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Evaluation of the MEPDG Dynamic Modulus Prediction Models for Asphalt Concrete Mixtures S. M. El-Badawy1, Ph. D. Research Fellow, A. Awed2, Graduate Research Assistant, and F. M. Bayomy3, Ph. D., P.E., Professor 1
National Institute for Advanced Transportation Technology (NIATT), University of Idaho, P.O. Box 441022, Moscow, Idaho 83844-1022; PH (208) 885-6818; FAX (208) 885-6608; email:
[email protected] , Permanent Address: Mansoura University, Public Works Eng., Dept., Mansoura, Egypt 2 Department of Civil Engineering, University of Idaho, P.O. Box 441022, Moscow, Idaho 83844-1022; PH (208) 885-6784; FAX (208) 885-6818; email:
[email protected] 3 Department of Civil Engineering, University of Idaho, P.O. Box 441022, Moscow, Idaho 83844-1022; PH (208) 885-6784; FAX (208) 885-6608; email:
[email protected] ABSTRACT HMA dynamic modulus (E*) is one of key inputs to the Mechanistic-Empirical Pavement Design Guide (MEPDG). There are two different E* models in the MEPDG; the NCHRP 1-37A viscosity-based model, and the NCHRP 1-40D, which is based on the binder shear modulus. This paper focuses on evaluating the influence of the binder characterization input level on the predicted E* in MEPDG. Laboratory E* tests were conducted on samples from 15 different HMA plant-produced mixtures. The shear modulus (G*) and phase angle (δ) for each binder were also determined in the laboratory. Results showed that MEPDG levels 1and 3 binder characterization inputs with both E* predictive models yielded E* values that are in excellent to fair agreement with laboratory measured E*. However, the 1-37A model showed better results than the 1-40D model. On the other hand, high bias in E* values was observed when level 1 binder characterization data was used. INTRODUCTION The most important hot-mix asphalt (HMA) property influencing the structural response of a flexible pavement is the HMA dynamic modulus (E*). It is the primary stiffness property for the characterization of asphalt concrete (AC) mixtures in all of the hierarchical input levels of MEPDG. Critical stresses, strains, and deflections in the AC layer(s) are calculated as a function of the AC modulus (E*) using the pavement response model incorporated in MEPDG software. In the current MEPDG software (version 1.10), level 3 E* values at different temperatures and loading frequencies can be estimated using two different predictive models according to the user’s choice. The first model is the NCHRP1-37A viscosity-based E* (ARA, 2004). The second model is the NCHRP1-40D binder shear modulus G*based model. The first model was implemented in the MEPDG in its first release (Version 0.7) while the second one was added to the MEPDG in version 1.0 (Witczak
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et al. 2006). These two models predict E* as a function of mixture volumetric properties, gradation, loading frequency and binder stiffness. For binder characterization, MEPDG utilizes three hierarchical input levels. In level 1 (same as level 2 in this case), laboratory measured binder G* and phase angle (δ) at an angular frequency of 10 rad/s at different temperatures are required. In level 3, the only input required is the binder Superpave performance grade (in case of Superpave binders). On the other hand, the binder viscosity grade is required input for binders classified based on viscosity while the binder penetration grade is the required input for binders classified according to penetration. The objective of this paper was to compare the predicted E* by these two models to the actual measured E* values and study the effect of binder characterization on such prediction. The predicted E* values using each model were conducted based on two different sets of binder characteristics. One set is based on level 1 G*-δ binder data at 10 rad/s angular loading frequency and at least three different temperatures as per MEPDG input requirements. The other set is based on MEPDG level 3 default binder properties based on superpave performance binder grade. A secondary objective of this paper is to compare the prediction accuracy of the two E* predictive models incorporated in MEPDG based on the data collected