Download - 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)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
achievedreductionhazardtimprovementheoftannualized
essEffectivenCost cos
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Glennon (1974) (cont.)
• Determine the effectiveness:E = H (before) - H (after)
• Compute cost-effectiveness:
achievedreductionhazardtimprovementheoftannualized
essEffectivenCost cos
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Warranting Methods
• Charts• Flow charts• Guidance tables and figures
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Warranting Methods (cont.)• Charts
*this chart used for high volume roads Georgia DOT (1991)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Warranting Methods (cont.)
Georgia DOT (1991)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Warranting Methods (cont.)
Georgia DOT (1991)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Warranting Methods (cont.)
Georgia DOT (1991)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
Take corrective action
Take corrective action
Restore embedment
Tighten attachments
YES
YES
YES
YES
YES
YES
YES
NO
NO
NO
NO
NO
NO
NO
AASHTO Roadside Design Guide (1989)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
AASHTO Roadside Design Guide (1989)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Warranting Methods (cont.)
DISTANCE FROM EDGE OF TRAVELED WAY TO ROADSIDE OBSTACLE (FEET)
METRIC CONVERSIONS1 mph = 1.61 Kmph1 ft = 0.305 m
Figure III-A-3
AASHTO Roadside Design Guide (1989)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Experiences of Traffic Agencies
• New York State• Ohio• California• Minnesota• Wyoming• Alaska
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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”
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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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