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 11Phase A: Evaluation of Mix Resistance to DeformationTask A1 – Review of previous studies and available data Task A2 – Analytical AnalysisTask A3 – Experimental Design, Binder and Agg. Eval.Task A4 – Prep and Evaluation of Asphalt Mixtures Task A5 – Data AnalysisPhase B: Evaluation of Mix Resistance to Fracture and Fatigue Task B1 – Literature ReviewTask B2 – Finite Element AnalysisTask B3 – Development of the Fracture Test ProcedureTask B4 – Prep and Evaluation of Asphalt Mixtures Task B5 – Data AnalysisTask B6 – Reliability AnalysisPhase C: Implementation of Research Products and TrainingTask C1 – Development of Implementation PlanTask C2 – Training Program for ITD PersonnelReportingTasks A6, B7 and C3 – Quarter Reports for USDOT R1 R2 R3 R4 R5 R6 R7Final Report Prep and SubmittalPhase D: Final Report Review and SubmittalTask D1: External peer review of the final reportTask D2: Final report review by ITDTask D3: Final Submittal

Q2 Q3Calendar Yr 2007 Calendar Yr 2008 Calendar Yr 2009Q1 Q2

This

tim

e is

for e

xter

nal p

eer r

evie

w o

f the

fina

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ort

Year 3

This

per

iod

is fo

r ITD

revi

ew o

f fin

al re

port

and

fin

aliz

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the

rese

arch

team

Q1Q3 Q4 Q4Year 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

< 0.3x106 √ √ √* √ √*

0.3 - 3x106 √ √ √

3 - 30x106 √ √ √

-0.5 Opt 0.5 -0.5 Opt 0.5 -0.5 Opt 0.5

< 0.3x106 √ √ √

0.3 - 3x106 √ √* √ √* √

3 - 30x106 √ √ √

-0.5 Opt 0.5 -0.5 Opt 0.5 -0.5 Opt 0.5

< 0.3x106 √ √ √

0.3 - 3x106 √ √ √

3 - 30x106 √* √* √* √ √

√ - 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 41.5" *

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 laneBinder PG Grade 58-28 58-28 58-28 58-28

Design Method 75 35 50 GyratorySubgrade "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 50 514" 4"

Layer Depth 4" Drain(Inches) 3"

RestrictZone Coarse

Asphalt Binder 120/150 AC-20 AC-20 AC-20 AC-20 AC-20 120/150 120/150 120/150 120/150 Overlay OverlayBinder 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 35Subgrade "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 HMA1999 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 29 302.5'' 3.3'' 1'' 2.5'' 3.2'' 2''

1''

Layer Depth(Inches) Sand Clay

SandClay GCBD

ClayClay Clay

Clay Clay ClayClay Clay

Asphalt Binder 120/150 120/150 120/150 Oil n/a 120/150 Double Oil 120/150 Oil 120/150 120/150Binder 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 75Subgrade "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 34 353.3''

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 58-40Design Method 75 Gyratory n/a Gyratory n/a Gyratory n/a Gyratory

Subgrade "R" Value 12 12 12 12 12 12 12 12Construction 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 1cClass 1f

5.1''

10''

5.1''

Class-4 Sp.

Reclaimed HMACrushed Stone

Class 1

Class-6 Sp.

4''

6''Class 5

Clay

12''

13''

4''

6''Class 5

Clay

14''

4''4'' 6''

Material LegendSuface Materials Base Materials

Class-3 Sp.Hot Mix Aspalt3.9''6''

8''

3.1"

4"

5.2" 5.9"

Oil Gravel Class-5 Sp.6"

4''

PSABDouble Chip Seal

3.9''

Low Volume RoadHot 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

oEεσ

=* (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,

EaVa

EpVp

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,

⎟⎟⎠

⎞⎜⎜⎝

⎛+−+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

=EaVa

EpVpx

VaEaVpEpx

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.

( )( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

+−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ −=

EaEpVaVaEpVa

Ec /1111 (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

cKGKKKK

mppm

mmmpm −++

+−+=

33434

* (Eq. 6)

)(1)1(1

* ση ycGG m

L −+= (Eq. 7)

( ))(1)1(1* εη ycGG mU −+= (Eq. 8)

m

p

GG

=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 +−+=

( ) ( ) 4.15

4.04 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,

5.0optac2110 )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 02774.06V

017033.02001 ++−+= η

[ ]1.110102 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,

K2200200 )(00000101.0008225.0261.0log PPE −+−=

Kabeff

beffa VV

VVP

+−−+ 415.003157.000196.0 4

)log725.0log716.0exp(10164.0)(001786.00000404.0002808.087.1 34

238384

η−−++−++

+f

PPPP (Eq.12)

where,

Appendix B, Page 8

E = dynamic modulus of mix, 105 psi. P200 = percent aggregate passing #200 sieve. P4 = percent aggregate retained on #4 sieve. P38 = percent aggregate retained on 3/8 inch sieve. P34 = percent aggregate retained on 3/4 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.

