KLK479_Progress Report_May 2007

Development and Evaluation of Performance Tests to Enhance
Superpave Mix Design and Implementation in Idaho
NIATT Project No. KLK479
USDOT Assistance No. DTOS59-06-G-00029
Progress Report
May 2007
Submitted to
Kyle Gracey
U.S. Department of Transportation
Submitted by
Fouad Bayomy
Research Team:
Dr. Fouad Bayomy, PI
Dr. S. J. Jung, Co-PI
Dr. Richard Nielsen, Co-PI
Dr. Thomas Weaver, Co-PI
Mr. Ahmad Abu Abdo, Graduate Research Assistant
University of Idaho
National Institute for Advanced Transportation Technology
Center for Transportation Infrastructure

1
Introduction
This project addresses the implementation of the Superpave in the state of Idaho. It is a
partnership between USDOT, the Idaho Transportation Department (ITD) and the
University of Idaho (UI). The project funding is provided by the USDOT and matching
funds are provided by the ITD and the University. The project focuses on developing
asphalt mix tests and tools that that can be conducted at the mix design stage to assess the
mix quality and performance. These tests and tools will not replace but intended to
augment the current Superpave mix design procedures. The products of this project are
expected to address two performance indicators; deformation resistance and fracture
resistance of asphalt mixes. The project scope has included two major phases, one for
deformation evaluation and another for fracture evaluation. In addition, a third phase was
planned to develop training program to aid the ITD engineers to implement the products
of the research. Detailed plans for these phases have been presented in the project
proposal.
This report summarizes the progress since the inception of the USDOT assistance
contract. The report focuses on activities done during the past period. It is important to
note that as of this date, the ITD contract for the matching funds is not in place yet, but is
expected very soon (Expected to start July 1, 2007). Thus this report summarizes the
status as far as the USDOT contract. Future reports will be developed quarterly and will
be submitted to the USDOT and to ITD. Other reports requirements by ITD will also be
observed once the ITD contract is in place.
This brief report addresses the following:
1. Project management and team assignments,
2. Equipment requisition,
3. Design of experiment,
4. Material procurement, and
5. Literature review that has been conducted as of May 2007.
1. Project Management and Team Assignments
The original proposal that was submitted to the USDOT in June 2005 was reviewed by
the collaborators from Idaho Transportation department (ITD). All comments from ITD
project coordinator (Mr. Mike Santi) were taken into consideration. In addition, a change
in the research team was made by adding Dr. Thomas Weaver, Assistant Professor of
Civil Engineering at the University of Idaho in place of Dr. Rafiqul A. Tarefder,
Assistant Professor of Civil Engineering, Idaho State University. Dr. Tarefder had left
Idaho to New Mexico prior to the start of this contract. The team decided that it is for the
best interest of the project and for Idaho to have Dr. Weaver added to the team to conduct
the tasks that were initially assigned to Dr. Tarefder. In addition, Mr. Ahmad Abu Abdo,
a PhD student at the University of Idaho was added to the project as a research assistant
starting in January 2007 (Spring semester).

2
During the past period, the team had looked into the time schedule for the tasks and
identified a lead person for each task. A new time schedule was developed to associate an
investigator for each task, and to adjust the time plan to be compatible with the expected
contract from ITD (future NIATT project KLK483). The new time schedule is included
in Table 1 below. The modified timeline is subject to approval by both USDOT and ITD.
The new time line includes a 4th
phase that is dedicated to the final report review process.
Accordingly, the team will request a time extension so that the task due dates and
submitted reports match both contracts.
Table 1 Modified Timeline to Accommodate ITD Contract
Phase / Task
Quarter
Month 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
Phase A: Evaluation of Mix Resistance to Deformation
Task A1 – Review of previous studies and available data
Task A2 – Analytical Analysis
Task A3 – Experimental Design, Binder and Agg. Eval.
Task A4 – Prep and Evaluation of Asphalt Mixtures
Task A5 – Data Analysis
Phase B: Evaluation of Mix Resistance to Fracture and Fatigue
Task B1 – Literature Review
Task B2 – Finite Element Analysis
Task B3 – Development of the Fracture Test Procedure
Task B4 – Prep and Evaluation of Asphalt Mixtures
Task B5 – Data Analysis
Task B6 – Reliability Analysis
Phase C: Implementation of Research Products and Training
Task C1 – Development of Implementation Plan
Task C2 – Training Program for ITD Personnel
Reporting
Tasks A6, B7 and C3 – Quarter Reports for USDOT R1 R2 R3 R4 R5 R6 R7
Final Report Prep and Submittal
Phase D: Final Report Review and Submittal
Task D1: External peer review of the final report
Task D2: Final report review by ITD
Task D3: Final Submittal
Q2 Q3
Calendar Yr 2007 Calendar Yr 2008 Calendar Yr 2009
Q1 Q2
Thistimeisforexternalpeerreviewofthefinalreport
Year 3
ThisperiodisforITDreviewoffinalreportand
finalizationbytheresearchteam
Q1Q3 Q4 Q4
Year 2Year 1
In summary, this project will be conducted under two NIATT project numbers KLK479
(from the USDOT side) and KLK483 (from ITD side). The funding has been shared
between the two as laid down in the original project proposal.
2. Equipment Requisition
A major testing equipment to test for the dynamic modulus test in accordance to the
NCHRP project 9-29 which led to the new AASTO TP62-03 (Dynamic Modulus Test)
was to be purchased. We have reviewed the protocols and possible vendors from which a
suitable testing machine can be procured. A set of specifications were developed and put
in a bid. The bid was recently completed (May 11, 2007). The delivery of the testing
machine is expected no later than end of July 2007. The research team is still working on
other equipment that will address the fracture testing (static and dynamic) at various
temperatures. Upgrading of the MTS system controller at the UI Labs and temperature
control chamber will be the focus of the research team in the forthcoming period. Other
equipment that is needed for sample preparations (such as coring and cutting as per the
AASHTO TP62-03) is still to be procured or may be developed in house.

