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 2i 2i 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 2i 2i t i cos t) t 12 12 Compound growth plus seasonality n zt 0 (1 1 ) ( i sin t i 1 2i 2i 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 4k 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 4k 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 4k 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 5.031.91 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? 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