Guidelines for Cost-Effective Safety Treatments of Roadside Ditches (2021)

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i CONTENTS LIST OF FIGURES ....................................................................................................................... iv LIST OF TABLES ....................................................................................................................... viii SUMMARY .................................................................................................................................... 1 CHAPTER 1. INTRODUCTION AND BACKGROUND ............................................................ 3 INTRODUCTION ...................................................................................................................... 3 LITERATURE REVIEW ........................................................................................................... 6 Slope Rollovers and Ditch Crashes ......................................................................................... 6 Ditch Geometry and Vehicle Dynamics ................................................................................. 7 Guardrail Need ...................................................................................................................... 14 Encroachment Simulation Studies ........................................................................................ 17 Cost-Effectiveness Methodology .......................................................................................... 22 NCHRP Project 17-11 ........................................................................................................... 25 Hydraulic Design Considerations ......................................................................................... 27 Maintenance and Vegetation ................................................................................................. 31 Channel Lining ...................................................................................................................... 32 CONCLUSIONS ...................................................................................................................... 35 CHAPTER 2. RESEARCH APPROACH .................................................................................... 36 CHAPTER 3. SURVEY OF STATES.......................................................................................... 38 INTRODUCTION .................................................................................................................... 38 Determining Barrier Need and Slope Combinations ............................................................ 39 Ditch Geometry ..................................................................................................................... 39 Foreslope and Backslope ...................................................................................................... 41 Slope Rounding ..................................................................................................................... 43 Formula Used for Slope Rounding ....................................................................................... 43 Surface Treatments ............................................................................................................... 43 Pavement Location ................................................................................................................ 44 Pavement Width .................................................................................................................... 44 CONCLUSIONS ...................................................................................................................... 45 CHAPTER 4. ANALYSIS OF EXISTING CRASH DATA........................................................ 46 INTRODUCTION .................................................................................................................... 46 Databases in Consideration ................................................................................................... 46 Relative Strengths and Limitations ....................................................................................... 47 Crash Data Screening ............................................................................................................ 47 FARS ........................................................................................................................................ 50 Time Trend ............................................................................................................................ 51 Presence of Appurtenances and Most Harmful Events ......................................................... 52 Highway Functional Class .................................................................................................... 53 Highway Type: Number of Lanes and Median Type ........................................................... 53 Roadside Versus Median Ditches/Culverts .......................................................................... 53 Posted Speed Limit ............................................................................................................... 54 Horizontal and Vertical Alignment ....................................................................................... 54 Lighting Condition ................................................................................................................ 54 Vehicle Body Type ............................................................................................................... 54 Deployment of Driver Side Airbags ..................................................................................... 58

