Conclusions

Report
Diversos Aspectos de la
Implementacion de la Guia
de Diseño MecanisticoEmpirico (MEPDG) en Texas
Dr. Jorge A. Prozzi
The University of Texas at Austin
Valparaiso, Chile, 10 November 2010
Presentation Outline
• Local Calibration of the Permanent Deformation
Performance Models
• Seasonal Time-Series Models for Supporting
Traffic Input Data
• Effect of WIM Measurement Errors on LoadPavement Impact Estimation
• Variability in Pavement Design and Its Effects
• Improving the Roughness (IRI) Predictions by
Correcting for Possible Bias
Local Calibration of the Permanent
Deformation Performance Models
for Rehabilitated Flexible
Pavements
Ambarish Banerjee
Jose Pablo Aguiar-Moya
Dr. Andre de Fortier Smit
Dr. Jorge A. Prozzi
Outline
•
•
•
•
•
•
•
•
Background
The MEPDG
LTPP
SPS-5
Analysis Inputs
Objectives and Approach
Results
Specific Conclusions
Historical Background
• Standard for Pavement Design in most regions of the
USA is the AASHTO 1993 Design Guide, which is an
empirical method
• Primarily based on results from the AASHO Road
Tests conducted in late 1950s, early 1960s
– Materials used for surface, base and subbase
layers were uniform throughout the test
– Test conducted in one location (soil, environment)
– Low levels of traffic (about 8 million ESALs max.)
Historical Background
Historical Background
• Deficiencies in the AASHTO Design Procedure
– Results from the AASHTO method cannot account
for different geographical locations
– AASHTO method somewhat antiquated based on
today's construction practices and materials
– Loads seen by pavements today are much greater
resulting in large extrapolations
– Mechanical-Empirical methods have gained
increasing popularity
The MEPDG
• Mechanistic-Empirical Pavement Design Guide
(MEPDG) is an analysis tool
– Sponsored by the AASHTO Joint task Force on
Pavements
– Assumes pavement is a layered structure with
each layer exhibiting elastic properties
– Like AASHTO method uses “national averages”
that need to be calibrated
Input Levels
• Three input levels:
– Level 1: Highest level of accuracy used for
site specific design
– Level 2: Intermediate level and can be
used for regional design
– Level 3: Least accurate and can be used
on a state level
LTPP Database
• Long Term Pavement Performance Database
– Established in 1987 as part of SHRP
– Monitors both in-use, new and rehabilitated
pavement
– Created a national database to share and
compare data
– General Pavement Studies (GPS)
– Specific Pavement Studies (SPS)
LTPP Database
• GPS
– Studies on pre-existing pavements, one section at
each location
– In-service and have a common design located
throughout the USA and Canada
• SPS
– To study the effects of specifically targeted factors
– SPS-5: Rehabilitation of Asphalt Concrete
Pavements
SPS-5 Experimental Design
• Eight or nine sections at each location
(depending on availability of control section)
• Factors Studied:
– Overlay Thickness: Thin vs. Thick (> 5
inches)
– Surface Preparation: Milling vs. No Milling
– Type of Asphalt Mixture: Virgin vs. RAP
Analysis Inputs - General
Location
Monitoring Start
Overlay
Const.
Opened to
Traffic
AADTT
Growth Rate
(%), Linear
Analysis
Period (yrs)
New Jersey
Nov ’91
Jul ’92
Aug ’92
840
5.9
14
Colorado
Jan ’87
Sep ’91
Oct ’91
799
2.4
9
Missouri
Jan ’98
Aug ’98
Sep ’98
569
3.1
8
Montana
Jan ’87
Sep ’91
Oct ’91
702
4.5
10
Texas
Jan ’87
Sep ’91
Oct ’91
301
16.1
14
Oklahoma
Jan ’87
Jul ’97
Aug ’97
292
4.0
10
LTPP SPS-5 sections
Analysis Inputs - Traffic
• Data available from counts, automatic vehicle
classification (AVC) systems and WIM stations
• Estimation of initial traffic and growth rate
Analysis Inputs – Vehicle Class
• Vehicle class distribution at each of the six SPS locations
Analysis Inputs – Axle Spectra
• Default values for each axle type, vehicle
class and month are already provided
• Site specific axle spectra for each month and
vehicle type was generated after averaging
over the number of years in the monitoring
period
Seasonal Variation in Axle Spectra
Axle Spectra for NJ SPS-5
location for January
Axle Spectra for NJ SPS-5
location for February
