sensitivity evaluation of the mepdg for flexible pavements trb webinar...
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SENSITIVITY EVALUATION OF THE MEPDG FOR FLEXIBLE PAVEMENTS TRB Webinar July 25, 2012
Presenter:
Charles W. Schwartz University of Maryland
Moderator:
Trenton Clark Virginia Asphalt Association
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University of Maryland
• Charles Schwartz (PI)
• Rui Li
NCHRP 1-47 Project Panel
• Kevin Hall, U AR (Chair)
• Michael Ayers, ACPA
• Imad Basheer, CA DOT
• Mohamed Elfino, VA DOT
• Laura Fenley, WI DOT
• Geoffrey Hall, MD SHA
• Kent Hansen, NAPA
• Tommy Nantung, IN DOT
• Richard Zamora, CO DOT
• Tom Yu, FHWA Liaison
• Stephen Maher, TRB Liaison
Iowa State University
• Halil Ceylan (Co-PI)
• Sung Hwan Kim
• K. Gopalakrishnan
NCHRP Staff
• Amir Hanna, Program Officer
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NCHRP 1-47 Final Report
http://onlinepubs.trb.org/onlinepubs/nchrp/docs/NCHRP01-47_FR.pdf
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Webinar Outline
• Study Objectives
• Sensitivity Analysis Concepts
• Design Inputs for Study
• Global Sensitivity Analysis (GSA) Methodology
• Results from GSA
• Key Findings and Conclusions
• Discussion
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5
Motivation
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“Research is needed to determine the degree of sensitivity of the performance predicted by the MEPDG to input parameter values… for specific climatic region and traffic conditions.... Users can [then] focus efforts on those input parameters that will greatly influence the pavement design.” − NCHRP 1-47 RFP
Traffic Volume Vehicle Mix
Vehicle Speed
HMA Thickness HMA Stiffness PCC Slab Geometry PCC Strength Base Thickness
Base Modulus Subgrade Modulus SWCC Parameters
Focus on Inputs under Control of Project Designer
Definable Refinable
6 6
QUESTION FOR AUDIENCE
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What is the Mechanistic-Empirical Pavement Design Guide (MEPDG)?
7
Empirical
TransferFunctions
INPUT
TRAFFIC
CLIMATE
PAVEMENT
Mechanistic
Analytic
International
Roughness Index
Asphalt Concr.
Rutting
Total Rutting
OUTPUTLongitudinal
Cracking
Alligator Cracking
Thermal Cracking
Mechanistic
Pavement
Analysis
Models
Empirical
Pavement
Analysis
Models
z
xy
z
y
x
z
xy
z
y
x
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MEPDG Software
8
Version 1.100 used for study
Not available at time of study Same models Same results
✔
✗
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Research Objective
Determine the sensitivity of the pavement performance predicted by the MEPDG to variability of the material property design input values for flexible pavements.
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MR
MR
ν
ν
SWCC
Groundwater Depth
SWCC (Soil Water Characteristic Curve)
P200, D60, PI
P200, D60, PI
volume, speed
SSA Va, Vbe, ν, PG, E*(α, δ),
thermal properties, etc.
Climate
h1
h2
Sensitivity is high Sensitivity is Low
(Flexible Pavement)
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Webinar Outline
• Study Objectives
• Sensitivity Analysis Concepts
• Design Inputs for Study
• Global Sensitivity Analysis (GSA) Methodology
• Results from GSA
• Key Findings and Conclusions
• Discussion
10
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Types of Sensitivity Analyses
Global Sensitivity Analyses
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Local Sensitivity Analyses
Ou
tpu
t y
Input x
Fre
qu
ency
(S
I)
Sensitivity Index SI
SI ,s
SI
• Each input varied one-at-a-time • Only evaluates sensitivity around
the reference value(s) • Ignores input correlations,
interactions • Employed in most past studies
• All inputs varied simultaneously • Evaluates sensitivity over the entire
problem domain • Can include input correlations • Can quanitify input interactions • Extremely computation intensive
Model: y = f (x)
(x
0, y
0)
SI =
f (x0+ Dx) - f (x
0- Dx)
2Dx
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Mo
del
Ou
tpu
t Y
Model Input X
Model Output
Regression
Mo
del O
utpu
t Y j
Model Input Xk
X1
X2
Sensitivity Metrics: The Past
r=1.0 ρ=1.0 Slope=0.1
r=1.0 ρ=1.0 Slope=1.0
Instantaneous Slope
Average Slope
Correlation Coefficients - Pearson r - Spearman ρ
Multivariate Linear Regression - Regression coefficients
(average slopes)
Sensitivity ΔY/ΔX ΔOutput/ΔInput !!
