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Publication Number:
FHWAHRT10035
Date: September 2011 
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The dynamic modulus, E*, is a fundamental property that defines the strain response characteristics of asphalt concrete mixtures as a function of loading rate and temperature. The significance of this material property is threefold. First, it is one of the primary material property inputs in the Mechanistic Empirical Pavement Design Guide (MEPDG) and software developed by National Cooperative Highway Research Program Project 137A.^{(1,2)} MEPDG uses a master curve and timetemperature shift factors in its internal modulus computation.^{(1)} In MEPDG, the master curve is constructed using a hierarchical structure of inputs ranging from estimates based on mixture volumetrics and binder tests to fullscale mixture E* testing. E* is one of the primary properties measured in the Asphalt Mixture Performance Test protocol that complements the volumetric mix design.^{(3,4)} Additionally, it is one of the fundamental linear viscoelastic material properties that can be used in advanced pavement response models based on viscoelasticity.
Given the significance of E*, this study evaluated existing prediction models, developed new models, and populated the LongTerm Pavement Performance database to provide a valuable data source for the pavement community. Supplementing the full suite of material properties, performance history, traffic, and climate with E* estimates will be advantageous in conducting MEPDG calibration, validation, and implementation.
Jorge E. PagánOrtiz
Director, Office of Infrastructure
Research and Development
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Technical Report Documentation Page
1. Report No.
FHWAHRT10035 
2. Government Accession No.  3 Recipient's Catalog No.  
4. Title and Subtitle
LTPP Computed Parameter: Dynamic Modulus 
5. Report Date September 2011 

6. Performing Organization Code  
7. Author(s)
Y. Richard Kim, B. Underwood, M. Sakhaei Far, 
8. Performing Organization Report No. 1240.10 

9. Performing Organization Name and Address Nichols Consulting Engineers, Chtd. 
10. Work Unit No. (TRAIS) 

11. Contract or Grant No. DTFH6102D00139 

12. Sponsoring Agency Name and Address
TurnerFairbank Highway Research Center 
13. Type of Report and Period Covered
Final Report 

14. Sponsoring Agency Code


15. Supplementary Notes Prepared in cooperation with the U.S. Department of Transportation, the Contracting Officer’s Technical Representative (COTR) was Larry Wiser, LongTerm Pavement Performance Team. 

16. Abstract
The dynamic modulus, E*, is a fundamental property that defines the stiffness characteristics of hot mix asphalt (HMA) mixtures as a function of loading rate and temperature. In spite of the demonstrated significance of E*, it is not included in the current LongTerm Pavement Performance (LTPP) materials tables because the database structure was established before E* was identified as the main HMA property in the Mechanistic Empirical Pavement Design Guide (MEPDG). The objective of this study was to use readily available binder, volumetric, and resilient material properties in the LTPP database to develop E* estimates. This report provides a thorough review of existing prediction models. In addition, several models have been developed using artificial neural networks for use in this project. This report includes assessments of each model, quality control checks applied to the data, and the final structure and format of the dynamic modulus data added to the LTPP database. A program was also developed to assist in populating the LTPP database, and the details of the program are provided in 

17. Key Words
Dynamic modulus, MEPDG, LTPP, Hot mix asphalt, Artificial neural network (ANN) 
18. Distribution Statement
Document is available to the U.S. public through the National Technical Information Service, Springfield, VA, 22161 

19. Security Classification Unclassified 
20. Security Classification Unclassified 
21. No. of Pages 263 
22. Price 
Form DOT F 1700.7  Reproduction of completed page authorized 
SI* (Modern Metric) Conversion Factors
*SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380.
(Revised March 2003)
A  Regression intercept 

