LINEAR VISCOELASTIC CHARACTERISTICS OF
MICHIGAN ASPHALT MIXTURES AND THE EFFECT
OF SAMPLE SIZE ON MATERIAL PROPERTIES
By
Anas Jamrah

A THESIS
Submitted to
Michigan State University
in partial fulfilment of the requirements
for the degree of
Civil Engineering - Master of Science
2013

ABSTRACT
LINEAR VISCOELASTIC CHARACTERISTICS OF MICHIGAN ASPHALT MIXTURES
AND THE EFFECT OF SAMPLE SIZE ON MATERIAL PROPERTIES
By
Anas Jamrah
The Mechanistic-Empirical Pavement Design Guide (M-E PDG) is becoming the stateof-the-practice in both newly constructed and rehabilitated pavement designs. A number of
different material inputs are required by the M-E PDG, and accurate measurement of these inputs
is crucial for the accuracy of the distress predictions. The main objective of the research study
presented in this thesis was to investigate linear viscoelastic characteristics of asphalt mixtures
and binders commonly used in Michigan. This is important for implementation of the M-E PDG
in Michigan and for accurate prediction of flexible pavement distresses. The second objective
was to develop analytical models in efforts to provide improved |E*| predictions of asphalt
mixtures used in the State of Michigan. For this, the Modified Witczak model was locally
calibrated. In addition, an Artificial Neural Network (ANN) model was developed and trained
for Michigan asphalt mixtures. Another objective of this study was to investigate the
Representative Volume Element (RVE) requirement for complex (dynamic) modulus (|E*|) of
asphalt mixtures. Small thin mixture beam (TBM) specimens (0.5”x0.25”x4.5”) were tested
using the Bending Beam Rheometer (BBR) testing machine to obtain the Creep Compliance
(D(t)). This study showed that there is a trend in D(t) values obtained from the BBR, but on the
other hand; the factor between |E*|-based and TBM-based D(t) values was not consistent and
ranged between 1.5 and 4 factors.

TO MY FAMILY...

iii

ACKNOWLEDGEMENTS
First and foremost, I would like to thank my advisor, Dr. M. Emin Kutay for his support,
guidance, and patience throughout my graduate studies. Dr. Kutay has always provided me with
the guidance and support that I needed. I consider myself very lucky to have had him as my
advisor.
I would also like to thank the other committee members of my advisory committee, Dr.
Neeraj Buch and Dr. Karim Chatti. Their knowledge and support has been very important
throughout this study. Special thanks are due to Dr. Syed Haider, and Dr. Gilbert Baladi for all
the research guidance and support.
I would also like to thank the Michigan Department of Transportation (MDOT) for their
financial support of this study. In addition, the efforts of and the comments made by the MDOT
research advisory panel members are sincerely appreciated.

iv

TABLE OF CONTENTS

LIST OF TABLES ..................................................................................................................... vii
LIST OF FIGURES ................................................................................................................... viii
1. INTRODUCTION. .................................................................................................................1
1.1 Objectives ............................................................................................................................ 2
1.2 Outline................................................................................................................................. 3
2. LITERATURE REVIEW ..................................................................................................... 5
2.1 Introduction and background on |E*| test .......................................................................... 5
2.2 Complex modulus (E*) ........................................................................................................ 6
2.3 Development of |E*| master curve ...................................................................................... 8
2.4 Relevance of |E*| to M-E PDG ........................................................................................ 12
2.4.1 Introduction ............................................................................................................. 12
2.4.2 |E*| as a design input in M-E PDG ......................................................................... 15
2.5 Dynamic modulus |E*| prediction models ....................................................................... 18
2.5.1 Original Witczak model (Andrei et al. 1999) – OW (NCHRP 1-37A) ................... 19
2.5.2 Modified Witczak model (Bari 2005) – MW (NCHRP 1-40D) ............................. 20
2.5.3 Hirsch model (Christensen et al. 2003) – HM ........................................................ 21
2.5.4 Law of mixtures parallel model (Al-Khateeb Model) ............................................ 23
2.5.5 Summary of inputs for |E*| prediction models ....................................................... 23
2.6 Sample geometry and Representative Volume Element (RVE) for |E*| ........................... 24
3. RESEARCH METHODOLOGY....................................................................................... 28
3.1 Introduction ...................................................................................................................... 28
3.2 Materials used .................................................................................................................. 28
3.2.1 Asphalt mixtures ..................................................................................................... 28
3.2.2 Asphalt binders ....................................................................................................... 29
3.3 Laboratory testing of materials collected ........................................................................ 29
3.3.1 Details of laboratory |E*| tests ................................................................................ 29
3.3.2 Details of laboratory |G*| tests ................................................................................ 30
3.4 Investigation of the Representative Volume Element (RVE) requirement for dynamic
modulus |E*| of asphalt mixtures using Thin Beam Mixtures (TBMs) ........................................ 32
4. LABORATORY TESTING: RESULTS & DISCUSSION ............................................. 35
4.1 Complex modulus |E*| testing of asphalt mixtures .......................................................... 35
4.1.1 Summary of |E*| values based on MDOT mix designation for each region ........... 39
4.1.2 Comparison of variation in |E*| master curves based on MDOT mix designation.. 39
4.1.3 Comparison of variation in |E*| master curve for HMA and WMA asphalt mixtures
43
4.2 Dynamic shear modulus |G*| testing of asphalt binders ................................................. 45
4.2.1 Comparison of variation in |G*| master curves based on binder PG grade ............. 46
v

5. |E*| PREDICTION MODELS: RESULTS AND DISCUSSION ..................................... 50
5.2 Evaluation and calibration of the Modified Witczak’s equation for Michigan asphalt
mixtures ........................................................................................................................................ 50
5.3 Validation of the calibrated Modified Witczak |E*| predictive model for MDOT asphalt
mixtures ........................................................................................................................................ 55
5.4 Evaluation of the ANNACAP software for predicting |E*| of MDOT mixtures ............... 57
5.5 Development and validation of a new ANN-based |E*| predictive model trained for
Michigan asphalt mixtures ........................................................................................................... 58
5.5.1 Structure of the ANN .............................................................................................. 59
5.5.2 Training the ANN ................................................................................................... 61
6. INVESTIGATION OF SAMPLE GEOMETRY & RVE REQUIREMENT FOR |E*|
USING THIN BEAM MIXTURES (TBMs) ............................................................................ 66
6.1 Materials Used ................................................................................................................. 66
6.2 Bending Beam Rheometer (BBR) testing on Thin Beam Mixtures (TBMs) ..................... 67
6.3 Results and Discussion .................................................................................................... 69
7. CONCLUSIONS & RECOMMENDATIONS ................................................................. 75
APPENDICES ............................................................................................................................ 77
APPENDIX A: VOLUMETRIC PROPERTIES AND AGGREGATE GRADATION OF THE
TESTED ASPHALT MIXTURES. ................................................................................................. 78
APPENDIX B: A LIST OF ASPHALT MIXTURE SAMPLES TESTED IN THIS STUDY
ALONG WITH THE CORRESPONDING AIR VOID LEVEL OF EACH SAMPLE ................... 85
APPENDIX C: |E*| MASTER CURVES OF THE TESTED ASPHALT MIXTURES
GROUPED BASED ON THE MDOT MIX DESIGNATION ..................................................... 93
APPENDIX D: |G*| MASTER CURVES GROUPED BASED ON THE PG GRADE ......... 102
REFERENCES ......................................................................................................................... 108

vi

LIST OF TABLES

Table 2.1: A and VTS values reported in Birgisson et al. (2005). ................................................ 14
Table 2.2: Parameters used in different |E*| predictive models. ................................................... 23
Table 4.1: HMAs tested for |E*| master curve............................................................................... 34
Table 4.2: HMAs tested for |E*| master curve (GGSP and LVSP Mixtures) ................................ 36
Table 4.3: HMAs tested for |E*| master curve (SUPERPAVE) – Mixtures that do not follow
MDOT specifications but are permitted to be used. ...................................................................... 37
Table 4.4: HMAs tested for |E*| master curve (GGSP and LVSP Mixtures) - Mixtures that do not
follow MDOT specifications but are permitted to be used. .......................................................... 37
Table 4.5: Summary of |E*| values for different asphalt mixture types in NGBSU Regions ....... 40
Table 4.6: Summary of |E*| values for different asphalt mixture types in the Metro Region ....... 41
Table 4.7: Summary of |E*| values for different asphalt mixture types in Superior Region ......... 42
Table 4.8: List of binder PGs tested in this study.......................................................................... 46
Table 5.1: Comparison between coefficients used in the original and optimized models. ........... 55
Table 6.1: List of TBMs tested along with their volumetric properties and NMAS ..................... 68
Table A.1: Volumetric properties and aggregate gradation of the tested asphalt mixtures. .......... 79
Table B.1: List of HMAs tested and their air voids……………………………………………...86

vii

LIST OF FIGURES

Figure 2.1: Illustration of cyclic loading of an asphalt specimen and corresponding strain response
(for interpretation of the references to color in this and all other figures, the reader is referred to the
electronic version of this thesis). ..................................................................................................... 7
Figure 2.2: Unshifted (original) |E*| data at different temperatures versus frequency. ................ 10
Figure 2.3: Illustration of shifted |E*| data at different temperatures versus reduced frequency to
obtain the master curve. ................................................................................................................. 10
Figure 2.4: Shift factor (a(T)) coefficients at different temperatures for an asphalt mixture. (a) |E*|
master curve. (b) Shift factor polynomial curve. ........................................................................... 11
Figure 2.5: Illustration of two typical |E*| mastercurves and expected fatigue and rutting

performance trends for these |E*| master curves........................................................................... 17
Figure 3.1: Asphalt Mixture Performance Tester (AMPT) ........................................................... 29
Figure 3.2: Illustration of the Dynamic Shear Rheometer (DSR) testing machine ....................... 30

Figure 3.3: Illustration of stress-strain relationship of asphalt binders when they are subjected to
cyclic shear load ............................................................................................................................ 31
Figure 3.4: Illustration of Thin Beam Mixture sample preparation and testing. ........................... 33
Figure 4.1: Dynamic Modulus master curves of all tested asphalt mixture specimens. The plot in
log-log scale is to show the differences in low frequency/high temperature, and the plot in linearlog scale is to show the differences in high frequency/low temperature. ...................................... 38
Figure 4.2: |E*| master curves of four 3E3 mixtures, 3 of which (26* mixes) are from same region.
NGBSU = North, Grand, Bay, Southwest and University Regions. ............................................. 43

viii

Figure 4.3: WMA versus HMA |E*| master curves for (3E30) MDOT mixture .......................... 44
Figure 4.4: WMA versus HMA |E*| master curves for (LVSP) MDOT mixture ......................... 44
Figure 4.5: Aggregate gradation of WMA and HMA mixtures ((LVSP) MDOT mixture) .......... 45
Figure 4.6: |G*| Master curves of seven different PG64-28 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions ................................................................................................ 47
Figure 4.7: Illustration of the effect of variation in |G*| and  on Longitudinal cracking predictions
in the M-E PDG software. ............................................................................................................. 48
Figure 4.8: Illustration of the effect of variation in |G*| and  on alligator cracking predictions in
the M-E PDG software. ................................................................................................................. 48
Figure 4.9: Illustration of the effect of variation in |G*| and  on IRI predictions in the M-E PDG
software. ........................................................................................................................................ 49
Figure 4.10: Illustration of the effect of variation in |G*| and  on rutting predictions in the M-E
PDG software. ............................................................................................................................... 49
Figure 5.1: The modified Witczak’s equation developed as part of the NCHRP 1-40D. The plot
shows the predicted versus measured values before calibration for MDOT mixtures. Se/Sy =
2
2
0.5084, R = 0.7881 (linear-linear plot), and Se/Sy = 0.446, R = 0.8369 (log-log plot). ............ 53
Figure 5.2: The modified Witczak’s equation developed as part of the NCHRP 1-40D. The plot
shows the predicted versus measured values after calibration for MDOT mixtures. S e/Sy = 0.3029,
2

2

R = 0.9248 (linear-linear plot), and Se/Sy = 0.2053, R = 0.965 (log-log plot). ......................... 54
Figure 5.3: The modified Witczak’s equation developed as part of the NCHRP 1-40D. The plot
shows the predicted versus measured values for MDOT mixtures using the calibrated coefficients.
2
Se/Sy = 0.3749, R = 0.885 (log-log plot). .................................................................................... 56

ix

Figure 5.4: Predicted versus measured values for MDOT mixtures using the ANNACAP software:
(a) Linear-Linear plot, (b) Log-Log plot. ...................................................................................... 57
Figure 5.5: Structure of the ANN model. ...................................................................................... 60
Figure 5.6: Error versus the epochs in the ANN model developed in this study .......................... 63
Figure 5.7: Predicted versus measured |E*| values for Training, Validation and Testing datasets as
well as all the data (for mixtures used during development of the model). .................................. 64
Figure 5.8: Predicted versus measured values for MDOT mixtures using the MSU-ANN model for
mixtures not used during development of the model .................................................................... 65
Figure 6.1: 3-point testing concept on asphalt mixtures. ............................................................... 67
Figure 6.2: Comparison between |E*|-based D(t) values and TBM-based D(t) values for 25.0mm
NMAS. ........................................................................................................................................... 71
Figure 6.3: Comparison between |E*|-based D(t) values and TBM-based D(t) values for 19.0mm
NMAS. ........................................................................................................................................... 71
Figure 6.4: Comparison between |E*|-based D(t) values and TBM-based D(t) values for 12.5mm
NMAS. ........................................................................................................................................... 72
Figure 6.5: Comparison between |E*|-based D(t) values and TBM-based D(t) values for 9.5mm
NMAS……………………………………………………………………………………………...72
Figure 6.6: Comparison between |E*|-based D(t) values and TBM-based D(t) values for all
mixtures and NMASs……………………………………………………………………………. 73
Figure C.1: Dynamic modulus |E*| master curves for 3E30 mixes……………………….....….94
Figure C.2: Dynamic modulus |E*| master curves for 3E3 mixes……………………………. ... 94

x

Figure C.3: Dynamic modulus |E*| master curves for 3E10 mixes……………………………...95
Figure C.4: Dynamic modulus |E*| master curves for 4E30 mixes……………………………...95
Figure C.5: Dynamic modulus |E*| master curves for 4E3 mixes……………………………….96
Figure C.6: Dynamic modulus |E*| master curves for 4E10 mixes……………………………...96
Figure C.7: Dynamic modulus |E*| master curves for 4E1 mixes……………………………….97
Figure C.8: Dynamic modulus |E*| master curves for 5E10 mixes………………………. ......... 97
Figure C.9: Dynamic modulus |E*| master curves for 5E03 mixes..…………………. ............... 98
Figure C.10: Dynamic modulus |E*| master curves for 5E3 mixes..………………. ................... 98
Figure C.11: Dynamic modulus |E*| master curves for 5E1 mixes..………………. ................... 99
Figure C.12: Dynamic modulus |E*| master curves for 2E3 mixes..………………. ................... 99
Figure C.13: Dynamic modulus |E*| master curves for 5E30 mixes..………………. ............... 100
Figure C.14: Dynamic modulus |E*| master curves for ASCRL mixes………………...............100
Figure C.15: Dynamic modulus |E*| master curves for GGSP mixes………………. ................101
Figure C.16: Dynamic modulus |E*| master curves for LVSP mixes..………………. ...............101
Figure D.1: |G*| master curves of different PG70-28P binders. NGBSU = North, Grand, Bay,
Southwest and University Regions..………………. ................................................................... 103

xi

Figure D.2: |G*| master curves of different PG64-28 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions..……………. ....................................................................... 103
Figure D.3: |G*| master curve of a PG70-28 binder. NGBSU = North, Grand, Bay, Southwest and
University Regions..……………. ............................................................................................... 104
Figure D.4: |G*| master curves of different PG64-34P binders. NGBSU = North, Grand, Bay,
Southwest and University Regions..……………. ....................................................................... 104
Figure D.5: |G*| master curves of different PG64-22 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions..……………. ....................................................................... 105
Figure D.6: |G*| master curves of different PG70-22P binders…………………………… ...... 105
Figure D.7: |G*| master curves of different PG58-22 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions..…………… ........................................................................ 106
Figure D.8: |G*| master curves of different PG58-28 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions..…………… ........................................................................ 106
Figure D.9: |G*| master curves of different PG58-22 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions. …………… ........................................................................ 107
Figure D.10: |G*| master curves of different PG58-34 binders………………………………...107

xii

INTRODUCTION
Complex (Dynamic) Modulus |E*| is a unique viscoelastic material property that defines
the stress-strain relationship of asphalt mixtures when they are loaded in a cyclic mode. The |E*|
is also used as a measure of stiffness and to compute the primary response (i.e., response to low,
non-damaging stress) of asphalt pavements at different temperatures and loading rates. In
addition, |E*| is directly related to the expected pavement performance (i.e., rutting and fatigue
cracking) in the field. The Mechanistic-Empirical Pavement Design Guide (M-E PDG) pavement
design software developed under the NCHRP Project 1-37A is becoming the state-of-thepractice in both newly constructed and rehabilitated pavement designs. The M-E PDG utilizes
semi-mechanistic and semi-empirical models to predict the distresses such as fatigue cracking,
rutting and thermal cracking in asphalt pavements. The design software determines the modulus
of asphalt materials at different temperatures and loading rates from a “master curve” generated
to combine the effects of frequency and temperature on |E*|. Once |E*| values are measured at
different temperatures (T) and loading frequencies (f), the |E*| master curve is obtained using the
time-temperature superposition (TTS) principle (Kim 2009). Laboratory test data at different
temperatures and loading frequencies are shifted with respect to time to form a good sigmoid fit
to the |E*| data. This constructed master curve describes the time (and frequency) dependency of
the material. The amount of shifting for each test data at each temperature describes the
temperature dependency of the material (NCHRP 9-19 2005). Development of |E*| master curve
is very useful because once the sigmoid coefficients, shift factor coefficients, and reference
temperature are known, |E*| at any temperature (T) and frequency (f) can be computed.