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Selected Sensitivity Metric: Design Limit Normalized Sensitivity Index (NSI)
baseline value of design input k
change in design input k about the baseline
change in predicted distress j corresponding to change of design input
the design limit of the distress j
Design Limit Normalized Sensitivity Index for Design Input k and Distress j
Sjk
DL =DY
j/ DL
j( )DX
k/ X
k( )
Example: Total Rutting Distress, Design Limit (DL) =0.75 in. Normalized Sensitivity of Total Rutting to Base MR = -0.50 What is change in Total Rutting if Base MR is increased by ΔX/X = 20%? Change in Total Rutting ΔY = (-0.50)(20%)(0.75 in) = -0.075 in.
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Webinar Outline
• Study Objectives
• Sensitivity Analysis Concepts
• Design Inputs for Study
• Global Sensitivity Analysis (GSA) Methodology
• Results from GSA
• Key Findings and Conclusions
• Discussion
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Base Cases
• 5 pavement types x 5 climates x 3 traffic levels
• Total number of base cases = 75
Note: HMA/JPCP on Stiff Foundation is intended to represent both new construction/reconstruction on stabilized foundations or rehabilitation on underlying HMA/PCC layers.
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Climate Categories
Climate
Category Location Weather Station Months
of Data
Binder Grade
Baseline Range
Hot-Wet Orlando FL ORLANDO
INTERNATIONAL ARPT
116 PG 70-10 PG 64-10
PG 76-10
Hot-Dry Phoenix AZ PHOENIX SKY HARBOR
INTL AP
116 PG 76-10 PG 70-10
PG 82-10
Cold-Wet Portland ME PORTLAND INTL
JETPORT ARPT
116 PG 52-28 PG 52-34
PG 52-22
Cold-Dry International
Falls MN
FALLS INTERNATIONAL
ARPT
112 PG 58-28 PG 58-34
PG 58-22
Temperate Los Angeles CA LOS ANGELES INTL
AIRPORT
108 PG 58-10 PG 52-10
PG 64-10
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Binder Grades
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Climate Baseline PG PGHigh- PGLow+ PGLowTC PGLowTC+
Cold-Dry PG 52-40 NA PG 58-34 PG 52-28 PG 52-22
Cold-Wet PG 52-28 NA PG 52-22 PG 52-16 PG 52-10
Hot-Dry PG 76-10 PG 70-10 NA NA NA
Hot-Wet PG 70-10 PG 64-10 NA NA NA
Temperate PG 58-10 PG 52-10 NA NA NA
PGLowTC, PGLowTC+ used for Thermal Cracking sensitivity analyses.
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Traffic Levels
Traffic
Category
Baseline Inputs
AADTT Range AADTT1
AADTT in
Design
Lane
Est. ESALs
(Flexible)5
Est. ESALs
(Rigid)6
Low 1,000 3752 2M 5M 500-5,000
Medium 7,500 2,0633 10M 25M 5,000-10,000
High 25,000 6,2504 30M 75M 20,000-30,000
1Based on MEPDG Interstate Highway TTC4 Level 3 default vehicle distribution. Potential correlations between operating speed and AADTT have been ignored.
250% directional split, 2 lanes per direction, 0.75 lane factor for design lane.
350% directional split, 3 lanes per direction, 0.55 lane factor for design lane.
450% directional split, 3 lanes per direction, 0.50 lane factor for design lane.
5Based on 15 year design life.
6Based on 25 year design life.