AASHTO  American Association of State Highway and Transportation Officials 
AC  Asphalt concrete 
ALF  Accelerated loading facility 
AMPT  Asphalt mixture performance tester 
ANN  Artificial neural network 
ANNACAP  Artificial Neural Networks for Asphalt Concrete Dynamic Modulus Prediction 
ASTM  American Society for Testing and Materials 
AVTS  Regression interceptregression slope of viscosity temperature susceptibility 
BBR  Bending beam rheometer 
CAM  Christensen Anderson Marasteanu 
DSR  Dynamic shear rheometer 
FHWA  Federal Highway Administration 
GGR  G* binder and gradationbased 
GPL  Generalized power law 
GPS  General Pavement Study 
GR  Gradation 
GV  Preliminary G*based model used in phase 1 of the study 
GV  G*based model using consistent aged binder data 
GVPAR  G*based model using inconsistent aged binder data of pressureaging vessel and rolling thin film oven aging conditions 
HMA  Hot mix asphalt 
IDT  Indirect tensile 
LOE  Line of equality 
LTOA  Longterm oven aging 
LTPP  LongTerm Pavement Performance 
LVE  Linear viscoelastic 
MEPDG  Mechanistic Empirical Pavement Design Guide 
NCDOT  North Carolina Department of Transportation 
NCHRP  National Cooperative Highway Research Program 
NCSU  North Carolina State University 
NMSA  Nominal maximumsized aggregate 
pANN  Pilot artificial neural network 
PAV  Pressureaging vessel 
PG  Performance grade 
QC  Quality control 
R&BT  Ring and ball temperature 
RTFO  Rolling thin film oven 
SHRP  Strategic Highway Research Program 
SPS  Specific Pavement Study 
STOA  Shortterm oven aging 
TFHRC  TurnerFairbank Highway Research Center 
TP  Test protocol 
VFA  Percentage of voids filled with asphalt 
ViscGR  Viscositygradation model 
ViscV  Viscosityvolumetric model 
VMA  Percentage of voids in mineral aggregate 
VTS  Slope of temperature susceptibility relationship 
VV  Viscositybased model 
VVgrade  Viscositybased model using specification grade of the asphalt binder as recommended in the Mechanistic Empirical Pavement Design Guide 
WLF  WilliamsLandelFerry Model 
WRI  Western Research Institute 
E*  Dynamic modulus 