ii Driver Alcohol Use ............................................................................................................... 59 Seat Belt Use ......................................................................................................................... 59 Travel Speed Distribution by Posted Speed Limit ................................................................ 60 NASS GES ................................................................................................................................ 62 Frequency and Severity Distributions of Ditch-Initiated Crashes ........................................ 63 Posted Speed Limit ............................................................................................................... 64 Travel Speed Distribution by Posted Speed Limit ................................................................ 65 NASS CDS ............................................................................................................................... 66 NCHRP PROJECT 17-22 DATABASE ................................................................................... 69 HSIS .......................................................................................................................................... 70 SEVERITY AND COST OF DITCH-INITIATED CRASHES ............................................... 71 Crash Data and Screening Criteria ........................................................................................ 72 Crash Cost Data .................................................................................................................... 73 Cost per Crash by Severity Level ......................................................................................... 73 Costs of Rollover and Non-rollover Crashes ........................................................................ 75 Underreporting of Minor Crashes ......................................................................................... 76 Average Annual Crash Cost and Conclusions ...................................................................... 77 CHAPTER 5. BENEFIT-COST ANALYSIS METHODS .......................................................... 78 INTRODUCTION .................................................................................................................... 78 CONCEPT AND BASIC FRAMEWORK ............................................................................... 79 Roadway and Roadside Specification ................................................................................... 82 Encroachment Rate Model .................................................................................................... 82 Encroachment Characteristics Model ................................................................................... 85 Ditch Traversal and Impact Model (CarSim) ....................................................................... 87 Impact-Severity Model ......................................................................................................... 88 Crash Cost Model ................................................................................................................. 89 MODEL PARAMETER CALIBRATION PROCEDURE ...................................................... 90 CHAPTER 6. SIMULATION ANALYSIS METHODS ............................................................. 95 INTRODUCTION .................................................................................................................... 95 SIMULATION TOOLS ............................................................................................................ 95 VEHICLE BODY-TO-TERRAIN CONTACT ........................................................................ 97 WRAPPER PROGRAM ........................................................................................................... 98 WRAPPER PROGRAM STRUCTURE AND OVERVIEW .................................................. 99 Inputs Generation Module .................................................................................................. 103 Simulation Stopping Conditions ......................................................................................... 105 Simulation Outputs ............................................................................................................. 106 SOIL-FURROWING FORCES .............................................................................................. 108 SENSITIVITY STUDIES ....................................................................................................... 111 Maximum Lateral Friction Coefficient ............................................................................... 112 Perception-Reaction Time .................................................................................................. 112 Encroachment Yaw Rate ..................................................................................................... 113 EVALUATION OF FRICTION MODEL AND LATERAL COEFFICIENT ...................... 114 Effectiveness of the Friction Ellipse Model ........................................................................ 117 Selection of Appropriate Lateral Friction Coefficient ........................................................ 119 VEHICLE MODELING AND VALIDATION ..................................................................... 121 Field Testing for Vehicle Model Validation ....................................................................... 121