from 15 different HMA mixtures commonly used in Idaho. MEPDG E* PREDICTIVE MODELS The two E* models adopted in MEPDG were developed by Witczak and his colleagues. These two models are the most commonly used when direct laboratory E* measurements are unavailable (Harran and Shalaby 2009; Ceylanet et al. 2009). Details of these models are presented next. NCHRP 1-37A viscosity-based E* model This model was implemented in the first version of the MEPDG (version 0.7). The model was developed based on 2750 measured E* data points from 205 different HMA mixtures, including modified and unmodified binders, that have been periodically collected by Witczak and his colleagues since 1969 (Andrei et al. 1999). It predicts E* at different temperatures as a function of the mix aggregate gradation, volumetric properties, loading frequency and binder viscosity. The model is presented by Equation 1 (ARA 2004): log10 E* = −1.249937 + 0.02923ρ 200 − 0.001767( ρ 200 ) 2 − 0.002841ρ 4 − 0.058097Va − 0.82208
Vbeff Vbeff + Va
+
3.871977 − 0.0021ρ 4 + 0.003958ρ 38 − 0.000017( ρ 38 ) 2 + 0.00547ρ 34 1 + e( −0.603313−0.313351 log f −0.393532 logη )
(1)
where E*=dynamic modulus, 105 psi; ρ34=cumulative % retained on the ¾ in sieve; ρ38= cumulative % retained on the 3/8 in sieve; ρ4=cumulative % retained on the No. 4 sieve; ρ200=% passing the No. 200 sieve; Vbeff=effective binder content, % by volume; Va=air void content, %; f=frequency of loading, Hz; and η=viscosity at the age and temperature of interest, 106 Poise.
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NCHRP 1-40D G*-based E* model The main disadvantage of the 1-37A model presented above is that it characterizes the binder in terms of conventional viscosity rather than the dynamic shear modulus and phase angle of the binder (Garcia and Thompson 2007; Ceylan et al. 2009). The binder G* and δ are commonly used as a part of the superpave performance grade (PG) binder specification. Thus, to overcome this disadvantage, the MEPDG flexible pavement research team incorporated, in addition to the 1-37A model, another E* predictive model which characterizes the binder in terms of G* and δ. This was done as a part of the NCHRP 1-40D (02) project which is the Technical Assistance to NCHRP and NCHRP Project 1-40A: Versions 0.9 and 1.0 of the M-E Pavement Design Software. This model is a modified version of the Bari and Witczak’s E* predictive model originally developed in 2005 (Witczak et al. 2007). It is implemented in the MPEDG since version 1.0. The E* database used in this model development contains 7400 data points from 346 mixtures. This database included the data used for the development of the 1-37A model. The model is presented below:
(
log10 E* = 0.02 + 0.758 | Gb * | −0.0009
⎛ 6.8232 − 0.03274ρ 200 + 0.00431ρ 200 2 + 0.0104ρ 4 − 0.00012ρ 4 2 ⎞ ⎜ ⎟ ⎟ ×⎜ ⎛ ⎞ V beff ⎟ ⎟ ⎜ + 0.00678ρ 38 − 0.00016ρ 38 2 − 0.0796Va − 1.1689 ⎜ ⎜V +V ⎟ ⎟ ⎜ beff ⎠ ⎠ ⎝ a ⎝
)
(2)
⎛ Vbeff ⎞ ⎟ + 0.00891ρ 38 − 0.00007 ρ 38 2 − 0.0081ρ 34 1.437 + 0.03313Va + 0.6926 ⎜ ⎜V +V ⎟ beff ⎠ ⎝ a + 1 + e ( − 4.5868−0.8176 log|Gb *| + 3.2738logδ )
where |Gb*|=dynamic shear modulus of binder (G*), psi; and δ= phase angle of the binder, degrees. All other variables are as previously defined in Equation 1. The presented models (Eq. 1 & 2) follow the form of a segmoidal function. Both models relate E* to mix gradation parameters, volumetric properties, frequency of loading and binder properties. As mentioned earlier, the main difference between the two models, is the parameters included for binder characterization. MEPDG E* prediction methodology As discussed before, both presented E* predictive models are function of the binder characteristics. There are two levels for binder input in MEPDG; level 1 and level 3 (level 2 is the same as level 1). For level 1 binder characterization, MEPDG requires the G* and δ of the binder (aged at RTFO condition) at different temperatures and one angular frequency of 10 rad/s. The software then uses the following relationship to compute the viscosity at different temperatures as a function of G* and δ ( ARA 2004). G *⎛ 1 ⎞ η= ⎜ ⎟ 10 ⎝ sin δ ⎠
4.8628
(3)
where G* = binder complex shear modulus, Pa; δ =binder phase angle, degrees; and η= viscosity, Pa.s.