G*  Dynamic shear modulus 
M_{R}  Resilient modulus 
tT  Timetemperature shift factors 
ρ_{200}  Percentage of aggregate passing #200 sieve 
ρ_{4}  Percentage of aggregate retained #4 sieve 
ρ_{3/8}  Percentage of aggregate retained ^{3}/_{8}inch sieve 
ρ_{¾}  Percentage of aggregate retained ¾inch sieve 
V_{a}  Percentage of air void 
V_{beff}  Percentage of effective asphalt content (by volume of mix) 
f  Loading frequency 
η  Binder viscosity 
G*_{b}  Dynamic shear modulus of asphalt binder 
δ_{b}  Binder phase angle associated with G*_{b} 
f_{s}  Dynamic shear frequency 
T  Temperature 
T_{R}  Temperature in Rankine scale 
E*_{m}  Dynamic modulus of hot mix asphalt (pounds per square inch) 
Pc  Aggregate contact volume 
ø  Phase angle of hot mix asphalt 
G*_{g}  Dynamic shear modulus of asphalt binder at the glassy state 
V_{mix}  Air voids by volume of the mix 
ω  Angular frequency in radians per second 
t  Time 
f_{R}  Reduced frequency 
m_{e}  Fitting coefficient 
k  Fitting coefficient 
δ  Binder phase angle (degree) 
G_{mb}  Bulk specific gravity 
G_{mm}  Maximum specific gravity 
SSE  Sum of squared error 
Sy  Standard deviation 
Se  Standard error 
σ_{a}  Applied stress 
ε_{r}  Recoverable strain 
ν  Poisson's ratio 
P  Applied load 
U  Recoverable horizontal displacement 
V  Recoverable horizontal displacement 
k_{1}  Constant value in NCHRP 128 elastic solution for Poisson's ratio 
k_{2}  Constant value in NCHRP 128 elastic solution for Poisson's ratio 
k_{3}  Constant value in NCHRP 128 elastic solution for Poisson's ratio 
k_{4}  Constant value in NCHRP 128 elastic solution for Poisson's ratio 
E  Young's modulus 
D  Compliance 
R  Radius of specimen 
χ  Horizontal distance from center of specimen 
E'  Storage modulus 
E"  Loss modulus 
E_{∞}  Equilibrium modulus 
ω_{r}  Angular reduced frequency 
E_{i}  Modulus of the ith Maxwell element 
ρ_{i}  Relaxation time of the ith Maxwell element 
A_{kj}  Matrix element in the kth row and jth column of matrix A 
B_{k}  Vector element in the kth row of vector B 
τ_{j}  Retardation time of the jth Voigt element determined a priori 
t_{k}  Time of interest 
α_{1}  Shift factor coefficient 1 
α_{2}  Shift factor coefficient 2 
α_{3}  Shift factor coefficient 3 
(logE*_{ANN})_{i}  Logarithm of the modulus determined from the ANN models at a particular temperature frequency combination 
(logE*_{fit})_{i}  Logarithm of the modulus determined from the optimized sigmoidal fit 
(logE*_{avg})_{i}  Logarithm of the average modulus determined from the ANN models for a given layer 
A  Intercept of temperature susceptibility relationship 
T_{critical}  Temperature in Rankine at which the viscosity is exactly equal to 2.7 x 10^{12} cP (0.0027 x 10^{12} Pas) 
PEN  Penetration number at given test temperature 
ν  Kinematic viscosity (cSt) 
ρ  Density (oz/in^{3} (g/cm^{3})) 
a_{T}  Timetemperature shift factor 
ω_{T}  Frequency at the physical temperature 
ω_{TR}  Reduced frequency of ω_{T} at the reference temperature 
ω_{c}  Fitting coefficient 
C_{1}  Fitting coefficient 
C_{2}  Fitting coefficient 
C_{3}  Fitting coefficient 
S(t)  Beam stiffness 
D_{0}  Regression coefficient 
D_{1}  Regression coefficient 
D*  Dynamic axial creep compliance 
∂G*/∂T  Derivative G* with respect to time 
E(t)  Uniaxial relaxation modulus 
E'(ω)  Storage modulus 
D(t)  Creep compliance 
K_{T}  Temperature factors 
K_{ω}  Frequency factors 
β_{1}  Second order polynomial coefficient 
β_{2}  Second order polynomial coefficient 
β_{3}  Second order polynomial coefficient 
f(T)  Transfer function 
Value of the nodes at the first hidden layer  
Transferred value of the nodes at the first hidden layer  
Value of the nodes at the second hidden layer  
Transferred value of the nodes at the second hidden layer  
Value of output node l (M_{R} ANN)  
Value of the output node (GV ANN and VV ANN)  
Transferred value of the output node l, normalized output (M_{R} ANN)  
Transferred value of the output node, normalized output (GV ANN and VV ANN)  
P_{i}  Input variables 
Weight factors for the first hidden layer  
Weight factors for the second hidden layer  
Bias factors for the first layer  
Bias factors for the second layer  
Bias factors for the outer layer (M_{R} ANN)  
B^{0}  Bias factor for the outer layer (GV ANN and VV ANN) 
(Sig_{l})_{max}  Maximum value for sigmoidal coefficient l in the trained data (M_{R} ANN) 
(Sig_{l})_{min}  Minimum value for sigmoidal coefficient l in the trained data (M_{R} ANN) 
log E*_{max}  Maximum log E* of the trained data (GV ANN and VV ANN) 
log E*_{min}  Minimum log E* of the trained data (GV ANN and VV ANN) 
Normalized value for given input variable, i  
MIN_{i}  Minimum value of variable, i, in calibration dataset 
MAX_{i}  Maximum value of variable, i, in calibration dataset 
Sig_{1}  First sigmoidal function coefficient 
Sig_{2}  Second sigmoidal function coefficient 
Sig_{3}  Third sigmoidal function coefficient 
Sig_{4}  Fourth sigmoidal function coefficient 