3
3. Hot-Mix Asphalt (HMA) Selection - Design of Experiment
To achieve the goals of Tasks A3, A4, and B4 several mixes are to be selected. Lab
mixes will be developed to address the variability of mix design. The variables
considered include: aggregates (gradation, texture, size, and shape), binder (grade and
content). For the lab mixes, three different Superpave mixes will be prepared and
evaluated in the lab. The fundamental difference between these three mixes is the
aggregate structure as suggested by the Superpave specifications. The lab mixes will
allow for varying binder grades and contents.
Field mixes will be selected to assess the various mix properties so that design values can
be developed.
Raw materials for lab mixes (aggregate and binders) as well as field mixes from selected
Superpave projects in Idaho will be provided by ITD, once the ITD contract begins. The
material requirements and project selection shall be in full coordination with ITD. Details
of the developed experiment design are provided in Appendix A.
4. MnRoad Material Procurement
In preparation for this project, during fall 2006, contacts were made with the MnDOT
authorities to acquire MnRoad samples from selected test sections at MnRoad. Seven
sections were identified and selected; four from mainline test sections and three from the
low volume road test sections. Those sections are identified in Appendix A. We received
over 700 lbs of asphalt mixes from the seven sections selected. In addition, data
published by MnRoad authorities that are related to these sections are obtained. Due to
the limited amount of materials from MnRoad sections, mixes are stored to be used at a
later stage in the project for verification purposes since field performance for these mixes
are done in MnRoad studies.
5. Literature Review
Limited Literature review has been conducted during the past period. The review focused
on the Dynamic Modulus test and the fracture testing procedures. This review is provided
in Appendix B.
Appendices
Appendix A: Selection of Asphalt Mixes and Experiment Design
Appendix B: Literature Review

Appendix A, Page 1
Appendix A
Selection of Asphalt Mixes and Experiment Design
Lab Mixes
The main objective of lab mixes is to study (under controlled conditions) the effect of
various changes in the mix design such as aggregate structure/gradation, binder grade,
and content on the asphalt mix performance. Based on these requirements a matrix of
planned mixes is proposed as shown in Table A1.
Table A1: Proposed Mix Matrix
PG High
Grade
-0.5 Opt 0.5 -0.5 Opt 0.5 -0.5 Opt 0.5
< 0.3x10
6
√ √ √* √ √*
0.3 - 3x10
6
√ √ √
3 - 30x10
6
√ √ √
-0.5 Opt 0.5 -0.5 Opt 0.5 -0.5 Opt 0.5
< 0.3x10
6
√ √ √
0.3 - 3x10
6
√ √* √ √* √
3 - 30x10
6
√ √ √
-0.5 Opt 0.5 -0.5 Opt 0.5 -0.5 Opt 0.5
< 0.3x10
6
√ √ √
0.3 - 3x10
6
√ √ √
3 - 30x10
6
√* √* √* √ √
√ - Required Mixes √* - PG binder dependes on JMF
58
-34 -28 -22
PG Low Grade -34 -28 -22
AC%
Agg.
Structure
(ESALs)
70
PG Low Grade
64
AC%
Agg.
Structure
(ESALs)
AC%
Agg.
Structure
(ESALs)
PG Low Grade -34 -28 -22
At least three mixes with different aggregate structure shall be procured with the
help of ITD. To ensure that the aggregate structure is different, each mix shall be
designed for different equivalent single axial load (ESALs) as follow,
1. Mix 1 shall be designed for < 0.3x106
ESALs.
2. Mix 2 shall be designed for 0.3 – 3x106
ESALs.
3. Mix 3 shall be designed for < 3 – 30x106
ESALs.

Appendix A, Page 2
To evaluate the effects of the binder on the asphalt mix properties, three asphalt
contents shall be studied; optimum asphalt content, +0.5% and -0.5% optimum asphalt
content. In addition, the matrix allows for nine binder grades to be selected depending on
the mix design to evaluate changing of the upper binder grade and the lower binder grade
on the asphalt mix behavior. The following are tentative binder grades proposed.
Variation from these grades could be made based on the actual used binders in selected
projects.
1. PG 70 – 34, PG 70 – 28, and PG 70 – 22.
2. PG 64 – 34, PG 64 – 28, and PG 64 – 22.
3. PG 58 – 34, PG 58 – 28, and PG 58 – 22.
To evaluate the properties of the aggregates, binders, and asphalt mix properties,
the following tests shall be conducted,
1. Binder Evaluation:
a. Rotational viscosity (AASHTO T316-06) at temperatures that match
temperatures for E* test.
b. Shear modulus, G* (AASHTO T315-06) at different temperatures and
loading frequencies that match the E* test. Samples will be sent out for
external testing since UI does not have DSR. ( possible labs are WSU or
ITD headquarter)
2. Aggregate Evaluation:
Aggregate properties: texture, angularity, and sphericity using AIMS.
Aggregate samples will be sent for external testing by AIMS (possible lab
is TTI or UT, Austin).
3. Asphalt Mix Evaluation:
a. Mix Structure determined using the Gyratory Stability (GS) parameter.
Previous test results showed that the Gyratory Stability could capture the
changes in aggregate structure and gradation in asphalt mixes.
b. Number of aggregate contacts and orientations, using either X-Ray
Tomography or Image analysis of sliced samples, this test shall be
conducted in WSU or Texas A&M lab.
c. Dynamic modulus, E* test at different temperatures and loading
frequencies as per NCHRP Report 9-29.
d. APA Rut Depth test this test shall be conducted at ITD headquarter lab.
e. Fracture and Fatigue tests using the Semi Circle Notched Beam (SCNB) at
different temperatures.
f. Tri-axial test. This test shall only be conducted, if it is required by the
finite element analysis, to determine the developed model parameters.
The estimated amount of material to prepare all required samples is about 3787 lbs of
aggregates per mix and 128.5 lbs of binder per binder grade (Table A2).

Appendix A, Page 3
Table A2: Required Materials of Lab Mixes
Test Aggregates
(lbs)
Binder (lbs) Number of
Specimens
GS / SCNB 2096.8 66.3 165
E* 419.4 13.3 22
APA 419.4 13.3 22
X-Ray 419.4 13.3 33
Tri-axial 419.4 13.3 33
AIMS 12.6 - -
G* and η - 9.0 -
Total 3787.0 128.5 275
Field Mixes
The main objective at this stage is to evaluate as many asphalt mixes as possible,
to determine thresholds for Superpave mixes using the developed performance
parameters such as the Gyratory Stability (GS), J-Integral (Jc), APA rut depth, and the
dynamic modulus (E*) test results. The properties of these mixes will depend on each
project specifications. These mixes shall be obtained directly from the project sites, and
thus no modifications shall be done on these mixes in the lab. The following tests are
planned for asphalt mix evaluations:
1. Gyratory stability
2. E* test at different temperatures and loading frequencies as per NCHRP Report 9-
29..
3. APA Rut Depth test this test shall be conducted at ITD HQ lab.
4. Fracture and Fatigue tests using the Semi Circle Notched Beam test (SCNB) at
different temperatures.
The required materials to conduct the above tests shall be 255 lbs (per mix) as shown in
Table A3.
Table A3: Required Materials of Field Mixes per Mix
Test Asphalt Mix (lbs) Number of
Specimens
GS / SCNB 182.0 15
E* 36.5 2
APA 36.5 2
Total 255.0 19
MnRoad Materials
The attached figure shows the selected test sections at MnRoad from which asphalt mixes
were procured.