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Once this step is completed, the ASTM viscosity-temperature relationship is established (Eq. 4). Then A and VTS parameters are determined by conducting linear regression using Equation 4 (ARA 2004).
log log η = A + VTS log TR
(4)
where η=viscosity, cP; TR=temperature in Rankine at which the viscosity was estimated; and A= regression intercept VTS=regression slope of the ViscosityTemperature Susceptibility. The above relationship is then used directly to estimate the binder viscosity at the temperature of interest and then use the 1-37A model (Eq. 1) for E* computation. For the 1-40D Model, once the A and VTS are determined, the following equations (Eq. 5 to 10) are used to compute Gb* and δb at the temperature and frequency of interest in order to compute the E* at these temperatures and frequencies (Witczak et al. 2007): loglogηf s , T = A'+ VTS' log TR
(5)
A' = 0.9699 * f
(6) (7)
-0.0527 s -0.0575 s
VTS' = 0.9668 * f
*A * VTS
f s = f c /2π
(8)
δ b = 90 − 0.1785 * log (ηfs , T ) 2.3814 * (f s ) (0.3507+0.0782VTS')
(9)
| G b * | = 1.469 *10 −9 * log( η f s ,T )12.0056 * f s
0.7418
(sin δ )0.6806
(10)
where A′=adjusted A (adjusted for loading frequency); VTS′=adjusted VTS (adjusted for loading frequency); fs= loading frequency in dynamic shear loading mode as used in the DSR test to measure |Gb*| and δ, Hz; fc=loading frequency of a dynamic loading in “compression” mode (as used in the E* test of HMA mixtures), Hz; and ηfs, T=viscosity of the asphalt binder as a function of both loading frequency in DSR (fs) and temperature (TR), cP. Equations 5 through 10 were developed based on asphalt binder properties database containing 8940 data points from 41 different virgin and modified asphalt binders (Bari&Witczak 2007; Witczak et al. 2007; Bari&Witcak, 2006). Finally, E* at any temperature and frequency can then be calculated using Equation 2. It must be noted that the G*-based E* predictive model was developed based on estimated, rather than laboratory measured, G* and δ at the same temperature and frequency of E* from default A and VTS values (based on conventional binder characterization testing) (Far et al. 2009). For Level 3, binder input, the program uses its internal default values of A and VTS for the selected binder grade. Then it follows the previous procedure explained for Level 1 to predicts E* either from Eq. 1 or Eq. 2 as selected by the user. In summary, the above analysis indicates that the E* prediction methodology, in MEPDG using either the 1-37A or 1-40D E* predictive models, is based on the ASTM A-VTS regression parameters for binder characterization. The 1-37A model, estimates the binder viscosity as a function of temperature (no influence of frequency on binder viscosity) through Equation 4. On the other hand, the 1-40D model
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estimates G* and δ at different temperatures and frequencies form A and VTS through a series of regression equations (Eq. 5 through 10). It is important to note that the A and VTS used in the development of both E* predictive models are the default values in the MEDPG which were based on conventional viscosity binder testing data. Some researchers questioned the validity of the typical (default) A and VTS values in MEPDG to superpave performance grade binders, since the Superpave binders use DSR data (Harran and Shalaby 2009, Birgisson et al. 2005, Dongre′ et al. 2005). MATERIALS AND METHODS HMA mixtures tested A total of 15 different plant produced asphalt concrete mixtures commonly used by Idaho Transportation Department (ITD) in pavement construction projects in the state of Idaho were used in the analysis. These mixtures contain five different superpave performance grade binder types, varied mix aggregate gradation, and volumetric properties. Specimen preparation for dynamic modulus testing For each investigated mixture, two replicate samples from each loose mix were compacted in a Servopac gyratory compactor to achieve 