability consideration. Some design parameters are subject to local or project requirements. For example, ditch depth needs to be varied to maintain a desirable longitudinal slope and to keep the runoff from the design year storm below the top of the subgrade. As is discussed in more detail later, the minimum depth requirement for cut slope sections varies by state and by highway class, and many states require a depth of at least 2 ft below the edge of the shoulder point. It is also a common practice for designers to add freeboard or other engineering safety factors to the design to allow for an extra margin of structural stability or for the uncertainties in analysis, design, and construction that cannot be fully or readily considered. To summarize, several decision variables, such as environmental impact and land development, are highly area-dependent, and monetization of their costs and benefits is difficult and highly variable. These variables are out of the scope of this study. Some ditch design variables can be highly site-dependent, such as soil/rock condition and choice of cut and filled slopes. In addition, certain design parameters, such as minimum ditch depth and choice of safety margin, are subject to local requirements and designer discretion. The economic considerations of most of these design variables and constraints are also beyond the scope of this study. While a reasonably wide range of ditch geometric configurations were explored and evaluated in this project, some of the configurations may not meet the specific need of individual projects when other variables and constraints are taken into account. The developed BCA method, and thus the

79 resulting guidelines, should be viewed with this scope in mind. The designerâs discretion is essential when applying the developed guidelines to local projects. In a similar vein, for those projects that treat already-built ditches, it is important to make sure that the alternatives in consideration are viable and that their impacts in terms of losing the already-demonstrated benefits of the existing ditches is minimized and acceptable to the community involved. In this study, the development of guidelines focused on motorist safety, and the BCA method was developed accordingly. Crash cost is used to evaluate the relative effectiveness of various ditch configurations and mitigation treatments in reducing crash frequency and severity. The benefit associated with non-crash related factors, such as soil stability, are not considered by the BCA method. For example, because V-shaped ditches are more susceptible to erosion, trapezoidal ditches may have added benefits in areas with erosive soil conditions. The BCA method is comprised of five major component models, including the vehicle dynamics code CarSim, to predict vehicle performance during ditch traversal. The concept and basic framework of the BCA method are presented below. The component models utilized in the BCA method contain many variables. The best data available to estimate the parameters involved in characterizing these variables come from different sources. Recognizing the imprecision of the data and assumptions involved in obtaining some of the estimated parameters, sensitivity analysis was used to understand how the analysis results, such as vehicle stability and crash cost, are affected by the uncertainty of the estimate. A complete mathematical description of the BCA method and procedures involved is provided in Appendix A. Both cost estimation and guideline development are described. It was prepared to serve two purposes: To add precision and clarity to the description provided in the main sections, especially on the computational and procedural aspects of the method. To lay out mathematical details for developing a software tool to perform the required computations (beyond the CarSim simulations). CONCEPT AND BASIC FRAMEWORK The developed BCA method takes an encroachment-based approach. Each possible encroachment outcome is probability-weighted to reflect the real-world encroachment condition. If a vehicle encroaches onto the roadside, a more forgiving shoulder and roadside ditch configuration provides the vehicle with a higher chance of recovery and reduces the severity of the crash if a recovery is not possible and a collision must occur. As previously discussed, crash data indicate that when an encroached vehicle strikes a ditch as the FHE, the most consequential event for SVROR crashes is a rollover. Thus, to reduce costly high-severity ditch crashes, the design must be able to reduce the rollover probability of errant vehicles. The BCA method is comprised of five major component models, including the vehicle dynamics simulation model CarSim. They are: Encroachment rate (ER) model. Encroachment characteristics model. Ditch traversal and impact model (CarSim). Impact-severity model. Crash cost model.

80 Figure 5.1 provides the basic framework of the BCA method at a glance. It is presented as a schematic flow chart containing an outline of the component models, variables, and data involved in the method and their relationships. This basic framework for the BCA was adopted from the RSAP software (46). At the time it was being considered for this project, RSAP incorporated a simplistic vehicle traversal and trajectory model that assumes no tire-terrain friction and a straight-line trajectory with no driver control input throughout the encroachment. This model was particularly problematic for use in evaluating vehicle performance on complex and highly variant ditch geometries. Furthermore, the impact-severity relationships in RSAP were based on crash data in the 1970s and early 1980s (when vehicles were not equipped with airbags and the seat belt usage rate was extremely low). Another limitation was that it did not explicitly consider rollover in its crash prediction and impact-severity models for any roadside feature except for longitudinal barriers struck by heavy trucks. This was a serious limitation for studying ditch design since a significant number of ditch-initiated crashes result in rollover. Although the RSAP software was being redeveloped under NCHRP Project 22-27 to address some of these issues, it was not immediately available for use under this project. The BCA method starts with a specification of roadway and roadside conditions to study. For a given specification, the five component models are applied sequentially to estimate crash cost. What follows is an overview of the basic framework presented in Figure 5.1. A brief description is first given regarding the specified roadway, roadside, and traffic elements. Then, each of the five component models is introduced. Specific specifications and supporting data are also described.