Analysis Inputs – Material
New Jersey section 0-502, No milling
Layer
Type
1
2
Asphalt
3
4
Binder
Content
(%)
Air
Voids
(%)
Material
HMA
1.9”
AC 40
8.1
7.3
Existing
HMA
2.7”
AC 30
10.0
3.6
6.2”
AC 10
7.7
2.7
5
Granular
Base
A-1-b
6
Subgrade
A-2-4
5.2”
20.5”
semi-inf
Modulus
(psi)
Binder
Grade
Thicknes
s
26500
21500
Gradation for both asphalt and unbound layers were also available
Atterberg’s limits, MDD and OMC was available for unbound layers
Objective
• Determination of Level 2 bias correction
factors for rehabilitated pavements for
the permanent deformation
performance models.
Approach
• Performance data available from the
SPS-5 sections will be compared to
predicted pavement performance from
the MEPDG
• Bias correction factors are adjusted to
reduce difference between the observed
and predicted values
AC Rutting Transfer Function
p
k 
k 
 k z  r 10k T
N
r
1
2 r2
3 r3
1
k z  (C1  C2 * depth) * 0.328196depth
C1  0.1039* H ac2  2.4868* H ac  17.342
C2  0.0172* H ac2  1.7331* H ac  27.428
Hac = Total AC thickness (inches)
εp = Plastic Strain (in/in)
εr = Resilient Strain (in/in)
T = Layer Temperature
N = Number of Load Repetitions
kz, k2, k3 = Laboratory Constants
βr1, βr2, βr3 = Calibration Coefficients
Methodology
• βr1 is a shift factor
– Governs the initial rut depth
• βr3 accounts for the bias due to the number of load
repetitions
– Slope of the transfer function
• βr2 is the bias correction factor for temperature
susceptibility of hot mix asphalt
– Not calibrated due to unavailability of data
Level 2 Bias Correction Factors
County
State
Lincoln
Colorado
Sweet
Grass
Montana
Monmouth
New
Jersey
Taney
Missouri
Kaufman
Texas
Comanche
Oklahoma
Climate
Dry
Freeze
Wet
Freeze
Wet No
Freeze
βr1
βr3
βs1
Standard
Error (in)
%
Reduction
238
0.142
0.3
0.055
62
320
0.138
0.3
0.105
61
112
0.122
0.7
0.055
25
129
0.140
0.7
0.083
41
80.0
0.444
0.5
0.075
59
107
0.252
0.4
0.081
50
Comparison of Results
Calibrated V/s Uncalibrated Predictions
(Section: 48-A502, Texas)
Comparison of Results
Calibrated V/s Uncalibrated Predictions
(Section: 30-0509, Montana)
Conclusions
• Level 2 bias correction factors for
rehabilitated pavements were proposed
• Significant differences with new pavements
• More test sections are needed to improve the
confidence in the bias correction factors
• Validation of bias correction factors is
currently being done
Alguna Pregunta?
Seasonal Time Series Models
for Supporting Traffic Input
Data for the MechanisticEmpirical Design Guide
Feng Hong
Jorge A. Prozzi
Outline
•
•
•
•
•
•
•
Introduction
Objective of this Study
Time Series Models
Data Source
Case Study
Implication
Conclusions
Introduction
 Pavement design approach: E or M-E
 Traffic components for pavement design and analysis
 Traffic load
 ESAL
 Load spectra
 Traffic volume
 Predicted traffic growth (long-term)
 Seasonal variation (short-term)
 Others
Traffic Input in M-E Guide
Objectives of This Study
 Facilitate traffic volume input required by MEPDG
 Develop mathematical model to incorporate both
truck volume components
 Long-term growth trend
 Short-term variation
 Investigate class-based truck volume statistical
characteristics
Seasonal Time Series Model
 Additive decomposition model
zt  Tt  St   t
 Trend component
Tt  T0  (1  r  t )
Tt  T0  (1  r )t
 Seasonal component
2i
2i
St   ( i sin
t   i cos
t)
s
s
i 1
n
Seasonal Time Series Model
 Linear growth plus seasonality
n
zt   0  1t   ( i sin
i 1
2i
2i
t   i cos
t)  t
12
12
 Compound growth plus seasonality
n
zt   0 (1  1 )   ( i sin
t
i 1
2i
2i
t   i cos
t)  t
12
12
Model Estimation Approach
 Linear growth + seasonality model
 Ordinary Least Square (OLS)
 Compound growth + seasonality model
 Nonlinear Least Square (NLLS)
Available Data Source
 Nation level: Long-Term Pavement
Performance: so far 20 years of records
 State level traffic monitoring program
 California: over 100 WIMs
 Texas: counts, AVCs, 20 WIMs
 Other resources
 PMS, freight database, e.g., TLOG
Case Study
 Data Used
 Location: Interstate Highway 37,
Corpus Christi, Texas
 Equipment: Weigh-in-Motion
 Duration: Jan. 1998 – May. 2002
Model Estimation Results
