Development and Evaluation of Performance Tests to Enhance Superpave Mix Design and Implementation in Idaho

USDOT Assistance No. DTOS59-06-G-00029 (NIATT Project No. KLK479)

ITD Project No. RP 181 (NIATT Project No. KLK483)

Quarterly Progress Report – QR2 For the period

Oct 1st to Dec. 31st, 2007

Submitted to Ashley Bittner

U.S. Department of Transportation

Ned Parrish Research Manager

Idaho Transportation Department

and

Michael J. Santi Assistant Material Engineer

Idaho Transportation Department

UI Research Team Dr. Fouad Bayomy, PI Dr. S. J. Jung, Co-PI Dr. Thomas Weaver, Co-PI Dr. Richard Nielsen, Co-PI Mr. Ahmad Abu Abdo, Graduate Research Assistant Mr. Seung II Baek, Graduate Research Assistant Mr. Srinivas Rao Gone, Graduate Research Assistant University of Idaho National Institute for Advanced Transportation Technology Center for Transportation Infrastructure

January 7, 2008

1

Introduction This project addresses the implementation of the Superpave mix design system in the state of Idaho. It is a partnership between the USDOT, the Idaho Transportation Department (ITD) and the University of Idaho (UI). It is co-funded by USDOT and ITD with match funds from the UI. The project focuses on developing asphalt mix tests and tools that would be conducted at the mix design level 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 a training program to aid the ITD engineers to implement the products of the research into the mix design process. Detailed plans for these phases have been presented in the project proposal. A progress report was submitted to the USDOT in May 2007, which summarized the progress since the inception of the USDOT assistance contract. A copy of that progress report was also sent to ITD. A new adjusted time schedule was submitted in May. With the inception of the ITD contract on July 1, 2007, a regular quarterly report is planned to be submitted at the end of each quarter, which is reflected in the new project schedule. This is the first quarterly report in which a summary of the project activities during the period July 1, 2007 to Sept 30, 2007 is presented.

1. Project Management Since the inception of the contract with ITD on July 1st, two new graduate students were recruited and they had started working with the team in fall 2007. Mr. Seung II Baek, will be mainly working on phase B of the project assisting Dr. Jung. He will also participate in the mix preparation tasks in Phases A and B. Mr. Srinivas Rao Gone, will be mainly working on research activities related to finite element analysis (FEA) and constitutive modeling in Phases A and B of the project. He will be assisting Dr. Weaver and Dr. Nielsen, and will also participate in the mixture testing activities of phase A. Work progress as measured by % task completed is estimated on monthly basis and is shown in Table 1.

2

Table 1 Approximate Level of Work Completed by Task at the end of Quarter 1

2. Progress by Task The chart in Table 1 summarizes the progress as % work completed as of Sept 30, 2007. Description of work performed during the report period in the various project tasks are provided below: Task A1 – Review of previous studies and available data Work in this task addresses review of work related to the developments in the dynamic modulus (E*) test and how the E* is used as a fundamental mix property. Most of the work reviewed on this subject was presented in the progress report that was submitted in May 2007. In this quarter, the work was focused on the protocol of the E* test, and training on how to conduct the test using the new SPT (Superpave Performance Tester) that has been recently installed in the lab. The work completed in this task is estimated to be about 22%. Task A2 – Analytical Analysis The focus of this task is on the development of constitutive models that relate the mix properties to the properties of its constituents. Thus, the effort here is to try to relate E* of the mix to the G* (shear modulus) of the binder and aggregate properties. Review of the literature and initial analysis is presented in Appendix A of this report. The work completed in this task is estimated to be about 12% Task A3 – Experimental Design, Binder and Aggregate Evaluation Lab Mixes: Modifications to the initial experiment design included reduction in the number of asphalt binders to be used in the mix matrix from 9 to 8 binders. The asphalt binder grade PG 58-22 is not available and is not used by ITD. Typically the binder for mixes that required PG 58-22 is