81 Roadway Characteristics â¢ Roadway Type: 2-lane undivided and 4-lane divided highways â¢ Speed Limit and AADT: 55 and 65 mph; low to high volumes â¢ Horizontal and Vertical Alignment: 0, 4.5 & 6 deg; 0, 4 & 6% Roadside Characteristics â¢ Shoulder: 3 width and surface material combinations â¢ Ditch Geometry: see simulation matrix in Chapter 7 â¢ Beyond the Ditch: flat open field with a 6% upgrade Roadside Encroachment Rates â¢ Encro Rates (in number of encro per mile per year) by Roadway Type, Speed Limit, Horizontal Curvature, Vertical Grade and AADT Vehicle Type â¢ 4 Types: Passenger Car, Midsize Sedan, SUV, and Pickup â¢ Distribution: based on crash data Vehicle Encroachment Characteristics at POD â¢ Encroachment Speed Distribution â¢ Encroachment Angle Distribution Driver Control Input â¢ Vehicle Tracking Status at Point of Departure (POD) â¢ Steering and Braking Behaviors at and after POD â¢ Perception-Reaction Time after POD Tire-Terrain Friction â¢ Coefficients of Friction (X & Y directions) CarSim Model (Vehicle Dynamics, Body-Terrain Contact & Veh Stability) Vehicle Performance Measures â¢ Status Indicators & Distances: safe return to travelway, rest on roadside, cross entire ditch; long-lat distances â¢ Stability: rollover or non-rollover (stable, sideslip, spin out) â¢ Severity Index (SI) Impact-Severity Relationships â¢ Rollover Crashes: severity distribution based on crash data â¢ Non-Rollover Crashes: severity distribution based on SI Crash Cost Estimates â¢ Cost of Rollover Crashes â¢ Cost of Non-Rollover Crashes â¢ Cost per Crash & Cost per Mile per Year (for each main- lane/traffic/roadside specification) Figure 5.1. Basic framework of the BCA method. Roadway & Roadside Specifications Encroachment Rate Model Encroachment Characteristics Model Ditch Traversal & Impact Model Impact-Severity Model Crash Cost Model

82 Roadway and Roadside Specification The BCA method starts with a selection of highways to study based on highway types and PSLs. The goal is to select a small number of combinations of highway types and PSLs that cover a significant percentage of the severe roadside ditch-initiated crashes. The selection is based on the crash data analysis results. While the majority of highway sections are relatively flat and straight, increased HC and vertical grade, especially on the outer side of the curve and in the downgrade direction, are known to have elevated rates of encroachments. A selected number of HCs and vertical grades are included in the study, focusing on roadside ditches built at the outside of the curve and in the downgrade travel direction. For a particular highway specification, the number of roadside encroachments per mile per year depends on the traffic volume, alignment, and other factors. An appropriate range of traffic volumes, in terms of average annual daily traffic (AADT) for the selected type of highways, are then chosen for study. Roadside specifications include shoulder width and type and ditch geometry, which are the design parameters of most interest to this study. Ditch geometry is specified according to its foreslope ratio, foreslope width, bottom width (equal to 0 for V-ditch), backslope ratio, and backslope width. A reasonably wide range of ditch slope and width combinations are considered in this study, which should cover most designs considered in practice. All reasonable combinations of the design parameters constitute a design space that was explored and evaluated to develop design guidelines. Encroachment Rate Model Encroachment rates vary from highway section to section depending mainly on main-lane characteristics and traffic volumes, including number of lanes, median type, PSL, horizontal and vertical alignment, and AADT. Given main-lane characteristics, the ER component model determines the expected number of encroaching vehicles on a relatively homogeneous stretch of highway. The rate is typically expressed in number of encroachments per million vehicle miles traveled (enc/MVMT) or per mile per year (enc/mi/yr). Unless indicated otherwise, the latter expression is used in this report. A curved section with a higher curvature and the downgrade travel direction of a section are expected to have a higher number of encroachments per mile per year. The best available encroachment rate data are listed in Tables 5.1 to 5.3, including base rates and adjustment factors for horizontal curvature and vertical grade. The base encroachment rates in Table 5.1 were calculated from two encroachment rate models developed by NCHRP 22-27 Roadside Safety Analysis Program Update project. Negative binomial regression models were used in the development of these models and encroachment data from Cooper were used (47, 48, 49). The source data for the adjustment factors are also shown in Figures 5.2 and 5.3 (50).