Appendix A, Page 4
Selected Test Sections from MnRoad
5-Year 1 2 3 4
1.5" *
Layer Depth 4" 4"
(Inches)
Asphalt Binder 120/150 120/150 120/150 120/150 * 2006 1.5" PG52-34 HMA Inlay in the driving lane
Binder PG Grade 58-28 58-28 58-28 58-28
Design Method 75 35 50 Gyratory
Subgrade "R" Value 12 12 12 12
Construction Date Sept-93 Sept-93 Sept-93 Sept-93
10-Year 14 15 16 17 18 19 20 21 22 23 50 51
4" 4"
Layer Depth 4" Drain
(Inches) 3"
Restrict
Zone Coarse
Asphalt Binder 120/150 AC-20 AC-20 AC-20 AC-20 AC-20 120/150 120/150 120/150 120/150 Overlay Overlay
Binder PG Grade 58-28 64-22 64-22 64-22 64-22 64-22 58-28 58-28 58-28 58-28 58-28 58-28
Design Method 75 75 Gyratory 75 50 35 35 50 75 50 35 35
Subgrade "R" Value 12 12 12 12 12 12 12 12 12 12 12 12
Construction Date Jul-93 Jul-93 Jul-93 Jul-93 Jul-93 Jul-93 Jul-93 Jul-93 Jul-93 Sept-93 Jul-97 Jul-97
12"
Drain
28" 28"
23"
9"
6.1" 6.3"
9.1"4.5"
Material Legend
33"
Suface Materials Base Materials
28"
33"
Hot Mix Aspalt Class-3 Sp.
Concrete Class-4 Sp.
Oil Gravel Class-5 Sp.
Double Chip Seal Class-6 Sp.
PSAB Reclaimed HMA
1999 Micro 2003 Micro/MiniMac
2004 Micro
10.9" 11.1"
8" 7.9"
28" 28"
7.9" 7.8" 7.8"
9"
18"
7.9" 7.9" 9.2"
9"
MainLine
Hot Mix Asphalt Test Sections
Selected Mixes are from
Cells 16, 17, 19 and 20
24 25 26 26 26 27 27 27 27 28 28 28 29 30
2.5'' 3.3'' 1'' 2.5'' 3.2'' 2''
1''
Layer Depth
(Inches) Sand Clay
Sand
Clay GCBD
Clay
Clay Clay
Clay Clay Clay
Clay Clay
Asphalt Binder 120/150 120/150 120/150 Oil n/a 120/150 Double Oil 120/150 Oil 120/150 120/150
Binder PG Grade 58-28 58-28 58-28 Gravel 58-28 58-28 Chip Gravel 52-34 58-28 Gravel 52-34 58-28 58-28
Design Method 35 50 50 Gyratory 50 Seal Gyr-60 35 Gyr-60 50 75
Subgrade "R" Value 70 70 12 12 12 12 12 12 12 12 12 12 12 12
Construction Date Aug-93 Aug-93 Aug-93 Sep-00 May-04 Aug-93 Aug-99 Sep-00 Aug-06 Aug-93 Aug-99 Aug-06 Aug-93 Aug-93
31 31 33 33 34 34 34 35
3.3''
Layer Depth
(Inches)
Clay Clay Clay
Clay Clay Clay Clay
Binder PG Grade 58-28 64-34 n/a 58-28 n/a 58-34 n/a 58-40
Design Method 75 Gyratory n/a Gyratory n/a Gyratory n/a Gyratory
Subgrade "R" Value 12 12 12 12 12 12 12 12
Construction Date Aug-93 Sep-04 Sep-96 Aug-99 Sep-96 Aug-99 Sep-96 Aug-99
4''
12'' 14''
6''
11''
14''
12''
Concrete
12''12'' 12''
Clay
4''
12''
6''
6''
Class 1c
Class 1f
5.1''
10''
5.1''
Class-4 Sp.
Reclaimed HMA
Crushed Stone
Class 1
Class-6 Sp.
4''
6''
Class 5
Clay
12''
13''
4''
6''
Class 5
Clay
14''
4''
4''
6''
Material Legend
Suface Materials Base Materials
Class-3 Sp.Hot Mix Aspalt
3.9''
6''
8''
3.1"
4"
5.2" 5.9"
Oil Gravel Class-5 Sp.
6"
4''
PSAB
Double Chip Seal
3.9''
Low Volume Road
Hot Mix Asphalt Test Sections
Selected Mixes are from
Cells 33, 34 and 35

Appendix B, Page 1
Appendix B
Literature Review
This brief review addresses two areas:
1. The dynamic modulus as a main property of the asphalt mix and the various
developments in its modeling.
2. The fracture evaluation of asphalt mixes using the semi-circular notched sample in
bending.
1. Dynamic Modulus
The dynamic modulus is defined as the absolute value of the Complex Modulus (E*),
which is the stress-to-strain relationship for a linear viscoelastic material. Mathematically the
Dynamic Modulus is equal to the stress amplitude (σo) divided by the recoverable strain
amplitude (εo) as shown in Equation 1 and Figure 1.
o
o
E
ε
σ
=* (Eq.1)
Figure 1: Sinusoidal Loading for the E* Test (after Witczak 2002)
The Dynamic Modulus Test protocol AASHTO TP 62-03 indicates that the test shall be
conducted under a series of temperatures (14, 40, 70, 100 and 130 °F) and loading frequencies
(0.1, 0.5, 1, 5, 10 and 25 Hz) at each temperature.
Methods for Predicting of the Dynamic Modulus, E*
In addition to laboratory tests, the dynamic modulus could be estimated using two
approaches; the first approach is to predict the dynamic modulus using numerical and analytical
modeling. Many models were developed under this approach. Some of these models were
borrowed from rock and concrete models and modified to account to the different behavior of
asphalt mixes. The second approach is to predict the dynamic modulus using models developed