( )K0052.010 |*|754.0349.0*log −+−= bGE

L⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−−−+

−+++×

abeff

beffa VV

VVPP

PPPP

06.108.0)(00014.0006.0

)(0001.0011.0)(0027.0032.065.62

3838

244

2200200

)log8834.0|*|log5785.07814.0exp(1

01.0)(0001.0012.071.003.056.2 342

3838

bb

abeff

beffa

G

PPPVV

VV

δ+−−+

+−++

++

+ (Eq.13)

where, E* = dynamic modulus of mix, 105 psi. P200 = percent aggregate passing #200 sieve. P4 = percent aggregate retained on #4 sieve. P38 = percent aggregate retained on 3/8 inch sieve. P34 = percent aggregate retained on 3/4 inch 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

1001000,200,4|*| VMAVFAGVMAPcE b

Appendix B, Page 9

1

|*|3000,200,41001)1(

−

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎠

⎞⎜⎝

⎛ −−+

bGVFAVMAVMAPc (Eq. 14-a)

58.0

58.0

|*|3650

|*|320

⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛ +

=

VMAGVFA

VMAGVFA

Pcb

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

R2 = 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

R2 = 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,rtP

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,

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−=

ra

raYI 045.7exp063.0219.1782.4 (Eq. 2)

t2s2r

aP

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.

zHfEE

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.

( )322

110 CTCTCT

++=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 + 4.4193R2 = 0.9823

y = -0.0002x2 - 0.0192x + 4.146R2 = 0.9998

2

2.5

3

3.5

4

4.5

0 10 20 30 40 50 60Temperature, °C

Dyn

amic

Mod

ulus

log

E

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 + 0.9746R2 = 0.9822

y2 = -7E-05x2 - 0.0052x + 1.17R2 = 0.9995

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

0 10 20 30 40 50 60Temperature, °C

Dyn

amic

Mod

ulus

log

(E /

E@ T

r)

Mix 1

Mix 2

Poly. (Mix 1)

Poly. (Mix 2)

Figure 16: Normalized Dynamic Modulus versus Temperature

Let,

( )322

110 CTCTCTT

++== 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, ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−=

ra

raYI 045.7exp063.0219.1782.4

a: notch depth. r: sample radius.

σc: applied critical stress,rtP

c 2=σ

P: applied vertical load. t: sample thickness. (KIC)T: critical stress intensity factor at any temperature (T).

αT: temperature shift factor, ( )322

110 CTCTCTT

++== 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. Master Thesis, University of Idaho, Moscow, Idaho, 2005.

Aboudi, J.. Mechanics of Composite Materials, a Unified Micromechanical Approach. Elsevier, 1991.

Al-Rousan, T., E. Masad, L. Myers and C. Speigelman. A New Methodology for Shape Classification of Aggregates in Asphalt Mixes. Transportation Research Record 1913, Washington D.C., 2005.

Bari J. and M.W. Witczak. Development of a New Revised Version of the Witczak E* Predictive Model of Hot Mix Asphalt Mixtures. Journal of the Association of Asphalt Paving Technologist, Volume 75, 2006.

Barksdale, R.D., J. Alba, N.P. Khosla, R. Kim, P.C. Lambe and M.S. Rahman. Laboratory Determination of Resilient Modulus for Flexible Pavement Design. Georgia Tech Project E20-634, 1997.

Bayomy, F., E. Masad, and S. Dessouky. Development and Performance Prediction of Idaho Superpave Mixes, Interim Report ITD-NIATT Project KLK464, National Institute for Advanced Transportation Technology, University of Idaho, Moscow, Idaho, 2002.

Christensen, D.W., T. Pellinen and R.F. Bonaquist. Hirsch Model for Estimating the Modulus of Asphalt Concrete. Journal of the Association of Asphalt Paving Technologist, Volume 72, 2003.

Counto, V.J.. The Effect of the Elastic Modulus of the Aggregate on the Elastic Modulus, Creep, and Creep Recovery of Concrete. Magazine of Concrete Research, Volume 62, No. 48, 1964.

Cundel, P.A.. A Computer Model for Simulating Progressive Large Scale Movement in Blocky Rock Systems. Proceeding of the Symposium of the International Society of Rock Mechanics, Volume 1, France, 1971.

Dessouky, S., E. Masad, and F. Bayomy. Prediction of Hot Mix Asphalt Stability Using the Superpave Gyratory Compactor, Journal of Materials in Civil Engineering, Vol. 16, No. 6, 2004.

Appendix B, Page 20

Fletcher, T., C. Chandan, E. Masad, K. Sivakumar. Aggregate Imaging System (AIMS) for Characterizing the Shape of Fine and Coarse Aggregates. Transportation Research Record 1832, Washington D.C., 2003.