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Baseline Flexible Pavement Sections
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Traffic
Level
Input
Parameter
Low Traffic Medium Traffic High Traffic
Baseline Min Max Baseline Min Max Baseline Min Max
AADTT-Nominal 1000 500 5000 7500 5000 10000 25000 20000 30000
Design Lane 375 188 1875 2063 1375 2750 6250 5000 7500
HMA Thickness (in) 6.5 5 8 10 8 12 12.5 10 15
Base Thickness (in) 6 1 10 7 1 14 9 1 18
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Design Inputs For Evaluation
Initial Triage - Literature review - Engineering judgment
OAT Local Sensitivity Analyses
(Nearly) All MEPDG Design Inputs
> Sensitive MEPDG Design Inputs
Global Sensitivity Analyses
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Design Inputs Given Special Consideration
• Unbound Material Properties
– Gradation, plasticity inputs for soil water characteristic curve (SWCC) correlated to resilient modulus MR
• HMA Dynamic Modulus
– Synthetic Level 1 dynamic modulus |E*| data
• HMA Low Temperature Properties
– Creep compliance correlated with stiffness
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Soil Water Characteristic Curve (SWCC)
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Unbound Material Properties
A design input value for Mr is selected first and then gradation data giving compatible values of P200 and D60 are determined via correlations along with compatible values for PI and LL.
SWCC – function of: • Percent passing the No. 200 sieve (P200) • D60 gradation parameter
• Plasticity index (PI)
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Unbound Material Properties
P200 D60
%Pass =100
eb+g log
10Size( )
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HMA Dynamic Modulus
δ = lower shelf stiffness
δ+α = upper shelf stiffness
f = loading frequency (from traffic speed)
η = binder viscosity (from binder grade, temperature);
used to generate synthetic Level 1 G*, ϕ
Design Input = Synthetic Level 1 Dynamic Modulus Data
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Design Inputs (New HMA)
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Webinar Outline
• Study Objectives
• Sensitivity Analysis Concepts
• Design Inputs for Study
• Global Sensitivity Analysis (GSA) Methodology
• Results from GSA
• Key Findings and Conclusions
• Discussion
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Global Sensitivity Analyses Procedure
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Sample the Entire Problem Domain
• Latin Hypercube
MEPDG GSA Simulations
• Over 40,000 MEPDG runs (Each run takes up to 0.5 hr on a single computer)
Respond Surface Modeling (RSM)
• Continuous response surface model (RSM) for the randomly located GSA simulation results.
Sensitivity Index Statistics
• Based on 10,000 RSM evaluations/base case
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Sampling with Complete Coverage
x1
x1
x1
x2
x2
x2
Monte Carlo n=25
Monte Carlo n=100
Latin Hypercube n=25
??
✔
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AutoIt Windows Scripting • Automates “manual” entry of input values to MEPDG.
• Extracts results from MEPDG output spreadsheets.
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6000+ lines of codes.
…
Cloud Storage
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“Parallel Processing”
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UMD Pavement Materials Lab
ISU Jelling Lab
40,000+ MEPDG Runs
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Predicted Distresses Span Wide Range
New HMA Cold-Wet Climate 1300 Simulations
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Respond Surface Modeling for Derivatives
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• Continuous response surface model (RSM) fit to the randomly located GSA simulation results
• Enables computation of sensitivity index derivatives
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10
y
x
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Respond Surface Modeling Artificial Neural Networks
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Input Layer
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Hidden Layer
5
Output Layer
1
Outputs
1
p1
p2
p23
…
p3
Σ
Σ
Σ
Σ
Σ
f 1
f 1
f 1
f 1
f 1
Σ f 2
iw1,1
0,1
iw23,5
0,1
b1
1
b2
1
b3
1
b4
1
b5
1
n1
1
n2
1
n3
1
n4
1
n5
1
a1
1
a2
1
a3
1
a4
1
a5
1
iw1,1
1,2
iw5,1
1,2
b1
2
n1
2
a1
2
Climate Type, Traffic Speed,
Pavement structure, etc…
Rutting Depth
36 Excellent Performance of ANN RSMs 36
MEPDG Predicted
RSM
Pre
dic
ted
Long Cracking Alligator Cracking AC Rutting Total Rutting IRI
CD
CW
T
HW
HD
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Spreadsheet for Quick MEPDG Calculation
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Webinar Outline
• Study Objectives
• Sensitivity Analysis Concepts
• Design Inputs for Study
• Global Sensitivity Analysis (GSA) Methodology
• Results from GSA
• Key Findings and Conclusions
• Discussion
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QUESTION FOR AUDIENCE
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GSA Sensitivity Index Distributions
New HMA – AC Rut Depth All Climate Zones, Traffic Levels 10,000 Simulations w/ Censoring
Sensitivity Metric for Ranking: NSIμ+2σ=Mean SI + 2 Standard Deviations
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Design Input Maximum NSIm +2s Values (ANN RSMs)
Long.
