TECHBRIEF LTPP Computed Parameter: 

Dynamic Modulus

FHWA Publication No.: FHWA-HRT-11-018.

FHWA Contact: Larry Wiser, HRDI-30, 202-493-3079, 

larry.wiser@dot.gov.

This document is a technical summary of the Federal 

Highway Administration (FHWA) report LTPP Computed 

Parameter: Dynamic Modulus, FHWA-HRT-10-035.

Introduction

The dynamic modulus, |E*|, is a fundamental property of 

asphalt concrete mixtures that defines strain response 

characteristics 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 (NCHRP) Project 1-37A.(1) The MEPDG 

uses a master curve and time-temperature shift factors 

in its internal computations of modulus. In the MEPDG, 

the master curve is constructed using a hierarchical 

structure of inputs ranging from estimates based on 

mixture volumetrics and binder tests to physical tests of 

a particular asphalt concrete mixture. Second, |E*| is one 

of the primary properties measured in the Asphalt Mixture 

Performance Test protocol that complements volumetric 

mix design with mechanical properties (the testing 

equipment is illustrated in figure 1). Third, |E*| is one of the 

fundamental linear viscoelastic material properties that can 

be used in advanced pavement response models based on 

viscoelasticity.

The emergence of |E*| as the main hot-mix asphalt (HMA) 

property in the MEPDG occurred long after the materials 

tables were developed and populated for the Long-Term 

Pavement Performance (LTPP) program. It is not practical 

to perform MEPDG Level 1 laboratory |E*| tests on material 

samples from LTPP test sections due to a lack of materials, 

budget limitations, and the absence of an accepted test 

method for field samples obtained from relatively thin 

Research, Development, and 

Technology

Turner-Fairbank Highway 

Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

www.tfhrc.gov

The Long-Term Pavement Performance 

(LTPP) program is a 20-year study of inservice pavements across North America. 

Its goal is to extend the life of highway 

pavements through various designs of 

new and rehabilitated pavement structures, using different materials and under 

different loads, environments, subgrade 

soil, and maintenance practices. LTPP was 

established under the Strategic Highway 

Research Program and is now managed 

by the Federal Highway Administration.
2

pavement structures. However, the LTPP 

database contains data that could be used 

to estimate the |E*| master curve and 

associated shift factors, which estimate |E*| 

at specific load durations and temperatures, 

and thereby develop inputs to the models 

contained in the MEPDG. 

Given the significance of |E*|, populating 

the LTPP database provides a valuable 

data source for the pavement community. 

Supplementing the full suite of material 

properties, performance history, traffic, and 

climate with |E*| estimates is advantageous 

in conducting MEPDG calibration, validation, 

and implementation.

Objective

The primary objective of this project was to 

develop estimates of the dynamic modulus of 

HMA layers on LTPP test sections following 

the models used in the MEPDG. These data will 

provide a means of linking MEPDG inputs (for 

HMA analysis) to known field performance as 

measured on LTPP test sections. As part of 

this project, existing models used to estimate 

|E*| values were evaluated, and additional 

models were developed based on the use of 

Artificial Neural Networks (ANNs). The models 

utilize readily available mixture and binder 

information to estimate dynamic modulus.

Analysis

An extensive and independent database 

was required to develop the ANN models 

and assess the predictive capabilities of 

each model. At the outset of the project, 

the most comprehensive material database 

available was one compiled through the 

efforts of Dr. Matthew Witczak at Arizona 

State University. The Witczak database was 

modified to include only materials for which 

measured binder shear modulus values, 

|G*|, were found. Additional databases were 

developed to include mixture information 

collected as part of the FHWA Mobile 

Asphalt Materials Testing Laboratory 

projects and by Transportation Pooled Fund 

Study TPF-5(019), Full-Scale Accelerated 

Performance Testing for Superpave and 

Structural Validation, as well information 

from North Carolina State University.(2) In 

addition to compiling a mixture database, 

binder properties were compiled into a 

similarly expansive database.

Existing predictive equations, including the 

original Witczak equation (NCHRP 1-37A), the 

modified Witczak equation (NCHRP 1-40D), 

the Hirsch model, and the law of parallel 

mixtures model, were evaluated for accuracy 

and potential bias.(1,2) This effort showed that, 

although each model has certain benefits, no 

single model is capable of highly accurate 

predictions over the complete range of 

necessary conditions. Furthermore, none of 

these existing predictive models could predict 

the |E*| values using only resilient modulus 

(Mr). As a result, the research team developed 

ANN models that yield reasonable and 

accurate predictions for the complete range 

of conditions needed. The most accurate ANN 

model was found to be the one that utilizes Mr

as its primary input parameter. Mr, formerly 

the material property of choice for asphalt 

pavement strength characterization, was 

available for a number of LTPP sites and has 

been widely collected by highway agencies. 

Figure 1. Dynamic Modulus Test Setup in the 

Asphalt Mixture Performance Tester.
3

Two additional ANN models were developed 

using mixture volumetric properties and 

a binder property as input variables. One 

model, the VV ANN, uses the binder viscosity 

and input frequency, whereas another 

model, the GV ANN, uses |G*|. The model 

hierarchy used to compute |E*| values from 

information contained in the LTPP database 

is shown in figure 2. The GV (|G*| and 

mixture volumetrics) and GV-PAR (pressure 

aging vessel (PAV) and rolling thin film oven 

(RTFO) aging) models, like the VV (viscosity 

and mixture volumetrics) and VV-Grade 

(binder grade) models, represent the same 

trained network, but they are identified 

by different terms due to the binder values 

used in each case. In the GV-PAR model, 

the binder values are based on two aging 

conditions, PAV and RTFO. In the VV-Grade 

model, the binder viscosity temperature 

susceptibility regression values are based on 

the specification grade of the asphalt binder, 

as recommended in the MEPDG.

