dr. jorge a. prozzi the university of texas at austin valparaiso, chile, 10 november 2010

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

• 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

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

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

• 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

(%), 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

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 – MaterialNew Jersey section 0-502, No milling

Layer Type Material Thickness

Modulus (psi)

Binder Grade

Binder Content

Air Voids (%)

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

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

428.27*7331.1*0172.0

342.17*4868.2*1039.0

328196.0*)*(

depthz

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

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 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

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 Mechanistic-Empirical Design Guide

Feng HongJorge 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

Trend component

Seasonal component

)1(0 trTTt

tt rTT )1(0

iiit t

)2cos2sin(

tttt STz

Seasonal Time Series Model

Linear growth plus seasonality

Compound growth plus seasonality

iiit tititz

122cos

122sin(

tt titiz

122cos

122sin()1(

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

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

Observed Vs. Predicted Traffic (2)

0 10 20 30 40 50 60

Time (month)

Linear growth + Time series Compound growth + Time series Linear trend Compound trend

Observed Vs. Predicted Traffic (1)

0 10 20 30 40 50 60

Time (month)

Linear growth + Time series Compound growth + Time series Linear trend Compound trend

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

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 HongJorge 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

0.10.15

0.20.25

0.30.35

-40 -30 -20 -10 0 10 20 30 40

WIM errors (%)

Sigma=1.5% Sigma=5% Sigma=10%

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

Data Source

• Texas 21 WIM stations

Axle types

Single Tandem Tridem

Axle Load Spectra

Single axle Tandem axle

Statistical Characteristics

Load-pavement impactm

r qLxLSF

LdxxfxLSF

444 84exp)ln(

skkk LWLSF 4284exp

Load equivalency factor

Load spectra factor (discrete)

Load spectra factor (continuous)

Load-pavement impact under random error: derivation

')163(

sxXX L

42244'

4 84exp163')('' sk

kkksXXXE LWLdxdxxfxxgxLSF

xXX LxXXE

dxxxgxLSF

Load-pavement impact under random error: result

Load-pavement impact under both errors: derivation

424224

84exp1163

'')()''(''

sXXXbE

LdxdxxfxxgxLSF

Load-pavement impact under both errors: result

Sensitivity analysis

-60.00%

-40.00%

-20.00%

20.00%

40.00%

60.00%

80.00%

100.00%

-20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00%

WIM Calibration Bias (alpha)

sigma = 0% sigma = 5% sigma = 10% sigma = 15% sigma = 20%

Comparison with FHWA-RD-98-104 results

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

Alguna Pregunta?

Variability in Pavement Design and Its Effects on the

Performance Predictions of the MEPDG

José P. Aguiar-MoyaDr. Jorge A. ProzziDr. Lance Manuel

• 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

• 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

• 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

• 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

• 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

1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5

Thickness (in)

Normal DistributionActual DataCritical Tail

• 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 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

• 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

• 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

3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5

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).

• 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

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

Air Void Content (%)

Normal DistributionActual DataCritical Lower TailCritical Upper Tail

• 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.

• 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

12,500 12,750 13,000 13,250 13,500 13,750 14,000

Resilient Modulus (psi - 2 psi Confining Pressure)

• 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.

• 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

722 725 728 731 734 737 740 743 746 749 752 755 758 761 764 767 770 773

Resilient Modulus (ksi - 80.6oF)

Uniform DistributionNormal DistributionActual DataCritical Tail

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).

• 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

• 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

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

• 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

• 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

• 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

Alguna Pregunta?

Improving the Flexible Pavement IRI Predictions by Correcting for Possible Bias

José P. Aguiar-MoyaHarold von QuintusDr. Jorge A. Prozzi

• Background– M-E IRI Model

• IV Regression– Panel Data Models

• Dataset for Model Estimation• IRI Estimation Model Results• Conclusions

• 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

• IRI measurement has improved– Highway speeds (profiler)

• Empirical Models to directly predict IRI– M-E PDG

– Initial, Distress, Frost-heave, Swelling

SFD0 IRIIRIIRIIRIIRI

Background

• IRI Prediction Model

RD40.0TC0.0080FC0.400SF0.0150IRIIRI Total0

1FI0.0006361Precip0.0079471PI0.02003AgeSF

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

M-E IRI Model

• OLS

• OLS Assumptions– E(X') = 0 (exogeneity)– Nonautocorrelation (uncorrelated errors)

ii4i3iTotal2i10i εRDβTCβFCβSFββIRI

OLS Regression (M-E PDG)

• 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)

• 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

• 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

• 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

• Random-Effects

it Totalit4it3itTotal2it1iiit εRDβTCβFCβSFβαDIRI

it Totaliit4it3itTotal2it1it εμRDβTCβFCβSFβIRI

Panel Data Models

• Joint SF-IRI Fixed-Effects

1FIβ1Precipβ1PIβAgeβαDIRI i7i6i5it1iiit

it Totalit4it3itTotal2 εRDβTCβFCβ

Panel Data Models

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)

Dataset for Model Estimation

(*) 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

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

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

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

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

• 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

• 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

• 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

Muchisimas Gracias

Preguntas? Comentarios?

Visite Texas!!!

dr. jorge a. prozzi the university of texas at austin valparaiso, chile, 10 november 2010

pavementsassumes pavement

aashto design procedureresults

common design

rigid pavementssps

aashto joint task force

empirical methodprimarily

intermediate level

highest level of accuracy

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