Download - Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010
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Diversos Aspectos de la Implementacion de la Guia
de Diseño Mecanistico-Empirico (MEPDG) en Texas
Dr. Jorge A. ProzziThe University of Texas at Austin
Valparaiso, Chile, 10 November 2010
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• Local Calibration of the Permanent Deformation Performance Models
• Seasonal Time-Series Models for Supporting Traffic Input Data
• Effect of WIM Measurement Errors on Load-Pavement Impact Estimation
• Variability in Pavement Design and Its Effects• Improving the Roughness (IRI) Predictions by
Correcting for Possible Bias
Presentation Outline
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Local Calibration of the Permanent Deformation Performance Models
for Rehabilitated Flexible Pavements
Ambarish BanerjeeJose Pablo Aguiar-MoyaDr. Andre de Fortier Smit
Dr. Jorge A. Prozzi
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Outline• Background• The MEPDG• LTPP• SPS-5• Analysis Inputs • Objectives and Approach• Results• Specific Conclusions
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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.)
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Historical Background
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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
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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
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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
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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)
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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
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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
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Analysis Inputs - General
Location Monitoring Start Overlay Const.
Opened to Traffic AADTT Growth Rate
(%), LinearAnalysis
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
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LTPP SPS-5 sections
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Analysis Inputs - Traffic• Data available from counts, automatic vehicle
classification (AVC) systems and WIM stations• Estimation of initial traffic and growth rate
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Analysis Inputs – Vehicle Class
• Vehicle class distribution at each of the six SPS locations
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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
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Seasonal Variation in Axle Spectra
Axle Spectra for NJ SPS-5 location for January
Axle Spectra for NJ SPS-5 location for February
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Analysis Inputs – MaterialNew Jersey section 0-502, No milling
Layer Type Material Thickness
Modulus (psi)
Binder Grade
Binder Content
(%)
Air Voids (%)
1
Asphalt
HMA 1.9” AC 40 8.1 7.3
2 Existing HMA
2.7” AC 30 10.0 3.6
3 6.2” AC 10 7.7 2.7
4 Granular Base A-1-b
5.2”26500
5 20.5”
6 Subgrade A-2-4 semi-inf 21500
Gradation for both asphalt and unbound layers were also availableAtterberg’s limits, MDD and OMC was available for unbound layers
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Objective
• Determination of Level 2 bias correction factors for rehabilitated pavements for the permanent deformation performance models.
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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
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AC Rutting Transfer Function
428.27*7331.1*0172.0
342.17*4868.2*1039.0
328196.0*)*(
10
22
21
21
33221
1
acac
acac
depthz
kkkrz
r
p
HHC
HHC
depthCCk
NTk rr
Hac = Total AC thickness (inches)εp = Plastic Strain (in/in)εr = Resilient Strain (in/in)T = Layer TemperatureN = Number of Load Repetitionskz, k2, k3 = Laboratory Constantsβr1, βr2, βr3 = Calibration Coefficients
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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
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Level 2 Bias Correction Factors
County State Climate βr1 βr3 βs1Standard Error (in) % Reduction
Lincoln ColoradoDry
Freeze
238 0.142 0.3 0.055 62
Sweet Grass Montana 320 0.138 0.3 0.105 61
Monmouth New Jersey Wet
Freeze
112 0.122 0.7 0.055 25
Taney Missouri 129 0.140 0.7 0.083 41
Kaufman Texas Wet No Freeze
80.0 0.444 0.5 0.075 59
Comanche Oklahoma 107 0.252 0.4 0.081 50
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Comparison of Results
Calibrated V/s Uncalibrated Predictions(Section: 48-A502, Texas)
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Comparison of Results
Calibrated V/s Uncalibrated Predictions(Section: 30-0509, Montana)
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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
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Alguna Pregunta?