1

A number of different material inputs are required by the M-E PDG, and accurate
measurement of these inputs is crucial for the accuracy of the distress predictions. Many State
Departments of Transportation (DOTs) (including the Michigan Department of Transportation
(MDOT)) do not have a testing program to measure certain key inputs required by the M-E PDG.
In flexible (asphalt) pavement design, the most important and hard-to-obtain material inputs for
the Level 1 analysis are: (i) complex (dynamic) modulus (|E*|) master curve of asphalt mixture,
(ii) complex (dynamic) shear modulus (|G*|) master curve of asphalt binder, (iii) Indirect Tensile
(IDT) Strength and creep compliance (D(t)) of the asphalt mixture. The |G*| master curve, which
defines the linear viscoelastic property of an asphalt binder, is required by both Level 1 and
Level 2 analyses of the M-E PDG. In Level 1 analysis, |G*| is primarily used in asphalt aging
models, whereas in Level 2, it is used in both aging models and in predicting the |E*| master
curve of the asphalt mixture using Witczak’s predictive equation. It is noted that Witczak’s
equation predicts the |E*| of the mixture from the binder |G*| as well as mixture volumetrics such
as the aggregate gradation, binder content etc. Level 3 analysis in M-E PDG does not require
testing of |E*| and |G*| and uses typical values based on the binder performance grade (PG).
However, in all levels (Levels 1, 2 and 3), thermal cracking prediction model requires the
Indirect Tensile Strength (IDT) as well as the Creep Compliance (D(t)) values.

1.1 Objectives
The main objective of the research study presented in this thesis was to investigate linear
viscoelastic characteristics of typical asphalt mixtures and asphalt binders used in Michigan. This

2

is important for implementation of the M-E PDG in Michigan and for accurate prediction of
flexible pavement distresses.
The second objective was to develop analytical models that can better predict the
dynamic modulus |E*| of asphalt mixtures commonly used in the State of Michigan. For this, the
Modified Witczak model was locally calibrated. In addition; an Artificial Neural Network
(ANN) model was developed and trained in an effort to develop a more improved |E*| predictive
model. An ANN-based model was developed using the data generated as part of this study using
similar inputs and volumetric properties required in the Modified Witczak model.
Another objective of this study was to investigate the Representative Volume Element
(RVE) requirement for dynamic modulus |E*| of asphalt mixtures. Small thin mixture beam
(TBM) specimens (0.5”x0.2”x4.5”) were tested using the Bending Beam Rheometer (BBR)
testing machine to obtain the Creep Compliance (D(t)). Using the basic theory of viscoelasticity,
|E*| laboratory measurements on regular size specimens were converted to D(t) values and
compared with the values measured using the BBR machine on the TBMs. Once the RVE
requirement is investigated and verified, this will serve as a foundation for a study of the effect
of aging on the material properties, and on pavement performance.

1.2 Outline
This thesis is organized as follows: Chapter 2 presents a literature review on the dynamic
modulus (|E*|) test background and development of the |E*| master curve. Also, a discussion on
the relevance of this material characteristic to the M-E PDG software and how it effects the
distress predictions is shown. Chapter 2 also discusses different |E*| predictive models and the
3

effect of sample geometry on the |E*| test and the Representative Volume Element (RVE)
requirement for the |E*| test. Chapter 3 is the methodology used in this study and shows all of the
materials used in the analysis. Chapters 4 and 5 present the results and discussion part on the
laboratory testing and |E*| predictive models, respectively. Chapter 6 shows a study on the RVE
requirement for asphalt mixtures and addresses the feasibility of using the Bending Beam
Rheometer (BBR) test on thin asphalt mixture beams to obtain fundamental engineering material
properties.

4

2. LITERATURE REVIEW
2.1 Introduction and background on |E*| test
The complex modulus testing for asphalt mixtures is a relatively old concept. Papazian
(1962) was one of the first to use the triaxial cyclic complex modulus test in an effort to describe
viscoelastic characterization of asphalt mixtures. A sinusoidal stress was applied to a cylindrical
specimen at a given frequency, and the resulting sinusoidal strain response at the same frequency
was measured (Clyne et al. 2003). He concluded that viscoelastic concepts could be applied to
asphalt pavement design and performance. About fifty years later, we are still using the same
concept to better understand the performance of pavement materials.
The most comprehensive research effort towards the complex modulus as a material
property started in mid-90s as part of the NCHRP Project 9-19 “Superpave Support and
Performance Models Management” and NCHRP Project 9-29 “Simple Performance Tester for
Superpave Mix Design” (NCHRP 9-19 2005, and NCHRP 9-29 2002). This research effort was
directed towards proposing new guidelines for the proper test specimen geometry and size.
Specimen preparation, testing procedure, loading pattern, and empirical models were also
addressed in the mentioned projects. After running numerous complex modulus tests, the
research panel recommended using 100mm diameter cored specimens from 150mm diameter
gyratory compacted specimens, with a saw cut final height of 150mm. In addition, fully
lubricated end plates were found useful to minimize end restraint on specimens. The research
projects also concluded that the |E*| test provides necessary input for structural analysis and is

5

tied to the M-E PDG design tool, and is a rational way to establish guidelines, and performance
criteria (NCHRP Project 9-29).

2.2 Complex modulus (E*)
The complex modulus E* defines the stress-strain relationship of asphalt mixtures when
they are loaded in a cyclic mode. Figure 2.1 shows a typical response of a cylindrical asphalt
specimen when subjected to a haversine loading. As shown, the measured strain also has a
haversine shape, with a delay in the peak as compared to the peak of the stress. This time delay is
used to calculate the phase angle of the material. For perfectly elastic materials, the phase angle
is zero; for perfectly viscous materials (e.g., fluids), the phase angle is 90 degrees. It should be
noted that the behavior seen in Figure 2.1 is linear viscoelastic and only observed if the loading
level does not result in strain levels larger than 100-120 microstrain. At higher load levels,
plastic deformation occurs at high temperatures (40-70oC) and microcracking initiates at
intermediate (10-30oC) temperatures.
The understanding of linear viscoelasticity concepts is vital for comprehension of the
complex modulus test (Clyne et al. 2003). Based on the fundamental concepts of linear
viscoelasticity, the one dimensional case of sinusoidal loading can be represented by the
following equation (Ferry 1980):

[2.1]
where σ◦ is the stress amplitude and  is the angular frequency related to the frequency f by the
following equation:

[2.2]
6

Figure 2.1: Illustration of cyclic loading of an asphalt specimen and corresponding strain
response (for interpretation of the references to color in this and all other figures, the
reader is referred to the electronic version of this thesis).

The resulting steady state strain is expressed by the following equation:

[2.3]
where ◦is the strain amplitude, andis the phase angle of the material caused by the time delay
between applied stress and resulting strain shown in Figure 2.1. Complex modulus (E*) is
defined as:

[2.4]

7

where (E’’) is the loss modulus, and (E’) is the storage modulus. The loss modulus describes the
viscous component and the storage modulus describes the elastic component expressed as
(Birgisson et al., 2004):

[2.5]
[2.6]
The phase angle of the material () can be expressed as:

(

)

[2.7]

The dynamic modulus is the absolute value of the complex modulus defined as (Yoder &
Witczak, 1975):

[2.8]
where peak and peak are the peak stress and strain, respectively.

1.2 Development of |E*| master curve
Asphalt mixtures have different |E*| values at different temperatures and loading
frequencies. The |E*| increases with increasing frequency, decreases with increasing temperature.
In order to be able to combine the effects of frequency and temperature on |E*|, a master curve is
generated. Once |E*| values are measured at different temperatures (T) and loading frequencies
(f), the |E*| master curve is obtained using the time-temperature superposition (TTS) principle
(Kim 2009). Figure 2.2 shows a graph of |E*| values at different temperatures and frequencies

8

that is generated from raw |E*| data. Based on the TTS principle, a single |E*| master curve can
be obtained by shifting the |E*| data obtained at different temperatures horizontally as shown in
Figure 2.3. Once shifted, the parameter in x-axis is called reduced frequency (fR), which is
defined as follows:

[2.9]
where f is the frequency of the load and aT(T) is the shift factor coefficient for a given
temperature T. As shown in Figure 2.4, the shift factor coefficient (aT(T)), i.e., the amount of
horizontal shift for each temperature is different. During shifting process, the shift factors at each
temperature are varied until a good sigmoid fit to the |E*| data of all temperatures is obtained.
Typically the following sigmoid function is used:

|

|

[2.10]

where b1, b2, b3, and b4 are the sigmoid coefficients, and fR is the reduced frequency.
After the shifting is completed and the shift factor coefficients (aT(T)) are determined,
they are plotted against each temperature (T) as shown in Figure 2.4b. Then a second order
polynomial is fitted to the data (also shown in Figure 2.4b) to obtain the polynomial coefficients
a1 and a2 in the following equation:

(

)

[2.11]

where aT(T) is the shift factor coefficient, a1, and a2 are the polynomial fit constants, and Tref is
the reference temperature.

9

Figure 2.2: Unshifted (original) |E*| data at different temperatures versus frequency.

Figure 2.3: Illustration of shifted |E*| data at different temperatures versus reduced
frequency to obtain the master curve.

10

Figure 2.4: Shift factor (a(T)) coefficients at different temperatures for an asphalt mixture.
(a) |E*| master curve. (b) Shift factor polynomial curve.

Development of |E*| master curve is very useful because once b1, b2, b3, b4, a1, a2 and
Tref are known, |E*| at any temperature (T) and frequency (f) can be computed.
11

2.4 Relevance of |E*| to M-E PDG
2.4.1 Introduction
After inception of M-E PDG, several States conducted asphalt mixture characterization
studies in support of M-E PDG (Flintsch et al. 2008, Mohammad 2010, Clyne et al. 2003,
Flintsch et al. 2005, Birgisson et al. 2005). The key objective of these studies was to obtain the
fundamental material characteristics of asphalt mixtures that are required by the M-E PDG
software.
In support of M-E PDG implementation in Virginia, Flintsch et al. (2008) conducted |E*|
tests on 11 different asphalt mixture types. The research team concluded that |E*| of the mixtures
common in VA is sensitive to the constituent properties of asphalt mixture (aggregate type,
asphalt content, percentage of recycled asphalt pavement, etc.). They also found that M-E PDG’s
level 2 |E*| prediction equation reasonably estimated the measured dynamic modulus; however,
it did not capture some of the differences between the mixes as found in the measured data. They
used the Original Witzcak’s (OW) equation (which is based on the viscosity of asphalt binder) to
predict |E*| and compared it to their measurements. The authors did not measure viscosity values
at different temperatures; instead, they used empirical equations to calculate the viscosity at
different temperatures.
Mohammad et al. (2007) conducted |E*| tests on 13 different asphalt mixture types
common to Louisiana. The research team evaluated the Witczak and Hirsch models and found
that predictions of the dynamic modulus |E*| values were reasonable. They indicated that the
Witczak model accuracy increases for higher Nominal Maximum Aggregate Size (NMAS),
12

whereas the Hirsch model accuracy increases for lower NMAS. They did not specify how they
determined the viscosity or |G*|/d values for binder for use in Witczack’s or Hirsch models.
Clyne et al. (2003) performed |E*| tests on four different asphalt mixtures commonly
used in Minnesota from the MnROAD site. |E*| and phase angle vs. frequency mastercurves
generated from the test data were compared to results obtained from Witczak’s predictive
equations. The modulus values calculated using the Original Witczak (OW) predictive equation
provided a reasonable prediction of the dynamic modulus for only two of the four mixtures
evaluated. It was stated that the 2000 predictive equation should be used with caution. However,
smooth master curves for phase angle could not be obtained, and use of the same shift factors as
for the complex modulus master curves did not result in smooth master curves for the phase
angle. The authors also indicated that sample preparation techniques affect the results of dynamic
modulus testing. The recommended procedure (NCHRP 9-29) of coring and cutting test
specimens led to a lower modulus than that of specimens compacted directly to size for the
mixture investigated. The authors indicated that the potential reason for this is that the cored
specimens likely had rather uniform air voids throughout the specimen. The compacted
specimens probably contained density gradients axially and radially throughout the specimens.
Birgisson et al. (2005) focused on the evaluation of the dynamic modulus predictive
equation used in the M-E PDG for mixtures typical to Florida. The research program consisted of
dynamic modulus testing of 28 different mixtures. The results showed that the predictive
equation used appeared (on the average) to work well for Florida mixtures. However; they
recommended a multiplier to account for the uniqueness of local mixtures. The results of the

13

study also identified optimal viscosity-temperature relationships that result in the closest
correspondence between measured and predicted dynamic modulus values. The authors
developed regression relationships that can be used to correct the predicted modulus values on
the average (Table 2.1). It was found that the dynamic modulus predictions using input
viscosities obtained from the Dynamic Shear Rheometer (DSR) test results were lower than the
measured values. Hence, consistent with the recommendations by Witzcak et al. (2002), if the
user wants to underestimate the dynamic modulus slightly, it was recommended that viscositytemperature regression coefficient (A and VTS) values used to generate input viscosities for the
predictive equation be obtained from the DSR test. The study also indicated that the viscositytemperature regression coefficients (A and VTS) should be obtained from the Brookfield
rotational viscometer test or alternatively the mix/ laydown conditions proposed by Witzcak and
Fonseca (1996). The results also showed that dynamic modulus predictions at higher
temperatures are generally closer to measured values than modulus predictions at lower
temperatures.

Table 2.1: A and VTS values reported in Birgisson et al. (2005).
Regression
Constants
A
VTS

From Brookfield
Rotational Viscometer
Test Results
-3.4655
10.407

From Dynamic Shear
Rheometer Test
Results
-3.0165
9.0824

14

From Mix/Laydown
Conditions suggested by
Witczak and Fonseca
-3.56455
10.6768

2.4.2 |E*| as a design input in M-E PDG
The |E*| is one of the main parameters used in the bottom-up, top-down fatigue cracking
and the rutting model for the mechanistic-empirical design procedure. Laboratory measured |E*|
data are needed to develop master curves and shift factors based on Equation 2.8 and Equation
2.9 for the Level 1 analysis in the M-E PDG. The Modified Witczak predictive equation
developed as part of the NCHRP Project 1-40D is used to predict |E*| using binder test data for
Level 2 analysis. Level 3 analysis uses the Superpave binder Performance Grade (e.g., PG 64-22)
to predict |E*| based on A-VTS relationship using the Original Witczak predictive equation
developed as part of the NCHRP Project 1-37A.
Summary of procedure used by the M-E PDG for fatigue cracking and rutting
predictions
The M-E PDG divides the pavement structure into sublayers and divides the analysis
period (i.e., the performance prediction period) into one month intervals, then for each period:
1) The Enhanced Integrated Climatic Model (EICM) predicts the temperature variation with
depth for each sublayer.
2) An equivalent frequency is chosen based on the traffic speed, type of road facility
(interstate, urban street etc.) and depth of each sublayer.
3) From the temperature and frequency (steps 1 and 2 above), an |E*| is selected/computed
and used as elastic modulus E = |E*| in a layered elastic pavement model called JULEA.

