1. Encroachment Probability Model (cont.) Annual accident costs arising from run-off-road traffic accidents within the region of interest ($/year) Uncontrolled encroachment frequency Summation over all encroachment vehicle sizes, velocities, angles, ranges Accident costs associated with an accident involving a vehicle of size W, striking a hazard at speed V and angle  Sicking and Hayes (1986)

2. Expected Accident Cost - Simplified • E(AC) = Expected accident cost • V = traffic volume, ADT • P(E) = P(encroachment) • P(A|E) = P(accident given an encroachment) • P(Ii|A) = P(injury severity i given an accident) • C(Ii) = cost associated with injury severity i • n = number of injury severity levels Mak et al. (1998)

3. Glennon (1974) 1. Determine effectivenes: E = Hazard(before) - Hazard(after) 2. Compute cost-effectiveness:

4. Glennon (1974) • Model considers: • vehicular roadside encroachment frequencies, a function of ADT • the percentile distribution for the lateral displacement of encroaching vehicles • the lateral placement of the roadside obstacle • the size of the obstacle • the accident severity associated with the obstacle

5. Glennon (1974) (cont.) Hazard index; expected number of fatal plus nonfatal injury accidents per year Vehicle exposure; number of vehicles per year passing through section L Probability that a vehicle will encroach on the roadside within section L; encroachment per vehicle Probability of a collision given that an encroachment has occurred, accidents per encroachment Probability of an injury (fatal or nonfatal) accident, given a collision, fatal plus nonfatal injury accidents per year

6. Simplified Hazard Model • Ef= encroachment frequency, number of roadside encroachments per year • S = severity index, number of fatal and nonfatal injury accidents per total accidents • l = longitudinal length of the roadside obstacle • y = lateral displacement of encroaching vehicle, feet Glennon (1974) • s = lateral placement of obstacle, feet • w = lateral width of the roadside obstacle • n = number of analysis increments for the hazard associated with the obstacle width • j = number of the obstacle-width increment under consideration

7. Lateral Extent Distribution PROBABILITY OF ENCROACHMENT EQUALING OR EXCEEDING LATERAL MOVEMENT, P, (%) LATERAL EXTENT OF MOVEMENT, X, (FEET) Glennon (1974)

8. Glennon (1974) (cont.) • Determine the effectiveness: E = H (before) - H (after) • Compute cost-effectiveness:

9. Warranting Methods • Charts • Flow charts • Guidance tables and figures

10. Warranting Methods (cont.) • Charts *this chart used for high volume roads Georgia DOT (1991)

11. Warranting Methods (cont.) Georgia DOT (1991)

12. Warranting Methods (cont.) Georgia DOT (1991)

13. Warranting Methods (cont.) Georgia DOT (1991)

14. Warranting Methods (cont.) • Flow charts: AASHTO Roadside Design Guide (1989)

15. NO 1. Is barrier warranted? Remove barrier YES 2. Can hazard be reduced YES Eliminate or reduce hazard or eliminated so that barrier and remove barrier is no longer needed? NO NO 3. Does barrier meet Take corrective action strength and safety standards? YES NO 4. Does the lateral Take corrective action placement of the barrier meet suggested criteria? YES NO 5. Is rail height proper Take corrective action distance above ground? YES NO 6. Are posts firmly Restore embedment embedded? YES NO 7. Are rails firmly attached Tighten attachments to posts? YES End of check Warranting Methods (cont.) AASHTO Roadside Design Guide (1989)

16. Warranting Methods (cont.) • Guidance tables and figures: AASHTO Roadside Design Guide (1989)

17. Warranting Methods (cont.) AASHTO Roadside Design Guide (1989)

18. Warranting Methods (cont.) AASHTO Roadside Design Guide (1989) DISTANCE FROM EDGE OF TRAVELED WAY TO ROADSIDE OBSTACLE (FEET) METRIC CONVERSIONS 1 mph = 1.61 Kmph 1 ft = 0.305 m Figure III-A-3

19. Experiences of Traffic Agencies • New York State • Ohio • California • Minnesota • Wyoming • Alaska

20. New York State DOT • Guardrail called “guide rail” because NYSDOT lost a case when the judge agreed that the rail did not “guard” a plaintiff • “Over-simplification” - • For each project they determine an appropriate clear zone • Then they shield potential hazards that can not be made crash-worthy • Site guide rail wherever clear zone is not wide enough

21. New York State DOT (cont.) • “Complex reality” - • All possible roadside and traffic conditions are a continuous spectra • Roadway curvature, side slopes, shoulder widths, curbing, ditches, location of hazards are highly variable • Cultural, historic, financial, or environmental value of potential hazards can vary significantly and there may be restrictions on what can be removed • Courts have provided a remedy - • Courts will not second guess the opinions of experts • Courts will not accept the opinion of other experts as invalidating the opinion of an expert civil engineer • Courts look for “professional judgement”

22. New York State DOT (cont.) • Various observations: • Accident history ~ prime factor • Tort liability is a significant concern • $9 billion in pending liability • Trials may occur many years after planning of site so good documentation is essential • Complaints that using methodologies are too time consuming, analysts would rather use own expert judgement • Need indication of areas instead of absolute

23. Ohio DOT • Only use prioritization when upgrading • Projects are prioritized and a guardrail may come along with the project • Using their own Roadside Design Guide, they determine if a guardrail is warranted. If so, the guardrail is installed • Possess a multitude of guardrail

24. California DOT • Do not do a benefit/cost calculation • Rely on their Traffic Manual and crash history and potential, geometrics, ADT, and the slope severity curve • “HQ Reviewers” ensure that safety device applications are applied uniformly statewide • They analyze various resources and if guardrail is recommended, they install

25. Minnesota DOT • First choice is to correct or remove the hazard • Will guardrail present a greater hazard? • AASHTO’s guide and common sense is utilized