150 mm diameter and 170 mm high cylindrical specimen. Dynamic modulus specimens were cored from the center of the gyratory specimens and the ends were sawed to obtain a cylindrical specimen of 100 mm diameter and 150 mm high in accordance to the AASHTO PP 60-09 procedures. HMA dynamic modulus testing Dynamic modulus tests were performed in the University of Idaho Laboratory using the Simple Performance Tester (SPT). All tests were conducted according to AASHTO TP 62-07. All tests were run on two replicate samples at temperatures of 4.4, 21.1, 37.8, and 54.4 oC and loading frequencies of 0.1, 0.5, 1, 5, 10, and 25 Hz at each temperature. Three on-specimen vertical LVDT’s were used to monitor the axial deformation of each specimen. The total number of E* measurements for the 15 mixtures is 720 points. Binder dynamic shear rheometer testing Dynamic Shear Rheometer (DSR) tests were conducted on the five PG binders used in the mixtures to determine binder G* and δ. The DSR tests were run according to AASHTO T315-06 (AASHTO 2006). All tests were performed at the same temperature and frequency sweep of the E* testing. Before testing, all binders were aged using Rolling Thin Film Oven (RTFO) to simulate mix aging during mixing and field compaction. The tested binder grades are PG 58-28, PG 64-28, PG 70-28, PG 64-34, and PG 76-28. DATA RESULTS AND ANALYSIS AND
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E* prediction based on level 3 binder data For Level 3 binder data, typical default A and VTS values at RTFO condition for each investigated binder were taken from MEPDG. For the 1-37A model, Equation 3 was used to compute binder viscosity at different temperatures, then E* values were estimated at different temperatures and frequencies by Equation 1. For the 1-40D model, Equations 5 through 10 were used to compute Gb* and δ, at the same temperature and frequency values used in DSR and E* testing, based on the binder A and VTS. Then Equation 2 was used to estimate E* values at the same temperatures and frequencies. E* prediction based on level 1 binder data For each investigated binder, equation 3 was used to calculate binder viscosity at different temperatures using data corresponding to angular loading frequency of 10 rad/s. Then the A and VTS parameters, for each binder, were determined by performing linear regression on Equation 4 as shown in Figure 1. Steps explained in the previous subsection were then followed to compute E* based on the 1-37A and 140D models. One may surmise from Figure 1 that the ASTM A-VTS linear relationship is not as accurate for the PG 64-28 and PG 70-28. Furthermore, the A and VTS parameters based on level 1 binder data were found to be significantly different from the typical MEPDG A and VTS for the investigated binders. This may be due to the fact that MEPDG default A and VTS values are based on conventional viscosity testing data rather than binder G* and δ from DSR testing. 1.05 y58-28 = -3.1857x + 9.5932 R² = 0.9936 y64-28 = -2.448x + 7.579 R² = 0.9637 y 64-34= -2.811x + 8.5631 R² = 0.9937
Log Log η (cP)
1.00 0.95 0.90 0.85 0.80 0.75 2.69
y70-28 = -2.4356x + 7.5538 R² = 0.9778 y76-28 = -2.7064x + 8.3107 R² = 0.9999
PG 58-28 PG 64-28 PG 64-34 PG 70-28 PG 76-28 Linear (PG 58-28) Linear (PG 64-28) Linear (PG 64-34) Linear (PG 70-28) Linear (PG 76-28) 2.70
2.71
2.72
2.73
2.74
2.75
2.76
2.77
2.78
Log TR (Rankine)
Figure 1 A-VTS determination based on level 1 binder data Accuracy and bias in MEPDG E* predictions Laboratory measured E* values were compared to the predicted ones using the two predictive models incorporated in MEPDG. Figures 2 and 3 show a comparison between measured and predicted E* (based on MEDPG level 3 binder AVTS) using the 1-37A and 1-40D models respectively. These figures are presented in both arithmetic and logarithmic scales. On the other hand, laboratory measured versus predicted E* values based on level 1 binder characterization inputs using the 1-37A and 1-40D models are shown in Figures 4 and 5 respectively.
