Encroachment Probability Model (cont.)

Center for Risk Management of Engineering Systems University of Virginia, Charlottesville

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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

fiW

VWV

iWV

iVW

EACECPAAC ,,,

,, )|(

AAC

iVW

fE

)|( ,,

,WV

iWV ECP

Sicking and Hayes (1986)


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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

n

iii ICAIPEAPEPVACE

1

)(*)|(*)|(*)(*)(

Mak et al. (1998)


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1. Determine effectivenes:

E = Hazard(before) - Hazard(after)

Glennon (1974)

n

j

f

njwsyP

nw

syPsyPlSE

H

1

]2

)12(6[14.5]3[4.31][

560,10

2. Compute cost-effectiveness:

achievedreductionhazardtimprovementheoftannualized

essEffectivenCost cos


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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




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Glennon (1974) (cont.))]|()][|()][([ CIPECPEPVH

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

H

V

)|( ECP

)(EP

)|( CIP


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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

n

j

f

njwsyP

nw

syPsyPlSE

H

1

]2

)12(6[14.5]3[4.31][

560,10

• 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

Glennon (1974)


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Lateral Extent Distribution

LATERAL EXTENT OF MOVEMENT, X, (FEET)

PRO

BA

BIL

ITY

OF

ENC

RO

AC

HM

ENT

EQU

ALI

NG

OR

EX

CEE

DIN

G L

ATE

RA

L M

OV

EMEN

T, P

, (%

)

Glennon (1974)


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Glennon (1974) (cont.)

• Determine the effectiveness:E = H (before) - H (after)

• Compute cost-effectiveness:




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Warranting Methods

• Charts• Flow charts• Guidance tables and figures


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Warranting Methods (cont.)• Charts

*this chart used for high volume roads Georgia DOT (1991)


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Warranting Methods (cont.)

Georgia DOT (1991)


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Georgia DOT (1991)


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Georgia DOT (1991)


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Warranting Methods (cont.)• Flow charts:

Is barrier warranted by FigureIII-A-1?

Are roadside obstacles within theclear zone as determined by

Figure III-A-3?

Barrier NotWarranted

Is barrier warranted basedon Table III-A-1 and/or

Table III-A-2?

Can hazard be removed orreduced so that barrier shielding

is unnecessary?

Barrier Warranted

YES

YES

YES

YES

NO

NO

NO

NO

AASHTO Roadside Design Guide (1989)


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Warranting Methods (cont.)1. Is barrier warranted?

2. Can hazard be reducedor eliminated so that barrieris no longer needed?

6. Are posts firmlyembedded?

7. Are rails firmly attachedto posts?

3. Does barrier meetstrength and safetystandards?

5. Is rail height properdistance above ground?

4. Does the lateralplacement of the barriermeet suggested criteria?

End of check

Remove barrier

Eliminate or reduce hazardand remove barrier

Take corrective action



Restore embedment

Tighten attachments

YES

YES

YES

YES

YES

YES

YES

NO

NO

NO

NO

NO

NO

NO



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Warranting Methods (cont.)• Guidance tables and figures:

Traffic Barrier RequiredNontraversable Hazard WithinClear Zone as Determined By

Figure III-A-3Yes No

Rough Rock Cuts X1

Large Boulders XStreams or permanent bodies of

water less than 2 ft. in depthX

Streams or permanent bodies ofwater more than 2 ft. in depth

X

Shoulder drop-off with slopesteeper than 1:1

a. Height greater than 2 ft. Xb. Height less than 2 ft. X

1 All roadside obstacles within the clear zone should be removed if possible, otherwise provide barrierprotection



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Warranting Methods (cont.)Traffic Barrier RequiredFixed Objects Within Clear Zone

as Determined By Figure III-A-31

Yes No

Sign, traffic signal, and luminairesupports2

a. Breakaway or yielding designwith linear impulse:3

1. less than 1,100 lb-sec X2. greater than 1,100 lb-sec X4

b. Concrete base extending 6 in.or more above ground

X

Fixed sign bridge supports XBridge piers and abutments at

underpassesX

Retaining walls and culverts XTrees with diameter greater than

6 in.X4

Wood poles or posts with areagreater than 50 in.2

X4

1 Fixed object should be removed or relocated so that a barrier is unnecessary if practical2 Breakaway or yielding design is desirable regardless of distance from traveled way3 See discussion in text4 A judgement decision AASHTO Roadside Design Guide (1989)


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DISTANCE FROM EDGE OF TRAVELED WAY TO ROADSIDE OBSTACLE (FEET)

METRIC CONVERSIONS1 mph = 1.61 Kmph1 ft = 0.305 m

Figure III-A-3



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Experiences of Traffic Agencies

• New York State• Ohio• California• Minnesota• Wyoming• Alaska


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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


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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”


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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


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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


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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


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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

Documents

Encroachment Probability Model (cont.)