Appendix B, Page 2
based on correlation and regression of actual test results of the dynamic modulus to the physical
and mechanical properties of the asphalt mixes.
Numerical and Analytical Predictive Models
The development of numerical models to predict the elastic modulus of composite
materials has been going for decades. Since the asphalt mix is considered a composite material
consisting of aggregates bound with mastic (fine aggregate and asphalt binder), the response of
the asphalt mix depends on the response of the aggregate, the mastic, and their interaction to the
loads. In this section a short summary of some models that has been developed for composite
materials.
Voigt in 1889 (Aboudi 1991) introduced his famous model for determining the elastic
modulus for a composite material. This model was developed for a two phase series system
(Figure 2). The elastic modulus can be easily computed using the following equation,
EaVaEpVpEc += (Eq. 2)
where,
Ec = elastic modulus for the composite material.
Ep = elastic modulus for the mastic.
Vp = volume fraction for the mastic.
Ea = elastic modulus for the aggregates.
Va = volume fraction for the aggregates.
Reuss et al. in 1929 developed a model to predict the elastic modulus for a composite
material in parallel (Figure 2). This model was developed for a two phase parallel system,
Ea
Va
Ep
Vp
Ec
+=
1
(Eq. 3)
Figure 2: Simple Elastic Modulus Predictive Models (after You 2003)
Voigt Model Reuss Model Hirsch Model Counto Model

Appendix B, Page 3
When applying the above two models to asphalt mixes, it was found (You 2003) that at
high temperatures, an asphalt mix follows Reuss model (lower bound). At low temperatures,
Voigt model is more applicable (upper bound). In 1962 Hirsch suggested a model that include
both models the two phase series system and two phase parallel system (Figure 2), this model
can be represented as follows,
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+−+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
=
Ea
Va
Ep
Vp
x
VaEaVpEp
x
Ec
)1(
11
(Eq. 4)
where x and (1-x) are the relative proportions of material. Changes in x and (1-x) are assumed to
capture the response of the composite material at different conditions. But the solution of this
model is confined between the upper and lower bound of the above two models. Counto (1964)
represented another model that is based on the assumption that a cover of mastic encloses a block
of aggregates (Figure 2). The model is illustrated in Equation 5.
( )( ) ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+−
+⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ −
=
EaEpVaVaEp
Va
Ec /1
111
(Eq. 5)
All the above models were developed mainly for concrete mix. Unlike concrete mixes,
the response of the asphalt mix is affected by the temperature and loading conditions due to the
viscoelastic properties that binder exhibits. In 1964 Hashin developed a model that based on the
assumption that the composite material consists of spherical particles engulfed by the mastic. In
addition, the model assumed that the particles are surrounded by a constant shell thickness
(Figure 3).
Figure 3: Composite Sphere Model (after Hashin 1964)
Utilizing the shear and bulk moduli for the particles and mastic, He was able to determine
an exact solution for the bulk modulus (K*) and upper and lower bound solution for the shear
modulus (G*) of the composite material. The model is as follows,
( )( )
( )cKKKG
cKGKK
KK
mppm
mmmp
m
−++
+−
+=
334
34
* (Eq. 6)
)(
1)1(1
* σ
η yc
G
G m
L
−+
= (Eq. 7)
( ))(
1)1(1*
ε
η ycGG mU −+= (Eq. 8)
m
p
G
G
=η (Eq. 9)
where,
K*, G* = bulk and shear moduli of the composite material.

Appendix B, Page 4
Km, Gm = bulk and shear moduli of the mastic.
Kp, Gp = bulk and shear moduli of the particles.
c = volume concentration of particles = (a/b)3
.
a, b = radii of particles and concentric mastic.
y1
(σ)
, y1
(ε)
= functions of elastic constants.
With the development of numerical software based on Finite Element Analysis (FEA)
and Discrete Element Modeling (DEM) many models have been developed to capture the
response of asphalt mixes under different loading conditions. Uddin (1999) developed a
micromechanical analysis model for determining the creep compliance of asphalt mix on a
microscopic level using the elastic properties of the aggregates and the viscoelastic properties of
the binder at a given temperature. This model was based on Method of Cells (MOC) (Aboundi
1991), to predict the viscoelastic response of an asphalt mix. Then the model was incorporated in
a microcomputer program that predicts the mix stiffness. Many other models have been
developed to predict the elastic modulus of the asphalt mixes using FEA. However, most of these
models are only used for a specified loading condition and test setup, and they are based on the
assumption that the binder and aggregates only exhibit linear elastic properties at that condition.
Recently, more attention is directed to the Discrete Element Modeling (DEM) of asphalt
mixes, even though that DEM was introduced in 1971 (Cundall 1971) where it was used to
analyze rock mechanics problems. The discrete element algorithm is a numerical technique that
derives solution by modeling problems as a system of distinct, interacting, and general-shaped
particles, subjected to motion and deformation, more information on DEM can be found in
Cundall (1971).
When using DEM, the complex constitutive behavior of a material is simulated by
associating simple constitutive models with each particle contact, the overall material behavior is
simulated by DEM packages. Shear and normal stiffness, static and sliding friction, and
interparticle cohesion are three of the simpler contact models which can be employed (You
2003).
You et al. (2006) argued that DEM procedure is a fundamental way of looking at the
complex behavior and heterogeneity of asphalt mixes, thus it can be used to simulate the asphalt
mixes responses under different loading and temperature conditions. They represented a DEM
approach as a research tool for modeling asphalt mix microstructure. It utilizes a high resolution
optical imaging of the asphalt mix to create a synthetic, reconstructed mechanical model (Figure
4). Manipulating the images, the components of the asphalt mix was simulated as distinct
elements (Figure 5). Two phases were modeled the aggregates and mastic, where the mastic was
assumed to be a combination of binder and fine aggregates passing 2.36mm sieve. Their results
showed that this 2-D model appears to capture the complex behavior of the asphalt mixes. It has
the ability to predict the dynamic modulus of mixtures across a range of temperature and loading
frequencies. For some fine asphalt mixes, it was found that the DEM approach provides a low
prediction compared to actual laboratory tests.
Further, You (2003) argues that when calibrating this model at one temperature and
frequency, this model can accurately predict (extrapolate) the dynamic modulus of an asphalt
mix at other loading and temperature conditions. It is expected that when this model is expanded
to 3-D DEM, it will yield without much calibration more accurate results.

Appendix B, Page 5
Figure 4: Optical Scanning Image of an Asphalt Mixture Specimen (after You et al. 2006)
Figure 5: Mastic Elements and Aggregate Elements in the DEM Model for a slice of mixture (after You et al.
2006)
Abbas et al. (2007) have utilized DEM to developed micromechanical model that
accounts for the viscoelastic behavior of asphalt mixtures to predict the dynamic modulus and
phase angle for these mixes. The asphalt mix microstructure was captured using grayscale
images of vertically cut sections of the compacted samples. Then these images were processed
into black and white as shown in Figure 6.