83 Table 5.1. Base encroachment rates for one side of the highway by highway type and projected bidirectional AADT. Projected Bidirectional AADT (veh/day) Two-Lane Two-Way Undivided Highways (enc/mi/yr) Projected Bidirectional AADT (veh/day) Four-Lane Divided Highways (enc/mi/yr) PSL: 55 mph PSL: 65 mph PSL=55 mph PSL=65 mph 0 0.00000 0.00000 0 0.00000 0.00000 500 0.46007 0.32320 2,500 0.83930 0.71188 1,000 0.82875 0.58220 5,000 1.51402 1.28415 2,500 1.51384 1.06349 10,000 2.46333 2.08934 5,000 1.79463 1.26074 15,000 3.00590 2.54954 7,500 1.59562 1.12094 20,000 3.26043 2.76542 10,000 1.26105 0.88590 25,000 3.31548 2.81211 12,500 0.93434 0.65638 30,000 3.23661 2.74521 15,000 0.66459 0.46688 35,000 3.07184 2.60546 Data source: Encroachment rate models developed by NCHRP 22-27 Roadside Safety Analysis Program Update project. The following assumptions are used: (1) Assuming 12-ft (3.6 m) lanes. (2) Assuming a directional AADT distribution of 50-50. (3) Assuming a straight and flat section (i.e., horizontal curvature â¤ 3 deg and vertical grade â¤2 percent). (4) Assuming a rural or suburban environment with one major access point per mi for two-lane undivided highways and 0.5 access points per mi for four-lane divided highways (see Table 2, FDOT (49). Table 5.2. Encroachment rate adjustment factors for horizontal curvatures (50). Horizontal Curvature (deg/100 ft arc) Horizontal Curvature Adjustment Factor (AHC) â¤ 3 1.0 4.5 2.5 â¥ 6 4.0

84 Figure 5.2. Encroachment rate adjustment factors for curved sections (50). Table 5.3. Encroachment rate adjustment factors for vertical grades (50). Vertical Grade (percent) Vertical Grade Adjustment Factor (AVG) â¤ 2 1.0 4 1.5 â¥ 6 2.0 Figure 5.3. Encroachment rate adjustment factors for vertical grades (50).

85 Encroachment Characteristics Model For a specific roadside condition, the probability of an encroached vehicle involved in a crash of a certain severity level depends on a number of encroachment characteristics. Based on available encroachment and crash data, the encroachment characteristics component model establishes real-world encroachment conditions at the POD and the driverâs vehicle maneuvering behaviors during the traversal. More specifically, this component model contains a probability- weight matrix, estimated from the best available data, that specifies how often an encroachment that possesses certain encroachment characteristics is expected to occur in the field. The set of encroachment characteristics considered by this study include vehicle type, encroachment speed, encroachment angle, driver control input (i.e., braking and steering), vehicle tracking status, and perception-reaction time. Vehicle Type Distribution For each encroachment, the encroachment characteristics considered by this study include four vehicle types, four encroachment speeds, three encroachment angles, and five driver control input and vehicle tracking status, a total of 240 possible combinations (=4Ã4Ã3Ã5) of encroachment characteristics. Their probability distributions are presented in Tables 5.4 to 5.7. Single-vehicle run-off-the-road (SV ROR) crashes involving roadside ditches from NASS GES from 2004 to 2009 were selected by this study to generate vehicle type distribution. Each of the four simulated vehicle type was used to represent a set of vehicle body types coded in the NASS GES based on vehicle weight and size (see Table 5.4). Crashes were then assigned to each simulated vehicle type according to their coded body type. Probability-weighted estimates were generated using the statistical method developed for analyzing complex survey data (e.g., 35, 36). Table 5.4. Vehicle type distribution. Simulated Vehicle Type Represented Vehicle Body Types Probability (%) 2,425-lb Passenger Car 2/3-door sedan/coupe/hardtop/hatchback 14.8 3,300-lb Passenger Car 4/5-door sedan/coupe/hardtop/hatchback, auto-based pickup, station wagon 38.3 Small Sport/Utility Vehicle small and midsize utility vehicle, compact pickup 25.0 5,000-lb Pickup Truck standard pickup, large utility, utility station wagon, minivan, large/step van, 21.9 Total 100.0 Data source: This Study, NASS GES data, 2004-2009 Encroachment Speed Distribution The following steps were taken by this study to estimate encroachment speed distribution presented in the Table 5.5. Step 1: Travel speed data for single-vehicle ROR crashes involving roadside ditches from NASS GES were selected for modeling. Qualified crashes were first grouped by the posted speed limit