Crack
Alligator
Crack
Thermal
Crack
AC Rut
Depth
Total Rut
Depth IRI Max
HMA E* Alpha Parameter
-29.52 -15.94 -0.58 -24.40 -8.98 -3.58 -29.52
HMA E* Delta Parameter
-23.87 -13.18 2.41 -24.43 -8.99 -2.80 -24.43
HMA Thickness -10.31 -7.46 -0.86 -4.21 -1.58 -1.11 -10.31
HMA Creep Compliance m Exponent N.A. N.A. -4.85 N.A. N.A. N.A. -4.85
Base Resilient Modulus -4.72 -2.73 -0.17 0.14 -0.15 -0.36 -4.72
Surface Shortwave Absorptivity 4.32 1.28 -0.20 4.65 1.67 0.67 4.65
HMA Air Voids 4.47 3.39 1.33 -0.05 0.03 0.29 4.47
HMA Poisson’s Ratio -2.38 -1.01 0.23 -4.33 -1.46 -0.43 -4.33
Traffic Volume (AADTT) 3.72 3.94 0.02 1.87 0.66 0.51 3.94
HMA Effective Binder Volume -3.88 -2.93 -0.17 0.05 0.06 -0.24 -3.88
Subgrade Resilient Modulus -2.07 -3.41 0.15 0.08 -0.28 -0.44 -3.41
Base Thickness -2.40 -1.02 -0.03 0.22 0.04 -0.09 -2.40
Subgrade Percent Passing No. 200 -1.71 -0.68 0.08 -0.10 -0.10 -0.12 -1.71
HMA Tensile Strength at 14oF N.A. N.A. -1.59 N.A. N.A. N.A. -1.59
Operational Speed -1.26 -0.83 -0.04 -1.06 -0.39 -0.15 -1.26
HMA Creep Compliance D Parameter N.A. N.A. -1.03 N.A. N.A. N.A. -1.03
HMA Unit Weight -0.88 0.97 -0.76 -0.88 -0.30 -0.08 0.97
Base Poisson’s Ratio 0.91 0.90 0.18 -0.19 -0.05 0.09 0.91
HMA Heat Capacity -0.76 -0.55 -0.77 -0.81 -0.28 -0.14 -0.81
Subgrade Liquid Limit -0.67 -0.79 -0.10 -0.10 0.07 0.03 -0.79 Binder Low Temperature PG 0.56 0.09 -0.74 0.25 0.09 0.02 -0.74
HMA Thermal Conductivity -0.53 -0.40 -0.67 0.20 0.04 0.02 -0.67
Binder High Temperature PG -0.60 -0.48 0.00 -0.66 -0.25 -0.09 -0.66 Subgrade Poisson’s Ratio 0.44 -0.59 0.16 0.08 0.07 0.04 -0.59
Groundwater Depth 0.20 -0.16 0.08 0.01 -0.02 -0.02 0.20
Subgrade Plasticity Index -0.15 0.11 0.03 0.01 0.02 0.00 -0.15
Aggregate Coef. Of Thermal Contraction N.A. N.A. -0.07 N.A. N.A. N.A. -0.07
Hypersensitive Very Sensitive Sensitive Non-Sensitive
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Design Input Maximum NSIm +2s Values (ANN RSMs)
Long.