Appendix B, Page 6
Figure 6: Unprocessed Grayscale Image (a) versus Processed Black and White Image (b) of an Asphalt Mix
Sample (after Abbas et al. 2007)
The microstructure images were used to construct the DEM model geometry. To estimate
the parameters for the viscoelastic contact models that represent the interaction within the
sample, the dynamic shear modulus for the tested binders (obtained using the dynamic shear
rheometer) were used. The DEM models were subjected to loading conditions to simulate the
Simple Performance test (SPT). The developed models tended to over estimate the dynamic
modulus for mixes made with neat binders, and under estimate the dynamic modulus for mixes
made with modified binders. In addition, the DEM models over predicted the phase angles for all
mixes.
Empirical Predictive Models
The concept behind the development of most empirical models to predict the dynamic
modulus is using the physical and mechanical properties of the asphalt mixtures using available
correlations (Barksdale et al. 1997).
The most famous empirical predictive model that was used as a base for most predictive
models is the Asphalt Institute Method (Shook and Kallas (1969). This method was developed
by using a cyclic triaxial loading setup. They have investigated the effects of the variation of the
asphalt mixture properties, temperature, and loading frequency on the dynamic modulus. They
utilized their results to develop an empirical equation to predict the dynamic modulus with an R-
square equal to 0.968 at a loading frequency of 4 cycles per seconds (cps). This equation is,
( ) ( ) ( )K32110 X068142.0X0318606.0X020108.054536.1|E*|log +−+=
( ) ( ) 4.1
5
4.0
4 XX00127003.0− (Eq. 10)
where,
|E*| = dynamic modulus of mix, 105
psi (4 cps loading frequency).

Appendix B, Page 7
X1 = percent aggregate passing #200 sieve.
X2 = air voids percent in the mix.
X3 = asphalt viscosity at 70 °F, 106
poises.
X4 = percent asphalt by weight of mix.
X5 = test temperature, °F.
This equation was later modified by Witczak (1978) using an expanded data base which
relates the dynamic modulus of asphalt mixes to the mix properties, temperature, and various
loading frequencies (Barksdale et al. 1997). Since this data base was developed for asphalt mixes
of crushed stone and gravel, Miller et al. (1983) refined Witczak equation to include a wide
range of asphalt mixes and predict the dynamic modulus for these mixes with an R-square equal
to 0.928. The modified equation is as follows,
5.0
optac2110 )4PP(CC|E*|log +−+= (Eq. 11)
where,
|E*| = dynamic modulus of mix, 105
psi.
)f/0931757.0()70,10(070377.0V03476.0)f/P(028829.0553833.0C 02774.06
V
017033.0
2001 ++−+= η
[ ]1.1
10102 f/)flog498253.1exp(T00189.0)flog49825.03.1exp(T000005.0C +−+=
P200 = percent aggregate passing #200 sieve.
f = loading frequency, Hz.
VV = volume of air voids in the mix.
η = asphalt viscosity at 70 °F, 106
poises.
T = test temperature, °F.
Pac = percent asphalt by weight of mix.
Popt = percent optimum asphalt content.
More models were developed by modifying the above equations (Witczak and Fonesca
1996) by adding more regression coefficients to relate more asphalt mix properties such as
percent asphalt absorption, effective asphalt binder content, and percent of aggregates retained
on sieve 3/4 inch and 3/8 inch and passing no. 4 sieves.
Witczak and Fonesca (1996) argued that these models have three major limitations. The first
limitation is that all the models were developed using conventional asphalt binder. Modified
binders were not studied. The response of mixes containing these binders to loading and
temperature varies for traditional mixes. The second limitation is that these models are based on
freshly prepared mixes that don’t account for aging, thus they can not be used to predict the
dynamic modulus for the in-placed mixes. Finally the third limitation is that all the models were
developed for test data generated with a temperature range of 5 to 40 °C. Therefore, when
predicting the dynamic modulus outside this range the results are commonly off. Witczak and
Fonesca (1996) have developed another model to address the above limitations and to predict the
dynamic modulus for asphalt mixes with an R-square equal to 0.930,
K2
200200 )(00000101.0008225.0261.0log PPE −+−=
K
abeff
beff
a
VV
V
VP
+
−−+ 415.003157.000196.0 4
)log725.0log716.0exp(1
0164.0)(001786.00000404.0002808.087.1 34
2
38384
η−−+
+−++
+
f
PPPP
(Eq.12)
where,

Appendix B, Page 8
E = dynamic modulus of mix, 105
psi.
P4 = percent aggregate retained on #4 sieve.
P38 = percent aggregate retained on 3/8 inch sieve.
Va = percent of air voids in the mix by volume.
Vbeff = percent of effective binder content by volume.
f = loading frequency, Hz.
η = asphalt viscosity at any temperature and degree of aging, 106
poises.
It is believed that the shear modulus of the binder (G*) and the phase angle (δ) are more
representative of the binder response to different loading conditions than the binder viscosity (η).
The shear modulus of the binder (G*) and the phase angle (δ) is measured using the Dynamic
Shear Rheometer test (AASHTO T315-06). A new modified Witczak model has been developed
to incorporate the binder shear modulus and phase angle instead of the binder viscosity and
loading frequency (Bari and Witczak 2006) as shown in Equation 12.
( )K0052.0
10 |*|754.0349.0*log −
+−= bGE
L
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
+
−−−+
−+++
×
abeff
beff
a
VV
V
VPP
PPPP
06.108.0)(00014.0006.0
)(0001.0011.0)(0027.0032.065.6
2
3838
2
44
2
200200
)log8834.0|*|log5785.07814.0exp(1
01.0)(0001.0012.071.003.056.2 34
2
3838
bb
abeff
beff
a
G
PPP
VV
V
V
δ+−−+
+−+
+
++
+ (Eq.13)
where,
E* = dynamic modulus of mix, 105
psi.
P4 = percent aggregate retained on #4 sieve.
Va = percent of air voids in the mix by volume.
Vbeff = percent of effective binder content by volume.
Gb* = binder dynamic shear modulus, psi.
δb = binder phase angle associated with Gb*, degree.
Christensen et al. (2003) have argued that the most effective model is the simplest. They
developed a model to predict the dynamic modulus of the asphalt mix using binder modulus and
volumetric composition such as VMA and VFA. Their model is based on an existing version of
the law of mixtures, called the Hirsch model (Hirsch 1962), which combines series and parallel
elements of phases (Figure 2). In spite that the Hirsch model was developed originally for
concrete mixes, Christensen et al. argued that it can be used effectively to predict the dynamic
modulus for asphalt mixes, by assuming that when applying the Hirsch model to asphalt mix, the
relative proportion of material in parallel arrangement, called the contact volume, is not constant
but varies with time and temperature. The outcome of their study is called the modified Hirsch
model,
K⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛ ×
+⎟
⎠
⎞
⎜
⎝
⎛
−=
000,10
|*|3
100
1000,200,4|*|
VMAVFA
G
VMA
PcE b