86 of the highways where crashes occurred. These travel speeds were estimated by the investigating officer (30). For each posted speed limit, gamma and normal distribution functions were used to fit the travel speed distribution. The model with a better goodness-of-fit statistically was selected. For crashes on highways with a posted speed limit of 55 mph, gamma model was found to have a better fit and selected. For highways with a 65 mph posted speed limit, a normal distribution was selected. Given a large sample size is available for performing both estimates, the modeling results were statistically reliable. Step 2: By comparing 210 crashes from NASS CDS in 2002 and 2003, for which event data recorder (EDR) data were available, Korpu (2008) concluded that the mean travel speed reported by the investigating officer is practically close to the mean EDR recorded vehicle speed (51). Out of the 210 crashes compared, the EDR speed was on average about 9% higher than the travel speed reported by the investigating officer. Therefore, each of travel speed distribution obtained in Step 1 was increased by 9% to adjust for the underestimation by investigating officers. Step 3: Analyzing 210 vehicle roadside encroachment cases with an analytical roadside vehicle trajectory model, together with a review of an earlier study by Perchonok (52), Cooper (48) suggested that the average encroachment speed should be about 80% of the average travel speed. Thus, the adjusted travel speed distributions obtained in Step 2 were multiplied by 0.8 to estimate the encroachment speed distributions. The cumulative distribution of the estimated encroachment speeds were used to generate the interval-probabilities presented in Table 5.5. Table 5.5. Encroachment speed distribution. Simulated Encro. Speed (mph) Represented Range (mph) Probability (%) 2-Lane Undivided 4-Lane Divided PSL=55 mph PSL=65 mph PSL=55 mph PSL=65 mph 45 < 50 79.20 41.02 79.20 41.02 55 [50,60] 16.66 39.92 16.66 39.92 65 [60,70] 3.62 16.66 3.62 16.66 75 > 70 0.52 2.40 0.52 2.40 Total 100.0 100.0 100.0 100.0 Data source: This Study, NASS GES data, 1999-2009, Korpu (51), and Cooper (48) Encroachment Angle Distribution NCHRP 22-27 Roadside Safety Analysis Program Update project reanalyzed the Cooper data to develop probability models for encroachment angles (47, 48). Commonly used regression models in scientific and engineering applications for modeling continuous and positive valued random variables, including Weibull, gamma, and lognormal regression models, were tested statistically. Among the three types of models, the Weibull model was found to have the best overall performance. A variant of the Weibull regression models, called truncated random effect Weibull-gamma regression models (53, 54, 55), were found to have the best statistical performance. The cumulative distributions of the models were used to generate the interval-probabilities in Table 5.6.