Hashin, Z.. Viscoelastic Behavior of Heterogeneous Media. Journal of Applied Mechanics, Trans. ASME, No. 9, 1965.

Hirsch, T.J.. Modulus of Elasticity of Concrete Affected by Elastic Moduli of Cement Paste 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 Modulus Predictive Equation. Transportation Research Record 911, Washington D.C., 1983.

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 Compaction and Shearing Resistance of Asphalt Mixtures. Transportation Research Record 1789, Washington, D.C., 2002.

Uddin, W.. A Micromechanical Model for Prediction of Creep Compliance and Viscoelastic Analysis of Asphalt Pavement. Presented at the 78th Annual TRB Meeting, Washington D.C., 1999.

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, D.C., 2002.

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 Stiffness Using The Discrete Element Method. PhD Dissertation, University of Illinois at Urbana-Champaign, 2003.

You, Z., W.G. Buttlar. Micromechanical Modeling Approach to Predict Compressive Dynamic Moduli of Asphalt Mixtures Using the Distinct Element Method. Transportation Research Record 1970, Washington D.C., 2006.

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 Fracture of Asphalt Mixtures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1034, TRB, National Research Council, Washington, D.C., 1985, pp. 112-123.

Bayomy, F., A. Abdo, M. Mull, and M. Santi, “Evaluation of Hot Mix Asphalt (HMA) Fracture Resistance Using J-Integral,” in the TRB Compendium of Papers CD-ROM of the 85th Transportation Research Board Annual meeting, January 2006, Washington, DC, paper No. 06-2745.

Bayomy, F., A. Abdo, Mary Ann Mull, and M. Santi, “Evaluation of Fracture Resistance of Hot-Mix-Asphalt,” the International Conference on Advanced Characterizations of Pavement and Soil Engineering Materials. Athens, Greece, June 20-22, 2007

Bhurke, A., E. Shin and L. Drzal, "Fracture Morphology and fracture toughness measurement of polymer modified asphalt concrete", TRB 76th annual meeting Jan 1997, Paper no. 970942.

Dongre, R., M.G. Sharma, and D.A. Anderson. Development of Fracture Criterion for Asphalt Mixes at Low Temperatures. In Transportation Research Record: Journal of the Transportation Research Board, No.1228, TRB, National Research Council, Washington, D.C., 1989, pp. 94-105.

Huang, B., W. Kingery, Z. Zhang, and G. Zuo. Laboratory Study of Fatigue Characteristics of HMA Surface Mixtures Containing Rap. Presented at 83rd Annual Meeting of the Transportation Research Board, Washington, D.C., 2004.

L.N. Mohammad, Z. Wu, and M. A. Mull. Characterization of Fracture and Fatigue Resistance on Recycled Polymer-Modified Asphalt Pavements. 5th RILEM International Conference on Cracking in Pavements, Limoges, France, May 5-8, 2004.

Li, X., and M. Marasteanu. Evaluation of Low Temperature Fracture Resistance of Asphalt Mixture Using the Semi Circular Bend Test. Journal of the Association of Asphalt Paving Technologists, Vol. 73, 2004, pp. 401-426.

Lim, I.L., I.W. Johnston, S.K. Choi, and J.N. Boland. Fracture Testing of a Soft Rock with Semi-Circular Specimens Under Three-point Bending. Part 1-Mode I. International Journal of Rock Mechanics and Mining Science, Vol. 31, No. 3, 1994, pp. 185-197.

Lim, I.L., J.W. Johnston, and S.K. Choi. Stress Intensity Factors for Semi-Circular Specimens Under Three-Point Bending. Engineering Fracture Mechanics, Volume 44, No. 3, 1993.

Little, N. and K. Mahboub. Engineering Properties of First Generation Plasticized Sulfur Binders and Low Temperature Fracture Evaluation of Plasticized Sulfur Paving Mixtures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1034, TRB, National Research Council, Washington, D.C., 1985, pp. 103-111.

M. A. Mull, A. Othman, and L. Mohammad. Fatigue Crack Propagation Analysis of Chemically Modified Crumb Rubber Asphalt Mixtures. Journal of Elastomers and Plastics. Vol 37: 2004, pp. 73-87.

Molennar, A., A. Scarpas, X. Liu, and G. Erkens. Semi Circular Test; Simple but Useful?. Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp.

Mull, M., K. Stuart, and A. Yehia. Fracture Resistance Characterization of Chemically Modified Crumb Rubber Asphalt Pavement. Journal of Materials Science, Vol. 37, 2002, pp. 557-566.

Appendix B, Page 22

Rice, J.R. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, Vol. 35, 1968, pp. 379-386.

Van de Ven, M., A. de Fortier Smit, and R. Krans. Possibilities of a Semi-Circular Bending Test, Proceedings of the Eighth International Conference on Asphalt Pavements, Vol. II, Seattle, WA., 1997, pp. 939-950.