iii Vehicle Models ................................................................................................................... 135 SUMMARY AND CONCLUSIONS ..................................................................................... 135 CHAPTER 7. SIMULATION SCENARIOS AND RESULTS ................................................. 137 INTRODUCTION .................................................................................................................. 137 SIMULATION MATRIX ....................................................................................................... 137 EXAMPLE SIMULATION CASE ........................................................................................ 140 CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES ......................................... 150 PROBABILITY-WEIGHTED SIMULATION RESULTS AS A FUNCTION OF LATERAL DISTANCE ..................................................................................................................... 150 Exceedance Probability ....................................................................................................... 151 Cumulative Rollover Probability ........................................................................................ 151 Cumulative Encroachment Cost.......................................................................................... 152 GUIDELINE DEVELOPMENT ............................................................................................ 159 Cost Contour Maps with an Equal Contour Interval .......................................................... 159 Envelope Adjustment Factors for Baseline Design Condition ........................................... 160 Development of Cost Contour Maps .................................................................................. 162 Benefit-Cost Analysis Results and Preliminary Guideline Development .......................... 173 CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS ......................... 197 INTRODUCTION .................................................................................................................. 197 SLOPE ROUNDING .............................................................................................................. 197 Slope Rounding Parameters ................................................................................................ 199 Simulated Ditch Configurations.......................................................................................... 201 Benefit-Cost Analysis ......................................................................................................... 201 Estimation Procedure and Assumptions ............................................................................. 202 Summary for Guideline Development ................................................................................ 205 SURFACE TREATMENTS ................................................................................................... 213 CHAPTER 10. GUIDELINE DEVELOPMENT ....................................................................... 215 INTRODUCTION .................................................................................................................. 215 GUIDELINE DEVELOPMENT PROCESS .......................................................................... 215 PROPOSED DESIGN GUIDELINES FOR ROADSIDE DITCH DESIGN ......................... 218 CHAPTER 11. SUMMARY AND CONCLUSIONS ................................................................ 228 REFERENCES ........................................................................................................................... 230 APPENDIX A. MATHEMATICAL DESCRIPTION OF THE BENEFIT-COST ANALYSIS METHOD ................................................................................................... A-1 APPENDIX B. CARSIM WRAPPER PROGRAM USERS’ GUIDE ....................................... B-1 APPENDIX C. SIMULATION OUTCOMES ........................................................................... C-1 APPENDIX D. PROPOSED GUIDELINES .............................................................................. D-1

iv LIST OF FIGURES Figure 1.1. Number of fatal crashes and fatalities involving vehicles striking ditches as FHE, from 1994 to 2008. .................................................................................................... 4 Figure 1.2. Percentage of fatal crashes involving vehicles striking ditches as FHE, from 1994 to 2008. ...................................................................................................................... 5 Figure 1.3. Recommendations for design of roadside slope combinations. ................................. 10 Figure 1.4. Recommendations for design of roadside slope combinations to permit vehicle traversal at speeds up to 60 mph (96 km/h) and encroachment angles up to 25 degrees. ........................................................................................................................ 11 Figure 1.5. Preferred cross-sections for parallel ditches with abrupt and gradual slope changes in RDG (4). ......................................................................................................... 13 Figure 1.6. Trajectories for two points—front, right bumper corner and hood corner—for a pickup truck traversing a 4H:1V slope (22). .................................................................. 22 Figure 1.7. Typical open-channel ditch configurations. ............................................................... 30 Figure 1.8. Rigid concrete channel lining. .................................................................................... 33 Figure 1.9. Vegetative lining. ....................................................................................................... 33 Figure 1.10. Cobble channel lining. .............................................................................................. 34 Figure 1.11. Rip rap channel lining. ............................................................................................. 34 Figure 1.12. Erosion control blanket. ............................................................................................ 35 Figure 3.1. Responding U.S. states and Canadian provinces........................................................ 38 Figure 3.2. Type of ditch typically used. ...................................................................................... 40 Figure 3.3. Symmetry of the ditch. ............................................................................................... 40 Figure 3.4. Ditch configuration for typical nonsymmetric ditches. .............................................. 