Because the LTPP database has a range of data 

available for different test sites, a hierarchal 

approach was used to select the best model to 

use for the available data, as shown in figure 2.

Application

The LTPP database was populated with |E*| 

values at five temperatures and six frequencies 

by using the prioritized ANN models. More 

than 1,000 layers in the LTPP database now 

have |E*| estimate information available as a 

result of this study. These populated values will 

allow users of the LTPP database to develop a 

master curve for independent analysis or for 

Resilient Modulus Resilient Modulus

Viscosity and Volumetric 

Properties

Viscosity and Volumetric 

Properties

No Yes

Y

N Y

Prediction Models Prediction Models

Available Information and Temperature 

and Frequency of Interest

Available Information and Temperature 

and Frequency of Interest

|G*| and Volumetric Properties 

at Consistent Age

|G*| and Volumetric Properties 

at Consistent Age

Data Processing and 

Surrogate Models

Data Processing and 

Surrogate Models

t-T Shift 

Factor

VV MR

A-VTS

GV-PAR No Prediction 

Possible

t-T Shift 

Factor

PAR 

Model

Isochronal 

Analysis

Binder Grade and Volumetric 

Properties

Binder Grade and Volumetric 

Properties N Y

M-E PDG 

Values

VVGrade

|G*| and Volumetric Properties 

at Inconsistent Age

|G*| and Volumetric Properties 

at Inconsistent Age

N Y

GV

t-T Shift 

Factor

Isochronal 

Analysis

N

Resilient Modulus Resilient Modulus

Viscosity and Volumetric 

Properties

Viscosity and Volumetric 

Properties

No Yes

Y

N Y

Prediction Models Prediction Models

Available Information and Temperature 

and Frequency of Interest

Available Information and Temperature 

and Frequency of Interest

|G*| and Volumetric Properties 

at Consistent Age

|G*| and Volumetric Properties 

at Consistent Age

Data Processing and 

Surrogate Models

Data Processing and 

Surrogate Models

t-T Shift 

Factor

VV MR

A-VTS

GV-PAR No Prediction 

Possible

t-T Shift 

Factor

PAR 

Model

Isochronal 

Analysis

t-T Shift 

Factor

PAR 

Model

Isochronal 

Analysis

Binder Grade and Volumetric 

Properties

Binder Grade and Volumetric 

Properties N Y

M-E PDG 

Values

VVGrade

|G*| and Volumetric Properties 

at Inconsistent Age

|G*| and Volumetric Properties 

at Inconsistent Age

N Y

GV

t-T Shift 

Factor

Isochronal 

Analysis

t-T Shift 

Factor

Isochronal 

Analysis

N

Figure 2. Dynamic Modulus Prediction Model Hierarchy.
4

Researchers—This study was performed by Nichols Consulting Engineers, Chtd. and North 

Carolina State University under contract No. DTFH61-02-D-00139.

Distribution—This TechBrief is being distributed according to a standard distribution. Direct 

distribution is being made to the Divisions and Resource Center.

Availability—This TechBrief may be obtained from the FHWA Product Distribution Center 

by email to report.center@dot.gov, fax to 814-239-2156, phone to 814-239-1160, or online at 

http://www.fhwa.dot.gov/pavement/ltpp/index.cfm.

Key Words—LTPP Data, Dynamic modulus, M-E Pavement Design Guide, Artificial Neural 

Networks.

Notice—This document is disseminated under the sponsorship of the U.S. Department of 

Transportation in the interest of information exchange. The U.S. Government assumes no 

liability for the use of the information contained in this document. The U.S. Government does 

not endorse products or manufacturers. Trademarks or manufacturers’ names appear in this 

report only because they are considered essential to the objective of the document.

Quality Assurance Statement—The Federal Highway Administration (FHWA) provides 

high quality information to serve the Government, industry, and public in a manner that 

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November 2010 FHWA-HRT-11-018

HRDI-30/11-10(1M)E

input directly into the MEPDG. In addition, 

master curve sigmoidal parameters and 

temperature shift factors were computed and 

included in the population effort. These layers 

have binder data available at a combination of 

different aging conditions: unaged (original), 

RTFO-aged, PAV-aged, or field-aged. 

Additionally, user-friendly software was 

developed to facilitate dynamic modulus 

computations. The executable software can 

batch process data from a file to compute 

large quantities of dynamic modulus 

estimates in accordance with the model 

hierarchy. The program also has a feature 

that allows the user to manually input known 

parameters and select a model to use in 

computing dynamic modulus. 

As part of this project, seven new tables were 

added to the testing module (TST) of the LTPP 

database. These tables include the inputs 

used in the predictions, |E*| estimates at five 

temperatures and six frequencies, sigmoidal 

functions (size and shape of the master curve), 

and shift factors. These new tables were 

made available in Standard Data Release 24 

in January 2010. The software can be obtained 

at no cost from the LTPP Customer Support 

Service Center at ltppinfo@dot.gov or at 

202-493-3035.

References

1. Advanced Research Associates. (2004). 

Guide for Mechanistic-Empirical Design 

of New and Rehabilitated Pavement 

Structures, NCHRP 1-37A Project, National 

Cooperative Highway Research Program, 

National Research Council, Washington, DC.

2. Kim,Y.R., Underwood, B., Far, M.S., 

Jackson, N., and Puccinelli, J. (2010). LTPP 

Computed Parameter: Dynamic Modulus, 

Report No. FHWA-HRT-10-035, Federal 

Highway Administration, Washington, DC.