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1.0E+05 1-37A Model (Level 3 Binder Inputs)
1-37A Model (Level 3 Binder Inputs)
Predicted E* Values (MPa)
Predicted E* Values (MPa)
2.5E+04 2.0E+04 1.5E+04 1.0E+04 5.0E+03 Line of Equality 0.0E+00 0.0E+00 5.0E+03 1.0E+04 1.5E+04 2.0E+04 2.5E+04
1.0E+04
1.0E+03
1.0E+02
1.0E+01 1.0E+01
Line of Equality 1.0E+02
1.0E+03
1.0E+04
1.0E+05
Measured E* Values (MPa)
Measured E* Values (MPa)
a) Arithmetic Scale b) Logarithmic Scale Figure 2 Predicted versus Measured E* based on the 1-37A model (level 3 binder data) 1.0E+05 1-40D Model (Level 3 Binder Inputs)
2.0E+04 1.5E+04 1.0E+04 5.0E+03 Line of Equality 0.0E+00 0.0E+00 5.0E+03 1.0E+04 1.5E+04 2.0E+04 2.5E+04
Predicted E* Values (MPa)
Predicted E* Values (MPa)
2.5E+04
1-40D Model (Level 3 Binder Inputs) 1.0E+04
1.0E+03
1.0E+02
1.0E+01 1.0E+01
Line of Equality 1.0E+02
1.0E+03
1.0E+04
1.0E+05
Measured E* Values (MPa)
Measured E* Values (MPa)
a) Arithmetic Scale b) Logarithmic Scale Figure 3 Predicted versus measured E* based on the 1-40D model (level 3 binder data) 1.0E+05
Predicted E* Values (MPa)
1-37A Model (Level 1 Binder Inputs) 2.0E+04 1.5E+04 1.0E+04 5.0E+03 Line of Equality 0.0E+00 0.0E+00 5.0E+03 1.0E+04 1.5E+04 2.0E+04 2.5E+04
Predicted E* Values (MPa)
2.5E+04
1-37A Model (Level 1 Binder Inputs) 1.0E+04
1.0E+03
1.0E+02 Line of Equality 1.0E+01 1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
Measured E* Values (MPa)
Measured E* Values (MPa)
a) Arithmetic Scale b) Logarithmic Scale Figure 4 Predicted versus Measured E* based on the 1-37A model (level 1 binder data) 2.5E+04
1.0E+05
Predicted E* Values (MPa)
Predicted E* Values (MPa)
1-40D Model (Level 1 Binder Inputs) 2.0E+04 1.5E+04 1.0E+04 5.0E+03 0.0E+00 0.0E+00 5.0E+03 1.0E+04 1.5E+04
Line of Equality 2.0E+04 2.5E+04
Measured E* Values (MPa)
1-40D Model (Level 1 Binder Inputs) 1.0E+04
1.0E+03
1.0E+02
1.0E+01 1.0E+01
Line of Equality 1.0E+02
1.0E+03
1.0E+04
1.0E+05
Measured E* Values (MPa)
a) Arithmetic Scale b) Logarithmic Scale Figure 5 Predicted versus measured E* based on the 1-40D model (level 1 binder data)
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Se, (GPa), eavg (GPa), (1-Slope), Intercept (GPa)
The goodness-of-fit statistics shown in these figures were calculated with reference to the line of equality where Sy= standard deviation of the measured E* values about the mean measured; e=error between the predicted and measured E* values; Se=standard error (i.e., standard deviation of error); R2=coefficient of determination. Both Se/Sy and R2 are measures of the model accuracy (degree of scatter with reference to the line of equality) while Se and the average error (eavg) are measures of the bias in predictions. The line of equality is a line with slope constrained to unity and intercept constrained to zero. Thus, the overall bias in prediction can also be assessed by measuring how close are the slope and intercept of the unconstrained linear regression between measured and predicted E* values to 1 and 0, respectively (Ceylan et al. 2009). Figure 6 compares the overall bias measures for each model. All bias parameters shown in this figure are calculated based on the arithmetic values of E* rather than the logarithmic values. The model with the lowest overall bias is the one with all parameters shown in Figure 6 are close to zero. 5 4 3 2 1 0 -1 -2 -3 -4 -5
Se (GPa)
Level 3
eavg (GPa)
Level 1
1-37A Viscosity-Based Model
D Slope =(1-Slope)
Level 3
Intercept
Level 1
1-40D Gb*-Based Model