Appendix B, Page 9
1
|*|3000,200,4
1001
)1(
−
⎥
⎦
⎤
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+⎟
⎠
⎞
⎜
⎝
⎛ −
−+
bGVFA
VMAVMA
Pc (Eq. 14-a)
58.0
58.0
|*|3
650
|*|3
20
⎟
⎠
⎞
⎜
⎝
⎛
+
⎟
⎠
⎞
⎜
⎝
⎛
+
=
VMA
GVFA
VMA
GVFA
Pc
b
b
(Eq. 15-b)
where,
E* = dynamic modulus of mix, 105
psi.
Gb* = binder dynamic shear modulus, psi.
VMA = voids in mineral aggregates.
VFA = voids filled with asphalt.
Factors Affecting the Dynamic Modulus of Asphalt Mixes
Asphalt Binder Rotational Viscosity (η)
Viscosity is a fundamental property of asphalt binders. It relates the applied shear stress
to the rate of shear strain of the material. It changes with temperature; at high temperatures
asphalt binders will behave as Newtonian fluids, on the other hand at low temperatures it
behaves as non-Newtonian fluids. Therefore, asphalt viscosity is an important measurement that
represents binder workability at mixing and compaction stages. Using the Brookfield Viscometer
(Figure 7) asphalt viscosity can be easily measured (AASHTO T316-06). In addition temperature
susceptibility of an asphalt binder can be easily determined by measuring the binder viscosity at
different temperatures (Roberts et al. 1996).
Figure 7: Brookfield Viscometer (UI lab)

Appendix B, Page 10
Asphalt Binder Shear Modulus (G*)
The binder shear modulus (G*) is defined as the complex shear modulus. It can be
considered as the total resistance of the binder to deformation when repeatedly sheared. The
shear modulus consists of two parts; an elastic part (G’) and a viscous (non-recoverable) part
(G”) as shown in Figure 8. Mathematically the shear Modulus is equal to the maximum shear
stress (τmax) divided by the maximum recoverable strain (γmax) as shown in Figure 9.Both
temperature and frequency of loading affect the values of G* and phase angle (δ) for asphalt
binder. Asphalt binders behave elastically at very low temperatures and viscous fluid at high
temperatures (Roberts et al 1996). G* can be easily determined using the Dynamic Shear
Rheometer (AASHTO T315-06) as shown in Figure 10.
Figure 8: Binder Complex Modulus Components (after Roberts et al. 1996)
Figure 9: Stress-Strain Response of Asphalt Binders (after Roberts et al. 1996)

Appendix B, Page 11
Figure 10: Dynamic Shear Rheometer (WSU Lab)
Aggregates Structure
One of the most important factors that affect the performance of asphalt mixes the
aggregate skeleton and its stability under loading. The Gyratory Stability (GS) parameter, which
was developed at the University of Idaho Lab (Bayomy et al. 2002), has high potentials to
measure of the aggregate structure stability in asphalt mixes. Utilizing the evaluated shear stress
and the energy used to develop contacts between aggregates while compaction the Gyratory
Stability was developed. The Gyratory Stability can be easily determined directly from the
compaction data output files of the Superpave Gyratory Compactor (SCG) once the sample is
compacted.
Results have shown that the Gyratory Stability can capture the change in aggregate
source, structure, and changes in asphalt content. It can identify mixes with weak aggregate
structure. (Bayomy et al. 2002, Dessouky et al. 2004, and Abu Abdo 2005). Recent experiment
results showed a relationship exist between the Gyratory Stability and the dynamic modulus
(Figure 11). Thus, the Gyratory Stability can be used to predict the dynamic modulus.

Appendix B, Page 12
R
2
= 0.76
0
5
10
15
20
25
0 100 200 300 400 500 600 700 800 900
a) E*/sin Φ @ 130°F, MPa
GS,kN.m
R
2
= 0.65
0
5
10
15
20
25
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
b) E*/sin Φ @ 100°F, MPa
GS,kN.m
Figure 11: Relationship of GS versus E*/sin φ
Aggregate Shape Characteristics
Studies (Masad et al. 2000, Stakston et al. 2002, and Masad 2003) have shown that
aggregate properties play a major role in the performance of asphalt mixes. Aggregate shape
characteristics can be quantified using the following indices; texture, angularity and roundness or
form (Figure 12).

Appendix B, Page 13
Figure 12: Schematic diagram of aggregate shape properties (after Masad et al. 2001)
These characteristics can be easily measured using imaging systems. Masad (2003) has
developed the Aggregate Imaging System (AIMS) for measuring the shape characteristics of
coarse and fine aggregates. AIMS measures the texture, angularity and shape of aggregates.
Texture is analyzed using the wavelet transform, which captures the changes of texture on gray
scale images. The wavelet transform gives a higher texture index for particles with rougher
surfaces. Aggregate angularity is measured using the gradient method. In this method, the
changes in the gradients on the boundary of a two-dimensional projection of a particle are
calculated (Masad 2003). Rounded particles have small gradients while angular particles have
higher gradients. Shape is quantified using the sphericity index which is equal to 1 for particles
that have equal dimensions, and decreases as particles become more flat and elongated. More
details on AIMS features and analysis methods are available in references (Masad 2003 and Al-
Rousan et al. 2005). Masad et al. (2001) showed that aggregate texture has a very strong
correlation with the asphalt mix performance. Stakston et al. (2002) showed that a consistent
trend of higher resistance to compaction with higher Fine Aggregate Angularity (FAA) exists.
2. Fracture Test using Semi-Circle Asphalt Sample
This test was initially developed during the NIATT research project KLK482 (ITD RP#175).
Two papers have been published on this test procedure (see Bayomy, et. al. 2006, 2007). Figure
13 shows a schematic of the test set-up. Brief review of published literature on related research
follows.