87 Table 5.6. Encroachment angle probability distribution. Simulated Encro. Angle (deg) Represented Range (deg) Probability (%) 2-Lane Undivided 4-Lane Divided PSL=55 mph PSL=65 mph PSL=55 mph PSL=65 mph 10 < 15 37.0 50.0 35.0 44.0 20 [15,25] 39.0 35.0 40.0 38.0 30 > 25 24.0 15.0 25.0 18.0 Total 100.0 100.0 100.0 100.0 Data source: Cooper (47, 48), NCHRP 22-27 Roadside Safety Analysis Program Update project. Driver Control Input and Vehicle Tracking Status Distribution A database developed by NCHRP 17-11 and FHWA Rollover Causation Project was used by this study to generate the distribution (13, 39). Out of the 559 cases in the database, driver control input was provided for 545 cases and vehicle tracking status were available for 544 cases. These cases were used to develop the distributions of driver control input and vehicle tracking presented in Table 5.7. Table 5.7. Driver Control Input and vehicle tracking status distribution at the point of departure and after the encroachment Driver Control Input/Vehicle Tracking Status Relative Frequency (%) No control input (freewheeling), tracking, and with a perception-reaction time (PRT) (representing, e.g., distracted and drowsy drivers) 26.7 Panic return-to-road steering, tracking, and with PRT 20.3 Panic return-to-road steering, non-tracking with yaw rate of 15 deg/sec, and no PRT 12.5 Combined return-to-road steering and full ABS braking, tracking, and no PRT 25.0 Combined return-to-road steering and full ABS braking, non-tracking with yaw rate of 15 deg/sec, and no PRT 15.5 All 100.0 Data source: This Study. Database developed by NCHRP 17-11 (13). FHWA Rollover Causation Project (39) Ditch Traversal and Impact Model (CarSim) The vehicle dynamics simulation code CarSim is the component model used to predict vehicle performance in response to driver controls when an encroached vehicle traverses a given roadside configuration. An appropriate pair of lateral and longitudinal tire-terrain friction values was determined from the literature and through a sensitivity analysis. For each design configuration, all possible combinations of encroachment characteristics discussed above were simulated with CarSim. For every possible set of encroachment

88 characteristics, CarSim was programmed to output key vehicle performance measures during the ditch traversal, which were subsequently used to determine crash severity. These performance measures included extent of lateral and longitudinal encroachments, an indicator variable indicating whether a full recovery of the vehicle is attained, vehicle stability (e.g., rollover or non-rollover), vehicleâs path, speed, and acceleration as a function of time during the encroachment. The number of simulation runs can increase exponentially and quickly become unmanageable if the total number of combinations of ditch geometry and encroachment characteristics are not properly constrained. One of the challenges in the development of the BCA method was to select ditch configurations and encroachment characteristics that strike a balance between covering a wide range of designs, maintaining reasonable fidelity, and keeping computational time practical. Chapter 6 describes the detailed simulation matrix that includes the ditch and shoulder configurations, encroachment characteristics, and main-lane alignments that were simulated. Impact-Severity Model This component model takes the outputs from CarSim, such as vehicle stability and acceleration, decides whether a reportable crash occurs and, if a crash occurs, predicts an injury severity distribution. For example, if a rollover encroachment is predicted by CarSim, then the impact-severity model assumes the severity distribution is the same as the distribution of real- world ditch-initiated rollover crashes, which was described in the previous chapter. On the other hand, if a non-rollover encroachment is predicted by CarSim, an injury probability distribution is determined from the maximum roll angle and acceleration the vehicle experiences. For this purpose, the results of the simulation are used to determine a severity index using the following formula, modified from Ross et al. (20): Where: SI = Severity index a = Maximum resultant vehicle acceleration during any 50 ms period (gâs), and Ï = Maximum vehicle roll angle (deg) (Ï = 90 if rollover) The severity index calculated in the above manner is then converted to police-reported severity level. This conversion is performed using Table 5.8. In the table, the severity index of 7 corresponds to the severity distribution obtained from ditch-initiated rollover crashes from FARS and NASS GES data (2004-2009). While the severity index of 2 corresponds to the distribution obtained from ditch-initiated non-rollover crashes of the same data sources and the assumption that 40% of the encroachments do not result in reportable crashes.