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Seasonal Time Series Models for Supporting Traffic Input Data for the Mechanistic-Empirical Design Guide
Feng HongJorge A. Prozzi
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Outline
• Introduction• Objective of this Study• Time Series Models• Data Source• Case Study• Implication• Conclusions
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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
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Traffic Input in M-E Guide
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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
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Seasonal Time Series Model Additive decomposition model
Trend component
Seasonal component
)1(0 trTTt
tt rTT )1(0
n
iiit t
sit
siS
1
)2cos2sin(
tttt STz
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Seasonal Time Series Model
Linear growth plus seasonality
Compound growth plus seasonality
t
n
iiit tititz
110 )
122cos
122sin(
t
n
iii
tt titiz
110 )
122cos
122sin()1(
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Model Estimation Approach
Linear growth + seasonality model Ordinary Least Square (OLS)
Compound growth + seasonality model Nonlinear Least Square (NLLS)
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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
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Case Study
Data Used Location: Interstate Highway 37,
Corpus Christi, Texas Equipment: Weigh-in-Motion Duration: Jan. 1998 – May. 2002
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Model Estimation Results Parameter Estimates of Seasonal Time Series Models with Two Harmonics
Class 4 Class 5 Class 9 Others Entire Trucks Model Type 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 0.7 0.000 12.9 0.000 2.4 0.081 1.9 0.000 18.0 0.000
1 2.7 0.223 78.7 0.016 79.8 0.004 25.8 0.000 187.0 0.000
1 -9.0 0.000 -176.9 0.000 37.4 0.177 1.0 0.826 -147.5 0.000
2 -5.5 0.024 44.4 0.184 -49.6 0.075 10.5 0.031 -0.2 0.995
Linear
2 1.8 0.421 -53.2 0.097 10.2 0.694 -15.7 0.001 -56.9 0.067
0 70.1 0.000 489.9 0.000 1908.9 0.000 351.5 0.000 2791.2 0.000
1 7.9E-03 0.000 1.7E-02 0.000 1.2E-03 0.059 4.8E-03 0.000 5.5E-03 0.000
1 2.5 0.218 72.5 0.009 79.6 0.001 25.5 0.000 183.7 0.000
1 -9.0 0.000 -180.3 0.000 37.4 0.137 1.0 0.827 -148.7 0.000
2 -5.6 0.010 45.3 0.122 -49.9 0.047 10.3 0.019 -1.1 0.971
Compound
2 1.9 0.356 -50.6 0.070 10.3 0.665 -15.5 0.000 -55.2 0.049
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Observed Vs. Predicted Traffic (2)
2000
2500
3000
3500
4000
4500
0 10 20 30 40 50 60
Time (month)
Volu
me
Linear growth + Time series Compound growth + Time series Linear trend Compound trend
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Observed Vs. Predicted Traffic (1)
2000
2500
3000
3500
4000
4500
0 10 20 30 40 50 60
Time (month)
Volu
me
Linear growth + Time series Compound growth + Time series Linear trend Compound trend
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Further Implication Integrating long- and short- term traffic information
Correlation Metrics of Parameters in the Models for Entire Trucks
Model Type Parameters 0 1 1 1
0 1.00 -0.91 -0.17 0.06
1 -0.91 1.00 0.09 -0.03
1 -0.17 0.09 1.00 -0.10
Linear growth
(plus time series)
1 0.06 -0.03 -0.10 1.00
0 1.00 -0.92 -0.16 0.07
1 -0.92 1.00 0.09 -0.05
1 -0.16 0.09 1.00 -0.10
Compound growth
(plus time series
1 0.07 -0.05 -0.10 1.00
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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
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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
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Alguna Pregunta?
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Effect of Weigh-In-Motion System Measurement Error on
Load-Pavement Impact Estimation
Feng HongJorge A Prozzi
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Outline
• Background– Traffic data collection– WIM measurement error
• Dataset– Data source– Statistical characteristics
• Methodology– Load-pavement impact– Incorporating measurement error
• Conclusions
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Introduction
• Pavement design inputs– Soil and material properties– Environmental conditions– Traffic load
• Empirical approach: ESALs• Mechanistic-empirical approach: axle
load spectra
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Traffic load data collection
• Static scale– Limited sample size – Accurate
• Weigh-in-Motion (WIM) scale– Continuous data collection– Accuracy?
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WIM classification
• Based on sensor technology
– Load cell– Bending plate– Piezo-electronic
Accuracy Cost
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WIM measurement error
• Percentage difference
• WIMWeight: weight measured by WIM scale• StaticWeight: weight measured by static scale
(assumed to be real weight)
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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
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Random error
00.05
0.10.15
0.20.25
0.30.35
-40 -30 -20 -10 0 10 20 30 40
WIM errors (%)
Sigma=1.5% Sigma=5% Sigma=10%
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Systematic error
00.010.02
0.030.040.050.060.07
0.080.090.1
-40 -30 -20 -10 0 10 20 30 40
WIM errors(%)
-10% biased ideal calibration +10% biased
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Data Source
• Texas 21 WIM stations
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Axle types
Single Tandem Tridem
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Axle Load Spectra
Single axle Tandem axle
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Statistical Characteristics
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Load-pavement impactm
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Load-pavement impact under random error: derivation
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Load-pavement impact under random error: result
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Load-pavement impact under both errors: derivation
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![Page 63: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/63.jpg)
Load-pavement impact under both errors: result
![Page 64: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/64.jpg)
Sensitivity analysis
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sigma = 0% sigma = 5% sigma = 10% sigma = 15% sigma = 20%
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Comparison with FHWA-RD-98-104 results
![Page 66: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/66.jpg)
Summary
• Investigate axle load spectra statistical characteristics
• Establish WIM error’s effect on load-pavement impact estimation– Both errors affect result– The result is more sensitive to systematic error
• Application – Pavement life estimation– WIM equipment selection
![Page 67: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/67.jpg)
Alguna Pregunta?