Appendix B, Page 14
Figure 13. Semi Circular Notched Bending Fracture Test
The use of the fracture-based concept in asphalt mix design has been investigated over several
decades. Little & Mahboub (1985) used the Jc concept to evaluate the mix fracture properties to
compare the fracture resistance of asphalt mixes prepared with and without plasticized sulfur
binder employing notched three point bending beams. Dongre et al. (1989) evaluated the fracture
resistance of asphalt mixes at low temperatures using bending beam specimens; their study
showed that Jc is a promising fracture characterization parameter for asphalt mixes at low
temperatures. Furthermore, the study concluded that Jc is sensitive to asphalt mix stiffness and it
is a better fracture characterization parameter than the plane strain critical stress intensity factor
(KIc). Abdulshafi et al. (1985) used V-shaped notched circular samples to determine Jc for
different asphalt mixes. They proposed a model based on Jc to predict the fatigue life of asphalt
mixes. They speculated that Jc could be related to the stress-intensity factor, KIC of the mix.
Bhurke et al. studied polymer modified asphalt concrete using the Jc fracture resistance approach
employing three point bending beam specimens (1997). Four different polymer additives,
including styrene-butadiene-styrene (SBS), an epoxy-based system and styrene-butadiene rubber
were studied as modifiers in a viscosity graded AC-5 asphalt. They concluded that the tests were
repeatable and were sensitive to material differences due to polymer modification.
With the introduction of the Superpave Gyratory Compactor (SGC), many studies were initiated
to utilize the gyratory compacted samples in a three point bending test. Ven et al. (1997), Li et al.
(2004), and Molennar et al. (2002) adopted the semi-circular bending test set-up using SGC
samples to determine tensile strength of asphalt mixtures in an effort to replace the indirect
tensile test. They, however, used un-notched samples and did not calculate fracture resistance
parameters. In a study of rock mechanics, Lim et al. (1994) used a semi-circular notched
specimen in a bending test to evaluate the fracture properties of natural rocks by determining the
KIC parameter. Mull et al. (2002) adopted this semi-circular bending test with notched specimens
to measure fracture toughness properties of asphalt mixtures. Hence, they introduced the Semi-
Circular Notched Bending Fracture (SCNBF) test. They determined Jc, to evaluate the fracture
resistance of chemical crumb rubber asphalt (CMCRA) mixes. Based on Jc, the fracture
resistance of the CMCRA was found to be twice that of a crumb rubber asphalt (CRA) mix, and
much higher than that of a control mix. Underlying micromechanical damage features as seen in

Appendix B, Page 15
scanning electron micrographs of the fracture surface of each mix confirmed these results. Huang
et al. (2004) used Mull’s test set-up and procedures to study the fracture properties of various
reclaimed asphalt pavement (RAP) mixes. Their analysis showed that the fracture resistance
measured by Jc has increased with an increase of RAP content in the mix until a certain point
after which the fracture resistance decreased significantly. Mohammed et al. (2004) used the
SCNBF test geometry to study the effect of recycled polymer modified asphalt cement
(RPMAC) content on the fracture resistance, Jc. They found out that as the percent of RPMAC
was increased the stiffness and maximum sustained load increased, with a slight decrease in the
deflection at maximum load. This resulted in increasing values of Jc with increasing RPMAC
content suggesting that the semi-circular fracture test used in conjunction with Jc analysis may
provide a valuable correlative tool.
Recently Mull et al. (2004) extended the concept of the SCNBF test to study fatigue crack
propagation of asphalt mixes. They found that the SCNBF test geometry provides a suitable
geometry for fatigue crack propagation analysis of asphalt mixes. In addition, they showed that
the fatigue lifetime of CMCRA mixes increased as compared to an unmodified crumb rubber
mixture and a control mixture. The results of the fatigue study on the crumb rubber modified
mixtures have confirmed the static Jc results generated earlier by Mull et al. (2002). This
suggests that the SCNBF geometry provides a simple yet reliable geometry for both static and
dynamic evaluation of hot asphalt mixtures.
In summary, most of these studies reveal that Jc can be determined by various methods and holds
promise as a useful correlative parameter, which can be used as indicator of the material’s
fracture resistance to crack propagation.
Further to the development documented in KLK482 report, the team studied the factors that
affect the fracture parameter Jc.
Stress Intensity Factor
The stress intensity factor is defined as,
aYEGK ccIC πσ== (Eq. 1)
where,
KIC: critical stress intensity factor.
E: elastic modulus.
Gc: strain energy release.
Y: shape factor.
σc: applied critical stress,
rt
P
c
2
=σ
P: applied vertical load.
r: sample radius.
t: sample thickness.
a: notch depth.

Appendix B, Page 16
Geometry Effect
For a semi circle sample under three points bending with span ratio (s/r) = 0.8, a shape factor has
been developed (Lim et al. 1993) using the following equation,
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
+⎟
⎠
⎞
⎜
⎝
⎛
−=
r
a
r
a
YI 045.7exp063.0219.1782.4 (Eq. 2)
t2s
2r
a
P
Figure 14: SCNB Test Setup
Temperature Effect
The behavior of asphalt mixes is a function of temperature, as per Equation 1 the stress intensity
factor is a function of the elastic modulus which is a function of the temperature. At low
temperature the asphalt mix is much stiffer that leads to higher fracture toughness. To determine
the stress intensity factor at different temperatures using test data at a reference temperature (Tr)
a shift factor is introduced (αT) as shown in Equation 3 and 4.
( ) aYK cTIC r
πσ= (Eq. 3)
( ) ( ) rTICTTIC KK α= (Eq. 4)
where (KIC)Tr is the stress intensity factor determined at testing temperature (reference
temperature) and (KIC)T is the stress intensity factor at any temperature (T) . To determine the αT
we will utilize the data from the dynamic elastic modulus test (AASHTO TP 62-03), where the
dynamic elastic modulus is determine at different loading frequencies (0.1, 1, 5, 10 and 25Hz)
and at different temperatures (-10, 4, 21.1, 37.8 and 54.4 °C). This method is based on the
assumption that the elastic modulus E is equal to the dynamic modulus E* at test frequency of 5

Appendix B, Page 17
Hz (Equation 5), this value has been used (NCHRP reports 465 and 513) to determine the
performance of asphalt mixes.
zHf
EE 5
* =
= (Eq. 5)
The first step to determine αT is to determine the dynamic modulus at SCNB testing temperature.
The SCNB test is commonly conducted at room temperature ≈ 25 °C, this temperature is defined
as the reference temperature (Tr). However, the dynamic modulus test is not conducted at the
same temperature. Therefore, the E* results from the test is plotted against the temperature, using
best fit line equation (Figure 2), then E* at the reference temperature is determined.
The next step is to normalized E* at different temperatures using E* at the reference temperature
as shown in Figure 3. Using best fit line equation we can determine a shift factor βT (Equation 6)
that can be incorporated in Equation 1 to account for the changes in temperatures as shown in
Equation 7. βT shall be equal to 1.0 at the reference temperature.
( )32
2
1
10 CTCTC
T
++
=β (Eq. 6)
where,
βT: shift factor.
T: required temperature.
C1,C2 and C3: constants that are a function of the asphalt mix (Figure 3).
aYEGK TccTIC πβσβ == (Eq. 7)
y = 0.0002x2
- 0.0439x + 4.4193
R2
= 0.9823
y = -0.0002x2
- 0.0192x + 4.146
R2
= 0.9998
2
2.5
3
3.5
4
4.5
0 10 20 30 40 50 60
Temperature, °C
DynamicModulus
logE
Mix 1
Mix 2
Poly. (Mix 1)
Poly. (Mix 2)
Figure 15: Dynamic Modulus versus Temperature