Parameter Estimates of Seasonal Time Series Models with Two Harmonics
Model
Type
Linear
Compound
Class 4
Class 5
Class 9
Others
Entire Trucks
Parameters estimate p-value estimate p-value estimate p-value estimate p-value estimate p-value
0
67.9
0.000
434.2
0.000
1906.4
0.000
347.6
0.000
2756.2
0.000
1
1
1
2
2
0
1
1
1
2
2
0.7
0.000
12.9
0.000
2.4
0.081
1.9
0.000
18.0
0.000
2.7
0.223
78.7
0.016
79.8
0.004
25.8
0.000
187.0
0.000
-9.0
0.000
-176.9
0.000
37.4
0.177
1.0
0.826
-147.5
0.000
-5.5
0.024
44.4
0.184
-49.6
0.075
10.5
0.031
-0.2
0.995
1.8
0.421
-53.2
0.097
10.2
0.694
-15.7
0.001
-56.9
0.067
70.1
7.9E-03
2.5
-9.0
-5.6
1.9
0.000
0.000
0.218
0.000
0.010
0.356
489.9
1.7E-02
72.5
-180.3
45.3
-50.6
0.000
0.000
0.009
0.000
0.122
0.070
1908.9
1.2E-03
79.6
37.4
-49.9
10.3
0.000
0.059
0.001
0.137
0.047
0.665
351.5
4.8E-03
25.5
1.0
10.3
-15.5
0.000
0.000
0.000
0.827
0.019
0.000
2791.2
5.5E-03
183.7
-148.7
-1.1
-55.2
0.000
0.000
0.000
0.000
0.971
0.049
Observed Vs. Predicted Traffic (2)
4500
4000
Volume
3500
3000
2500
2000
0
10
20
30
40
50
Time (month)
Linear growth + Time series
Compound growth + Time series
Linear trend
Compound trend
60
Observed Vs. Predicted Traffic (1)
4500
4000
Volume
3500
3000
2500
2000
0
10
20
30
40
50
Time (month)
Linear growth + Time series
Compound growth + Time series
Linear trend
Compound trend
60
Further Implication
 Integrating long- and short- term traffic information
Correlation Metrics of Parameters in the Models for Entire Trucks
Model
Type
Linear
growth
(plus time
series)
Compound
growth
(plus time
series
Parameters
0
1
1
1
0
1
1
1
0
1
1
1
1.00
-0.91
-0.17
0.06
-0.91
1.00
0.09
-0.03
-0.17
0.09
1.00
-0.10
0.06
-0.03
-0.10
1.00
1.00
-0.92
-0.16
0.07
-0.92
1.00
0.09
-0.05
-0.16
0.09
1.00
-0.10
0.07
-0.05
-0.10
1.00
Conclusions
 Linear or compound plus time series model is
capable of capturing traffic growth trend and
seasonal variation accurately
 Traffic seasonal variation is statistically
significant, hence, it should be accounted for
 Two harmonics are sufficient for representing
seasonality
 One harmonic may be used for simplicity
Conclusions
 Both traffic growth and seasonality differ
among varying truck classes
 Short- and long-term traffic information can
be effectively and efficiently integrated to
accommodate volume input required by
MEPDG
Alguna Pregunta?
Effect of Weigh-In-Motion
System Measurement Error on
Load-Pavement Impact
Estimation
Feng Hong
Jorge A Prozzi
Outline
• Background
– Traffic data collection
– WIM measurement error
• Dataset
– Data source
– Statistical characteristics
• Methodology
– Load-pavement impact
– Incorporating measurement error
• Conclusions
Introduction
• Pavement design inputs
– Soil and material properties
– Environmental conditions
– Traffic load
• Empirical approach: ESALs
• Mechanistic-empirical approach: axle
load spectra
Traffic load data collection
• Static scale
– Limited sample size
– Accurate
• Weigh-in-Motion (WIM) scale
– Continuous data collection
– Accuracy?
WIM classification
• Based on sensor technology
– Load cell
– Bending plate
– Piezo-electronic
Accuracy
Cost
WIM measurement error
• Percentage difference
• WIMWeight: weight measured by WIM scale
• StaticWeight: weight measured by static scale
(assumed to be real weight)
Measurement error types
• Random error
– An indicator of WIM system accuracy
– Intrinsic: equipment design (sensors)
– Means of improvement: via manufacturer
• Systematic error
– persistent measurement shift
– External: roadway, vehicle & environmental fcts.
– Means of improvement: calibration
Random error
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-40
-30
-20
-10
0
10
20
30
WIM errors (%)
Sigma=1.5%
Sigma=5%
Sigma=10%
40
Systematic error
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
-40
-30
-20
-10
0
10
20
WIM errors(%)
-10% biased
ideal calibration
+10% biased
30
40
Data Source
• Texas 21 WIM stations
Axle types
Single
Tandem
Tridem
Axle Load Spectra
Single axle
Tandem axle
Statistical Characteristics
Load-pavement impact
 xr 
LEFr   
 LS 
m
Load equivalency factor
4
x 
LSF    r  qr
r 1 Ls 
Load spectra factor (discrete)
R
LSF 
4
 x f ( x)dx
Ls
4
E X 4  M 4