Phase / TaskQuarter

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

Task A1 – Review of previous studies and available data 10% 10% 5% 25%

Task A2 – Analytical Analysis 8% 8%Task A3 – Experimental Design, Binder and Agg. Eval. 15% 10% 25%

Task A4 – Prep and Evaluation of Asphalt Mixtures 5% 5%

Task A5 – Data Analysis 0%

Task B1 – Literature Review 10% 15% 5% 30%

Task B2 – Finite Element Analysis 0%Task B3 – Development of the Fracture Test Procedure 10% 10%

Task B4 – Prep and Evaluation of Asphalt Mixtures 0%

Task B5 – Data Analysis 2% 2%

Task B6 – Reliability Analysis 0%

Task C1 – Development of Implementation Plan 0%

Task C2 – Training Program for ITD Personnel 0%

Tasks A6, B7 and C3 – Quarter Reports for USDOT R1 R2 R3 R4 R5 R6 R7 Final 0%

Task D1: External peer review of the final report 0%

Task D2: Final report review by ITD 0%

Task D3: Final Report Submittal 0%

Phase D: Final Report Review and Submittal

Year 3

Phase B: Evaluation of Mix Resistance to Fracture and Fatigue Cracking

Phase A: Evaluation of Mix Resistance to Deformation

Phase C: Implementation of Research Products and Training

Reporting

Year 1 Year 2

Tot

al %

T

ask

Com

plet

ed

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4Calendar Yr 2007 Calendar Yr 2008 Calendar Yr 2009

3

replaced by PG 58-28 instead. In addition, the aggregate structures selected were reduced from 3 to 2 as designated by Mix 1 and Mix 2, where Mix 1 represents medium traffic (from 3 to 30 million ESALs where Mix 2 for high traffic with more than 30 million ESALs. The reason for that change was that we could not identify a single ITD mix that fits low traffic with less than 3 million ESALs. The new mix matrix is presented in Table 2.

Table 2 Modified Lab Mix Matrix and Selected Binders

All eight PG asphalt binders have been procured from Idaho Asphalt Supply. Binder testing in G* and viscosity is in progress. The initial viscosity-temp susceptibility curves as provided by the supplier are shown in Figure 1. It is important to note that the selection of the binders was to use various grades that have different temperature susceptibility.

PG High Grade

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

Mix 1 3 - 30x106 √ √ √

Mix 2 > 30x106 √ √ √ √ √

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

Mix 1 0.3 - 3x106 √ √ √ √ √

Mix 2 > 30x106 √ √ √

-0.5 Opt 0.5 -0.5 Opt 0.5

Mix 1 0.3 - 3x106 √ √

Mix 2 > 30x106 √ √

58

-34 -28 -22

PG Low Grade -34 -28

AC%

-34 -28 -22

70

PG Low Grade

64

AC%

AC%

PG Low Grade

Aggregatbeing siepresented

 

Test

GS/Jc

Jc (at 3 diff. low temp.)

Jc*

E*

APA

Tri-axial

X-Ray

AIMS

G* and η

Total

Fig

tes for Mix geved in the ITd in Table 3.

Aggregate (lb) Binde

37.3 6.4

111.9 19

37.3 6.4

37.3 6.4

37.3 6.4

37.3 6.4

37.3 6.4

12.4 -

- 1.7

348.1 59

gure 1 Temper

groups 1 andTD HQ lab. .

Table 3

er (lb)# of

Samples / test

4 3

.3 3

4 3

4 2

4 2

4 3

4 3

-

7 -

.8 19

rature Suscep

d 2 (raw matThe planned

3 Planned Test# of

Samples / mix

Totalwt (

45 559

27 100

27 335

30 559

30 559

9 111

9 111

- 12

-

177 325

ptibility Curve

terials) have d tests and th

ts and Materi

Agg (lb)

Total Bindewt (lb)