15

4) In the bottom-up fatigue cracking model, JULEA predicts the tensile strain at the base of
the asphalt and uses it in the MS-1 model to predict the number of cycles to failure (Nf)
for the given analysis period. Then this Nf is used in Miner’s damage accumulation law to
predict the damage caused by the bottom-up fatigue cracking.
5) In the top-down fatigue cracking model, JULEA predicts the tensile strain at the edge of
the tire and uses it in another MS-1 type empirical model to predict the number of cycles
to failure (Nf) for the given analysis period. Then this Nf is used in Miner’s damage
accumulation law to predict the damage because of top-down fatigue cracking.
6) In the rutting model, the resilient strain of the material is predicted by JULEA and used in
the empirical rutting model, along with the temperature and number of load repetitions.
The detailed description of JULEA, MS-1, Miner’s law and rutting models mentioned
above can be found in the M-E PDG documentation (Appendices GG, II, and RR).
Effect of |E*| master curve on fatigue and rutting predictions in M-E PDG
Figure 2.5 illustrates two conceptual |E*| master curves labeled as Mix-A and Mix-B. In
an |E*| master curve graph, the left side of the graph corresponds to high temperature and low
frequency, whereas the right side of the graph corresponds to low temperature and high
frequency, as illustrated in Figure 2.5. Typically, better fatigue resistance is expected if the |E*|
curve is relatively low on the right side of the curve. Conversely, better rutting resistance is
expected if the |E*| curve is relatively high in the left side of the curve. In Figure 2.5, Mix-A is
typically expected to perform better in both rutting and fatigue resistance as compared to Mix-B.
The middle of the |E*| master curve, for most mixtures, corresponds to 21oC (~70oF) at 0.1 Hz.
16

Therefore, relatively low temperatures (right side of the vertical dashed line in the middle of the
curves in Figure 2.5) corresponds to temperatures less than 70oF, the left side is the temperatures
higher than 70oF. It should be noted that this mid point (i.e., median temperature) can be slightly
different for different mixtures.
It should be noted that very soft mixes may not necessarily lead to better fatigue
resistance. The fatigue resistance, in addition to the |E*|, is also related to the tensile strain at the
base of the pavement structure being analyzed. Therefore, excessively soft asphalt mixtures may
lead to excessive tensile strain at the base of the asphalt layer, which can cancel out the
beneficial effect of low |E*| (see MS-1 model in the MEPDG documentation).

log (|E*|)

Low frequency &
High temperature

Mix-B
Mix-A

Better
rutting
resistance

Better
fatigue
resistance

High frequency &
Low temperature

log (fR)
Figure 2.5: Illustration of two typical |E*| mastercurves and expected fatigue and rutting
performance trends for these |E*| master curves.

17

2.5 Dynamic modulus |E*| prediction models
The dynamic modulus test is a tedious experiment and relatively expensive to perform
and may take several days to develop a master curve for a unique asphalt mixture (Birgisson et
al. 2005). In addition, costly equipment and trained personnel are needed for sample preparation,
testing, and data analyses (Azari et al. 2007). Given the significance of |E*| as a design parameter
in the M-E PDG software, and to overcome the difficulties of laboratory testing; several
researchers developed relationships between the characteristics of asphalt mixture constituents
(e.g., mix design parameters and binder characteristics) and |E*| master curve (Bonnaure et al.
1977, Andrei et al. 1999, Bari 2005, Christensen et al. 2003, Al-Khateeb et al. 2006).
2.5.1

Original Witczak model (Andrei et al. 1999) – OW (NCHRP 1-37A)

Andrei et al. (1999) developed a revised version of the original Witczak |E*| predictive
equation based on data from 205 mixtures with 2,750 data points. The predictive model is given
in the following equation:

| |
(

)

(
(

)
)
[2.12]

where:
|E*|

=

5

Asphalt mix modulus, psi (x10 ).

18

p200

=

Percentage of aggregate passing #200 sieve.

p4

=

Cumulative percentage of aggregate retained in #4 sieve.

p3/8

=

Cumulative percentage of aggregate retained in 3/8-inch (9.56-mm) sieve.

p3/4

=

Cumulative percentage of aggregate retained in 3/4-inch (19.01-mm) sieve.

Va

=

Percentage of air voids (by volume of mix).

Vbeff =

Percentage of effective asphalt content (by volume of mix).

f

=

Loading frequency (hertz).



=

Binder viscosity at temperature of interest (x10 poise).

6

The preceding equation is based on nonlinear regression analysis using the generalized
gradient optimization approach in Microsoft Excel Solver (Kim et al. 2011). This model is
currently one of two options for levels 2 and 3 analyses in the M-E PDG software (NCHRP 137A, 2004). The M-E PDG software converts all level 2 and level 3 inputs into A-VTS values to
develop the |E*| master curve (Kim et al. 2011).
One of the limitations of the Witczak equation is that it relies on other models to convert
the |G*| to binder viscosity. Also, extrapolation beyond the calibration database is restricted since
the predictive equation is based on regression analysis (Bari 2005). In addition, the need to
improve sensitivity of the model to mixture volumetrics was noted by Dongre et al. (2005).
2.5.2

Modified Witczak model (Bari 2005) – MW (NCHRP 1-40D)

In order to include binder |G*| and phase angle () in the predictive model, Witczak
reformulated the model as follows:
19

|

|
|

|
(

)

(
|

)

|
[2.13]

where:
|G*|b =

Dynamic shear modulus of asphalt binder (pounds per square inch).

b

Binder phase angle associated with |G*|b (degrees).

=

Because some of the mixtures in their database did not contain |G*|b data, Bari and
Witczak (2007) used the Cox-Mertz rule, using correction factors for the non-Newtonian
behaviors (see equations 2.14–2.16), was used to calculate |G*|b from A-VTS values:

|

|
[ 2.14]

(

)

[2.15]

[2.16]
20

where:
fs

=

Dynamic shear frequency.

b

=

Binder phase angle predicted from equation 2.14 (degrees).

fs,T

=

Viscosity of asphalt binder at a particular loading frequency (fs) and temperature

(T) determined from equation 2.15 (centipoise).
TR

=

Temperature in Rankine
2.5.3

Hirsch model (Christensen et al. 2003) – HM

A limited number of data points (206) was used to determine the calibration coefficients
in the Hirsch model, compared to 2750 and 7400 data points for the Original Witczak model and
Modified Witczak model, respectively (Kim et al. 2011). Christensen et al. (2003) examined four
different models based on the law of mixtures parallel model and incorporated the binder
modulus, Voids in the Mineral Aggregate (VMA), and Voids Filled with Asphalt (VFA) because
it provides accurate results in the simplest form (Christensen et al. 2003). The proposed |E*|
prediction model is in the following equations:


1  Pc 
 VFA *VMA 
 VMA 
| E*|m  Pc 4,200,000 1 
 3 | G*|b 



 100 
 10,000  1  VMA

VMA
100

4,200,000 3 | G*|b VFA





[2.17]
[2.18]

21

| |
| |
[2.19]
where:
|E*|m =

Dynamic modulus of asphalt mixture (psi).

Pc

=

Aggregate contact volume.



=

Phase angle of asphalt mixture.

An important strength of this model is the empirical phase angle equation (Equation
2.18), which is used for the interconversion of |E*| to the relaxation modulus (E(t)), or creep
compliance (D(t)). On the other hand; the model lacks strong dependency on volumetric
properties of the asphalt mixture, especially at low air void levels and VFA conditions (Kim et
al. 2011).
2.5.4 Law of mixtures parallel model (Al-Khateeb Model)
Similar to the Hirsch model, this formulation is based on law of mixtures for composite
materials. Al-Khateeb et al. (2006) later simplified the Hirsch model and introduced the
following revised formulation:

|

|

|

(

)

|

[

|
|

⁄

|

⁄

]

|
[2.20]

where |G*|b = dynamic shear modulus of asphalt binder at the glassy state (assumed to be
145,000 psi (999,050 kPa)).
22

This model addresses one of the primary limitations of the Hirsch model by improving
the ability to accurately predict |E*| of asphalt mixtures at low frequencies and high
temperatures. On the other hand, weaknesses of this model include lack of verification and the
fact that the authors developed this model based on |E*| tests at higher strain amplitudes (200
microstrain than recommended (75-150 microstrain) (Kim et al. 2011).
2.5.5

Summary of inputs for |E*| prediction models

Table 2.2 shows a summary of the required inputs for the previously mentioned
predictive equations.
Table 2.2: Parameters used in different |E*| predictive models.
Parameter

Description

VMA
VFA

Voids in mineral aggregate (%)
Voids filled with asphalt (%)
Aggregate passing #200 sieve (%)

P200
P4
P3/8
P3/4
Va
Vbeff
A &VTS
fs
|G*|b

Used in |E*| Predictive Model?
OW
MW
H
A






Aggregate passing #4 sieve (%)





Aggregate passing 3/8-inch sieve (%)





Aggregate passing 3/4-inch sieve (%)





Air voids (by volume) (%)





Effective asphalt content (by volume) (%)
Intercept & slope of viscosity-temperature
relationship of binder
Loading frequency (Hz)





Binder dynamic shear modulus









Binder phase angle

Note: OW = Original Witczak (Andrei et al. 1999), MW = Modified Witczak (Bari 2005),
H = Hirsch (Christensen et al. 2003), and A = Al-Khateeb (Al-Khateeb et al. 2006).
b

23

2.6 Sample geometry and Representative Volume Element (RVE) for |E*|
As stated earlier in this chapter, the most comprehensive research effort towards the
complex modulus as a material property started in mid-90s as part of the NCHRP Project 9-19,
and NCHRP Project 9-29 (NCHRP 9-19 2005, and NCHRP 9-29 2002). Part of this research
effort was directed towards proposing new guidelines for the proper test specimen geometry and
size.
Although a major cost in |E*| testing time and equipment arises from the need to core and
saw gyratory compacted specimens, the research panel of the NCHRP Project 9-19
recommended using 100mm diameter cored specimens from 150mm diameter gyratory
compacted specimens, with a saw cut final height of 150mm in the |E*| test. After running
numerous complex modulus tests, it was found that:
1. A minimum height-to-diameter ratio of 1.5 was recommended to ensure that the response
of test specimens represents a fundamental engineering property.
2. A minimum diameter of 100mm was recommended for all asphalt mixtures up to a
maximum aggregate size of 37.5mm.
3. Smooth, parallel-ended specimens were recommended to eliminate bending, end friction,
and boundary effects of the specimen during the test.
4. Less variability in |E*| test results were observed when 100mm diameter specimens were
used, as compared to 150mm diameter specimens. The reason behind that is the large
degree of nonhomogeneity of air voids within the larger specimens; which leads to
variability in |E*| test results.

24

Kim et al. (2004) investigated the possibility of using IDT testing to measure the |E*| of
existing asphalt pavements by comparing the |E*| values from the IDT tests with |E*| values from
axial compression tests on standard cylindrical specimens. It was found that IDT testing is
suitable for a wide range of mixtures and statistically proven to be similar to the master curves
obtained from axial compression tests. Considering the relatively small thickness of IDT
specimens (38mm), IDT test is a valid option for characterizing pavement materials for existing
pavements (Kim et al. 2008). In addition, Kim et al. (2008) investigated prismatic specimen
geometry and found that the prism and cylindrical specimens produce |E*| values that are
statistically the same.
Research performed by Zofka et al. (2007) suggested the use of much smaller sample
geometry to measure asphalt mixture creep compliance at low temperatures on thin mixture
beams (127×12.7×6.35mm) using the Bending Beam Rheometer (BBR) testing machine. Using
statistical analysis, a regression equation was derived and it was shown that this relation gives
good predictions for IDT from the BBR results.
The research methodology suggested by Zofka et al. (2007) and Velasquez et al. (2009)
was explored in this research study by running the BBR tests on thin beam mixtures to obtain
mixture creep compliance D(t). The basic theory of viscoelasticity was used to convert |E*|
values obtained from the typical cylindrical test specimens (100mm×150mm) to D(t) values and
were then compared to D(t) values measured using the BBR testing machine.
A major drawback of testing thin beam mixtures is the fact that the thickness of the beam
(6.35mm) is smaller than the maximum aggregate size for most mixtures, which violates the
RVE concept. The geometry and size of a test specimen play a significant role at high
25

temperatures when the asphalt mixture components have major different mechanical properties
(Zofka et al. 2007). On the other hand, asphalt binders start behaving as brittle linear viscoelastic
materials at low temperatures, and the mismatch between the aggregate and the binder modulds
becomes less significant. This agrees well with Romero and Masad (2001), who reported this
phenomenon and suggested that the RVE can be significantly reduced at lower temperatures.
It is desirable to study the effect of aged material properties on pavement performance.
Recent research showed that current laboratory aging protocols lead to aging gradients within the
regular-size (100mm diameter, 150mm tall) samples (Houston et al. 2005). Test samples become
non-homogeneous and anisotropic. Such samples are no longer useful for performance testing.
Therefore, once the RVE requirement is verified for the thin beam mixtures, this will serve as a
foundation for the aging study since small samples will be much less susceptible to aging
gradients.

26

3. RESEARCH METHODOLOGY
3.1 Introduction
The main objective of this research was to evaluate the complex modulus of asphalt
mixture materials commonly used in the State of Michigan. A total of 64 asphalt mixtures and 44
asphalt binders were characterized in this study. A detailed description of the materials used in
this research is provided in following section.

3.2 Materials used
3.2.1

Asphalt mixtures

A total of 64 asphalt mixtures (59 Hot Mix Asphalt (HMA) mixtures and 5 Warm Mix
Asphalt (WMA) mixtures) commonly used in the State of Michigan were characterized in this
research. Appendix A shows a list of volumetric properties and aggregate gradation for the tested
asphalt mixtures. All test samples were prepared in accordance with AASHTO PP60
“Preparation of Cylindrical Performance Test Specimens Using the Superpave Gyratory
Compactor (SGC)”. The air voids of all samples tested were within the range of 7%  0.5%,
which is the recommended range of air voids for most performance tests in the AASHTO
specifications. This air void level is typically the median air void level expected in the field right
after the construction. Running the |E*| experiments at different air void levels may lead to
different |E*| values, but, such investigation was not within the scope of this study. It should be
noted that very limited |E*| tests at lower air void levels were run, and resulted in very similar

27

|E*| values as compared to the |E*| values of the samples compacted to 7% air voids. A complete
list of air voids of all mixtures tested in this study is given in Appendix B.
3.2.2 Asphalt binders
A total of 44 unique asphalt binders commonly used in the State of Michigan were
characterized in this study. Virgin asphalt binders, as well as modified asphalt binders were
tested to obtain the dynamic shear modulus (|G*|) master curve and phase angle d of asphalt
binders. The |G*| master curve and phase angle are required inputs in the M-E PDG software for
prediction of asphalt mixture complex modulus.

3.3 Laboratory testing of materials collected
3.3.1 Details of laboratory |E*| tests
Figure 3.1 shows a picture of the Asphalt Mixture Performance Tester (AMPT)
equipment used in this study for testing |E*| of the asphalt mixtures. The |E*| tests were
conducted in accordance with AASHTO T342 “Determining Dynamic Modulus Mastercurve of
Hot Mix Asphalt (HMA)”. The tests were conducted at temperatures of -10, 10, 21, 37 and 54
degrees C. At each temperature, tests were run at frequencies of 25, 10, 5, 1, 0.5 and 0.1 Hz. The
entire series of temperatures and frequencies were run on 3 different gyratory compacted
specimens. The average of the 3 replicates was used to develop the master curve representing
each asphalt mixture. A detailed explanation of determination of |E*| master curves from the
laboratory data can be found in AASHTO PP62-10 “Developing Dynamic Modulus
Mastercurves for Hot Mix Asphalt (HMA)”.

28

Figure 3.1: Asphalt Mixture Performance Tester (AMPT)

3.3.2 Details of laboratory |G*| tests
The |G*| tests were conducted in accordance with AASHTO T315 “Determining the
Rheological Properties of Asphalt Binder Using a Dynamic Shear Rheometer (DSR)” on Rolling
Thin Film Oven (RTFO) aged residue. Frequency sweep tests were conducted at temperatures of
15, 30, 46, 60 and 76 degrees C. At each temperature, tests were run at 11 frequencies varying
between 1.0 and 100.0 Rad/sec. Three replicate asphalt binder samples were tested at each
temperature and frequency. The average of the 3 replicates was used to develop the |G*| master
curve.
The dynamic shear modulus (|G*|) is a parameter that defines the stress-strain
relationship of asphalt binders when they are subjected to cyclic shear load.

The |G*| is

measured using the Dynamic Shear Rheometer (DSR) shown in Figure 3.2. The |G*| is defined
as:
29

 peak
| G* | peak

where τ

peak

peak

and γ

[3.1]

are peak shear stress and strain, respectively (see Figure 3.3). The steps in

generating the |G*| master curve are identical to the steps described in the previous sections for
the |E*| master curve. Because of the strong relationship between the |G*| and |E*|, Levels 2 and
3 analyses in the M-E PDG software utilize the |G*| master curve (along with other inputs) to
predict the |E*| master curve. Level 1 analysis in M-E PDG also requires |G*| as input, because
|G*| is used to compute the viscosity-temperature relationship (a.k.a. A-VTS relationship) of the
binder. The A-VTS relationship is needed in the global aging system model of the M-E PDG to
predict the aging of the asphalt mixture over time.