89 Table 5.8. Relationship Between Severity Index and Severity Distribution Severity Index (SI) Encroachments Not Resulting in Reportable Crash (%) Police-Reported Injury Severity Level PDO C B A K 0 100.00 0.00 0.00 0.00 0.00 0.00 0.5 85.00 15.00 0.00 0.00 0.00 0.00 1 70.00 20.10 6.90 3.00 0.00 0.00 2 40.00 45.11 6.52 5.22 2.98 0.17 3 10.00 58.50 13.50 10.80 6.48 0.72 4 0.00 55.00 17.00 15.00 11.50 1.50 5 0.00 50.63 17.79 17.19 12.38 2.01 6 0.00 46.25 18.58 19.39 13.26 2.52 7 0.00 41.88 19.37 21.58 14.14 3.03 8 0.00 27.92 12.91 14.39 9.43 35.35 9 0.00 13.96 6.46 7.19 4.71 67.68 10 0.00 0.00 0.00 0.00 0.00 100.00 By determining the severity index of a particular encroachment using the simulation output data, Table 5.8 is then used to determine the police-level injury severity distribution for non-rollover enchroachments. Crash Cost Model Given the rollover status and police-level injury severity distribution obtained from the impact-severity component model, the crash cost component model computes the expected cost of an encroachment. Average costs per crash by injury severity level for ditch-initiated rollover and non-rollover crashes have been estimated using the FARS and NASS GES data provided in the last chapter. In addition, it was estimated that a ditch-initiated rollover crash costs about $312,000, which is more than 6 times that of ditch-initiated non-rollover crash costs ($48,000). Given an encroachment, each combination of the encroachment characteristics discussed earlier has a certain probability of occurring, and its outcome in terms of crash cost is weighted accordingly. The expected cost of an encroachment is calculated as the sum of the probability- weighted cost over all possible combinations of the encroachment characteristics. Certain encroachment characteristics have a low probability of occurring in the field. But the consequence of the encroachment is likely to be a severe crash. For example, a high-speed and high-angle encroachment, though relatively rare (with a low probability of occurrence), is highly likely to result in a severe crash, such as a rollover crash. These events are often referred to as low-probability high-consequence events. It is important to make sure that these events and their outcomes are adequately represented in the encroachment characteristics model and properly accounted for in the crash cost model.

90 MODEL PARAMETER CALIBRATION PROCEDURE A procedure was developed to perform a calibration of some key parameters used in the encroachment characteristics, severity, and cost component models to make sure that the probability-weighted vehicle performance outcomes produced from the developed encroachment model, such as rollover probability, crash severity distribution, and crash cost, were generally consistent with the statistics generated from the crash records. A schematic flow chart of the calibration procedure is presented in Figure 5.4. The key parameters selected for calibration were the encroachment speed and angle distributions used in the encroachment characteristics model and the SI formula used in the severity model to determine the severity distribution of rollover and non-rollover encroachments. To facilitate the calibration procedure, a set of frequently used ditch configurations were identified from the configurations simulated in this study to represent real-world ditches. Based on the survey results presented in Chapter 3, 16 ditch configurations were identified and used in the calibration. These configurations are listed in Table 5.9. The following results from the survey were used to identify these ditch configurations: V-ditches were more common than trapezoidal ditches (53% of respondents indicated that they use V-ditches very frequently or frequently, while the corresponding percentage for trapezoidal ditches was 38%). Nonsymmetric ditches, where foreslope and backslope widths and slopes are not the same, are more common than symmetric ditches (65% versus 17%, indicating very frequent or frequent usage). For nonsymmetric ditches, the backslope is usually steeper than the foreslope (75% versus 9%, indicating very frequent or frequent usage). Typical foreslope ratios: 1V:4Hâ80%, 1V:6Hâ74%, and 1V:3Hâ48% (indicating very frequent, frequent, or somewhat frequent usage). Typical backslope ratios: 1V:3Hâ77%, 1V:4Hâ65%, and 1V:2Hâ50% (indicating very frequent, frequent, or somewhat frequent usage). Most typical foreslope widths: 8â12 ft (2.4â3.6 m). Most typical backslope widths: 8â12 ft (5â6 m). Note that the actual probability distribution of ditch configurations in the field is unknown. The survey only provides a clue of what types of ditches and characteristics of ditch elements are frequently used. In the parameter calibration, the 16 selected ditches were weighted equallyâimplying equal representation in the fieldâwhen calculating the performance statistics of interest, such as average rollover probability and encroachment cost. The calibration was an iterative procedure. The parameters were manually adjusted after reviewing the performance outcomes at each iteration until the performance outcomes were reasonably close to the outcomes derived from ditch-initiated crash data described in Chapter 4. For example, it was desirable to see the encroachments that result in reported crashes have an average rollover probability of about 34%, and encroachments that result in crashes have an average crash cost of about $127,000. Note that not all encroachments result in a ROR crash. From the available encroachment data, such as the Cooper data (1980), we know that a significant percentage of encroached vehicles did not show up in the crash reports, and presumably many were non-crash events in

91 which the vehicle was able to return to the road or stop safely on the roadside. The consequence of having a high percentage of non-crash encroachments is that a site with a higher ROR crash rate does not automatically indicate a higher ER. It could simply be an indication that the roadside condition of the site is worse than average. In our calibration, the percentage of non-crash vehicles varied from 30% to about 55% in different iterations over the course of the calibration as parameter values were adjusted. In the final calibration, the percentage of non-crash encroachments was about 43% for the 16 ditches selected to represent the population. It is also well-known that not all reportable crashes are reported and get recorded in the crash database. A 30% underreporting rate for PDO crashes was assumed in the calibration based on available studies on the underreporting rates of ROR crashes.