Appendix B, Page 18
y = 0.0002x2
- 0.0446x + 0.9746
R2
= 0.9822
y2 = -7E-05x2
- 0.0052x + 1.17
R2
= 0.9995
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
0 10 20 30 40 50 60
Temperature, °C
DynamicModulus
log(E/E@Tr)
Mix 1
Mix 2
Poly. (Mix 1)
Poly. (Mix 2)
Figure 16: Normalized Dynamic Modulus versus Temperature
Let,
( )32
2
1
10 CTCTC
TT
++
== βα (Eq. 8)
In summary the stress intensity factor for a semi circle notched bending test can be determined at
any temperature using the following Equations,
( ) aYK cITIC r
πσ= (Eq. 9)
( ) ( ) rTICTTIC KK α= (Eq. 10)
where,
(KIC)Tr: critical stress intensity factor at testing temperature (Tr).
YI: shape factor for SCNB test, ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
+⎟
⎠
⎞
⎜
⎝
⎛
−=
r
a
r
a
YI 045.7exp063.0219.1782.4
a: notch depth.
r: sample radius.
σc: applied critical stress,
rt
P
c
2
=σ
P: applied vertical load.
t: sample thickness.
(KIC)T: critical stress intensity factor at any temperature (T).
αT: temperature shift factor, ( )32
2
1
10 CTCTC
TT
++
== βα
C1,C2 and C3: constants determined from the dynamic modulus test.

Appendix B, Page 19
3. References
A. Dynamic Modulus (E*) for Hot-Mix Asphalt
AASHTO. Standard Method of Test For Determining Dynamic Modulus of Hot-Mix Asphalt
Concrete Mixtures. American Association of State Highway and Transportation Officials.
AASHTO TP 62-03, 2004.
AASHTO. Standard Method of Test for Determining the Rheological Properties of Asphalt
Binder Using a Dynamic Shear Rheometer (DSR). AASHTO T315-06, 2006.
AASHTO. Standard Method of Test for Viscosity Determination of Asphalt Binder Using
Rotational Viscometer. AASHTO T316-06, 2006.
Abbas, A., E. Masad, T. Papagiannakis, and T. Harman. Micromechanical Modeling of the
Viscoelastic Behavior of Asphalt Mixtures Using the Discrete-Element Method.
International Journal of Geomechanics, Volume 7, No. 2, 2007.
Abu Abdo, A., Development of Performance Parameters for the Design of Hot-Mix Asphalt.
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Aboudi, J.. Mechanics of Composite Materials, a Unified Micromechanical Approach. Elsevier,
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Al-Rousan, T., E. Masad, L. Myers and C. Speigelman. A New Methodology for Shape
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Bari J. and M.W. Witczak. Development of a New Revised Version of the Witczak E* Predictive
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Barksdale, R.D., J. Alba, N.P. Khosla, R. Kim, P.C. Lambe and M.S. Rahman. Laboratory
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Bayomy, F., E. Masad, and S. Dessouky. Development and Performance Prediction of Idaho
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Christensen, D.W., T. Pellinen and R.F. Bonaquist. Hirsch Model for Estimating the Modulus of
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6, 2004.

Appendix B, Page 20
Fletcher, T., C. Chandan, E. Masad, K. Sivakumar. Aggregate Imaging System (AIMS) for
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Hashin, Z.. Viscoelastic Behavior of Heterogeneous Media. Journal of Applied Mechanics,
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Matrix and Aggregates. Journal of the American Concrete Institute, Volume 59, No. 3,
1962.
Masad, E., D. Olcott, T. White, and L. Tashman. Correlation of Fine Aggregate Imaging Shape
Indices with Asphalt Mixture Performance. Transportation Research Record 1757,
Washington D.C., 2001.
Masad, E., The Development of A Computer Controlled Image Analysis System for Measuring
Aggregate Shape Properties. NCHRP-IDEA Project 77 Final Report, Transportation
Research Board, Washington, D.C., 2003
Masad, E., D. Little, R. and Sukhwani. Sensitivity of HMA Performance to Aggregate Shape
Measured Using Conventional and Image Analysis Methods. International Journal of
Road Materials and Pavement Design. Vol. 5, No. 4, 2004.
Miller, J.S., J. Uzan and M.W. Witczak. Modification of the Asphalt Institute Bituminous Mix
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Reuss, A. and Z. Aarsenault. In metal Matrix Composites, Pergamon, Oxford, 1929.
Roberts, F.L., P.S. Kandhal, E.R. Brown, D.Y. Lee, and T.W. Kennedy. Hot Mix Asphalt
Materials, Mixture Design, and Construction. National Center for Asphalt Technology,
NAPA, Second Edition, 1996.
Shook, J.F. and B.F. Kallas. Factors Influencing the Dynamic Modulus of Asphalt Concrete.
Proceeding of The Association of Asphalt Paving Technologists, Volume 38, 1969.
Stackston, A., J. Bushek, and H. Bahia. Effect of Fine Aggregates Angularity (FAA) on
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Witczak, M.W.. Development of Regression Model for Asphalt Concrete Modulus for Use in
MS-1 Study. Research Report, University of Maryland, Collage Park, 1978.
Witczak, M.W., K. Kaloush, T. Pellinen, M. Al-Basyouny, and H. Von Quintus. Simple
Performance Test for Superpave Mix Design, NCHRP Report 465, TRB, Washington,
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Witczak, M.W. and O.A. Fonseca. Revised Predictive Model for Dynamic (Complex) Modulus
of Asphalt Mixtures, Transportation Research Record 1540, Washington D.C., 1996.
You, Z.. Development of A Micromechanical Modeling Approach To Predict Asphalt Mixture
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Appendix B, Page 21
B. Fracture Toughness of Hot-Mix Asphalt
Abdulshafi, A. and K. Majidzadeh. J-Integral and Cyclic Plasticity Approach to Fatigue and
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Appendix B, Page 22
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