Torque
(shear) load

Top plate
Asphalt binder sample

Bottom plate (fixed)

Figure 3.2: Illustration of the Dynamic Shear Rheometer (DSR) testing machine

30

Figure 3.3: Illustration of stress-strain relationship of asphalt binders when they are
subjected to cyclic shear load

3.4 Investigation of the Representative Volume Element (RVE) requirement for
dynamic modulus |E*| of asphalt mixtures using Thin Beam Mixtures (TBMs)
In this study, a research methodology suggested by Zofka et al. (2007) and Velasquez et
al. (2009) for low temperature applications was followed to investigate the Representative
Volume Element (RVE) requirement for asphalt mixtures. Relatively small samples of asphalt
mixture beams (127×12.7×6.35mm) were cut from gyratory specimens (Figure 3.4) to

31

investigate the possibility of obtaining the |E*| master curve from a much smaller specimen
geometry as compared to the typical cylindrical test specimens (100mm diameter×150mm tall).
It is desirable to study the effect of oxidation/aging on pavement performance. Recent
research showed that current laboratory aging protocols lead to aging gradients within the
regular-size (100mm diameter, 150mm tall) samples. Test samples become non-homogeneous
and anisotropic. Such samples are no longer useful for performance testing. Therefore, it is
essential that the use of relatively smaller sample geometries be investigated since small samples
will be much less susceptible to aging gradients and will experience more homogeneity after
undergoing different laboratory aging processes.
The Bending Beam Rheometer (BBR) test was conducted on thin beam mixtures to
obtain mixture the creep compliance D(t) of the asphalt mixture. The basic theory of
viscoelasticity was then used to convert |E*| values obtained from the typical cylindrical test
specimens to D(t) values and were then compared to D(t) values measured using the BBR testing
machine. Figure 3.4 below illustrates the experimental setup of the TBMs.
A total of 10 unique asphalt mixtures with varying Nominal Maximum Aggregate Sizes
(NMASs) and Job Mix Formulas (JMFs) were tested. In addition, three replicates representing
the same unique asphalt mixture were tested in order to account for sample-to-sample variability.

32

Saw cutting regularsize performance
specimen in two
halves

Tile saw is used for cutting three Tile saw is used to cut
disks (center, middle, and edge) a TBM from each disk

Resulting asphalt thin mixture beam

BBR testing on TBM
Figure 3.4: Illustration of Thin Beam Mixture sample preparation and testing.
33

4. LABORATORY TESTING: RESULTS & DISCUSSION
4.1 Complex modulus |E*| testing of asphalt mixtures
Sampling of loose mixtures was conducted by MDOT during the summers of 2011 and
2012. The loose mixtures were collected from selected pavement projects in multiple regions in
the State of Michigan (North, Grand, Bay, Southwest and University Regions (NGBSU), Metro
Region, and Superior Region). A total of 64 unique asphalt mixtures were sampled and a wide
range of |E*| master curves that are representative of typical MDOT mixtures were obtained. A
total of 213 different specimens were prepared from 64 unique asphalt mixture types. The tested
asphalt mixture types are shown in Tables 4.1 through 4.4. The grey shaded cells in these tables
represent the HMAs collected and tested.

Base

Leveling

Leveling/Top

Top

Binder
PG

Binder
PG

5
8
13
16
21
24

Binder
PG

North, Grand, Bay, Southwest and University Regions (NGBSU)
64-22
1 64-22 2
70-28P
3
70-28P
4
70-28P
64-22
1 64-22 2
76-28P
6
76-28P
7
76-28P
64-22
9 64-22 10 70-28P 11 70-28P 12 70-28P
64-22
9 64-22 10 76-28P 14 76-28P 15 76-28P
58-22 17 58-22 18
64-28
19
64-28
20
64-28
58-22 17 58-22 18 70-28P 22 70-28P 23 70-28P
34

HMA#

Base

HMA#

5

HMA#

4

HMA#

3

HMA#

E30
E30
E50
E50
E10
E10

3

Binder
PG

M
HS
M
HS
M
HS

2

Binder
PG

Mix
Type

Layer:

Mix No:

Table 4.1: HMAs tested for |E*| master curve.

HMA#

Binder
PG

Top

HMA#

Leveling/Top

Binder
PG

Leveling

HMA#

Base

Binder
PG

Base

HMA#

5

Binder
PG

4

HMA#

3

Binder
PG

Mix No:

3

Mix
Type

2

Layer:

Table 4.1 (cont’d)

E30
E30
E50
E50
E10

North, Grand, Bay, Southwest and University Regions (NGBSU)
58-22 25
58-22
26
64-28
27
64-28
28
64-28
58-22 25
58-22
26 70-28P
30
70-28P
31
70-28P
58-22 33
58-22
34
58-28
35
58-28
36
58-28
58-22 33
58-22
34
64-28
38
64-28
39
64-28
58-22 41
58-22
42
58-28
43
58-28
44
58-28
58-22 41
58-22
42
64-28
46
64-28
47
64-28
Metro Region
64-22 1
64-22
2
70-22P
89
70-22P
90
70-22P
64-22 1
64-22
2
76-22P
92
76-22P
93
76-22P
64-22 9
64-22
10 70-22P
95
70-22P
96
70-22P
64-22 9
64-22
10 76-22P
98
76-22P
99
76-22P
58-22 17 *58-22
18
64-22
101
64-22
102
64-22

91
94
97
100
103

HS

E10

58-22

17

58-22

18

104

70-22P

105

70-22P

106

M
HS
M
HS
M
HS

E3
E3
E03
E03
E1
E1

58-22
58-22
58-22
58-22
58-22
58-22

25
25
33
33
41
41

58-22
58-22
58-22
58-22
58-22
58-22

64-22
70-22P
58-22
64-22
58-22
64-22

108
111
114
117
120
123

64-22
70-22P
58-22
64-22
58-22
64-22

109
112
115
118
121
124

M
HS
M
HS
M
HS

E10
E10
E3
E3
E03
E03

58-28
58-28
58-28
58-28
58-28
58-28

53
53
61
61
69
69

58-28
58-28
58-28
58-28
58-28
58-28

26
64-22
107
26 70-22P 110
34
58-22
113
34
64-22
116
42
58-22
119
42
64-22
122
Superior Region
54
58-34
55
54 64-34P
58
62
58-34
63
62 64-34P
66
70
58-34
71
70 64-34P
74

58-34
64-34P
58-34
64-34P
58-34
64-34P

56
59
64
67
72
75

58-34
64-34P
58-34
64-34P
58-34
64-34P

57
60
65
68
73
76

M
HS
M
HS
M
HS

E3
E3
E03
E03
E1
E1

M
HS
M
HS
M

70-22P

35

29
32
37
40
45
48

M E1 58-28 77
HS E1 58-28 82
Note: M=Mainline,
HS=High Stress

58-28
58-28

Superior Region
78
58-34
79
83 64-34P 84

58-34
64-34P

80
85

58-34
64-34P

81
86

Binder
PG

HMA#

Top

Binder
PG

Leveling/Top

HMA#

Leveling

Binder
PG

Base

HMA#

Base

HMA#

5

Binder
PG

4

HMA#

3

Binder
PG

Mix No:

3

Mix
Type:

2

Layer:

Table 4.1 (cont’d)

Table 4.2: HMAs tested for |E*| master curve (GGSP and LVSP Mixtures)

HMA Type

Layer:
Region:

North, Grand, Bay,
Southwest and
University Regions
(NGBSU)

Mix
Binder PG
Type
M
GGSP
70-28P
HS
GGSP
76-28P
M
LVSP
58-28
HS
LVSP
64-28
Note: M=Mainline, HS=High Stress

Leveling/Top
Metro

Superior

HMA#

Binder PG

HMA#

Binder PG

HMA#

49
50
51
52

70-22P
76-22P
58-22
64-22

125
126
127
128

-

-

58-34
64-34P

87
88

36

Table 4.3: HMAs tested for |E*| master curve (SUPERPAVE) – Mixtures that do not follow
MDOT specifications but are permitted to be used.
HMA
Type

Mix No:
2
3
Layer:
Base
Base
Mix
Binder
Binder
HMA#
HMA#
Type
PG
PG
M
E10
58-28
200
HS
E10
HS
E30
M
E3
58-28
205
M
E1
M
E1
Note: M=Mainline, HS=High Stress

4
Leveling/Top
Binder
HMA#
PG

5
Top
Binder
HMA#
PG

70-22P

64-22
70-22P

202
204

64-22
64-22

206
207

203

Table 4.4: HMAs tested for |E*| master curve (GGSP and LVSP Mixtures) - Mixtures that
do not follow MDOT specifications but are permitted to be used.
HMA
Type:

Layer:
Leveling/Top
Region:
NGBSU
Metro
Superior
Mix
Binder HMA# Binder HMA# Binder HMA#
Type
M
ASCRL 64-28
201
Note: M=Mainline

In order to illustrate the overall range of |E*| values for all mixtures tested, the |E*| master
curves were plotted in Figure 4.1. As shown, the difference between the lowest and highest |E*|
values is approximately 2 orders of magnitude.

37

Figure 4.1: Dynamic Modulus master curves of all tested asphalt mixture specimens. The
plot in log-log scale is to show the differences in low frequency/high temperature, and the
plot in linear-log scale is to show the differences in high frequency/low temperature.
38

4.1.1 Summary of |E*| values based on MDOT mix designation for each region
Table 4.5, Table 4.6, and Table 4.7 show a summary of the |E*| values at temperatures of
-10, 21 and 54oC, at a loading frequency of 10Hz. These tables are provided to illustrate the
relative differences in |E*| values of various asphalt mixture types used in MI. As shown in Table
4.5, 3E mixtures are generally stiffer than 4E and 5E mixtures (e.g., compare HMA# 18 versus
20 versus 21). However the trend is not always consistent in all temperatures (e.g., HMA# 31
versus 32 at -10oC). A clear trend should not be expected since there are many variables (e.g.,
aggregate gradation, binder |G*| master curve, VMA, VFA…etc.) that play a role in the
magnitude of |E*| at different temperatures and frequencies.
4.1.2 Comparison of variation in |E*| master curves based on MDOT mix designation
Figure 4.2 shows |E*| master curves of the 3E3 mixtures, where a single master curve is
not visible. Appendix C shows the |E*| master curves of all other mixtures grouped based on the
MDOT mix designation (e.g., 4E10, 3E03 etc.). The objective of plotting these graphs was to
investigate if MDOT mix types for a given region (e.g., 5E10 for Metro Region) exhibit same or
similar |E*| master curve values. After carefully analyzing the |E*| master curves, it was
concluded that it is not appropriate to come up with a single |E*| master curve for a given MDOT
mix, for a given region. The main reason is that the aggregate gradation plays a key role in |E*|
master curve and it is not unique for an MDOT mix type in a region (e.g., 3E3 in Metro). For
example, two 3E3 projects in Metro region may (and most probably will) have different
gradations (and mix designs).

39

Mainline /
High Stress

Table 4.5: Summary of |E*| values for different asphalt mixture types in NGBSU Regions

M
HS
M
HS
M
HS
M
HS
M
HS
M
HS

North, Grand, Bay, Southwest and University Regions (NGBSU)

Mix
No:
Layer:
Traffic
E30
E30
E50
E50
E10
E10
E3
E3
E03
E03
E1
E1

3

HMA #
2
2
10
10
18
18
26
26
34
34
42
42

4

Base
|E*| (MPa)
10Hz, 10Hz,
-10oC
21oC
24183
9108
24183
9108
26710
26710
21470
21470

7668
7668
5649
5649

10Hz,
54C
1175
1175
668
668
453
453

5

Leveling/Top
|E*| (MPa)
10Hz, 10Hz, 10Hz,
-10oC 21oC
54C
21668 5683
498

HMA #
4
7
12
15
20
23
28
31
36
39
44
47

24989
22232
22301
17363

698
475
449
437

20696
20879

40

7175
5300
5618
4834
4833
5707

440
536

HMA#
5
8
13
16
21
24
29
32
37
40
45
48

Top
|E*| (MPa)
10Hz,
10Hz, 10H,
-10oC
21oC
54C

19780
15287
17958
21282
18761

4893
4133
6068
4796
4017

398
444
605
399
214

15280
18204

4207
4659

429
369

Table 4.6: Summary of |E*| values for different asphalt mixture types in the Metro Region
Metro Region

Mainline /
High Stress

Mix
No:
Layer:
Traffic

M
HS
M
HS
M
HS
M
HS
M
HS
M
HS

E30
E30
E50
E50
E10
E10
E3
E3
E03
E03
E1
E1

3

4

Base
|E*| (MPa)
HMA #
2
2
10
10
18
18
26
26
34
34
42
42

5

Leveling/Top
|E*| (MPa)

10Hz, 10Hz, 10Hz,
-10C
21C
54C
24183
24183

9108
9108

1175
1175

26710
26710
21470
21470

7668
7668
5649
5649

668
668
453
453

HMA #
90
93
96
99
102
105
108
111
114
117
120
123

10Hz, 10Hz, 10Hz,
-10C
21C
54C
22256

7408

26014 10224
21314 7375
23374 8419
25192 9402

41

Top
|E*| (MPa)

913

1443
852
948
1434

HMA #
91
94
97
100
103
106
109
112
115
118
121
124

10Hz, 10Hz, 10Hz,
-10C
21C
54C

23603

7405

813

24044
21293
23442
20122

8588
6425
7706
6323

849
656
549
705

Table 4.7: Summary of |E*| values for different asphalt mixture types in Superior Region

Mainline /
High Stress

Mix No:
Layer:

M
HS
M
HS
M
HS
M
HS

3
Base
|E*| (MPa)

Traffic HMA#

E10
E10
E3
E3
E03
E03
E1
E1

Superior Region
4
Leveling/Top
|E*| (MPa)

54
54
62
62
70
70
78
83

10Hz,
-10C

19556
19556

10Hz, 10Hz, HMA#
21C
54C

4142
4142

241
241

10Hz,
-10C

56
59
64
67
72
75
80
85

5
Top
|E*| (MPa)

19103
19403

4519
3339

527
261

18831

42

10Hz
,
21C

10Hz,
54C

17663
16849

3193
3456

260
264

17265

3570

10Hz, 10Hz, HMA# 10Hz,
21C
54C
-10C

3483

297

57
60
*65
68
73
76
81
86

Mix type: 3E3

100,000

|E*| MPa

10,000
1,000
26A PG 58-22 (NGBSU & Metro)
26B PG 58-22 (NGBSU & Metro)
26C PG 58-22 (NGBSU & Metro)
62 PG 58-28 (Superior)

100
10
1.E-05

1.E-03

1.E-01
1.E+01
1.E+03
1.E+05
Reduced Frequency, fr=f*a(T)

1.E+07

Figure 4.2: |E*| master curves of four 3E3 mixtures, 3 of which (26* mixes) are from same
region. NGBSU = North, Grand, Bay, Southwest and University Regions.
As a result, |E*| can be very different. An evidence of this phenomenon is the three 3E3
mixtures (26A, 26B and 26C) that were tested as part of this study. As shown in Figure 4.2,
mixtures 26A, 26B and 26C exhibited different |E*| values. In fact, 26C had a very similar |E*|
master curve as 62, which has a different binder PG and was in a different region (Superior).
4.1.3 Comparison of variation in |E*| master curve for HMA and WMA asphalt mixtures
A limited number of warm mix asphalt mixtures (4 WMAs) were characterized in this
study. Two graphs comparing WMA and HMA |E*| master curves are shown in Figure 4.3 and
Figure 4.4. Figure 4.3 compares two different |E*| master curves for the same type of MDOT
mixture (3E30) and clearly shows that the WMA is softer than the HMA. In Figure 4.4, WMA is
shown as in-between HMAs (51A and 51B) of the same type of MDOT mixture (Low Volume
Superpave (LVSP)). However, it should be noted that when the JMFs were compared, the
gradation of 51A was much coarser than the 51B and 51C, which were almost identical (see

43

Figure 4.5). Therefore, it is more appropriate to compare 51B-HMA and 51C-WMA. As shown,
51C-WMA is slightly softer than the 51B-HMA.

100000

|E*| MPa

10000

1000

100

10
1.0E-04

2-HMA
2-WMA
1.0E-02

1.0E+00
1.0E+02
1.0E+04
Reduced Frequency, fr=f*a(T)

1.0E+06

Figure 4.3: WMA versus HMA |E*| master curves for (3E30) MDOT mixture
100000

|E*| (MPa)

10000

1000

100

10
1.0E-04

51A-HMA
51B-HMA
51C-WMA
1.0E-02

1.0E+00
1.0E+02
1.0E+04
Reduced Frequency, fr=f*a(T)

1.0E+06

Figure 4.4: WMA versus HMA |E*| master curves for (LVSP) MDOT mixture

44

Figure 4.5: Aggregate gradation of WMA and HMA mixtures ((LVSP) MDOT mixture)

4.2 Dynamic shear modulus |G*| testing of asphalt binders
The dynamic shear modulus test was run on RTFO aged residue to obtain the |G*| of 44
unique binders commonly used in the State of Michigan. Table 4.8 shows a list of the different
asphalt binder PG grades tested in this study. Frequency sweep tests were conducted at
temperatures of 15, 30, 46, 60 and 76 degrees C. At each temperature, tests were run at 11
frequencies varying between 1.0 and 100.0 Rad/sec.