41 Figure 3.5. Typically used foreslopes. .......................................................................................... 42 Figure 3.6. Typically used backslopes. ......................................................................................... 42 Figure 3.7. Usage of rounding as a mitigation strategy. ............................................................... 43 Figure 3.8. Types of surface treatments used. .............................................................................. 44 Figure 3.9. Use of ditch paving. .................................................................................................... 45 Figure 4.1. Number of fatal crashes involving ditches and other roadside features as FHE from 1991 to 2009. ............................................................................................................ 52 Figure 5.1. Basic framework of the BCA method. ....................................................................... 81 Figure 5.2. Encroachment rate adjustment factors for curved sections (50). .............................. 84 Figure 5.3. Encroachment rate adjustment factors for vertical grades (50). ................................. 84 Figure 5.4. Model parameter calibration procedure. ..................................................................... 92 Figure 6.1. Body-to-terrain contact forces. ................................................................................... 97 Figure 6.2. TTI’s CarSim wrapper program main flowchart. ..................................................... 101 Figure 6.3. Flowchart of the input generation module of TTI’s wrapper program. ................... 102 Figure 6.4. Flowcharts of the subroutines for generating CarSim (a) terrain/road inputs, and (b) event inputs (steering, braking, encroachment speeds, angles, rates, etc.). ........ 104 Figure 6.5. Flowchart of TTI’s code for applying body-to-terrain contact with CarSim. .......... 105 Figure 6.6. Properties of tires in CarSim. ................................................................................... 109 Figure 6.7. Friction ellipse model for modeling tire forces due to soil furrowing. .................... 110 Figure 6.8. Roadside ditch profile used for sensitivity analysis. ................................................ 111 Figure 6.9. Results of the sensitivity analyses for determining maximum lateral friction coefficient. ...................................................................................................................... 113

v Figure 6.10. Results of the sensitivity analyses for determining perception-reaction time. ....... 114 Figure 6.11. Results of the sensitivity analyses for determining encroachment yaw rate. ......... 114 Figure 6.12. Simulation matrix for evaluation of the friction ellipse model and determination of the lateral friction coefficient. ............................................................. 116 Figure 6.13. Lateral tire forces for small car and pickup truck with 25-mph initial speed, tracking initial conditions, and panic return-to-road steer after 1 second P/R time. ...... 118 Figure 6.14. Lateral tire forces for small car and pickup truck with 35-mph initial speed, non-tracking initial conditions, constant steer angle, and full ABS brakes. ................... 118 Figure 6.15. Lateral tire forces for small car and pickup truck with 55 mph initial speed, non-tracking initial conditions, constant steer angle, and full ABS brakes. ................... 119 Figure 6.16. Percentages and numbers of rollovers for different values of maximum lateral coefficient of friction. .......................................................................................... 120 Figure 6.17. Speed bump test setup. ........................................................................................... 122 Figure 6.18. Ditch traversal test setup. ....................................................................................... 123 Figure 6.19. Geometric and mass properties of the test vehicle. ................................................ 125 Figure 6.20. Location of tracked points (diamond-shaped) on pickup truck’s body. ................. 126 Figure 6.21. CarSim terrain incorporating two staggered speed bumps. .................................... 126 Figure 6.22. CarSim terrain for V-ditch testing. ......................................................................... 126 Figure 6.23. Typical CarSim speed bump traversal simulation. ................................................. 127 Figure 6.24. Speed bump traversal comparison for single speed bump with vehicle speed of 11.5 mph. .................................................................................................................... 129 Figure 6.25. Speed bump traversal comparison for single speed bump with vehicle speed of 21.7 mph. .................................................................................................................... 129 Figure 6.26. Speed bump traversal comparison for single speed bump with vehicle speed of 30.8 mph. .................................................................................................................... 130 Figure 6.27. Speed bump traversal comparison for two speed bumps with vehicle speed of 11.9 mph. .................................................................................................................... 130 Figure 6.28. Speed bump traversal comparison for two speed bumps with vehicle speed of 21.1 mph. .................................................................................................................... 131 Figure 6.29. Speed bump traversal comparison for two speed bumps with vehicle speed of 29.3 mph. .................................................................................................................... 131 Figure 6.30. CarSim simulation of MASH pickup traversing 5.5H:1V V-ditch. ....................... 132 Figure 6.31. Vehicle path comparison at 41.6 mph. ................................................................... 