4
C
Ls
   x
M E X
4

4
LSF   Wk exp 4k  8 k
k
2
Load spectra factor (continuous)
 1  ln(x)    2 
 dx  exp 4  8
exp  


2 x
 
 2
1
4
L
s
4

2

Load-pavement impact under random error:
derivation
 x '


m
LSFX4' X  x
4
X ' X x
LSF
g X ' X x' x dx'
Ls
4
E X ' X  x 
m

Ls
4
(3 4  6 2  1) x 4

4
Ls

LSF E   x'4 g X ' X x' x  f X ( x)dxdx' Ls  3 4  6 2  1 Wk exp 4k  8 k
4
k
2

Ls
4
Load-pavement impact under random error:
result
Load-pavement impact under both errors:
derivation
LSF E (b )   x' '4 g X '' X ( x' ' x) f X ( x)dxdx' ' Ls



4
 3 4  6 2 1     1     Wk exp 4k  8 k
2
4
k
2

Ls
4
Load-pavement impact under both errors:
result
Sensitivity analysis
100.00%
80.00%
60.00%
Estimation Error
40.00%
20.00%
-20.00%
-15.00%
-10.00%
0.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
-20.00%
-40.00%
-60.00%
WIM Calibration Bias (alpha)
sigma = 0%
sigma = 5%
sigma = 10%
sigma = 15%
sigma = 20%
20.00%
Comparison with FHWA-RD-98-104 results
Summary
• Investigate axle load spectra statistical
characteristics
• Establish WIM error’s effect on loadpavement impact estimation
– Both errors affect result
– The result is more sensitive to systematic error
• Application
– Pavement life estimation
– WIM equipment selection
Alguna Pregunta?
Variability in Pavement Design
and Its Effects on the
Performance Predictions of the
MEPDG
José P. Aguiar-Moya
Dr. Jorge A. Prozzi
Dr. Lance Manuel
Presentation Outline
• Introduction
• Variability in Pavement Design
• Variability Analysis
–
–
–
–
Pavement Layer Thickness
Asphalt Binder Content
Air Void Content
Modulus of Unbound Material Layers
– Modulus of HMA Layers
• Effect of Variability on MEPDG Predictions
• Conclusions
Introduction
• Many sources of variability have an impact on
pavement field performance:
–
–
–
–
–
Material properties
Environmental conditions
Traffic loading
Structural layout
Construction practices
Effect on Reliability (fiabilidad, confiabilidad)
Prior knowledge on the variability of the factors
affecting the performance is required!
Variability in Pavement Design
• Treating all the variables in a complex analysis
procedure, such as MEPDG, is unfeasible.
• A reduced set of variables has been used in the analysis:
–
–
–
–
–
–
–
–
–
–
Climatic region
Truck Traffic Classification (TTC)
Average Annual Daily Truck Traffic (AADTT)
Thickness of the HMA layer
Asphalt binder content
Air void content
Thickness of the base
Resilient modulus of the HMA layer
Modulus of the base
Modulus of the subgrade
Goodness-of-Fit Tests to evaluate Data
Distribution
• Skewness-Kurtosis Test
– Pools the skewness and kurtosis of the distribution
into a χ2 statistic, and compares it to that of a normal
distribution where the values are 0 and 3 respectively.
• Shapiro-Francia Test
– Function only of the expected order statistics.
– Allows for evaluating normality based on small
samples (n≥4)
Variability in Pavement Layer Thickness
• Darter et al. (1973) quantified this variability in Standard
Deviation (SD) as
–
–
–
–
–
HMA layers (0.41 in)
Cement-treated bases (0.68 in)
Aggregate bases (0.79 in)
Aggregate subbases (1.25 in).
The average Coefficient of Variation (CoV) was 10%.
• Selezneva et al. (2002) and Jiang (2003) studied layer
thickness using pavement elevation data from LTPP.
– 86% of the analyzed layers follow a normal distribution
– Mean CoV for asphalt layers around 10%.
Variability in Pavement Layer Thickness
• Unfortunately LTPP contains few core / elevation data
observation for each pavement section.
 Use GPR Data
• LTPP contains GPR data for selected SPS sections.
• For each section: 600 layer thickness measurements
along lane centerline and right wheelpath.
 Nearly continuous thickness observations for each
section
Variability in Pavement Layer Thickness
1
Normal Distribution
0.9
Actual Data
Critical Tail
Cummulative Density Function
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
Thickness (in)
3.3
3.5
3.7
3.9
4.1
4.3
4.5
Variability in Pavement Layer Thickness
• Skewness-Kurtosis goodness-of-fit tests were performed
to assess normality of the data:
– 99% confidence level was selected
– It was found that 88.5% of the HMA surface layers and
80.0% of the granular base layers follow a normal
distribution
Layer
HMA Surface Layer
HMA Binder Course Layer
Granular Base Layer
Average CV
0.072
0.138
0.103
Range
0.032 – 0.184
0.117 – 0.160
0.060 – 0.172
Variability in Asphalt Binder Content
• Increases in binder content are associated with
increased resistance to cracking, but reduced resistance
to permanent deformation in the asphalt layers.
• Prozzi et al. (2005) assumed that the asphalt binder
content follows a normal distribution.
• Hall and Williams (2002) showed that:
–
–
–
–
Asphalt binder content
Air void content
VMA
Field density
Follow normal
distributions
Variability in Asphalt Binder Content
• Detailed asphalt binder content information was
collected for the LTPP SPS-9 sections.
• SPS-9 was designed to evaluate the
performance of Superpave asphalt mixtures.
81 SPS-9 sections were queried from the LTPP
– For each of the SPS-9 the number of asphalt binder
observations ranged from 24 to 50
Variability in Asphalt Binder Content
1
0.9
Cummulative Density Function
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Normal Distribution
Actual Data
0.1
Critical Tail
0
3.5
3.7
3.9
4.1
4.3
4.5
4.7
Asphalt Binder Content (%)
4.9
5.1
5.3
5.5
Variability in Asphalt Binder Content
• Skewness-Kurtosis goodness-of-fit tests were
performed to assess normality of the data:
– 99% confidence level was selected
• 85.2% of the HMA layers have asphalt content
distributions that follow a normal distribution.
• The CoV for the analyzed asphalt layers was
found to be 0.063 on average (0.009 - 0.392).
Variability in Air Void Content
• The asphalt binder content is closely related to the
compaction effort applied during construction, and
therefore is also related to the density of the asphalt mix.
• LTPP contains air void content information for all the
flexible SPS sections and for many of the GPS sections.
 194 LTPP sections were queried from the LTPP
– For each of the LTPP section the number of asphalt binder
observations ranged from 6 to 17
Variability in Air Void Content
1
0.9
Cummulative Density Function
0.8
0.7
0.6
0.5
0.4
Normal Distribution
0.3
Actual Data
0.2
Critical Lower Tail
0.1
Critical Upper Tail
0
5.5
6.0
6.5
7.0
7.5
Air Void Content (%)
8.0
8.5
9.0
Variability in Air Void Content
• Shapiro-Francia goodness-of-fit tests were performed to
assess normality at 99% confidence level
– 98.8% of the HMA layers have air void content
distributions that follow a normal distribution.
• The CoV for the analyzed asphalt layers was found to be
0.051 on average (0.009 - 0.390).
• Negative correlation between the asphalt binder content
and the air void content of -0.175 was found.
Variability in Modulus of Unbound Layers
• The modulus of the supporting layers is required in
determining the response of a pavement structure.
• LTPP contains modulus of unbound material layers for
all flexible SPS sections and for many of the GPS
sections.
 Information from 1087 untreated subgrade layers and 16
untreated base was identified
Variability in Modulus of Unbound Layers
1
0.9
Normal Distribution
Actual Data
Cummulative Density Function
0.8
Critical Tail
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
12,500
12,750
13,000
13,250
13,500
Resilient Modulus (psi - 2 psi Confining Pressure)
13,750
14,000
Variability in Modulus of Unbound Layers
• Shapiro-Francia goodness-of-fit tests were performed to
assess normality at 99% confidence level
– 99.5% of the untreated subgrade layers and for 100.0% of
the untreated base layers follow a normal distribution.
• The CoV for the base layers was on average 0.101
(0.009 - 0.390), and for the subgrade layers 0.093
(0.008 – 0.896).
• There is positive correlation between the modulus of the
base and the subgrade in the order of 0.319.
Variability in Modulus of HMA Layers
• It was initially assumed that the resilient modulus of the
HMA layers follows a normal distribution.
The validity of the previous assumption is now evaluated.
• LTPP contains HMA modulus for all flexible SPS
sections and for many of the GPS sections.
 Information from 1137 HMA layers was identified
Variability in Modulus of HMA Layers
1
0.9
Cummulative Density Function
0.8
Uniform Distribution
Normal Distribution
Actual Data
Critical Tail
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
722 725 728 731 734 737 740 743 746 749 752 755 758 761 764 767 770 773
Resilient Modulus (ksi - 80.6o F)
Variability in Modulus of HMA Layers
 The data follows a uniform distribution.
• The CoV for the for the analyzed HMA
layers were found to be on average 0.028
(0.001 – 1.645).
Effect of Variability on MEPDG Predictions
• Three of the original SHRP climatic were selected:
– Cold climatic region (Salem, OR),
– Warm climate region (Destin, FL), and
– Hot climatic region (Imperial, CA)
• A three-layer structure was analyzed
• Two types of truck traffic distribution (TTC2, TTC12)
• Material / Structural properties:
Parameter
HMA Thickness (in)
Asphalt Binder Content (%)
Air Voids (%)
Base Thickness (in)
HMA Modulus at 80.6°F (ksi)
Base Modulus (psi)
Subgrade Modulus (psi)
Mean
4.5 / 10.0
5.0
7.0
14.0
760
22,000
10,000
Std. Dev.
0.33 / 0.72
0.32
0.36
1.44
20
2222
930
Distribution
Normal
Normal