45

Table 4.8: List of binder PGs tested in this study
Binder PG Grade
58-22
58-28
58-34
64-22
64-28
64-34P
70-22P
70-28
70-28P
TOTAL

Total number of binders
from different locations
3
9
2
9
7
4
4
1
5
44

4.2.1 Comparison of variation in |G*| master curves based on binder PG grade
As mentioned previously, there is a strong relationship between the binder |G*| and
corresponding mixture |E*|. Levels 2 and 3 in the M-E PDG utilize the |G*| master curve (along
with other inputs) to predict the |E*| master curve. Also, Level 1 analysis requires |G*| as input to
compute the A-VTS relationship of the binder that is needed in the global aging system model of
the M-E PDG to predict the aging of the asphalt mixture over time. Figure 4.6 shows the |G*|
master curves of seven different binders with same performance grade of PG 64-28. As shown, a
single PG in some cases showed significant variations and did not necessarily produce the same
|G*| master curve.

46

PG: 64-28

100,000,000
10,000,000

|G*| Pa

1,000,000
100,000
20B (NGBSU)
29B (NGBSU)
21 (NGBSU)
47 (NGBSU)
20C (NGBSU)
28B (NGBSU)
48 (NGBSU)

10,000
1,000
100
10
1.E-07

1.E-05

1.E-03
1.E-01
Reduced Frequency, fr=f*a(T)

1.E+01

Figure 4.6: |G*| Master curves of seven different PG64-28 binders. NGBSU = North,
Grand, Bay, Southwest and University Regions

In order to evaluate the effect of the |G*| master curve and phase angle ( on
performance prediction, a sensitivity analysis was run in the M-E PDG software. A HMA over
HMA base case was selected. All other inputs were held constant while the |G*| and  were used
to characterize the asphalt binder. The results showed that the variation in |G*| and  is
insignificant for cracking and International Roughness Index (IRI) (see Figure 4.7 to Figure 4.9).
However, it was observed that rutting is sensitive to asphalt binder characteristics as shown in
Figure 4.10. Therefore, it is recommended that |G*| master curves should not be grouped based
on PG grades or regions where the material was acquired from. The |G*| master curves grouped
based on the other asphalt binder PG grades tested in this study are given in Appendix D.

47

PG 64-28 (20C)
Threshold

Longitudinal cracking (ft/mi)

2500

PG 64-28 (29B)

2000
1500
1000
500
0

0

5

10
Pavement age (years)

15

20

Figure 4.7: Illustration of the effect of variation in |G*| and d on Longitudinal cracking
predictions in the M-E PDG software.

PG 64-28 (20C)
Threshold

Alligator cracking (%)

25

PG 64-28 (29B)

20
15
10
5
0

0

5

10
15
20
Pavement age (years)
Figure 4.8: Illustration of the effect of variation in |G*| and d on alligator cracking
predictions in the M-E PDG software.

48

IRI (in/mi)

200
180
160
140
120
100
80
60
40
20
0

PG 64-28 (20C)
Threshold

0

5

PG 64-28 (29B)

10
15
Pavement age (years)

20

Figure 4.9: Illustration of the effect of variation in |G*| and d on IRI predictions in the M-E
PDG software.
PG 64-28 (20C)
Threshold

0.6

PG 64-28 (29B)

Rutting (in)

0.5
0.4
0.3
0.2
0.1
0

0

5
10
Pavement age (years)

15

20

Figure 4.10: Illustration of the effect of variation in |G*| and d on rutting predictions in the
M-E PDG software.

49

5. |E*| PREDICTION MODELS: RESULTS AND DISCUSSION
A recent FHWA-funded research showed that the predictions of Witczak, Hirsch and AlKhateeb equations were inaccurate at low frequencies/high temperatures (Sakhaeifar et al. 2009,
Kim et al. 2010). Independent evaluations of these models were performed in various studies
(e.g., Azari et al. 2007, Robbins and Timm 2011, Singh et al. 2010). These studies consistently
showed inaccuracies of statistical models at certain frequencies and temperatures. This indicated
the need for either local calibration of the constants in these equations, or if necessary, employ
advanced computing tools such as the Artificial Neural Networks (ANNs) to develop models for
better prediction of |E*| values and use them as Level 1 inputs in the M-E PDG software. Such
models were developed by Kim et al. (2010) as part of a FHWA funded study.

5.2 Evaluation and calibration of the Modified Witczak’s equation for Michigan
asphalt mixtures
As seen in Table 4.1 and Table 4., there are numerous Michigan mixtures where |E*|
characterization could not be done as part of this study because they were not used in a field
project during the period of this research study. For these mixtures, |E*| predictive models, such
as the Witczak’s model or the ANN model, may be utilized to estimate the master curves. For
this, first, the modified Witczak (Bari 2005) model, which is implemented in the M-E PDG
software, was evaluated. The performance of Witczak’s model is evaluated using two different
approaches; goodness-of-fit statistics, and comparison of measured and predicted values with
respect to the line of equality (LOE) (visual inspection). The goodness-of-fit statistics include Se/
Sy (standard error of estimate /standard deviation), and the correlation coefficient (R2). The
50

ratio of Se/Sy is a measure of improvement in the accuracy of prediction due to the empirical
model. Smaller ratio of Se/Sy indicates better prediction by the model. On the other hand, R

2

measures model accuracy, values closer to one indicate better estimation by the model (Singh et.
2

al. 2010). It is noted that R is a better parameter for linear models with a large sample size.
However, for non-linear models, such as the empirical models, ratio of Se/Sy is a more rational
2

measure of prediction reliability (Kim et. al 2005). The goodness-of-fit statistics (Se/Sy, R )
were calculated using the following equations:

Se 

Sy 

ˆ
 ( y  y) 2

[5.1]

(n  k )

 ( y  y)2

[5.2]

(n  1)

(n  k )  S e

R2  1
(n  1)  S y







2

where:
Se: Standard error of estimate,
Sy: Standard deviation,
2

R : Correlation coefficient,
y: Measured dynamic modulus,
y: Predicted dynamic modulus,
y: Mean value of measured dynamic modulus,
n: Sample size,
k: Number of independent variables in the model. In this case, k=21 (Equation 5.4).
51

[5.3]

Figure 5.1 shows the predicted versus measured values based on the modified Witczak’s
equation developed as part of the NCHRP 1-40D, which is based on the nationally calibrated
coefficients. As shown, the goodness-of-fit statistics for the linear-linear plot are Se/Sy = 0.5084,
and R2 = 0.7881, and for the log-log plot Se/Sy = 0.446, and R2 = 0.8369. It should be recalled
that the smaller the Se/Sy and the larger the R2, the better the goodness-of-fit is. There are
significant differences in |E*| values at high temperature/low frequencies (lower left side of the
graph in Figure 5.1).
Using the laboratory |E*| data collected in this study, the MATLAB software was used to
calibrate the coefficients of the Modified Witczak’s equation. Figure 5.2 shows the predicted
versus measured |E*| values using the calibrated coefficients. The goodness-of-fit statistics for
the linear-linear plot are Se/Sy = 0.3029, and R2 = 0.9248, and for the log-log plot Se/Sy = 0.2053,
and R2 = 0.965 which are much better than the statistics shown in Figure 5.1. In addition, the
predicted values are much closer to the line of equality as compared to results shown in Figure
5.1. Table 5.1 shows a comparison between coefficients used in the original and optimized
models. Each coefficient in Table 5.1 is shown in the following equation (which is the Modified
Witczak equation):

log10 | E* | a1  a 2(| G* |b a3 ) *

a4  a5 p200  a6( p200 ) 2  a7 p4  a8( p4 ) 2  a9 p 3

 Vbeff
 a10( p 3 ) 2  a11Va  a12
 Vbeff  Va
8
8


 Vbeff 
  a16 p 3  a17( p 3 ) 2  a18 p 3
a13  a14Va  a15
8
8
4
 Vbeff  Va 



1  exp( a19  a 20 log | G* |b  a 21log  b )

52

[5.4]


)



Figure 5.1: The modified Witczak’s equation developed as part of the NCHRP 1-40D. The
plot shows the predicted versus measured values before calibration for MDOT mixtures.
2
2
Se/Sy = 0.5084, R = 0.7881 (linear-linear plot), and Se/Sy = 0.446, R = 0.8369 (log-log
plot).
53

Figure 5.2: The modified Witczak’s equation developed as part of the NCHRP 1-40D. The
plot shows the predicted versus measured values after calibration for MDOT mixtures.
2
2
Se/Sy = 0.3029, R = 0.9248 (linear-linear plot), and Se/Sy = 0.2053, R = 0.965 (log-log
plot).
54

Table 5.1: Comparison between coefficients used in the original and optimized models.
Coefficients
a1
a2
a3
a4
a5
a6
a7
a8
a9
a10
a11
a12
a13
a14
a15
a16
a17
a18
a19
a20
a21

|E*| Predictive model
Original
Optimized
model
model
-0.349
-0.97535
0.754
1.212316
-0.0052
0.009132
6.65
8.153804
-0.032
-0.00188
0.0027
0.001256
0.011
0.006975
-0.0001
-0.000019
0.006
0.011852
-0.00014
-0.00017
-0.08
-0.22348
-1.06
-4.84772
2.558
1.092204
0.032
0.074729
0.713
2.350258
0.0124
-0.03973
-0.0001
0.000576
-0.0098
0.014317
-0.7814
0.112725
-0.5785
-0.64427
0.8834
0.38239

5.3 Validation of the calibrated Modified Witczak |E*| predictive model for MDOT
asphalt mixtures
About 15% (9 out of 64) of the asphalt mixtures characterized in this study were used in
the independent validation of the calibrated Modified Witczak predictive model. These 9
mixtures were not used during the calibration of the model shown in Figure 5.2. Figure 5.3
shows a comparison between laboratory measured |E*| values and predicted |E*| values using the
model calibrated for MDOT mixtures. The calibrated model showed very good results as
55

compared to the measured laboratory data. The goodness-of-fit statistics for the log-log plot
2

Se/Sy = 0.3749, R = 0.885, are better than the statistics shown in Figure 5.1.

Figure 5.3: The modified Witczak’s equation developed as part of the NCHRP 1-40D. The
plot shows the predicted versus measured values for MDOT mixtures using the calibrated
2
coefficients. Se/Sy = 0.3749, R = 0.885 (log-log plot).
56

5.4 Evaluation of the ANNACAP software for predicting |E*| of MDOT mixtures
The ANNACAP software, which is an artificial neural network (ANN)-based |E*|
prediction model developed by FHWA’s Long Term Pavement Performance (LTPP) program
(FHWA 2011 (web link), Kim et al. 2010) was evaluated as part of this study. The ANNACAP
software was used to predict the |E*| values using the volumetric properties of the MDOT
mixtures tested, then compared with the laboratory-measured |E*| values. Figure 5.4 shows the
2

measured versus ANNACAP-predicted |E*| values, where the correlation coefficient (R ) was
0.775. As shown, the software, which was trained (i.e., calibrated) nationally, did not perform
very well in predicting |E*| values of MDOT mixtures tested in this study.

Figure 5.4: Predicted versus measured values for MDOT mixtures using the ANNACAP
software: (a) Linear-Linear plot, (b) Log-Log plot.

57

5.5 Development and validation of a new ANN-based |E*| predictive model trained
for Michigan asphalt mixtures
In the field of Computer Science, Artificial Neural Networks (ANNs) have been
extensively utilized for pattern recognition in images, with special emphasis to the application of
face detection (Propp and Samal 1992, Rowley et al. 1998, Sung and Poggio 1998). For road
materials, ANNs have been employed to classify aggregates size (Kim et al. 2004), predict
pavement layer moduli (Ceylan et al. 2007; Kim and Kim 1998), simulate rutting and fatigue
performance of asphalt mixtures (Huang et al., 2007; Tarefder et al. 2005a), estimate the
thickness of the pavement layers (Gucunski and Krstic 1996), approximate the resilient modulus
of base materials (Tutumluer and Seyhan 1998), and relate mixture variables to permeability and
roughness (Choi et al. 2004; Tarefder et al. 2005b). ANN models are very useful in predicting
certain engineering outputs (e.g., |E*|) from a number of input variables (e.g., asphalt volumetric
properties).
In an effort to develop an improved |E*| predictive model for the future MDOT mixtures
that are not similar to the ones tested in this study, an ANN model was developed using the data
generated as part of this study. In this study, an ANN was developed to predict |E*| at different
temperatures and frequencies using the following inputs:
(i)

p200 = Percentage of aggregate passing #200 sieve

(ii)

p4 = Cumulative percentage of aggregate retained in #4 sieve

(iii)

p3/8 = Cumulative percentage of aggregate retained in 3/8-inch sieve

(iv)

p3/4 = Cumulative percentage of aggregate retained in 3/4-inch sieve
58

(v)

Va = Percentage of air voids (by volume of mix)

(vi)

Vbeff = Percentage of effective asphalt content (by volume of mix)

(vii)

|G*|b = Dynamic shear modulus of asphalt binder (psi)

(viii) db = Binder phase angle associated with |G*|b (degrees)
(ix)

f = reduced frequency (Hz) corresponding to each |G*| and db.

It is noted that the ANN-algorithm developed in this study automatically generates the
|E*| master curve and determines the shift factor polynomial coefficients (i.e., a1 and a2 of
aT(T) – see Equation [2.11]) and uses them to calculate the reduced frequency (i.e., the input
(ix) above).
5.5.1 Structure of the ANN
A feed-forward (back-propagation) network of one hidden layer and one output layer was
determined to be the optimum network for the ANN model (Figure 5.5). This ANN structure was
obtained by a trial and error process that involves trial of many ANN structures (Demuth and
Beale 2004).
The steps below describe how the ANN shown in Figure 5.5 calculates output y (which is
the |E*| in this case) from a set of 9 inputs (which are p200, p4, |G*|, etc. shown in the previous
page). These steps are herein called “forward computation”.
1) Compute the output of the Hidden Layer ( aH ) using Equations [5.5] and [5.6]. The
variables in bold letters in these equations indicate that they are matrices (or vectors)

59

and the multiplication and summation in the equation are matrix operations. The
tansig function in Equation [5.6], however, is applied to each element of the vector.

n H  W Hp  b H

[5.5]

a H  tansig(n H )

[5.6]

where p is the input vector (9×1), WH is the weight matrix (8×9) and bH is the bias
vector (8×1) of the Hidden Layer, and the tansig is the transfer function given as:

tansig ( x) 

2
1
1  exp( 2 x)

[5.7]

Inputs

Va
Vbeff
p200
p4
p3/8
p3/4
IG*|b
δb
f

ANN

Input

Hidden Layer

Output:
|E*| = Dynamic
modulus

Output Layer

Output

aH W 0
a0
W 1H
0
H
y1x1
(1X8) n
(8x1) +n1
+
(9x1)
(8x1)
(1x1)
H
0
b1
b
(1x1)
(8x1)tansig
purelin
(8X1)
(1X1)
aH =tansig(WHp+bH) a0 =purelin(W0aH +b0)
P

Figure 5.5: Structure of the ANN model.
60

2) Compute the output of the Output Layer by using the output of the Hidden Layer (

)

as follows:

no  W oa H  bo
y = purelin(no ) = no

[5.8]
[5.9]

where y is the positive or negative scalar output of the entire network, aH is the
output of the Hidden Layer (8×1), Wo is the weight matrix (1×8) and bo is the bias
constant of the Output Layer.
5.5.2 Training the ANN
The training initiates with random weights (i.e., WH and Wo) and biases (i.e., bH and
bo). The forward computation described in the previous section is repeated many times while
adjusting these weights and biases. Each repetition is called an epoch, which continues until the
error between the predicted output from the ANN (i.e., y = |E*|predicted) and actual target output
(i.e., ytarget = |E*|measured) is minimized. The ANN model was trained by using 41 different Job
Mix Formulas (JMFs). It is noted that a JMF is the mix design the contractor uses when paving a
particular mix. For each JMF, 12 |G*| values and 12 phase angle values were used to cover a
wide range of frequencies and temperatures, which makes 492 data points. MATLAB’s ANN
toolbox was used for this purpose. In this toolbox, the mean square error between the measured
and predicted |E*| decreases as the number of epochs increases. It is noted that the training
dataset is divided into three subsets: Training (80% of the dataset), Validation (10% of the
dataset), and Test (10% of the dataset). The ANN primarily uses the information from the

61

Training dataset and adjusts the weights and biases accordingly. While doing so, it also looks at
the prediction accuracy of Validation dataset and makes sure that error in Validation data set is
close to the error from the Training dataset. If the error in Validation dataset is significantly
larger than the error in Training dataset, it means that the ANN is over trained to the Training
dataset and memorized the Training dataset rather than learning the overall interrelation between
the input and output. Lastly, the Testing dataset, which is not used during adjusting weights and
biases, is used as an independent validation of the model.
Figure 5.6 shows the change in the mean squared error as the epochs increase. As shown,
all curves (Training, Validation and Test) are close to each other, which means that the ANN
developed in this study learned from the training data, it did not memorize. Performance of the
ANN model was evaluated from the plot of the predicted versus measured values of |E*| for the
training, validation and testing datasets as shown in Figure 5.7. Coefficient of determination (R2)
with respect to the line of equality was computed, which is used to measure the goodness-of-fit
of the trend. As shown in Figure 5.7, ANN predictions lay around the line-of-equality with R2s
ranging from 0.951 to 0.963. Considering the sample-to-sample variability and other factors, this
is a good result and better than the Modified Witczak model (see Figure 5.3) and the ANNACAP
(see Figure 5.4). It should be noted that ANN models are trained and validated for local material
properties used in each developed model. Therefore ANN models that are developed nationally,
are not expected and will not provide |E*| predictions that are as accurate as those of models that
are independently developed for materials used in a specific State. Therefore; the ANN-based
|E*| prediction model developed in this study may not perform as well as shown above in
predicting |E*| values for materials used in other regions.
62

In order to further validate the ANN model developed in this study, 9 different asphalt
mixtures were set aside and not used in any of the ANN development process. Then these 9
mixtures were used in forward computation of |E*| values using the ANN developed. Figure 5.8
presents the predicted versus measured values using the independent data set. As shown,
independent validation of the ANN model exceeds the accuracy of the calibrated Modified
Witczak model (see Figure 5.3).