Figure 6 Bias in MEPDG E* prediction models for Idaho mixtures Figures 2 through 6 along with the goodness-of-fit statistics shown in the graphs reveal that the 1-37A model with level 3 binder characterization show the most accurate (R2=0.93, Se/Sy=0.26 in arithmetic scale) and least biased E* estimates. However, this model shows some bias and high scatter in the predictions at the high temperature values. The observed bias and scatter at the high temperature regime agree with several literature studies (Ceylan et al. 2009; Harran and Shalaby 2009; Schwartz 2005). On the other hand, the 1-40D model with levels 1 binder characterization resulted in E* estimates that are in excellent agreement with the measured data (R2=0.92, Se/Sy=0.29) while the 1-40D model with level 3 binder characterization showed lower accuracy (R2=0.61, Se/Sy=0.64). Despite the high accuracy of the 1-40D model with level 3 binder data, it showed vey high bias at the higher temperatures compared to the 1-37A model with level 3 binder data. It significantly over predicts E* at the high temperatures.
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With level 1 binder characterization, both E* models showed significant overall bias as shown in Figures 4, 5, and 6. The main reason for the high bias in the predicted E* can be attributed to the estimated A and VTS values from Gb* and δ calculated for the ASTM viscosity temperature relationship. The 1-37A model along with level 1 binder data was found to under predict E* values at low temperature and over estimates E* at higher temperatures. The E* estimates based on this model along with level 1 data showed the highest overall bias among all predictions as shown in Figure 6. It is suspected that the high bias in the estimated E* using both 1-37A and 1-40D models along with level 1 binder data and the low accuracy of the 1-37A model with level 1 binder data attributed to the fact that both models were calibrated based on the typical A and VTS values from viscosity testing of conventional binders rather than A and VTS estimated from superpave DSR testing. CONCLUSIONS A comparison between the MEPDG 1-37A η-based and Gb*-based dynamic modulus prediction models along with level 1 and level 3 binder characterization inputs have been completed for typical ITD HMA mixtures. Based on the analysis of E* data from 15 ITD Superpave mixtures with five different binder grades, mix aggregate gradation, and volumetric properties, the following conclusions were found: 1. The 1-37A η-based E* predictive model along with level 3 binder characterization produces reasonably accurate estimates of the dynamic modulus of ITD HMA mixtures although some bias in the E* estimates was found at the higher temperature values. 2. The 1-37A η-based E* predictive model along with level 1 binder characterization produced highly biased and less accurate estimates of the dynamic modulus of ITD mixes. This model was found to underestimate E* at low temperatures and overestimate E* values at high temperatures. 3. The 1-40D Gb*-based E* predictive model along with level 1 binder characterization produces excellent E* estimates at the lower temperatures. However, at the higher temperatures, this model shows a highly significant biased E* estimates for ITD HMA mixtures compared to the 1-37A model with level 3 binder data. 4. The 1-40D model along with level 3 binder data was found to overestimates E* especially at the high temperatures. The results of this study suggest that the 1-37A η-based E* model along level 3 binder characterization input data can be used to characterize ITD HMA mixes for MEDPG. It is not recommended to use MEPDG level 1 binder characterization for ITD mixes with level 3 E* prediction. Finally, MEPDG default A and VTS values for superpave PG grades should be revised based on binder G* and δ from DSR testing. If this is done, MEPDG E* predictive models should be recalibrated.