Normal
Normal
Uniform
Normal
Normal
MEPDG Performance Predictions
• Simulation with the MEPDG was performed considering
the previously defined design variables as random.
• Because the MEPDG has no closed-form solution
Response surface approach.
Fit a surface to the MEPDG predictions that can be
later used to predict the performance
• 1,000,000 repetitions for each of the design scenarios
were simulated.
• The effect of variability of the design parameters on
different types of deterioration was assessed:
– Rutting of the HMA layer, fatigue cracking, and IRI.
MEPDG Performance Predictions
Thin HMA Layer (4.5 in)
Thick HMA Layer (10.0 in)
Parameter Cool Climatic Region Warm Climatic Region Hot Climatic Region Cool Climatic Region Warm Climatic Region Hot Climatic Regi
TTC 2
TTC 12
TTC 2
TTC 12
TTC 2
TTC 12
TTC 2
TTC 12
TTC 2
TTC 12
TTC 2
TTC 1
Rutting of the HMA Layer (in)
Mean
0.2302
0.2272
0.3164
0.3147
0.2306
0.2338
0.3236
0.3217
0.2308
0.2267
0.2933
0.290
Std. Dev.
0.0373
0.0366
0.0154
0.0153
0.0311
0.0314
0.0155
0.0155
0.0436
0.0427
0.0156
0.015
Minimum
0.0358
0.0413
0.2445
0.2341
0.0866
0.0874
0.2501
0.2461
0.0294
0.0235
0.2126
0.210
Maximum
0.4123
0.4235
0.3933
0.3899
0.3782
0.3934
0.3973
0.3937
0.4328
0.4244
0.3660
0.362
Terminal IRI (in/mi)
Mean
108.53
109.63
138.78
141.57
92.75
93.35
118.35
119.89
127.46
128.55
162.06
167.5
Std. Dev.
64.11
63.78
2.93
3.20
36.64
38.25
2.19
2.34
145.76
145.55
4.78
5.31
Minimum
124.72
126.47
108.36
108.08
136.32
142.8
Maximum
398.27
435.39
153.45
156.51
277.49
300.31
128.70
131.23
868.56
813.80
185.09
194.4
Fatigue Cracking (%)
Mean
49.66
49.88
31.16
34.00
25.59
27.31
16.13
17.52
76.73
76.98
60.47
64.90
Std. Dev.
9.59
9.46
2.99
3.29
11.11
10.95
1.67
1.85
5.54
5.44
5.31
5.70
Minimum
3.48
0.21
16.41
18.56
8.30
6.87
52.09
50.50
34.15
38.57
Maximum
93.88
94.25
46.30
50.69
79.52
79.14
24.42
26.81
103.79
102.46
86.64
92.80
MEPDG Performance Predictions
• Rutting
– CV is on average 0.11 for the analyzed scenarios.
– Ranged from 90% below the mean to 87% above the
mean due to the variability of the design parameters.
• IRI
– CV was con average 0.37 for the analyzed scenarios.
– IRI in some of the cases was up to 581% above the
mean.
• Fatigue Cracking
– CV was con average 0.37 for the analyzed scenarios.
– Ranged from 100% below the mean to 211% above
the mean
Conclusions
• Most design and analysis tools assume that the input
parameters are deterministic
It has been shown that this assumption is unrealistic.
• When analyzing the variability and distributions of design
variables, it was identified that some of the variables
have considerable variation:
– Layer thickness and resilient modulus of different layers.
• It is strongly advised that the analysis or design of the
pavement structure be not only performed based on the
mean design values, but at several other critical values
of the variables that are expected to have a higher
impact on the performance of the pavement structure.
Conclusions
• Based on the different scenarios:
• For rutting and IRI
 Variability was higher on thin pavements in cool climatic
regions or on thick pavements in warm climatic
• For fatigue cracking,
 Variability was more severe on all pavement structures
under cool climatic regions.
Alguna Pregunta?
Improving the Flexible
Pavement IRI Predictions by
Correcting for Possible Bias
José P. Aguiar-Moya
Harold von Quintus
Dr. Jorge A. Prozzi
Presentation Outline
• Background
– M-E IRI Model
• IV Regression
– Panel Data Models
• Dataset for Model Estimation
• IRI Estimation Model Results
• Conclusions
Background
• Concept of Serviceability
– Related to pavement performance → PSR & PSI
PSI  5.031.91 log(1  SV)  0.01 C  P 1.38 RD2
0.5
• Serviceability is correlated to IRI
PSI  5  exp 0.26 IRI
Background
• IRI measurement has improved
– Highway speeds (profiler)
• Empirical Models to directly predict IRI
– M-E PDG
IRI  IRI0  IRID  IRIF  IRIS
– Initial, Distress, Frost-heave, Swelling
M-E IRI Model
• IRI Prediction Model
IRI  IRI0  0.0150  SF  0.400  FCTotal   0.0080  TC   40.0  RD
SF  Age  0.02003  PI  1  0.007947  Precip  1  0.000636  FI  1
M-E IRI Model
• Potential Problems:
– Extrapolation of IRI to time of construction
– Interpolation to match cracking/rutting observations
– IRI estimated based on regression results
• Initial IRI should be captured thru intercept of model
– Removes need for extrapolation
• Methods to account for correlation between regressors
and unobserved factors
OLS Regression (M-E PDG)
• OLS
IRI i  β 0  β 1  SFi   β 2  FC Total i   β 3  TC i   β 4  RD i   ε i
• OLS Assumptions
– E(X') = 0 (exogeneity)
– Nonautocorrelation (uncorrelated errors)
OLS Regression (M-E PDG)