Figure 5.6: Error versus the epochs in the ANN model developed in this study

63

Figure 5.7: Predicted versus measured |E*| values for Training, Validation and Testing
datasets as well as all the data (for mixtures used during development of the model).

64

Figure 5.8: Predicted versus measured values for MDOT mixtures using the MSU-ANN
model for mixtures not used during development of the model

65

6. INVESTIGATION OF SAMPLE GEOMETRY & RVE
REQUIREMENT FOR |E*| USING THIN BEAM MIXTURES (TBMs)
It is desirable to study the effect of aged material properties on pavement performance.
Recent research showed that current laboratory aging protocols lead to aging gradients within the
regular-size (100mm diameter, 150mm tall) samples (Houston et al. 2005). Test samples become
non-homogeneous and anisotropic. Such samples are no longer useful for performance testing,
especially for tests that are used to calibrate advanced models. Therefore, it is suggested in this
study that relatively smaller test geometries be used for that purpose. Thin Beam Mixtures
(TBMs) (127×12.7×6.35mm) were obtained from typical gyratory cored asphalt mixture
specimens to investigate the possibility of obtaining the complex modulus |E*| master curve from
the creep compliance D(t) using the Bending Beam Rheometer (BBR) testing machine and in
efforts of verifying the RVE requirement for asphalt mixtures. Once the RVE requirement is
verified for the thin beam asphalt mixtures, this will serve as a foundation for the aging study
since small samples will be much less susceptible to aging gradients. A similar study (NCHRPIDEA 151) by Marasteanu et al. (2012) showed the feasibility of using TBM samples for low
temperature cracking analysis.

6.1 Materials Used
As previously mentioned in the Chapter 3 (Research Methodology), it was intended to
verify the applicability of this methodology on a wider range of asphalt mixtures. Therefore; 10
asphalt mixtures commonly used in the State of Michigan with varying Nominal Maximum
66

Aggregate Sizes (NMASs) were tested. In addition, three replicates representing the same asphalt
mixture were tested in order to account for sample-to-sample variability which brings the total up
to 30 tested asphalt mixture beams as shown below in Table 6.1.

6.2 Bending Beam Rheometer (BBR) testing on Thin Beam Mixtures (TBMs)
As part of the binder PG specification; the BBR is used to determine the creep
compliance of asphalt binders using the 3-point bending setup commonly used in mechanics
(Zofka et al. 2007). This test method follows the method developed at the University of
Minnesota to determine the creep stiffness of thin mixture beams using the BBR testing
equipment used to determine the PG grade of asphalt binders. This procedure was developed into
a draft standard procedure under a NCHRP IDEA project led by Dr. Marasteanu.
Similar to BBR testing of asphalt binders, a constant force is applied in the middle of the
beam, and deflections with time are measured throughout the test. Using the deflections
measured during the test, and knowing the dimensions of the beam, the applied force and stress;
the resulting strain and creep compliance D(t) can be computed.
Applied load

TBM

Supports

Figure 6.1: 3-point testing concept on asphalt mixtures.
67

Table 6.1: List of TBMs tested along with their volumetric properties and NMAS
NMAS (mm)

HMA ID

Binder
PG

Maximum
Specific Gravity
Gmm

64-22

2.545

18A

58-22

2.534

58-28

2.415

58-34

2.511

90

70-22

2.547

64

58-34

2.462

206

64-22

2.503

21

64-28

2.481

29A

9.5

2.502

80

12.5

58-28

26B

19.0

205

2

25.0

64-28

2.457

N/M: Not measured

68

TBM ID

Air Voids
(AV) (%)

205-U-C
205-U-M
205-U-E
2-U-C
2-U-M
2-U-E
18A-U-C
18A-U-M
18A-U-E
26B-U-C
26B-U-M
26B-U-E
80-U-C
80-U-M
80-U-E
90-U-C
90-U-M
90-U-E
64-U-C
64-U-M
64-U-E
206-U-C
206-U-M
206-U-E
21-U-C
21-U-M
21-U-E
29A-U-C
29A-U-M
29A-U-E

14.09
11.85
12.66
12.23
8.49
9.03
8.63
7.21
5.82
9.79
8.77
6.50
N/M*
N/M*
9.39
10.85
4.11
8.03
12.81
8.40
9.30
9.94
8.28
6.22
9.18
10.34
12.47
13.31
12.71
10.38

Once the D(t) tests are completed at different temperatures, the Time-Temperature
Superposition (TTS) principle is used to compute the D(t) master curve. It should be noted that
the theory of viscoelasticity states that if one of the linear viscoelastic properties (i.e., complex
modulus |E*|, creep compliance D(t), and relaxation modulus E(t)) is known, the remaining
properties can be calculated through numerical inter-conversion procedures (Park and Schapery,
1999). Once the D(t) master curve is determined, the |E*| master curve can be computed using
the methods described by Park and Schapery (1999).

6.3 Results and Discussion
Due to the availability of limited samples; the TBM tests were only conducted at one
temperature (-10º C). This did not produce enough data points to obtain |E*| values for the
studied mixtures through inter-conversion processes. Instead, using the basic theory of
viscoelasticity; |E*| laboratory measurements on regular size specimens of the 10 HMAs under
study were converted to D(t) values and compared with the values measured using the BBR
machine on the TBMs.
Figure 6.2 through Figure 6.6 show comparisons between |E*|-based D(t) values and
TBM-based D(t) values for all TBMs tested in this study based on the NMAS of each asphalt
mixture. Visual inspection with respect to the line of equality (LOE) do not show a good
correlation between measured D(t) values using the TBM and D(t) values converted from |E*|
data run on the regular size specimens. A trend in D(t) values obtained from the BBR test on
TBMs was observed. On the other hand; the factor between |E*|-based and TBM-based D(t)

69

values was inconsistent and ranged between 1.5 and 4 factors. This was observed for all NMASs
used in this study.
Figure 6.2 shows a comparison between |E*|-based D(t) values and TBM-based D(t)
values for HMA #205 with a NMAS of 25.0mm. The factor between |E*|-based, and TBM-based
D(t) values was approximately 3 factors. Figure 6.3 shows comparisons for 19.0mm NMAS thin
beams. The factor between |E*|-based, and TBM-based D(t) values ranged between 1.5 and
approximately 4 factors. The data shown in Figure 6.2 for the 25.0mm NMAS represents one
asphalt mixture only. This is the reason why the 25.0mm NMAS showed less variability as
compared to the 19.0mm NMAS mixtures. Figure 6.4 shows comparisons for 12.5mm NMAS
thin beams. The factor between |E*|-based, and TBM-based D(t) values ranged between 1.5 and
less than 3 factors. Figure 6.5 shows comparisons for 9.5mm NMAS thin beams. The difference
between |E*|-based, and TBM-based D(t) values ranged between 1.6 and approximately 2
factors. In addition, Figure 6.6 shows a comparison between |E*|-based D(t) values and TBMbased D(t) values for all TBMs tested in this study. The overall plot shows a difference between
|E*|-based and TBM-based D(t) values that range between 1.5 and approximately 3 factors. It
should be noted that the variation could have also been caused by the different air void levels for
each TBM.

70

NMAS; 25.0mm

205-Avg AV; 12.86%
y = 0.3025x

D(t) from |E*| (1/psi)

2.0E-06

²

R = 0.9869

1.5E-06

3.41

1.0E-06

3.28

5.0E-07
0.0E+00
0.0E+00

5.0E-07

1.0E-06
1.5E-06
D(t) from TBM (1/psi)

2.0E-06

Figure 6.2: Comparison between |E*|-based D(t) values and TBM-based D(t) values for
25.0mm NMAS.

NMAS; 19.0mm

2.5E-06

D(t) from |E*| (1/psi)

2.0E-06

26B-Avg AV; 8.35% 2-Avg AV; 9.91% 18A-Avg AV; 7.22%
y = 0.6508x
y = 0.4355x
y = 0.2377x

²

R = 0.9913

²

R = 0.8886

²

R = 0.8723

1.5E-06
1.0E-06

2.48

1.5

3.96

5.0E-07
0.0E+00
0.00E+00

5.00E-07

1.00E-06
1.50E-06
D(t) from TBM (1/psi)

2.00E-06

2.50E-06

Figure 6.3: Comparison between |E*|-based D(t) values and TBM-based D(t) values for
19.0mm NMAS.

71

NMAS; 12.5mm

3.5E-06
3.0E-06

64-Avg AV; 10.17% 80-Avg AV; 9.39% 90-Avg AV; 7.66%
y = 0.3659x
y = 0.3279x
y = 0.5712x

²

2.5E-06
D(t) from |E*| (1/psi)

²

R = 0.8975

²

R = 0.9225

R = 0.859
2.96

2.0E-06
1.5E-06
1.48

1.0E-06
5.0E-07
0.0E+00
0.0E+00

1.0E-06

2.0E-06

3.0E-06

D(t) from TBM (1/psi)
Figure 6.4: Comparison between |E*|-based D(t) values and TBM-based D(t) values for
12.5mm NMAS.

NMAS; 9.5mm

D(t) from |E*| (1/psi)

2.0E-06

29A-Avg AV; 12.13% 206-Avg AV; 8.14% 21-Avg AV; 10.66%
y = 0.5128x
y = 0.517x
y = 0.566x

1.5E-06
1.0E-06

²

²

R = 0.78

R = 0.9837

²

R = 0.9172
2.13

1.61

5.0E-07
0.0E+00
0.0E+00

5.0E-07

1.0E-06
D(t) from TBM (1/psi)

1.5E-06

2.0E-06

Figure 6.5: Comparison between |E*|-based D(t) values and TBM-based D(t) values for
9.5mm NMAS.

72

All mixtures

3.5E-06

LOE
18A
64

D(t) from |E*| (1/psi)

3.0E-06

2
90
29A

80
21
205

206
26B

2.5E-06

2.96

2.0E-06
1.5E-06
1.0E-06

1.48

5.0E-07
0.0E+00
0.0E+00

1.0E-06

2.0E-06

3.0E-06

D(t) from TBM (1/psi)
Figure 6.6: Comparison between |E*|-based D(t) values and TBM-based D(t) values for all
mixtures and NMASs.

As shown from the simple analysis, D(t) values obtained from the BBR test are not very
comparable to the values obtained from regular size |E*| test specimens. It should be noted that
the BBR testing on TBMs is a bending mode of testing, and the |E*| testing on regular-size
performance specimens is a compression mode of testing. Therefore, the factors between |E*|based and TBM-based D(t) values are expected. In a similar study, Zofka et al. (2007) compared
D(t) values obtained from the BBR machine with D(t) values obtained from the Indirect Tensile
Strength (IDT) test. The difference in magnitude was close to the difference obtained in this
study at intermediate temperatures (-10º C). The difference observed was much less at lower
temperatures. The D(t) values obtained from the BBR test should correlate even better with those
obtained from the IDT test since it is a tension mode of testing. A trend was observed in TBM73

based D(t) values, but inconsistent factors of difference between |E*|-based and TBM-based
values do not support the use of this experimental procedure for producing fundamental
engineering material properties of asphalt mixtures.
Based on the limited analysis carried out in this study, it is concluded that the BBR test is
not very feasible for estimation of mixture creep compliance and therefore; not very reliable for
estimation of other linear viscoelastic properties (i.e., complex modulus |E*|, and relaxation
modulus E(t)) through numerical inter-conversion.
Better results were observed for asphalt mixtures with a NMAS of 12.5mm and less. It
should be noted that this experimental procedure was only conducted at one temperature (-10º
C). Variability in test data is expected to be less for test temperature less than -10° C. On the
other hand, much higher variability in the test data will probably be observed for materials tested
at higher temperatures. Further analysis is indeed required to form a better understanding and
validation of this experimental procedure.

74

7. CONCLUSIONS & RECOMMENDATIONS
This research investigated the linear viscoelastic characteristics of typical asphalt
mixtures and binders commonly used in the State of Michigan. Such material characterization is
very important for implementation of the M-E PDG in Michigan and for accurate predictions of
flexible pavement performance in the field. The Modified Witczak |E*| predictive model was
locally calibrated for Michigan, and an analytical model was developed to better predict
distresses for flexible pavements in Michigan through an Artificial Neural Network (ANN) that
was developed and trained for typical asphalt mixtures in Michigan. In addition, the
Representative Volume Element (RVE) requirement for dynamic modulus |E*| of asphalt
mixtures was investigated and verified. This study showed that the BBR testing machine is not
always feasible for obtaining mixture Creep Compliance (D(t)) of thin beams of asphalt mixtures
(0.5”×0.25”×4.5”), and therefore it may not be very reliable for estimation of other linear
viscoelastic properties (i.e, complex modulus |E*|, and relaxation modulus E(t)) through
numerical inter-conversion. Following is a summary of conclusions and recommendations that
were observed based on this study:
1. The Modified-Witczak (MW) model was calibrated for use in |E*| prediction of asphalt
mixtures commonly used in the State of Michigan to be used in the Level 1 analysis of
the M-E PDG software. The calibrated model performed well in comparison with the
laboratory measured data.
2. The ANNACAP software, which was developed by the FHWA’s LTPP program, was
evaluated for use in the |E*| prediction of asphalt mixtures commonly used in the State of
Michigan. The software did not perform well for MDOT mixtures in predicting |E*|.

75

3. A new ANN-based model was developed as part of this research. The new ANN-based
model did very well in predicting |E*| values of Michigan mixtures.
4. ANN models that are developed nationally are not expected and will not provide |E*|
predictions that are as accurate as those of models that are independently developed for
materials used in a specific State. Therefore; the ANN-based |E*| prediction model
developed in this study may not perform as well as shown above in predicting |E*| values
for materials used in other regions.
5. A summary of |E*| values based on MDOT mix designation was provided. As expected,
3E mixtures were generally stiffer than 4E and 5E mixtures. However the trend was not
always consistent in all temperatures. A clear trend should not be expected since there are
many variables that play a role in the magnitude of |E*| at different temperatures and
frequencies.
6. A comparison of variation in |E*| master curves based on MDOT mix designations (e.g.,
3E10) was carried out. Grouping mixtures based on MDOT mix designation and using
the average of |E*| values for the given designation is not recommended.
7. This study showed that the TBM-based D(t) values obtained from the BBR testing
machine do not match very well to |E*|-based D(t) values.
8. D(t) values obtained from the BBR testing machine showed a trend in estimated values
but the factor (ratio) between |E*|-based and TBM-based D(t) values was inconsistent.
9. Further investigation is needed for use of TBMs.

76

APPENDICES

77

APPENDIX A: VOLUMETRIC PROPERTIES AND AGGREGATE GRADATION
OF THE TESTED ASPHALT MIXTURES.