Resilient modulus at 41° F (5 °C), MPa  
Resilient modulus at 77° F (25 °C), MPa  
Resilient modulus at 104° F (40 °C), MPa  
R  Coefficient in WLF function 
E_{a}  Coefficient in WLF function 
t_{R}  Inverse of reduced frequency of loading (Hz) 
δ  Sigmoidal function fitting coefficient 
β  Sigmoidal function fitting coefficient 
D'  First vector component of D* 
D"  Second vector component of D* 
V_{be}  The effective volume of the binder 
The dynamic modulus, E*, is a fundamental property that defines the stiffness characteristics of hot mix asphalt (HMA) mixtures as a function of loading rate and temperature. Given the significance of E* in pavement engineering, this project was undertaken to provide the LongTerm Pavement Performance (LTPP) database with E* estimates using material properties currently available for LTPP test sections. In this report, existing models used to estimate E* values and additional models that have been developed based on the use of artificial neural networks (ANNs) were evaluated. Using the results of the model evaluation, the research team developed a model selection hierarchy and populated the LTPP database with E* estimates at five temperatures and six frequencies. It also developed shift factors and sigmodial functions that can be used to construct mastercurves.
The seven models identified at the outset of this project as potentially suitable for the task at hand include the following:
The existing predictive models (1–4 above) are collectively referred to in this report as “closedform models.” Specific comparisons are drawn regarding their forms and required input parameters.
An extensive independent database was required to develop the ANN models and to fairly assess the predictive capabilities of each model in the list of possible models. At the outset of the project, the most comprehensive material database available was compiled through the efforts of Dr. Matthew Witczak at Arizona State University. Witczak's database consists of 7,400 data points from 346 mixtures, all of which were used in the calibration of the NCHRP 140D predictive models.^{(5)} A smaller subset of the data (2,750 data points from 205 mixtures) was also used in developing the NCHRP 137A predictive model.^{(2)} In addition, the database contains G* data obtained from different materials and aging conditions. Through this research project, the Witczak database was combined with mixtures from other national projects and efforts undertaken at North Carolina State University (NCSU). The expanded mixture database currently includes 22,505 data points.
In addition to a mixture database, binder properties were compiled into a similarly expansive database. Substantial efforts have been expended to develop the appropriate binder data processing techniques. The required processing varied depending on the type of data available (i.e., G*, viscosity, or binder grade). Only the critical points are presented in this report, and the details are provided in the appendices.
Closedform models were compared using datasets that were not used in the calibration of the respective models. It was found that the law of mixtures parallel model shows a significant bias, but the Hirsch model shows reasonable predictions, except for insensitivity under extreme conditions.^{(7,6)} For the verification database, the Hirsch model shows slightly better statistical predictions than either of the Witczak models.^{(6)} This finding, along with other statistical analyses, led the research team to adopt the Hirsch model input parameters into the viscositybased (VV) and G*based ANN models.
Comparisons between the ANN models and the closedform models were made. Overall, the ANN models provide better predictability than any of the closedform solutions. Additionally, the ANN models are more sensitive to the input parameters. Based on these findings, the ANN models were chosen to populate the LTPP database moduli values. The primary advantage of using ANN modeling over statistical regression techniques is that the functional form of the relationship is not needed a priori. Considering that many variables affect E* values and their interactions, the ANN technique may capture complicated nonlinear relationships between E* and other mixture variables better than regression analysis.
Early in the project, concerns arose because the database combined moduli that had been measured using two different methods, the American Association of State Highway and Transportation Officials (AASHTO) test protocol (TP)62 and the asphalt mixture performance tester (AMPT) protocol.^{(8,9,4)} A study of the available databases revealed that the mixtures that are tested according to the AASHTO TP62 protocol tend to yield higher moduli values than similar mixtures tested using the AMPT protocol. Statistical analysis to assess the significance of the difference was not performed, but the two data ranges tend to overlap, suggesting a lack of statistical significance in their differences. A limited experimental study wherein the modulus of a single mixture was measured using the two protocols is also discussed. The study shows a statistically significant difference of about 12 percent in the measured moduli across all studied temperatures and frequencies. However, in light of the fact that both protocols are readily available and that neither of the available protocols can be discounted without a more comprehensive and controlled experimental program, the decision was made to include all available data from both the AMPT protocol and AASHTO TP62 in the calibration process.
