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S1SP ARA0127-1
Reliability in MechanisticReliability in Mechanistic--Empirical Pavement Design GuideEmpirical Pavement Design Guide
Flexible Pavement AnalysisFlexible Pavement Analysis
Presented By: Manuel Ayres Jr., Ph.D.
At: TRB Workshop 152
Date: Jan 21, 2007
Expanding the Realm of Possibility
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SummarySummary
1. MEPDG Performance Criteria
2. Components of Variability
3. Reliability Approaches
4. Input Variables
5. Calibration and Residuals
6. Modeling Variability
7. Advantages and Disadvantages of Current Approach
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Reliability Reliability -- DefinitionDefinition
� "The reliability of the pavement design-performance process is the probability that a pavement section
designed using the process will perform satisfactorily
over the traffic and environmental conditions for the
design period." (AASHTO, 1993)
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2006 2006 RecalibrationRecalibration: NCHRP 1: NCHRP 1--40D40D
� Recalibrated models for Bottom-Up, Top-Down and Transverse
Cracking, Perm Deform and IRI.
� Improvement of database
� Added 4-5 years of data
� Additional climatic data
� Lower model error
� Sg backcalculated moduli
� Lower model errors
� Rational sensitivity to changes in inputs
� Improved reliability
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MEPDG Performance MEPDG Performance CriteriaCriteriaFlexible PavementsFlexible Pavements
� Terminal IRI
� AC Surface Down Cracking
� AC Bottom Up Cracking
� AC Thermal Fracture
� AC Permanent Deformation
� Total Permanent Deformation
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Components Components of of VariabilityVariability
� Design Factors
� Environment
� Traffic
� Materials
� Drainage characteristics
� Construction
� Materials
� Equipment
� Procedures
� Experience
� Performance
� Model errors
� Simplified assumptions
� Calibration data
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Reliability Approaches EvaluatedReliability Approaches Evaluated
� Monte Carlo Simulation
� Obtain probability distribution
� Number of simulation runs required is high
� Time to run is high
� Rosenblueth Procedure
� Number of iterations = 2n
(n is # of stochastic variables)
� First Order Second Moment (FOSM)
� Closed form solution
� Require partial derivatives
� Distribution of Residuals
V f x x xf
xV xn
i
i
i
n
[ ( , , ... ) [ ]1 2
2
1
=
=
∑∂
∂
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Number Number of Input of Input Stochastic VariablesStochastic VariablesLevel Level 3 Design3 Design
� Traffic
� 159+39*10*12+ 39*10*12+ 31*10*12+ 31*10*12+56 = 17015
� Climate
� 19+5*24 = 139
� Structure
� AC – 14
� Unbound – 16
� CTB – 8
� PCC - 13
Simple Pavement: AC + Base + Sg
17200 SV
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Distribution of ResidualsDistribution of Residuals
Actual AC Rutting
Pre
dic
ted
AC
Ru
ttin
g
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Estim
ate
d A
C R
uttin
g
RT1
T1
RL
1-R
1-R
T0
RT0
AC Rutting Performance Criteria
1-R
Expected IRI
MEPDG MEPDG ReliabilityReliability ApproachApproach
R
R
Time
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Example MEPDG Output Example MEPDG Output -- PlotPlotPermanent Deformation: Rutting
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0 12 24 36 48 60 72 84 96 108 120 132
Pavement Age (month)
Ruttin
g D
epth
(in
)
SubTotalAC
SubTotalBase
SubTotalSG
Total Rutting
TotalRutReliability
Total Rutting Design Limit
AC Rutting Design Value =
0.25
Total Rutting Design Limit =
0.75
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Example MEPDG Output Example MEPDG Output -- TabularTabular
mo yr
1 0.08 October 0.0001 6 0.0032 0 0.0009 0 0.0193 0 0.0209
2 0.17 November 0.0001 6 0.0033 0 0.0009 0 0.0197 0 0.0216
3 0.25 December 0.0001 6 0.0033 0 0.0009 0 0.0197 0 0.0216