78

Table A.1: Volumetric properties and aggregate gradation of the tested asphalt mixtures.
Sample ID
2A
2-WMA
4
18A
18B
20A
20B
20C
21
23
24A
24B
26A
26B
26C
28A
28B
29A
29B
31A
31B
32A
32B
37
44

PG
Grade
64-22
64-28
70-28
58-22
58-22
64-28
64-28
64-28
64-28
70-28
70-28
70-28
58-22
58-28
58-28
64-28
64-28
64-28
64-28
70-28
70-28
70-28
70-28
58-28
58-28

% Asphalt
(Given)
4.90
4.90
5.31
5.20
5.04
5.23
5.53
5.58
6.01
4.94
6.29
5.78
5.60
5.30
5.43
5.40
5.43
5.99
5.92
5.62
5.40
5.99
6.08
6.01
5.35

VMA

VFA

Angularity

13.94
14.02
15.04
14.16
13.52
15.05
14.97
14.83
16.34
14.40
16.04
15.94
14.17
13.80
13.72
14.75
15.06
15.74
16.07
15.27
14.71
15.71
16.20
16.52
15.07

78.47
78.67
73.51
78.81
77.81
73.49
73.28
76.40
75.58
75.69
75.06
78.04
78.83
78.17
18.14
72.87
73.44
74.59
75.11
73.76
72.81
74.54
75.31
75.78
73.46

46.00
46.00
45.30
46.00
41.30
45.20
45.00
45.20
45.30
46.00
45.40
45.00
45.00
42.10
41.10
41.20
41.70
43.40
43.00
41.20
41.20
43.40
41.70
42.60
42.10
79

Gmm Gmb
2.545
2.508
2.510
2.534
2.502
2.506
2.485
2.489
2.481
2.578
2.426
2.531
2.538
2.490
2.473
2.471
2.490
2.457
2.463
2.471
2.472
2.458
2.450
2.494
2.475

2.469
2.433
2.410
2.458
2.427
2.406
2.386
2.402
2.382
2.488
2.329
2.422
2.462
2.415
2.398
2.372
2.390
2.359
2.364
2.372
2.373
2.360
2.352
2.395
2.376

Gb

Gse

Gsb

Pbe

1.027
1.029
1.025
1.018
1.023
1.029
1.029
1.032
1.029
1.030
1.031
1.030
1.018
1.020
1.017
1.028
1.028
1.028
1.028
1.017
1.031
1.031
1.017
1.032
1.020

2.755
2.708
2.732
2.760
2.710
2.722
2.710
2.715
2.727
2.796
2.668
2.779
2.785
2.709
2.694
2.686
2.711
2.696
2.700
2.701
2.686
2.696
2.696
2.743
2.692

2.728
2.691
2.686
2.715
2.665
2.684
2.651
2.663
2.676
2.763
2.599
2.737
2.708
2.653
2.629
2.632
2.661
2.632
2.650
2.642
2.632
2.632
2.636
2.696
2.648

4.55
4.70
4.62
4.72
4.73
5.33
5.33
4.62
4.55
4.55
4.66
4.76
5.12
5.24
4.83
4.66
5.12
5.27
5.39
4.75

Table A.1 (cont’d)

Sample
ID

1-1/2"

1"

3/4"

1/2"

3/8"

No. 4

No. 8

No. 16

No. 30

No. 50

No. 100

No. 200

2A
2-WMA
4
18A
18B
20A
20B
20C
21
23
24A
24B
26A
26B
26C
28A
28B
29A
29B
31A
31B
32A
32B
37
44

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

100.00
100.00
100.00
100.00
98.10
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

83.00
88.10
98.80
84.50
88.80
98.80
93.40
93.20
100.00
91.60
100.00
100.00
88.10
89.80
86.10
98.90
90.10
100.00
100.00
93.90
98.90
100.00
100.00
100.00
93.70

72.30
77.10
88.60
73.40
84.30
89.50
90.40
88.60
99.20
83.00
95.70
97.80
78.40
80.70
80.70
89.60
84.40
97.90
96.90
87.80
89.60
97.90
96.70
92.50
86.20

47.30
57.60
73.20
49.40
65.80
71.10
83.40
73.50
83.60
68.30
80.10
86.80
52.60
63.60
63.30
71.50
71.20
80.30
77.40
72.00
71.50
80.30
77.80
70.10
73.30

34.90
40.90
56.30
34.70
46.20
53.50
56.20
54.00
66.30
50.00
58.00
61.80
33.00
46.30
49.00
57.00
55.70
59.60
59.00
56.70
57.00
59.60
58.20
58.60
54.80

26.00
27.70
38.00
25.70
33.90
36.30
36.70
40.70
46.50
35.90
39.90
44.30
22.10
35.60
41.40
46.30
44.20
44.90
46.40
43.90
46.30
44.90
45.10
50.30
41.80

18.20
19.50
25.20
20.20
25.50
23.50
25.60
30.80
31.20
25.60
28.70
32.30
15.60
26.60
32.60
35.90
32.20
32.90
33.20
32.60
35.90
32.90
34.20
41.10
30.60

9.30
12.70
14.70
11.50
16.30
13.10
15.80
19.40
17.30
14.40
16.20
18.30
10.90
13.90
14.20
15.60
16.10
15.20
16.10
16.30
15.60
15.20
191.00
21.90
16.10

6.10
7.50
7.80
6.90
7.40
7.40
8.40
8.60
8.70
6.80
7.70
9.00
7.20
6.50
6.20
7.00
7.40
7.20
7.10
6.90
7.00
7.20
7.40
8.70
6.60

5.00
4.50
4.90
5.20
4.40
4.70
5.80
4.60
5.40
4.30
5.80
5.60
5.20
4.40
4.50
5.40
5.10
5.40
4.90
4.70
5.40
5.40
5.00
5.90
4.40

80

Table A.1 (cont’d)

Sample ID
45
47
48
49A
49B
49C
51A
51B
51C-WMA
62
64
65
67
68
80
81
85
86
90
97
102
103
105
106
108

PG
Grade
58-28
64-28
64-28
70-28
70-28
70-28
58-28
58-28
58-28
58-28
58-34
58-34
64-34
64-34
58-34
58-34
64-34
64-34
70-22
70-22
64-22
64-22
70-22
70-22
64-22

% Asphalt
(Given)
5.98
5.29
5.91
6.18
6.16
6.12
6.24
5.36
5.60
4.89
5.40
6.00
5.10
5.46
5.45
5.66
5.48
6.14
4.98
5.49
5.20
5.60
5.08
5.70
5.21

VMA

VFA

Angularity

16.22
14.88
16.02
17.59
18.19
17.94
16.51
14.72
15.37
14.17
15.00
16.10
15.40
15.78
15.20
16.11
15.20
16.00
14.73
15.92
14.96
16.06
15.23
16.02
15.05

75.38
73.12
75.03
77.35
78.01
77.70
75.80
76.22
77.33
78.82
73.30
75.20
74.10
75.65
73.70
75.20
77.00
81.20
76.23
74.88
73.25
75.10
73.74
75.04
73.43

42.40
42.60
41.90
48.90
46.30
48.70

42.90
41.00
43.20
42.10
42.80
41.80
42.80
43.20
42.50
47.00
46.00
46.00
45.00
46.00
46.30
46.00
81

Gmm Gmb
2.454
2.504
2.474
2.535
2.489
2.543
2.474
2.483
2.468
2.589
2.462
2.468
2.565
2.537
2.511
2.523
2.497
2.471
2.547
2.537
2.550
2.498
2.536
2.489
2.541

2.356
2.404
2.375
2.434
2.390
2.441
2.375
2.396
2.382
2.512
2.364
2.369
2.463
2.436
2.411
2.422
2.410
2.397
2.458
2.436
2.448
2.398
2.434
2.389
2.439

Gb

Gse

Gsb

Pbe

1.020
1.029
1.029
1.025
1.018
1.035
1.032
1.024
1.024
1.032
1.023
1.023
1.026
1.026
1.026
1.026
1.033
1.033
1.023
1.023
1.027
1.027
1.025
1.025
1.027

2.695
2.722
2.713
2.808
2.750
2.810
2.727
2.701
2.693
2.807
2.679
2.712
2.789
2.773
2.740
2.765
2.721
2.718
2.763
2.776
2.776
2.730
2.753
2.724
2.765

2.644
2.675
2.661
2.771
2.741
2.793
2.667
2.659
2.657
2.783
2.629
2.655
2.764
2.734
2.688
2.724
2.686
2.678
2.739
2.738
2.729
2.697
2.726
2.683
2.722

5.29
4.66
5.21
5.72
6.05
5.44

4.59
4.74
5.24
4.75
4.96
4.77
5.13

4.60
5.17
4.73
5.16
4.65

Table A.1 (cont’d)

Sample ID

1-1/2"

1"

3/4"

1/2"

3/8"

No. 4

No. 8

No. 16

No. 30

No. 50

45
47
48
49A
49B
49C
51A
51B
51C-WMA
62
64
65
67
68
80
81
85
86
90
97
102
103
105
106
108

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

100.00
100.00
100.00
100.00
99.90
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

100.00
93.50
100.00
94.60
92.50
96.10
94.80
91.90
91.20
86.50
95.00
100.00
95.90
100.00
98.20
100.00
93.70
100.00
98.20
100.00
98.50
100.00
99.30
100.00
98.70

96.60
87.10
99.70
70.00
77.10
79.70
83.20
84.80
85.70
76.10
86.90
97.40
84.30
95.40
89.90
97.40
84.40
97.00
85.60
99.70
88.60
99.90
88.30
99.50
87.30

77.40
76.40
83.30
26.60
27.40
31.80
58.70
72.40
71.40
56.90
72.50
75.20
64.80
73.60
69.30
75.20
66.40
80.20
63.60
77.70
65.10
75.90
63.00
76.20
65.10

57.80
57.20
6.30
20.50
19.00
22.10
44.60
57.20
56.70
45.40
56.70
56.70
56.20
59.90
54.00
56.40
53.50
62.20
44.20
53.90
45.00
54.70
42.20
47.70
46.50

45.10
41.30
49.80
16.60
15.30
17.80
35.90
45.40
43.90
34.40
43.50
42.50
45.00
47.80
41.10
43.60
42.60
47.80
31.00
37.20
30.30
39.10
28.10
32.70
32.30

34.40
29.90
36.70
13.00
12.70
14.40
27.40
35.50
30.80
23.10
32.20
31.10
30.90
33.90
30.00
31.00
26.90
33.80
22.00
26.20
21.50
29.50
19.40
23.20
23.30

18.60
16.60
20.00
10.40
10.70
11.80
14.00
19.50
14.80
14.60
15.50
15.50
20.10
21.60
18.60
16.80
11.20
18.20
14.00
14.80
13.50
18.00
12.90
14.70
14.90

82

No.
100
8.00
8.00
9.20
8.90
9.30
9.70
7.10
7.90
7.30
6.10
6.20
6.60
8.20
8.80
8.40
8.60
7.00
8.20
7.50
9.10
7.80
9.80
7.70
7.90
8.10

No.
200
5.40
5.30
6.10
8.20
8.20
8.10
4.70
5.20
4.50
3.50
4.50
4.80
5.00
5.20
5.60
5.80
5.40
5.70
5.60
6.20
5.60
6.00
5.50
5.40
5.70

Table A.1 (cont’d)

Sample ID
109
111
112
127
200
201
202
203
204
205
206
207
208WMA
209A-HMA
209B-WMA

PG
Grade
64-22
70-22
70-22
58-22
58-28
64-28
64-22
70-22
70-22
58-28
64-22
64-22
64-22
64-22
64-22

% Asphalt
(Given)
5.50
5.31
5.80
5.43
5.20
3.30
6.03
4.99
5.80
4.90
5.40
6.21
5.60
6.21
6.21

VMA

VFA

Angularity

16.08
15.09
16.39
15.23
13.70

75.12
73.50
75.59
73.74
78.22

45.00
46.00
45.00

16.19
14.85
15.77
13.23
16.08
16.04
14.75
15.89
15.89

75.36
73.07
74.63
77.32
75.13
75.06
76.27
77.97
77.97

43.20
3.30
45.60
47.00
47.00
42.10
45.00
43.70
45.00
45.00

83

Gmm Gmb
2.493
2.544
2.489
2.522
2.513
2.734
2.482
2.510
2.524
2.502
2.503
2.503
2.461
2.476
2.476

2.393
2.443
2.389
2.421
2.438
2.383
2.410
2.423
2.427
2.403
2.403
2.375
2.389
2.389

Gb

Gse

Gsb

Pbe

1.027
1.025
1.025
1.022
1.024
1.026
1.031
1.025
1.025
1.020
1.027
1.025
1.034
1.209
1.209

2.719
2.775
2.729
2.754
2.731
2.835
2.728
2.717
2.774
2.704
2.727
2.767
2.680
2.730
2.730

2.695
2.724
2.692
2.701
2.678
2.775
2.672
2.689
2.710
2.660
2.709
2.684
2.630
2.664
2.664

5.18
4.66
5.31
4.74
4.50
2.54
5.29
4.62
4.98
4.31
5.16
5.14

Table A.1 (cont’d)

Sample ID

1-1/2"

1"

3/4"

1/2"

3/8"

No. 4

No. 8

No. 16

No. 30

No. 50

109
111
112
127
200
201
202
203
204
205
206
207
208WMA
209A-HMA
209B-WMA

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

100.00
100.00
100.00
100.00
99.90
96.00
100.00
100.00
100.00
90.00
100.00
100.00
100.00
100.00
100.00

100.00
98.90
100.00
92.50
88.90
59.50
100.00
96.40
100.00
73.50
100.00
99.60
94.20
100.00
100.00

99.60
87.60
99.90
86.80
82.60
30.20
99.70
87.10
99.70
69.70
99.70
97.80
86.10
97.80
97.80

75.60
66.50
75.80
79.20
65.00
14.70
84.10
52.30
76.40
57.40
78.00
85.50
65.20
77.60
77.60

51.40
47.30
54.90
58.50
48.40
11.50
66.70
33.60
53.20
44.50
53.90
63.50
48.70
52.70
52.70

36.50
33.90
39.20
43.20
34.10
9.10
46.80
22.40
36.60
35.30
38.60
46.40
39.40
37.40
37.40

27.40
24.40
29.10
32.60
22.50
7.20
31.50
15.90
24.30
25.50
29.10
33.30
32.40
25.90
25.90

17.60
15.80
18.20
20.90
12.00
6.00
16.60
10.90
13.70
12.60
18.00
20.30
15.60
14.20
14.20

84

No.
100
9.60
8.20
8.40
10.30
7.30
4.60
8.70
7.10
8.70
5.90
9.60
9.70
6.40
7.30
7.30

No.
200
6.40
5.70
6.10
5.60
5.10
3.60
6.00
5.50
6.10
4.40
6.40
5.30
4.50
4.90
4.90

APPENDIX B: A LIST OF ASPHALT MIXTURE SAMPLES TESTED IN THIS
STUDY ALONG WITH THE CORRESPONDING AIR VOID LEVEL OF EACH
SAMPLE

85

Table B.1: List of HMAs tested and their air voids.
Unique
Sample#
HMA#

1

2

3

4

5

6

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

HMA
ID

Core
Avg.
AV%

STDEV
AV

5.7

0.3

5.9

SlabShearbox

7.37

0.005

6.4

Gyratory

6.7

0.2

2.7

SlabShearbox

9.1

0.4

4

SlabShearbox

7.57

0.001

1.3

Gyratory

8.3

0.4

4.3

SlabShearbox

7.0

0

0.6

SlabShearbox

4.4

0.3

7.5

SlabShearbox

7.03

0.7

9.8

Gyratory

4.1

0.3

8

SlabShearbox

4.7

4.7

-

-

Gyratory

6.5
6.2
6.6

6.4

0.2

2.9

SlabShearbox

Sample
AV%
ID

18-1
18-S1
18-2
18-3
18-4
18-S2
18-5
18-6
28-1
28(B)28-2
S1
28-3
29-1
29(A)S1
29-3
29-1
29(A)29-2
S2
29-3
44-1
44-S1
44-2
44-3
44-4
44-S2
44-5
44-6
49A-1
49AS1
49A-2
49A-1
49A49A-2
S2
49A-3
203-1
203203-2
S1
203-3
203203GYRO GYRO
203-4
203203-5
S2
203-6

5.7
6.1
5.4
7.9
7.1
7.1
6.6
6.9
6.5
8.9
9.4
7.5
7.6
7.6
8.0
8.2
8.7
7.0
7.0
6.9
4.2
4.6
6.4
6.9
7.8
3.8
4.4
4.2

86

COV Compaction
(%)
method

Table B.1 (cont’d)
Unique
HMA#

7

8

9

10

11

12

13

14

Sample#
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64

HMA
ID
204S1
204S2
205S1
205GYRO
205

24A

32B

37

67

81

51A

Sample
ID
204-1
204-2
204-3
204-1
204-2
205-1
205-2
205-3
205GYRO
205-1
205-2
205-3
24A-1
24A-2
24A-3
24A-4
32-1
32B-2
32B-3
32B-4
37-1
37-2
37-3
67-1
67-2
67-3
81-1
81-2
81-3
51A-1
51A-2
51A-3

6.4
6.2
6.2
6.9
6.8
9.0
8.8
8.6

STDEV
AV

COV
(%)

Compaction
method

6.3

AV%

Core
Avg.
AV%

0.1

1.9

SlabShearbox

6.86

0.07

1

Gyratory

8.8

-

-

Gyratory

0.27

4

Gyratory

6.9

0.2

2.8

Gyratory

7.1

0.7

10.2

Gyratory

7.3

0.29

3.9

Gyratory

7.2

0.5

6.9

Gyratory

8.0

0.4

5.2

Gyratory

7.3

87

SlabShearbox

6.74

7.0
6.7
6.5
6.7
7.1
6.7
7.0
8.2
7.2
6.6
6.6
7.3
7.6
7.0
6.7
7.7
7.2
8.3
7.6
8.2
7.7
6.9
7.2

2.7

8.9

8.9

0.2

0.4

5.6

Gyratory

Table B.1 (cont’d)
Unique
HMA#
15

16

17

18

19

20

21

22

23

24

Sample#
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94

HMA
ID
64

102

103

109

105

111

48

31B

45

21

Sample
ID

AV%

64-1
64-2
64-3
102-1
102-2
102-3
103-1
103-2
103-3
109-1
109-2
109-3
105-1
105-2
105-3
111-1
111-2
111-3
48-1
48-2
48-3
31B-1
31B-2
31B-3
45-1
45-2
45-3
21-1
21-2
21-3