IRIi  β 0  β1  SFi  ωSFi   β 2  FCTotali  ω FCTotal  β 3  TCi  ωTC i   β 4  RDi  ω RD i   ε i
i
IRIi  β 0  β1  SFi   β 2  FCTotali   β 3  TCi   β 4  RDi   ωSFi ,FCTotal ,TCi ,RDi  ε i
i
IRIi  β 0  β1  SFi   β 2  FCTotali   β 3  TCi   β 4  RD i   ε Total i
• The Total is correlated with the regressors!!
→ Exogeneity assumption is not met
→ Biased estimates
IV Regression
• IV Regression
IRIi  βX i  ε i
X i  f(Z i )  ω i
• Where  = [0, 1, 2, 3, 4],
X i' = [1,SFi,FCTotal i,TCi,RDi]
Z i' = exogenous variables
IV Regression
• IV Regression by means of 2SLS
– Project Z i on X i
– Run least squares using projection of X i
ˆ ε
IRIi  βX
i
i
ˆ  f(Z )
X
i
i
→ COV[Z i, i] = 0
→ Estimates theoretically are consistent and
unbiased
Panel Data Models
• Data used for calibrating the IRI models contains
– Cross-sectional observations
– Time series observations
• Panel Data
– Use time history of a pavement section as IV
– Account for heterogeneity
– Can use random-effects or fixed-effects approach
Panel Data Models
• Fixed-Effects
IRIit  D i α i  β1  SFit   β 2  FCTotal it   β 3  TC it   β 4  RD it   ε Total it
• Random-Effects
IRIit  β1  SFit   β 2  FCTotal it   β 3  TC it   β 4  RD it   μ i  ε Total it
Panel Data Models
• Joint SF-IRI Fixed-Effects
IRIit  Di α i  β1 Ageit β 5 PIi  1  β 6 Precipi  1  β 7 FIi  1
 β 2 FC Total it   β 3 TC it   β 4 RD it   ε Total it
Dataset for Model Estimation
Dataset for Model Estimation
• Instrumental Variables
–
–
–
–
–
–
–
–
–
Plasticity Index (PI) of the subgrade
Average annual precipitation in in. (Precip)
Frost Index (FI)
Age of the pavement in years (Age)
Gradation of the subgrade: material passing the 0.02
and 0.075 mm sieves (p02 and p075)
Thickness of the asphalt layer (hAC)
Thickness of the granular base (hGB)
Air voids (Va)
Asphalt binder content (Pb)
IRI Model Estimation Results
OLS
2SLS (*)
Parameter
Estimates
Std. Err.
t-value
Estimates
Std. Err.
t-value
Intercept
58.37
3.77
15.46
50.39
10.56
4.77
SF
1.18
0.36
3.24
0.24
1.05
0.22
FCTotal
34.84
16.22
2.15
318.83
80.70
3.95
TC
0.01
0.02
0.51
0.04
0.07
0.51
RD
51.14
9.30
5.50
35.26
34.01
1.04
(*) Using the 10 instrumental variables: PI, Precip, FI,
Age, p075, p02, hAC, hGB, Va, and Pb
IRI Model Estimation Results
Fixed-Effects
Random-Effects
Parameter
Estimates
Std. Err.
t-value
Estimates
Std. Err.
t-value
Intercept
56.35
3.30
17.1
54.08
4.32
12.5
SF
2.94
0.42
7.0
2.41
0.33
7.3
FCTotal
37.82
8.63
4.4
38.36
8.14
4.7
TC
0.02
0.02
1.1
0.02
0.02
1.0
RD
23.03
9.84
2.3
37.27
8.14
4.6
IRI Model Estimation Results
Joint Random-Effects
Parameter
Estimates
Std. Err.
t-value
Intercept
51.30
4.37
11.7
Age*(PI+1)
0.06
0.01
3.9
Age*(Precip+1)
0.63
0.27
2.3
Age*(FI+1)
0.0010
0.0003
3.7
FCTotal
28.49
8.55
3.3
TC
0.02
0.02
1.0
RD
32.92
8.15
4.0
IRI Model Estimation Results
Instrumental Variable Regression
Estimate
OLS
Joint Random-
2SLS
Fixed-Effects
Random-Effects
Effects