Details of the three ANN models, including the required input parameters, model structure, and input range, are presented in this report. The models are prioritized based on engineering judgment and statistical analysis. From this prioritization, a decision tree was developed for populating E* of the LTPP layers (see figure 1). A user may follow this decision structure and determine the best model to use for the available input parameters.
Figure 1. Illustration. Modulus prediction model decision tree.
At the end of phase I of this study, it was discovered that some State agencies report effective binder content by mass instead of by volume (i.e., gravimetric instead of volumetric). As a result, there were concerns about the use of a predictive model based on the volumetric properties of the asphalt mixtures. After reviewing the database and carrying out some volumetric computations, volumetricbased properties could still be calculated when gravimetric quantities were reported. Details of how these volumetricbased quantities were computed are provided in this report.
A key component to the prediction of moduli values is ensuring that the predicted values are rational and acceptable. To meet this criterion for the finalized ANN predictions, a set of quality control (QC) checks on both the input parameters and model predictions were performed. In total, seven QC checks were developed, one for the inputs and six for the modulus predictions, and are described in detail in section 6.2 of this report. Executable software, Artificial Neural Networks for Asphalt Concrete Dynamic Modulus Prediction (ANNACAP), was developed as part of this project for this purpose. The software can be run for individual layers (manual mode) or all layers simultaneously (batch mode). An unpublished manual for the software is provided in appendix E of this report.
Statistics for the population effort are also presented in this report. The LTPP database contains information for 1,806 layers that meet the criteria established for this project. These layers have binder data available at a combination of different aging conditions, including unaged or originalaged, rolling thin film oven (RTFO)aged, pressureaging vessel (PAV)aged, and fieldaged. For the fieldaged data, 2,223 records are available because some layer properties have been measured at different dates. The total resulting number of records is 7,641. Using the combined ANN models and requisite internal QC checks, modulus values are predicted for 363 records/layers in the originalaged level, 469 records/layers in the RTFOaged level, 1 record/layer in the PAVaged level, and 503 records in the fieldaged level. Combined, these numbers translate to predictions for 17.5 percent of the total number of records available. However, these records are distributed in such a way that a higher percentage of the layers has some sort of valid prediction. Of the 1,806 layers in the database, 1,010 layers, or 56 percent, have a modulus prediction for some aging condition. Of these 1,010 layers, 615 layers, or 34 percent of the total 1,806 layers, have reasonable predictions (i.e., an “A” grade), and 89 layers, or 4.9 percent of the total 1,806 layers, have unreasonable predictions (i.e., an “F” grade). The remaining 306 layers, representing 17 percent of the 1,806 layers, have questionable predictions (i.e., a “C” grade). Thus, the total percentage of layers with a completely valid or questionable prediction is 51 percent. The quality grading system referenced is different from the standard record status definition used in the LTPP database.^{(10)} The research team established strict QC checks to ensure that only the highest quality data were assigned an “A” grade. The data that did not achieve an “A” grade were not considered unusable data. All predictions are included in the database so that users can determine the data that are suitable for their needs. In addition, the Federal Highway Administration (FHWA) can revise the criteria used for the quality checks as deemed appropriate based on the opinions of its experts.
Topics: research, infrastructure, pavements and materials Keywords: research, infrastructure, pavements and materials, Dynamic modulus, MEPDG, LTPP, Hot mix asphalt, Artificial neural network (ANN) TRT Terms: research, facilities, transportation, highway facilities, roads, parts of roads, pavements Updated: 11/03/2011