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ACKNOWLEDGEMENT This study is partially funded by the National Science Foundation, Award No. 0612630. AC mixes were provided by the Idaho Transportation Department (ITD). Authors would like to acknowledge the technical and financial support of ITD and NSF. REFERENCES Andrei, D., Witczak, M., & Mirza, W. (1999). “Development of a Revised Predictive Model for the Dynamic (Complex) Modulus of Asphalt Mixtures.” Appendix CC-4, NCHRP 1-37A, National Research Council, Washington, DC. ARA, Inc., ERES Consultants Division. (2004). “Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures.” NCHRP 1-37A Final Report, Transportation Research Board, National Research Council, Washington, DC. Bari, J., and Witczak, M. W. (2006) “Development of a New Revised Version of the Witczak E* Predictive Models for Hot Mix Asphalt Mixtures.” Journal of the Association of Asphalt Paving Technologies,” Vol. 75, pp. 381-417. Bari, J., and Witczak, M. W. (2007). “New Predictive Models for the Viscosity and Complex Shear Modulus of Asphalt Binders for Use with the Mechanistic-Empirical Pavement Design Guide.” In Transportation Research Record, Journal of the Transportation Research Board, No. 2001, Washington, DC, pp. 9-19. Birgisson, B., Sholar, G., and Roque, R. (2005). “Evaluation of Predicted Dynamic Modulus for Florida Mixtures.” In Transportation Research Record, Journal of the Transportation Research Board, No. 1929, Washington, DC, pp. 200-207. Ceylan, H., Schwartz, C. W., Kim, S., & Gopalakrishnan, K. (2009). “Accuracy of predictive Models for Dynamic Modulus of Hot-Mix Asphalt.” Journal of Materials in Civil Engineering, pp. 286-293. Dongre′, R., Myres, L., D’Angelo J., Paugh, C., and Gudimettla, J. (2005) “Field Evaluation of Witczak and Hirsh Models for Predicting Dynamic modulus of Hot-Mix Asphalt.” Journal of the Association of Asphalt Paving Technologies,” Vol. 74, pp. 381-434. Far, M., Underwood, B., Ranjithan, S., Kim, R., and Jackson, N. (2009). “Application of Artificial Neural Networks for Estimating Dynamic Modulus of Asphalt Concrete.” In Transportation Research Record, Journal of the Transportation Research Board, No. 2127, Washington, DC, pp 173-183. Harran, G., and Shalaby, A. (2009). “Improving the Prediction of the Dynamic Modulus of Fine-Graded Asphalt Concrete Mixtures at High Temperatures.” Canadian Journal of Civil Engineering , 36 (2), pp. 180-190. Schwartz, C. W. (2005). “Evaluation of the Witczak Dynamic Modulus Prediction Model.” Proc., 84th Annual Meeting of The Transportation Research Board (CD-ROM), Transportation Research Board, Washington, D.C. Witczak, M., El-Basyouny, M., & El-Badawy, S. (2007). “Incorporation of the New (2005) E* Predictive Model in the MEPDG.” NCHRP 1-40D Final Report, Arizona State University, Tempe, AZ.
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