92 Figure 5.4. Model parameter calibration procedure. Initialization Encroachment Conditions: â¢ Speed, Angle, Driver Input, Vehicle Type Frequently Used Ditch Configurations (16 Selected from Simulation, Based on Survey Results) CarSim Model Vehicle Performance Measurements: â¢ Roll Angle & Resultant Acceleration Severity Index (SI) Formula SI to Police-Level Severity Distribution Table Weighted Outcomes: â¢ Rollover Probability â¢ Severity Index â¢ Encroachment Cost "Reality" Checks (Statistics from Crash Data Analysis) Adjust Any Calibration Parameters? Stop Probability Weight for Each Encro. Condition No Yes

93 Table 5.9. Set of simulated ditch configurations selected to represent frequently used configurations in the field. Ditch # Simulation Configuration # SHW (ft) FS FSW (ft) BTW (ft) BS BSW (ft) 1 51 6 1V:6H 8 0 1V:4H 8 2 53 6 1V:6H 8 0 1V:3H 8 3 59 6 1V:6H 8 4 1V:4H 8 4 75 6 1V:6H 16 0 1V:4H 8 5 77 6 1V:6H 16 0 1V:3H 8 6 83 6 1V:6H 16 4 1V:4H 8 7 99 6 1V:4H 8 0 1V:4H 8 8 107 6 1V:4H 8 4 1V:4H 8 9 125 6 1V:4H 16 0 1V:3H 8 10 127 6 1V:4H 16 0 1V:2H 8 11 133 6 1V:4H 16 4 1V:3H 8 12 149 6 1V:3H 8 0 1V:3H 8 13 151 6 1V:3H 8 0 1V:2H 8 14 157 6 1V:3H 8 4 1V:3H 8 15 173 6 1V:3H 16 0 1V:3H 8 16 175 6 1V:3H 16 0 1V:2H 8 Note: SHW = shoulder width; FS = foreslope; FSW = foreslope width; BTW = bottom width; BS = backslope; BSW = backslope width. Given the size of the simulation data that needed to be processed, the calibration process was time-intensive. The process included completing a calibration iteration, examining the results from the calibration iteration, deciding on key parameters to adjust and the magnitude of the adjustments, and setting up the input files for the next iteration run. Thus, the researchers knew it was not feasible to check all parameters and run all desired adjustments. Therefore, the calibration had to be carried out in a selective manner. The calibration was used to understand how sensitive each outcome variable is with respect to changes in key parameters in the encroachment characteristics and severity component models. The key parameters considered for adjustment included the mean of the encroachment speed distribution, the mean of the encroachment angle distribution, the constants in the SI formula, and the SI to police-level severity distribution table. As an example, the encroachment angle distribution was derived from the NCHRP 17-22 crash database. Those encroachments that result in crashes are expected to have a higher encroachment angle, on average, than those encroachments in which the vehicle is able to recover and result in non-crash encroachments. Thus, in some of the iterations, the mean of the encroachment angle distribution was adjusted lower by 5%, 10%, and 20% to see how these changes affected the statistics of key outcome variables. The final calibration results selected by the researchers for conducting the BCA had an average rollover probability (for the 16 selected ditches) of about 33% for reported crashes, which is close to the 34% from the crash statistics reported earlier. In terms of encroachments, the average rollover probability was about 16.5% per encroachment.

94 On a per crash basis, the final selected calibration had an average cost of $182,000 per crash, which was somewhat higher than the $127,000 obtained from the crash statistics in Chapter 4. Note that the researchers were unable to reduce the cost further through the adjustments in the calibration without significantly lowering the average rollover probability discussed above. Preference was given to keeping the rollover probability as close as possible to the crash data. In terms of the cost on a per-encroachment basis, the final calibration gave an average cost of about $104,000 per encroachment. Based on the percentage of non-crash encroachments from the calibration, which as indicated earlier was about 43%, the $127,000 per crash cost from the crash statistics was converted to a $72,480 per-encroachment cost that was used to represent the average real-world encroachment cost in the BCA and subsequent guideline developments.