6.1
7.7
7.2
7.2
7.9
8.4
7.0
7.3
7.4
7.8
7.5
7.6
6.4
7.1
7.1
7.5
7.7
6.3
7.3
7.3
7.0
7.2
7.5
7.7
7.2
7.2
7.1
7.4
7.2
7.6

88

Core
Avg.
AV%

STDEV
AV

7

0.8

11.4

Gyratory

7.8

0.6

7.6

Gyratory

7.2

0.2

3.1

Gyratory

7.6

0.2

2.2

Gyratory

6.8

0.4

6.2

Gyratory

7.2

0.8

10.6

Gyratory

7.2

0.2

2.3

Gyratory

7.5

0.3

3.5

Gyratory

7.2

0.1

0.8

Gyratory

7.4

0.16

2.2

Gyratory

COV Compaction
(%)
method

Table B.1 (cont’d)
Unique
HMA#
25

26

27

28

29

30

31

32

33

34

Sample#
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124

HMA
ID
62

112

206

108

68

207

47

127

106

4

Sample
ID

AV%

62-1
62-2
62-3
112-1
112-2
112-3
206-1
206-2
206-3
108-1
108-2
108-3
68-1
68-2
68-3
207-1
207-2
207-3
47-1
47-2
47-3
127-1
127-2
127-3
106-1
106-2
106-3
4--1
4--2
4--3

6.4
6.7
6.9
7.6
7.3
7.4
7.4
8.0
7.8
7.4
7.6
7.5
7.3
8.0
7.3
7.6
7.5
7.7
6.2
6.8
7.5
7.5
7.5
7.6
6.8
7.9
7.9
6.8
7.0
7.1

89

Core
Avg.
AV%

STDEV
AV

6.7

0.3

3.8

Gyratory

7.5

0.2

2.2

Gyratory

7.7

0.3

3.6

Gyratory

7.5

0.1

1.4

Gyratory

7.6

0.4

4.8

Gyratory

7.6

0.1

1.7

Gyratory

6.83

0.68

10

Gyratory

7.5

0.05

0.6

Gyratory

7.52

0.64

8.5

Gyratory

6.95

0.19

2.7

Gyratory

COV Compaction
(%)
method

Table B.1 (cont’d)
Unique
HMA#
35

36

37

38

39

40
41
42

43

44

45

Sample#
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156

HMA
ID
20A

2

20B

23

24B

26A
26B
26C

31A

32A

51B

Sample
AV%
ID
20A-1
20A-2
20A-3
2-1
2-2
2-3
20B-1
20B-2
20B-3
23-1
23-2
23-3
24B-1
24B-2
24B-3
26A-1
26A-2
26A-3
26B-1
26B-2
26C-1
26C-2
26C-3
31A-1
31A-2
31A-3
32A-1
32A-2
32A-3
51B-1
51B-2
51B-3

7.6
7.5
6.9
7.7
7.3
7.2
6.2
6.7
6.4
7.2
6.9
7.0
6.8
6.7
7.1
6.8
7.0
7.3
6.4
7.7
7.6
7.1
7.9
7.2
7.6
7.7
7.4
6.7
6.7
7.1
7.7
7.5
90

Core
Avg.
AV%

STDEV
AV

COV
(%)

Compaction
method

7.33

0.35

4.8

Gyratory

7.38

0.26

3.5

Gyratory

6.4

0.28

4.4

Gyratory

7.01

0.2

2.8

Gyratory

6.84

0.2

3.1

Gyratory

7.06

0.3

3.8

Gyratory

7.04

0.9

12.3

Gyratory

7.53

0.4

5

Gyratory

7.49

0.3

3.5

Gyratory

6.92

0.4

6

Gyratory

7.44

0.28

3.8

Gyratory

Table B.1 (cont’d)
Unique
HMA#
46

47

48

49

50

51

Sample#
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174

HMA
ID
65

80

97

200

201

202

175
52

176

WMA

177
53

54

55

178
179
180
181
182
183
184
185
186

90

208

49C

Sample
ID
65-1
65-2
65-3
80-1
80-2
80-3
97-1
97-2
97-3
200-1
200-2
200-3
201-1
201-2
201-3
202-1
202-2
202-3
WMA1
WMA2
WMA3
90-1
90-2
90-3
208-1
208-2
208-3
49C-1
49C-2
49C-3

AV%
6.8
7.7
7.1
7.4
6.8
7.2
7.0
6.8
6.7
8.0
6.8
7.0
11.4
11.5
11.2
7.4
7.4
7.9

Core
Avg.
AV%

STDEV
AV

COV
(%)

Compaction
method

7.2

0.46

6.4

Gyratory

7.15

0.28

4

Gyratory

6.82

0.12

1.8

Gyratory

7.25

0.63

8.7

Gyratory

11.4

0.12

1.1

Gyratory

7.57

0.3

4

Gyratory

7.27

0.45

6.2

Gyratory

9.1

Gyratory

6.8
7.3
7.7
7.48
6.50
7.77
7.29
6.70
6.59
7.23
6.58
7.11
91

7.25

0.66

6.86

0.003

5.5

Gyratory

6.97

0.003

4.9

Gyratory

Table B.1 (contd’)
Unique
HMA#
56

57

58

59

60

61

62
63
64

Sample#
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
211
212
213

HMA
ID
85

86

51C

2B

209A

209B

49B
29B
20C

Sample
ID

AV%

85-1
85-2
85-3
86-1
86-2
86-3
51C-1
51C-2
51C-3
2B-1
2B-2
2B-3
209A-1
209A-2
209A-3
209B-1
209B-2
209B-3
49B-1
49B-2
49B-3

7.53
7.41
7.46
7.73
6.22
6.15
7.36
7.33
6.93
7.33
7.24
7.18
6.88
7.21
7.11
7.19
7.25
7.02
6.15
6.61
6.28

29B-1

8.86

29B-2
20C-1
20C-2
20C-3

9.38
7.42
7.57
7.61

92

Core
Avg.
AV%

STDEV
AV

COV
(%)

Compaction
method

7.47

0.0006

0.9

Gyratory

6.70

0.009

13.3

Gyratory

7.21

0.0024

3.4

Gyratory

7.25

0.0007

1.04

Gyratory

7.07

0.17

7.153

0.119

1.7

Gyratory

6.35

0.24

4.0

Gyratory

9.12

0.4

4.0

Gyratory

7.53

0.1

1.0

Gyratory

2.4

Gyratory

APPENDIX C: |E*| MASTER CURVES OF THE TESTED ASPHALT MIXTURES
GROUPED BASED ON THE MDOT MIX DESIGNATION

93

Mix type: 3E30

100,000

|E*| MPa

10,000
1,000
100
10
1.E-05

HMA 2 PG 64-22 (University)
1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)

1.E+05

Figure C.1: Dynamic modulus |E*| master curves for 3E30 mixes.

Mix type: 3E3

100,000

|E*| MPa

10,000
1,000
26A PG 58-22 (NGBSU & Metro)
26B PG 58-22 (NGBSU & Metro)

100
10
1.E-05

26C PG 58-22 (NGBSU & Metro)
62 PG 58-28 (Superior)
1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)

Figure C.2: Dynamic modulus |E*| master curves for 3E3 mixes.

94

1.E+05

1.E+07

Mix type: 4E30

100,000

|E*| MPa

10,000

1,000

100

10
1.E-05

4 PG 70-28P (University)
203 PG 70-22P (Not Listed)
90 PG 70-22P (Metro)
1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)
Figure C.3: Dynamic modulus |E*| master curves for 3E10 mixes.

1.E+05

Mix type: 3E10

100,000

|E*| MPa

10,000

1,000

100

10
1.E-05

18 PG 58-22 (University)
200 PG 58-28 (Not Listed)
1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)

Figure C.4: Dynamic modulus |E*| master curves for 4E30 mixes.

95

1.E+05

1.E+07

Mix type: 4E3

100,000

|E*| MPa

10,000

1,000

31A PG 70-28P (University)
31B PG 70-28P (University)
108 PG 64-22 (Metro)
111 PG 70-22P (Metro)
64 PG 58-34 (Superior)
67 PG 64-34P (Superior)

100

10
1.E-06

1.E-04

1.E-02
1.E+00
1.E+02
Reduced Frequency, fr=f*a(T)
Figure C.5: Dynamic modulus |E*| master curves for 4E3 mixes.

1.E+04

1.E+06

Mix type: 4E10

100,000

|E*| MPa

10,000

1,000

20A PG 64-28 (University)
20B PG 64-28 (University)
102 PG 64-22 (Metro)
105 PG 70-22P (Metro)
23 PG 70-28P (NGBSU)

100

10
1.E-05

1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)

Figure C.6: Dynamic modulus |E*| master curves for 4E10 mixes.

96

1.E+05

1.E+07

Mix type: 4E1

100,000

|E*| MPa

10,000

1,000

100

10
1.E-05

44 PG 58-28 (University)
47 PG 64-28 (University)
80 PG 58-34 (Superior)
1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)

1.E+05

Figure C.7: Dynamic modulus |E*| master curves for 4E1 mixes.

Mix type: 5E10

100,000

|E*| MPa

10,000

1,000
21 PG 64-28 (University)
24 PG 70-28P (University)
103 PG 64-22 (Metro)
106 PG 70-22P (Metro)
202 PG 64-22 (Not Listed)

100

10
1.E-06

1.E-04

1.E-02
1.E+00
1.E+02
1.E+04
Reduced Frequency, fr=f*a(T)

Figure C.8: Dynamic modulus |E*| master curves for 5E10 mixes.

97

1.E+06

Mix type: 5E03

100,000

|E*| MPa

10,000

1,000

100

10
1.E-04

37 PG 58-28 (University)
1.E-02

1.E+00
1.E+02
1.E+04
Reduced Frequency, fr=f*a(T)

1.E+06

Figure C.9: Dynamic modulus |E*| master curves for 5E03 mixes.

Mix type: 5E3

100,000

|E*| MPa

10,000
29 PG 64-28 (University)
32A PG 70-28P (University)
32B PG 70-28P (University)
109 PG 64-22 (Metro)
112 PG 70-22P (Metro)
65 PG 58-34 (Superior)
68 PG 64-34P (Superior)

1,000

100

10
1.E-06

1.E-04

1.E-02
1.E+00
1.E+02
1.E+04
Reduced Frequency, fr=f*a(T)

Figure C.10: Dynamic modulus |E*| master curves for 5E3 mixes.

98

1.E+06

Mix type: 5E1

100,000

|E*| MPa

10,000
1,000
45 PG 58-28 (University)
100

48 PG 64-28 (University)
81 PG 58-34 (Superior)

10
1
1.E-06

206 PG 64-22 (Not Listed)
207 PG 64-22 (Not Listed)

1.E-04

1.E-02
1.E+00
1.E+02
1.E+04
Reduced Frequency, fr=f*a(T)

1.E+06

Figure C.11: Dynamic modulus |E*| master curves for 5E1 mixes.

Mix type: 2E3

100,000

|E*| MPa

10,000

1,000

100

10
1.E-05

205 PG 58-28 (Not Listed)
1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)

Figure C.12: Dynamic modulus |E*| master curves for 2E3 mixes.

99

1.E+05

Mix type: 5E30

100,000

|E*| MPa

10,000

1,000

100

10
1.E-05

204 PG 70-22P (Not Listed)
1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)

1.E+05

Figure C.13: Dynamic modulus |E*| master curves for 5E30 mixes.

Mix type: ASCRL

100,000

|E*| MPa

10,000

1,000

100

10
1.E-05

201 PG 64-28 (University)
1.E-03

1.E-01
1.E+01
1.E+03
Reduced Frequency, fr=f*a(T)

Figure C.14: Dynamic modulus |E*| master curves for ASCRL mixes.

100

1.E+05

Mix type: GGSP

100,000

|E*| MPa

10,000

1,000

100

10
1.E-06

49A PG 70-28P (University)
49B PG 70-28P (University)
1.E-04

1.E-02
1.E+00
1.E+02
Reduced Frequency, fr=f*a(T)

1.E+04

1.E+06

Figure C.15: Dynamic modulus |E*| master curves for GGSP mixes.

Mix type: LVSP

100,000

|E*| MPa

10,000

1,000

100

10
1.E-06

127 PG 58-22 (Metro)
51 PG 58-28 (University)
1.E-04

1.E-02
1.E+00
1.E+02
1.E+04
Reduced Frequency, fr=f*a(T)

Figure C.16: Dynamic modulus |E*| master curves for LVSP mixes.

101

1.E+06

APPENDIX D: |G*| MASTER CURVES GROUPED BASED ON THE PG
GRADE

102

PG: 70-28P

100,000,000
10,000,000

|G*| Pa

1,000,000
100,000
10,000

4 (NGBSU)
31A (NGBSU)
49A (NGBSU)
31B (NGBSU)
32A (NGBSU)

1,000
100
10
1.E-06

1.E-04

1.E-02
1.E+00
1.E+02
Reduced Frequency, fr=f*a(T)
Figure D.1: |G*| master curves of different PG70-28P binders. NGBSU = North, Grand,
Bay, Southwest and University Regions.

PG: 64-28

100,000,000
10,000,000

|G*| Pa

1,000,000
100,000

20B (NGBSU)
29B (NGBSU)
21 (NGBSU)
47 (NGBSU)
20C (NGBSU)
28B (NGBSU)
48 (NGBSU)

10,000
1,000
100
10
1.E-07

1.E-05

1.E-03
1.E-01
Reduced Frequency, fr=f*a(T)

1.E+01

Figure D.2: |G*| master curves of different PG64-28 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions.

103

10,000,000

PG: 70-28

1,000,000

|G*| Pa

100,000
10,000
1,000

100

24 (NGBSU)

10
1.E-06

1.E-04
1.E-02
1.E+00
1.E+02
Reduced Frequency, fr=f*a(T)
Figure D.3: |G*| master curve of a PG70-28 binder. NGBSU = North, Grand, Bay,
Southwest and University Regions.

10,000,000

PG: 64-34P

1,000,000

|G*| Pa

100,000
10,000
1,000

67 (Superior)
68 (Superior)
85 (Superior)
86 (Superior)

100
10
1.E-05

1.E-03
1.E-01
1.E+01
Reduced Frequency, fr=f*a(T)
Figure D.4: |G*| master curves of different PG64-34P binders. NGBSU = North, Grand,
Bay, Southwest and University Regions.

104

100,000,000

PG: 64-22

10,000,000

|G*| Pa

1,000,000
100,000

108 (Metro)
109 (Metro)
102 (Metro)
103 (Metro)
202 (Not Listed)
206 (Not Listed)
207 (Not Listed)
208 (Not Listed)
2 (NGBSU)

10,000
1,000
100
10
1.E-05

1.E-03
1.E-01
1.E+01
Reduced Frequency, fr=f*a(T)
Figure D.5: |G*| master curves of different PG64-22 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions.

100,000,000

PG: 70-22P

10,000,000

|G*| Pa

1,000,000
100,000
10,000
1,000
111 (Metro)
112 (Metro)
203 (Not Listed)

100

10
1.E-06

1.E-04
1.E-02
1.E+00
Reduced Frequency, fr=f*a(T)
Figure D.6: |G*| master curves of different PG70-22P binders.

105

1.E+02

100,000,000

PG: 58-22

10,000,000

|G*| Pa

1,000,000
100,000

10,000
1,000
26A (NGBSU)
127 (Not Listed)
18B (Metro)

100
10
1.E-06

1.E-04
1.E-02
1.E+00
1.E+02
Reduced Frequency, fr=f*a(T)
Figure D.7: |G*| master curves of different PG58-22 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions.

10,000,000

PG: 58-28

1,000,000

|G*| Pa

100,000
10,000

205 (Not Listed)
26C (Metro)
200 (Not Listed)
44 (NGBSU)
45 (NGBSU)
37 (NGBSU)
51A (Not Listed)
51B (Not Listed)

1,000
100
10
1.E-05

1.E-03
1.E-01
1.E+01
Reduced Frequency, fr=f*a(T)

Figure D.8: |G*| master curves of different PG58-28 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions.

106

PG: 58-22

100,000,000
10,000,000

|G*| Pa

1,000,000
100,000
10,000
1,000

26A (NGBSU)
127 (Not Listed)
18B (Metro)

100
10
1.E-06

1.E-02
1.E+00
1.E+02
Reduced Frequency, fr=f*a(T)
Figure D.9: |G*| master curves of different PG58-22 binders. NGBSU = North, Grand, Bay,
Southwest and University Regions.

10,000,000

1.E-04

PG: 58-34

1,000,000

|G*| Pa

100,000
10,000
1,000
100
10
1.E-06

65 (Superior)
80 (Superior)
1.E-04
1.E-02
1.E+00
Reduced Frequency, fr=f*a(T)

Figure D.10: |G*| master curves of different PG58-34 binders.

107

1.E+02

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108

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114