133 Figure 6.32. Vehicle path comparison at 49.9 mph. ................................................................... 133 Figure 6.33. Vehicle roll, pitch, and yaw comparison at 41.6 mph. ........................................... 134 Figure 6.34. Vehicle roll, pitch, and yaw comparison at 49.9 mph. ........................................... 134 Figure 7.1. Terrain modeled for the example simulation case. ................................................... 140 Figure 7.2. Vehicle response and path for simulation Case 1. .................................................... 142 Figure 7.3. Vehicle response and path for simulation Case 2. .................................................... 143 Figure 7.4. Vehicle response and path for simulation Case 3. .................................................... 144 Figure 7.5. Vehicle response and path for simulation Case 4. .................................................... 145 Figure 7.6. Vehicle response and path for simulation Case 5. .................................................... 146 Figure 7.7. Comparison of vehicle path. ..................................................................................... 147 Figure 7.8. Comparison of vehicle roll angle. ............................................................................ 147 Figure 7.9. Comparison of vehicle yaw angle. ........................................................................... 148 Figure 7.10. Comparison of vehicle sideslip angle. .................................................................... 148

vi Figure 8.1. Exceedance probability of the extent of lateral encroachments: ditches with various BTWs, SHW = 6 ft, FSW = 8 ft, BSW = 8 ft. ................................................... 153 Figure 8.2. Exceedance probability of the extent of lateral encroachments: V-ditches with various SHWs, FSW = 8 ft, BSW = 8 ft. ........................................................................ 154 Figure 8.3. Cumulative rollover probability as a function of lateral distance: ditches with various BTWs, SHW = 6 ft, FSW = 8 ft, BSW = 8 ft. ................................................... 155 Figure 8.4. Cumulative rollover probability as function of lateral distance: V-ditches with various SHWs, FSW = 8 ft, BSW = 8 ft. ........................................................................ 156 Figure 8.5. Cumulative encroachment cost as a function of lateral distance: ditches with various BTWs, SHW = 6 ft, FSW = 8 ft, BSW = 8 ft. ................................................... 157 Figure 8.6. Cumulative encroachment cost as a function of lateral distance: V-ditches with various SHWs, FSW = 8 ft, BSW = 8 ft. ................................................................ 158 Figure 8.7. An illustration of design points where normalized expected crash costs will be estimated for default design configuration. .................................................................... 160 Figure 8.8. An example cost contour map with equal contour interval. ..................................... 161 Figure 8.9. An illustration of the strategy to select preferred design envelope based on cost gradient. ................................................................................................................... 161 Figure 8.10. EAF moves preferred envelope for default design condition either inward or outward to stay neutral in crash cost. .............................................................................. 162 Figure 8.11. Rollover probabilities for varying ditch bottom widths. ........................................ 165 Figure 8.12. Rollover probabilities for varying shoulder widths. ............................................... 166 Figure 8.13. Encroachment costs for varying ditch bottom widths. ........................................... 167 Figure 8.14. Encroachment costs for varying shoulder widths. .................................................. 168 Figure 8.15. Normalized encroachment costs for varying ditch bottom widths. ........................ 169 Figure 8.16. Normalized encroachment costs for varying shoulder widths. .............................. 170 Figure 8.17. Cost contour maps for varying ditch bottom widths. ............................................. 171 Figure 8.18. Cost contour maps for varying shoulder widths. .................................................... 172 Figure 8.19. NCPE contour maps for base configurations. ........................................................ 174 Figure 8.20. NCPE contour maps for varying ditch bottom widths. .......................................... 176 Figure 8.21. NCPE contour maps for varying shoulder widths. ................................................. 177 Figure 8.22. NCPE contour maps for varying vertical grades. ................................................... 178 Figure 8.23. NCPE contour maps for varying HCs. ................................................................... 179 Figure 8.24. NCPE = 0.6 for varying BTW, FSW, and BSW. ................................................... 180 Figure 8.25. NCPE = 0.6 for varying HC, FSW, and BSW. ...................................................... 181 Figure 8.26. Initial design envelopes for sites with ERs of 0.3, 0.5, 1.0, 1.5, and 3.0 per mi-yr-side. ....................................................................................................................... 182 Figure 8.27. NCPE contour map for simulated V-ditches with varying FSW and BSW: 4D65. ............................................................................................................................... 186 Figure 8.28. Comparison of contour lines for NCPE=0.6 for four highway types—PSL combinations. .................................................................................................................. 187 Figure 8.29. Design envelopes for relatively straight sections by ER and foreslope width. ...... 188 Figure 8.30. Design envelopes for sections with an HC of ≥3 degrees and <6 degrees by ER and foreslope width. .................................................................................................. 191 Figure 8.31. Design envelopes for sections with an HC of ≥6 degrees by ER and foreslope width................................................................................................................ 194 Figure 9.1. Equal-tangent parabolic rounding. ........................................................................... 200

