Encroachment Probability Model (cont.)

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(AE) P(accident given an encroachment)
• P(IiA) 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
Glennon (1974)

• 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

• 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
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?
• AASHTOs guide and common sense is utilized