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Variability in Pavement Design and Its Effects on the
Performance Predictions of the MEPDG
José P. Aguiar-MoyaDr. Jorge A. ProzziDr. Lance Manuel
![Page 69: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/69.jpg)
• 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
Presentation Outline
![Page 70: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/70.jpg)
• 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!
Introduction
![Page 71: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/71.jpg)
• 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
Variability in Pavement Design
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• 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)
Goodness-of-Fit Tests to evaluate Data Distribution
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• 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
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• 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
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Variability in Pavement Layer Thickness
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Thickness (in)
Normal DistributionActual DataCritical Tail
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• 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
Variability in Pavement Layer Thickness
Layer Average CV Range HMA Surface Layer 0.072 0.032 – 0.184 HMA Binder Course Layer 0.138 0.117 – 0.160 Granular Base Layer 0.103 0.060 – 0.172
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• 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
Variability in Asphalt Binder Content
Follow normal distributions
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• 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
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Asphalt Binder Content (%)
Normal DistributionActual DataCritical Tail
Variability in Asphalt Binder Content
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• 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 Asphalt Binder Content
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• 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
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Air Void Content (%)
Normal DistributionActual DataCritical Lower TailCritical Upper Tail
Variability in Air Void Content
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• 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 Air Void Content
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• 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
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Resilient Modulus (psi - 2 psi Confining Pressure)
Normal DistributionActual DataCritical Tail
Variability in Modulus of Unbound Layers
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• 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 Unbound Layers
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• 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
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Resilient Modulus (ksi - 80.6oF)
Uniform DistributionNormal DistributionActual DataCritical Tail
Variability in Modulus of HMA Layers
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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).
Variability in Modulus of HMA Layers
![Page 90: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/90.jpg)
• 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:
Effect of Variability on MEPDG Predictions
Parameter Mean Std. Dev. Distribution HMA Thickness (in) 4.5 / 10.0 0.33 / 0.72 Normal Asphalt Binder Content (%) 5.0 0.32 Normal Air Voids (%) 7.0 0.36 Normal Base Thickness (in) 14.0 1.44 Normal HMA Modulus at 80.6°F (ksi) 760 20 Uniform Base Modulus (psi) 22,000 2222 Normal Subgrade Modulus (psi) 10,000 930 Normal
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• 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
![Page 92: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/92.jpg)
MEPDG Performance Predictions
TTC 2 TTC 12 TTC 2 TTC 12 TTC 2 TTC 12 TTC 2 TTC 12 TTC 2 TTC 12 TTC 2 TTC 12
Mean 0.2302 0.2272 0.3164 0.3147 0.2306 0.2338 0.3236 0.3217 0.2308 0.2267 0.2933 0.2900Std. Dev. 0.0373 0.0366 0.0154 0.0153 0.0311 0.0314 0.0155 0.0155 0.0436 0.0427 0.0156 0.0154Minimum 0.0358 0.0413 0.2445 0.2341 0.0866 0.0874 0.2501 0.2461 0.0294 0.0235 0.2126 0.2108Maximum 0.4123 0.4235 0.3933 0.3899 0.3782 0.3934 0.3973 0.3937 0.4328 0.4244 0.3660 0.3629
Mean 108.53 109.63 138.78 141.57 92.75 93.35 118.35 119.89 127.46 128.55 162.06 167.59Std. Dev. 64.11 63.78 2.93 3.20 36.64 38.25 2.19 2.34 145.76 145.55 4.78 5.31Minimum - - 124.72 126.47 - - 108.36 108.08 - - 136.32 142.86Maximum 398.27 435.39 153.45 156.51 277.49 300.31 128.70 131.23 868.56 813.80 185.09 194.47
Mean 49.66 49.88 31.16 34.00 25.59 27.31 16.13 17.52 76.73 76.98 60.47 64.90Std. Dev. 9.59 9.46 2.99 3.29 11.11 10.95 1.67 1.85 5.54 5.44 5.31 5.70Minimum 3.48 0.21 16.41 18.56 - - 8.30 6.87 52.09 50.50 34.15 38.57Maximum 93.88 94.25 46.30 50.69 79.52 79.14 24.42 26.81 103.79 102.46 86.64 92.80
Fatigue Cracking (%)
Thin HMA Layer (4.5 in) Thick HMA Layer (10.0 in)Parameter
Rutting of the HMA Layer (in)
Terminal IRI (in/mi)
Cool Climatic Region Warm Climatic Region Hot Climatic Region Cool Climatic Region Warm Climatic Region Hot Climatic Region
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• 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
MEPDG Performance Predictions
![Page 94: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/94.jpg)
• Most design and analysis tools assume that the input parameters are deterministicIt 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
![Page 95: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/95.jpg)
• 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.
