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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

2

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


3

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)


4

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

=

=

∑∂

∂


8

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


10

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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Bottom UpBottom Up Fatigue Fatigue CrackingCracking


14

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


15

BottomBottom--UpUp Cracking Cracking –– Groups and Groups and RangesRanges2003 Calibration2003 Calibration


16

Top Down Cracking Top Down Cracking –– Se Se ModelModel


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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


19

Sg Permanent DeformationSg Permanent DeformationSeRDSG = 0.1235 SGrut0.5012


20

Total Total Permanent DeformationPermanent Deformation


21

Top Down CrackingTop Down Cracking


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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


23

HMA HMA -- ResidualsResiduals forfor IRIIRI


24

HMA over PCC HMA over PCC -- ResidualsResiduals forfor IRIIRI


25

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


30

Thank You!Thank You!

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