vii Figure 9.2. NCPE for simulated ditch configurations with and without slope rounding treatments: 4D65, BTW = 4 ft. ....................................................................................... 206 Figure 9.3. NCPE contour maps constructed from simulated configurations with and without slope rounding treatments: 4D65, BTW = 4 ft. ................................................. 207 Figure 9.4. Contour lines for NCPE values of 0.2, 0.6, and 1.2 for ditches with and without slope rounding treatments: 4D65, BTW = 4 ft. ................................................. 208 Figure 9.5. NCPE contour maps constructed from simulated configurations with and without slope rounding treatments: 4D65, BTW = 0 ft. ................................................. 209 Figure 9.6. NCPE contour lines of 0.2, 0.6, and 1.2 for ditches with and without slope rounding treatments: 4D65, BTW = 0 ft. ........................................................................ 210 Figure 9.7. NCPE contour lines of 0.2, 0.6, and 1.2 for ditches with and without slope rounding treatments: 2U55, BTW = 4 ft. ........................................................................ 211 Figure 9.8. NCPE contour lines of 0.2, 0.6, and 1.2 for ditches with and without slope rounding treatments: 2U55, BTW = 0 ft. ........................................................................ 212 Figure 9.9. NCPE contour maps for varying surface treatments. ............................................... 214 Figure 10.1. Preferred design envelope graph for HC of less than 3 degrees, ditch bottom width of 0 to 4 ft, and ER of 0.75. .................................................................................. 216 Figure 10.2. Simplified design envelope graph containing a single curve that represents all the foreslope widths. .................................................................................................. 217 Figure 10.3. Curves of various ERs combined in a single graph. ............................................... 217 Figure 10.4. Roadside ditch design guidelines for ditch bottom width of less than 6 ft and HC of less than 3 degrees................................................................................................ 220 Figure 10.5. Roadside ditch design guidelines for ditch bottom width of greater than or equal to 6 ft and HC of less than 3 degrees..................................................................... 221 Figure 10.6. Roadside ditch design guidelines for ditch bottom width of less than 6 ft and HC of greater than or equal to 3 degrees and less than 6 degrees. ................................. 222 Figure 10.7. Roadside ditch design guidelines for ditch bottom width of greater than or equal to 6 ft and HC greater than or equal to 3 degrees and less than 6 degrees. ........... 223 Figure 10.8. Roadside ditch design guidelines for ditch bottom width of less than 6 ft and HC of greater than or equal to 6 degrees. ....................................................................... 224 Figure 10.9. Roadside ditch design guidelines for ditch bottom width of greater than or equal to 6 ft and HC of greater than or equal to 6 degrees. ............................................ 225 Figure 10.10. ER based on AADT for divided and undivided highway types. .......................... 226

viii LIST OF TABLES Table 1.1. Distributions of crashes by MHE: for fatal crashes involving vehicles striking ditches as FHE in 2008 (6). ................................................................................................. 6 Table 1.2. Hazard classifications and severity levels. .................................................................. 16 Table 1.3. Clear-zone distances for different AADT ranges. ....................................................... 24 Table 4.1. Relative strengths and limitations of databases to address research objectives. ......... 48 Table 4.2. Top five or six MHEs (FARS: 2004 to 2008). ............................................................ 53 Table 4.3. Frequency and relative percentage of fatal crashes by highway functional class (FARS: 2004 to 2008). ...................................................................................................... 55 Table 4.4. Frequency and relative percentage of fatal crashes by FHE and highway type (FARS: 2004 to 2008). ...................................................................................................... 56 Table 4.5. Frequency and relative percentage of fatal crashes by FHE and posted speed limit (FARS: 2004 to 2008). ............................................................................................. 57 Table 4.6. Frequency and relative percentage of fatal crashes by FHE and horizontal alignment (FARS: 2004 to 2008). ..................................................................................... 57 Table 4.7. Frequency and relative percentage of fatal crashes by FHE and vertical profile of highways (FARS: 2004–2008). .................................................................................... 57 Table 4.8. Frequency and relative percentage of fatal crashes by FHE and lighting condition (FARS: 2004–2008). ......................................................................................... 58 Table 4.9. Frequency and relative percentage of fatal crashes by FHE and vehicle body type (FARS: 2004–2008). ................................................................................................. 58 Table 4.10. Frequency and relative percentage of fatal crashes by FHE and the deployment of driver side air bags (FARS: 2004–2008). ................................................. 