Conclusions
![Page 96: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/96.jpg)
Alguna Pregunta?
![Page 97: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/97.jpg)
Improving the Flexible Pavement IRI Predictions by Correcting for Possible Bias
José P. Aguiar-MoyaHarold von QuintusDr. Jorge A. Prozzi
![Page 98: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/98.jpg)
• Background– M-E IRI Model
• IV Regression– Panel Data Models
• Dataset for Model Estimation• IRI Estimation Model Results• Conclusions
Presentation Outline
![Page 99: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/99.jpg)
• Concept of Serviceability– Related to pavement performance → PSR & PSI
• Serviceability is correlated to IRI
Background
25.0 38.101.0)1log(91.103.5 RDPCSVPSI
IRIPSI 26.0exp5
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• IRI measurement has improved– Highway speeds (profiler)
• Empirical Models to directly predict IRI– M-E PDG
– Initial, Distress, Frost-heave, Swelling
SFD0 IRIIRIIRIIRIIRI
Background
![Page 101: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/101.jpg)
• IRI Prediction Model
RD40.0TC0.0080FC0.400SF0.0150IRIIRI Total0
1FI0.0006361Precip0.0079471PI0.02003AgeSF
M-E IRI Model
![Page 102: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/102.jpg)
• 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
M-E IRI Model
![Page 103: Dr. Jorge A. Prozzi The University of Texas at Austin Valparaiso, Chile, 10 November 2010](https://reader035.vdocuments.net/reader035/viewer/2022062501/56815e07550346895dcc576d/html5/thumbnails/103.jpg)
• OLS
• OLS Assumptions– E(X') = 0 (exogeneity)– Nonautocorrelation (uncorrelated errors)
ii4i3iTotal2i10i εRDβTCβFCβSFββIRI
OLS Regression (M-E PDG)
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• The Total is correlated with the regressors!!→ Exogeneity assumption is not met→ Biased estimates
iiRDi4iTCi3iFCiTotal2iSFi10i εωRDβωTCβωFCβωSFββIRITotal
iRD,TC,FC,SFi4i3iTotal2i10i εωRDβTCβFCβSFββIRIiiiTotali
i Totali4i3iTotal2i10i εRDβTCβFCβSFββIRI
OLS Regression (M-E PDG)
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• IV Regression
• Where = [0, 1, 2, 3, 4], X i' = [1,SFi,FCTotal i,TCi,RDi] Z i' = exogenous variables
ii εIRI iβX
iii ωZX )f(
IV Regression
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• IV Regression by means of 2SLS– Project Z i on X i – Run least squares using projection of X i
→ COV[Z i, i] = 0→ Estimates theoretically are consistent and
unbiased
ii εˆIRI iXβ
)f(ˆii ZX
IV Regression
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• 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
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• Fixed-Effects
• Random-Effects
it Totalit4it3itTotal2it1iiit εRDβTCβFCβSFβαDIRI
it Totaliit4it3itTotal2it1it εμRDβTCβFCβSFβIRI
Panel Data Models
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• Joint SF-IRI Fixed-Effects
1FIβ1Precipβ1PIβAgeβαDIRI i7i6i5it1iiit
it Totalit4it3itTotal2 εRDβTCβFCβ
Panel Data Models
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Dataset for Model Estimation
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• 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)
Dataset for Model Estimation
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(*) Using the 10 instrumental variables: PI, Precip, FI, Age, p075, p02, hAC, hGB, Va, and Pb
IRI Model Estimation Results
Parameter OLS 2SLS (*)
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
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IRI Model Estimation Results
Parameter Fixed-Effects Random-Effects
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
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IRI Model Estimation Results
Parameter Joint Random-Effects
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
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IRI Model Estimation Results
Estimate OLS
Instrumental Variable Regression
2SLS Fixed-Effects Random-Effects Joint Random-
Effects
32.469 45.068 9.300 9.300 9.150
u - - 31.966 30.060 29.819
2u
2εw σσσ - - 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
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IRI Model Estimation Results
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IRI Model Estimation Results
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IRI Model Estimation Results
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IRI Model Estimation Results
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IRI Model Estimation Results
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• 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: 2
u = 0) to test validity of pooled data models indicates there is bias due to unobserved variables
Conclusions
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• 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
Conclusions
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• 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
Final Conclusions
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Muchisimas Gracias
Preguntas? Comentarios?
Visite Texas!!!