4 0.33 January 0.0001 0 0.0033 0 0.0009 0 0.0197 0 0.0216
5 0.42 February 0.0002 0 0.0034 0 0.0009 0 0.0197 0 0.0216
6 0.5 March 0.0003 0 0.0035 0 0.0009 0 0.0205 0 0.0229
7 0.58 April 0.0003 0 0.0043 0 0.0013 0 0.0282 0 0.0393
8 0.67 May 0.0003 0 0.0067 0 0.0019 0 0.0316 0 0.043
9 0.75 June 0.0008 6 0.0188 0 0.0039 0 0.0363 0 0.0474
10 0.83 July 0.0012 6 0.0256 0 0.0051 0 0.0377 0 0.0488
11 0.92 August 0.0013 6 0.0284 0 0.0056 0 0.0383 0 0.0493
Predicted Rutting: Project HMA-newPavement
age
Month
Maximum Rutting (inch)
AC1
Location
(in) AC2
Location
(in) AC3
Location
(in) GB4
Location
(in) SG5
0.0209 0 0.0768 0 0.0042 0.0193 0.0977 0.1212 0 0.1754
0.0216 0 0.0844 0 0.0042 0.0197 0.106 0.13 0 0.1862
0.0216 0 0.0851 0 0.0043 0.0197 0.1067 0.1307 0 0.1871
0.0216 0 0.0851 0 0.0044 0.0197 0.1067 0.1308 0 0.1872
0.0216 0 0.0851 0 0.0045 0.0197 0.1067 0.1309 0 0.1873
0.0229 0 0.0852 0 0.0047 0.0205 0.1081 0.1333 0 0.1901
0.0393 0 0.1284 0 0.0059 0.0282 0.1676 0.2017 0 0.2714
0.043 0 0.139 0 0.0089 0.0316 0.182 0.2225 0 0.2951
0.0474 0 0.1452 0 0.0235 0.0363 0.1926 0.2524 0 0.3281
0.0488 0 0.1481 0 0.0318 0.0377 0.197 0.2665 0 0.3441
0.0493 0 0.1498 0 0.0353 0.0383 0.1991 0.2726 0 0.351
Maximum Rutting (inch)
SG5
Location
(in) SG6
Location
(in)
SubTotalA
C
SubTotalB
ase
SubTotalS
G Total
Location
(in)
TotalRutR
eliability
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Residuals
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
-4 -3 -2 -1 0 1 2 3
Adjusted Damage
Err
or
(Pre
dic
ted - M
easure
d C
rackin
g)
Bottom UpBottom Up Cracking Cracking –– Distribution Distribution of of ResidualsResiduals
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BottomBottom--UpUp Cracking Cracking –– Groups and Groups and RangesRanges2003 Calibration2003 Calibration
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GB GB Permanent DeformationPermanent Deformation
Se = 0.1477 GBRut0.67
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AC AC Permanent DeformationPermanent Deformation
SeRDAC = 0 .24 ACrut0.8026
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Sg Permanent DeformationSg Permanent DeformationSeRDSG = 0.1235 SGrut0.5012
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IRI IRI ModelsModels� Flexible New or Rehab
� Flexible New or Rehab over PCC
� IRI = f(IRI0, Rutting, Fat. Crack, Transv. Crack, Site Factor)
� Site Factor = f(Subgrade, Climate, Age)
� Subgrade: % fine sand, silt, clay & PI
� Climate: Freezing index, precipitation
� Age (cycles hot/cold, wet/dry, freeze/thaw)
V f x x xf
xV xn
i
i
i
n
[ ( , ,... ) [ ]1 2
2
1
=
=
∑∂
∂
First-Order, Second-Moment (FOSM) method
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Thermal FractureThermal Fracture
Std.Dev (Thermal) = -0.0899 * Thermal + 636.97
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Advantages Advantages & & DisadvantagesDisadvantages
� Advantages
� Improvement relative AASHTO 1993
� Practical and more realistic
� Based on residuals from calibration
� May allow more economical design for localcalibration
� Disadvantages
� Does not allow to evaluate change in performance due to differences in variability of individual factors
� Currently variability and reliability analysis does not depend upon level of design
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T1
1-RAC Rutting Performance Criterion
1-R
Expected Rutting
MEPDG MEPDG ReliabilityReliability Approach Approach –– Level 3Level 3
R
AC Rutting
RutT1
Rutf
Time
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AC Rutting
RutT1
T1
Rutf1-RAC Rutting Performance Criterion
1-R
Expected Rutting
MEPDG MEPDG ReliabilityReliability Approach Approach –– Level 1Level 1Level 3 CalibrationLevel 3 Calibration
R
Time
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AC Rutting
RutT1
T1
RutfAC Rutting Performance Criterion
1-R
MEPDG MEPDG ReliabilityReliability Approach Approach –– Level 1Level 1Level 1 CalibrationLevel 1 Calibration
R
Expected Rutting
Time