59 Table 4.11. Frequency and relative percentage of fatal crashes by FHE and driver alcohol use (FARS: 2004–2008). .................................................................................................. 59 Table 4.12. Frequency and relative percentage of fatal crashes by FHE and seat-belt use. ......... 60 Table 4.13. Some characteristics of travel speed distribution and fitted probability density function by posted speed limit (FARS: 2004–2009; only SVROR crashes on the roadside area). ........................................................................................... 61 Table 4.14. Average numbers of injuries and damages involved in one ditch/culvert- initiated crash (FARS and GES databases, 2004–2009). .................................................. 64 Table 4.15. Estimated numbers and distribution of crashes by injury severity (FARS and GES databases, 2004–2009). ............................................................................................ 65 Table 4.16. Distribution of SVROR crashes that involved a roadside ditch/culvert as the FHE by posted speed limit. ......................................................................................... 65 Table 4.17. Some characteristics of travel speed distribution and fitted probability density function by posted speed limit (GES: 2002–2009; only SVROR crashes on the roadside area). ................................................................................................................... 66 Table 4.18. Number of sampled cases involving ditches as the FHE (CDS: 1997–2008). .......... 68 Table 4.19. Top rollover initiation objects contacted after striking the ditch as the FHE (CDS: 1997–2008). ........................................................................................................... 69 Table 4.20. Distribution of crash severities for rural two-lane highways (WA State: 1999– 2002). ................................................................................................................................ 71 Table 4.21. OST-recommended crash cost per injury and per property damage for various police-reported severity levels. ......................................................................................... 73

ix Table 4.22. Average cost per crash by police-reported injury severity level for ditch/culvert initiated crashes. .......................................................................................... 74 Table 4.23. Average cost per crash by police-reported severity level for rollover and non- rollover crashes. ................................................................................................................ 75 Table 4.24. Estimated per-crash cost for rollover, non-rollover, and all crashes. ........................ 76 Table 4.25. Per-crash cost adjusted for underreporting of non-rollover PDO crashes. ................ 77 Table 5.1. Base encroachment rates for one-side of the highway by highway type and projected bi-directional AADT. ........................................................................................ 83 Table 5.2. Encroachment rate adjustment factors for horizontal curvatures (50). ........................ 83 Table 5.3. Encroachment rate adjustment factors for vertical grades (50). .................................. 84 Table 5.4. Vehicle type distribution. ............................................................................................. 85 Table 5.5. Encroachment speed distribution. ................................................................................ 86 Table 5.6. Encroachment angle probability distribution. .............................................................. 87 Table 5.7. Driver Control Input and vehicle tracking status distribution at the point of departure and after the encroachment ............................................................................... 87 Table 5.8. Relationship Between Severity Index and Severity Distribution ................................ 89 Table 5.9. Set of simulated ditch configurations selected to represent frequently used configurations in the field. ................................................................................................ 93 Table 6.1. Simulation outcomes logged in the aggregate simulation results table. .................... 107 Table 6.2. Simulation output data saved for each simulation case. ............................................ 108 Table 6.3. Vehicle’s initial speed during speed bump tests. ....................................................... 123 Table 6.4. Vehicle’s initial speed on entering the ditch. ............................................................. 123 Table 6.5. Vehicle model’s mass moments of inertia. ................................................................ 124 Table 7.1. Vehicle dynamics simulation matrix. ........................................................................ 137 Table 7.2. Number of baseline and secondary ditch variables. .................................................. 138 Table 7.3. Encroachment conditions and driver behavior. ......................................................... 138 Table 7.4. Driver inputs. ............................................................................................................. 138 Table 7.5. Simulation outcomes summary. ................................................................................. 140 Table 9.1. AADT range for recommended slope rounding (20)................................................. 199 Table 9.2. Change in NCPE value by ditch configuration and slope rounding type (constant rounding, optimum rounding). ........................................................................ 202 Table 10.1. Adjustment Factors for ER Based on Horizontal Curvature ................................... 226 Table 10.2. Adjust Factors for ER Based on Vertical Grade ...................................................... 227