32.469
45.068
9.300
9.300
9.150
u
-
-
31.966
30.060
29.819
σ w  σ ε2  σ 2u
-
-
33.291
31.466
31.191
R 
0.4428
0.2873
0.9768
0.9763
0.9774
F
20.91
10.46
42.59
53.15
39.37
IRI Model Estimation Results
IRI Model Estimation Results
IRI Model Estimation Results
IRI Model Estimation Results
IRI Model Estimation Results
Conclusions
• Difference in estimates from OLS and IV
Regression
→ Endogeneity Bias
• S.E. for the panel data model increased
→ Unobserved section specific attributes
• Panel Data Model parameters are more
significant (by means of F-stat)
• LM test (H0: 2u = 0) to test validity of pooled
data models indicates there is bias due to
unobserved variables
Conclusions
• A Hausman test indicated that the assumptions
of the R-E Model are inappropriate
• The F-E and the joint SF-IRI F-E Models are
preferred
• Observed changes (OLS vs. F-E):
– an increase of 1 ft in the length of transverse cracks
has increased IRI by 38%
– an increase of 1 ft2 in the area of fatigue cracking has
decreased IRI by 15%
– an increase in the rut depth of 0.1 in. is associated
with a 25% decrease in IRI
Final Conclusions
• La Guia MEPDG esta aqui para quedarse
• Es el sistema de analysis de pavimentos mas
completo hasta hoy
• Muy importante valor academico
• Representa “state-of-practise”
• Necesita muchas mejoras:
–
–
–
–
Calibracion a condiciones locales
Revision de modelos
Nuevos modelos
Simplifiacion de datos de entrada
• Una buena base de datos es esencial
Muchisimas Gracias
Preguntas? Comentarios?
Visite Texas!!!

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