Crack
Alligator
Crack
Thermal
Crack
AC Rut
Depth
Total Rut
Depth IRI Max
HMA E* Alpha Parameter
-29.52 -15.94 -0.58 -24.40 -8.98 -3.58 -29.52
HMA E* Delta Parameter
-23.87 -13.18 2.41 -24.43 -8.99 -2.80 -24.43
HMA Thickness -10.31 -7.46 -0.86 -4.21 -1.58 -1.11 -10.31
HMA Creep Compliance m Exponent N.A. N.A. -4.85 N.A. N.A. N.A. -4.85
Base Resilient Modulus -4.72 -2.73 -0.17 0.14 -0.15 -0.36 -4.72
Surface Shortwave Absorptivity 4.32 1.28 -0.20 4.65 1.67 0.67 4.65
HMA Air Voids 4.47 3.39 1.33 -0.05 0.03 0.29 4.47
HMA Poisson’s Ratio -2.38 -1.01 0.23 -4.33 -1.46 -0.43 -4.33
Traffic Volume (AADTT) 3.72 3.94 0.02 1.87 0.66 0.51 3.94
HMA Effective Binder Volume -3.88 -2.93 -0.17 0.05 0.06 -0.24 -3.88
Subgrade Resilient Modulus -2.07 -3.41 0.15 0.08 -0.28 -0.44 -3.41
Base Thickness -2.40 -1.02 -0.03 0.22 0.04 -0.09 -2.40
Subgrade Percent Passing No. 200 -1.71 -0.68 0.08 -0.10 -0.10 -0.12 -1.71
HMA Tensile Strength at 14oF N.A. N.A. -1.59 N.A. N.A. N.A. -1.59
Operational Speed -1.26 -0.83 -0.04 -1.06 -0.39 -0.15 -1.26
HMA Creep Compliance D Parameter N.A. N.A. -1.03 N.A. N.A. N.A. -1.03
HMA Unit Weight -0.88 0.97 -0.76 -0.88 -0.30 -0.08 0.97
Base Poisson’s Ratio 0.91 0.90 0.18 -0.19 -0.05 0.09 0.91
HMA Heat Capacity -0.76 -0.55 -0.77 -0.81 -0.28 -0.14 -0.81
Subgrade Liquid Limit -0.67 -0.79 -0.10 -0.10 0.07 0.03 -0.79 Binder Low Temperature PG 0.56 0.09 -0.74 0.25 0.09 0.02 -0.74
HMA Thermal Conductivity -0.53 -0.40 -0.67 0.20 0.04 0.02 -0.67
Binder High Temperature PG -0.60 -0.48 0.00 -0.66 -0.25 -0.09 -0.66 Subgrade Poisson’s Ratio 0.44 -0.59 0.16 0.08 0.07 0.04 -0.59
Groundwater Depth 0.20 -0.16 0.08 0.01 -0.02 -0.02 0.20
Subgrade Plasticity Index -0.15 0.11 0.03 0.01 0.02 0.00 -0.15
Aggregate Coef. Of Thermal Contraction N.A. N.A. -0.07 N.A. N.A. N.A. -0.07
Hypersensitive Very Sensitive Sensitive Non-Sensitive
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GSA Results: New HMA Max |NSI| Values for Longitudinal Cracking
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GSA Results: New HMA Max |NSI| Values for Alligator Cracking
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GSA Results: New HMA Max |NSI| Values for AC Rutting
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GSA Results: New HMA Max |NSI| Values for Total Rutting
47
GSA Results: New HMA Max |NSI| Values for IRI
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Most Sensitive Inputs by Property Category: New HMA
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Webinar Outline
• Study Objectives
• Sensitivity Analysis Concepts
• Design Inputs for Study
• Global Sensitivity Analysis (GSA) Methodology
• Results from GSA
• Key Findings and Conclusions
• Discussion
49
50
Key Findings: Methodology
• “Mean + 2 standard deviations” NSI is the best and most robust ranking metric – Relates change in design input to corresponding change in
predicted distress relative to its design limit
– Captures both the average sensitivity and its variability
– Categories: • Hypersensitive (HS): NSIμ+2σ > 5
• Very Sensitive (VS): 1 < NSIμ+2σ < 5
• Sensitive (S): 0.1 < NSIμ+2σ < 1
• Nonsensitive (NS): NSIμ+2σ < 0.1
• Artificial Neural Network response surface models provide robust and accurate relationships between design inputs and outputs
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Key Findings: General
• Most NSI frequency distributions showed well-defined single peaks
– Indicates that NSI did not vary significantly over problem domain
• For all pavements, design inputs for the bound layers (i.e., HMA) exhibited the highest sensitivities
• Sensitivity values did not vary substantially or systematically across climate zones
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Key Findings for Designers: Flexible
• Only HMA properties were most consistently in the highest sensitivity categories:
– HMA dynamic modulus lower (δ), upper (δ+α) shelves
– HMA thickness
– Surface shortwave absorptivity
– Poisson’s ratio
• Sensitivity values were consistently higher for longitudinal cracking, alligator cracking, and AC rutting than for IRI and thermal cracking
• Little or no thermal cracking was predicted when correct binder grade used
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GSA of MEPDG using Level 3 dynamic modulus data.
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Level 1 Input Level 3 Input
Asp
hal
t M
ix
Dynamic Modulus at different
combination of Temperature and
Frequency
Cumulative % Retained 3/4 inch sieve: Cumulative % Retained 3/8 inch sieve: Cumulative % Retained #4 sieve: % Passing #200 sieve:
Asp
hal
t
Bin
der
Shear Modulus and Phase Angle at 10
rad/sec at different temperatures Superpave binder grading
Asp
hal
t G
ener
al Effective binder content (%)
Air voids (%) Total unit weight(pcf) Poisson's Ratio Thermal conductivity asphalt (BTU/hr-
ft-F) Heat capacity asphalt (BTU/lb-F)
Effective binder content (%) Air voids (%) Total unit weight(pcf) Poisson's Ratio Thermal conductivity asphalt (BTU/hr-
ft-F) Heat capacity asphalt (BTU/lb-F)
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Level 1 vs. Level 3 HMA |E*|
-35
-30
-25
-20
-15
-10
-5
0
5
10N
SI V
alu
es
(Me
an +
2 S
tDe
v)
Level 1
Level 3
55
Additional Key Findings: HMA Over Stiff
• Thermal conductivity and heat capacity of stabilized base are additional sensitive inputs
– Not inputs for non-stabilized base in flexible pavements
• Increased sensitivity of longitudinal cracking to operating speed
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Issues for Further Study
• Base, subgrade design inputs had significant sensitivities in only a small number of cases—realistic?
• Realism of unexpectedly high sensitivities for some inputs:
– |E*| lower (δ), upper (δ+α) shelves
– Poisson’s ratio for HMA
– Poisson’s ratio for base, subgrade
– HMA unit weight (especially for longitudinal cracking)
• Replace/eliminate low sensitivity inputs with internal default values?
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Sensitivity Analysis in Terms of Service Life
57
y = 0.1297x0.3347 R² = 0.9878
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 24 48 72 96 120 144 168 192 216 240 264
Ru
ttin
g D
ep
th (
in)
Pavement Age (month)
Permanent Deformation: Rutting
SubTotalAC
SubTotalBase
SubTotalSG
Total Rutting
TotalRutReliability
Total Rutting Design Limit Power (Total Rutting)
AC Rutting Design Value = 0.25
Total Rutting Design Limit = 0.75
Pavement Service Life
Distress at end of analysis period
58
Overall Conclusions
• Rigorous sensitivity analysis methodology is essential
• Very few surprises in results – This is a good thing!
• There were some surprises in results – Identify MEDPG areas that may merit further investigation
• Results provide practical guidance for pavement designer – Importance of Level 1 characterization for HMA
• Results suggest areas where MEPDG/DARWin-ME could be simplified – Eliminate some inputs/replace with internal defaults
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Webinar Outline
• Study Objectives
• Sensitivity Analysis Concepts
• Design Inputs for Study
• Global Sensitivity Analysis (GSA) Methodology
• Results from GSA
• Key Findings and Conclusions
• Discussion
59
Contact Info:
Dr. Charles W. Schwartz University of Maryland [email protected] +1.301.405.1962