9.4 24.2

06.9 43.5

5.6 14.5

9.4 24.2

9.4 24.2

1.9 4.8

1.9 4.8

2.4 -

2.0

57 140 per Binder Grade

es for the Selec

been procurhe required m

ial Requireme

er

e

Test at all conditio

Test at all conditio

Test at optimum Aaggregates struct

Test at optimum Aaggregates struct

Test at all conditio

Test at optimum Atemperatures (e.gconducted for PG

Test at optimum A

Test all PGs at di

cted Binders

red from thematerials fro

ents

ons

ons

AC% and at designeture

AC% and at designeture

Notes

ons

AC% and at 3 differg. for PG 64-28: test

G 64-22, 64-28 and 6

AC% and at all bind

fferent temp. and fr

4

field and arom each mix

ed PG for each

ed PG for each

rent Low PG ts will be 64-34°C)

er grades

equencies

re are

5

B.  Field Mixes Six mixes have been identified from various projects in Idaho. The Job Mix Formula (JMF) for all these mixes are available. Due to their large file size, it was omitted from this report. Summary of all mix design parameters are listed in Table 4. The mixes shall be procured as ready mixed from project sites. However, for Mixes 1 and 2, raw materials were also procured to construct the lab mixes as per Table 2. The work completed in this task is estimated to be about 30%.

Table 4 Summary of Properties of Field Mixes

Mix ID 1 2 3 4 5 6

ProjectJerome IC, IM-84-3 (074) 165

Topaz to Lava Hot Springs NH-A010 (455)

Lapwai to Spalding NH-411 (144)

US-20 MP 112.9 to 124.63 NH-3340 (109)

Int. US-26/SH 46 Gooding A008 (256)

Chester to Twin Groves S.B.L NH-6470

Key# 8896 10455 8353 9106 8256 8634

Class SP4 SP3 SP3 SP3 SP3 SP3

ESALs > 30x106 3 - 30x106 3 - 30x106 3 - 30x106 3 - 30x106 3 - 30x106

N-design 125 100 100 100 100 100

Gmm 2.449 2.424 2.568 2.448 2.351 2.281

AV% 4% 4% 4% 4% 4% 3.9%

Sample wt, gr 4700 4600 4800 4750 4610 4300

PG 70-28 64-34 70-28 70-28 70-28 64-34

Pb% 4.9% 4.35% 5.4% 5.12% 5.9% 5.8%

Gb 1.021 1.025 1.034 1.021 1.021 1.026

Mix Temp., °F 330 335 323 330 325 320

Comp. Temp., °F 305 307 293 305 303 293

Gsb 2.586 2.558 2.771 2.589 2.467 2.387

Gse 2.639 2.568 2.808 2.648 2.559 2.464

Absorption 1.3% 1.5% 1.9% 1.9% 2.9% 3.23%

%Passing, Sieves

25mm (1") 98% 100% 100% 100% 100% 100%

19 mm (3/4") 86% 100% 97% 100% 99% 99%

12.5mm (1/2") 73% 83% 83% 79% 85% 87%

9.5mm (3/8") 64% 65% 71% 66% 75% 73%

4.75mm (#4) 41% 37% 51% 45% 60% 48%

2.36mm (#8) 27% 25% 34% 32% 45% 33%

1.18mm (#16) 18% 18% 23% 23% 32% 22%

600um (#30) 13% 14% 16% 16% 22% 14%

300um (#50) 10% 11% 11% 9% 11% 11%

150um (#100) 5% 7% 8% 5% 5% 8%

75um (#200) 4% 4.7% 5.9% 4% 4.2% 6.4%

Mix Properties

Aggreagtes Properties

Binder Properties

6

Task A4 – Preparation and Evaluation of Asphalt Mixtures Work in this task has not started yet as far as mix preparation. However, the effort spent in procuring raw materials of aggregate and binders and the preparation work of these materials is estimated to be 5% work level in this task. The actual mixing will occur after all sieving is complete, which is expected to occur in the next quarter. Task A5 – Data Analysis Work in this task did not commence yet. Task B1 – Literature Review on Fracture Work in this task is focused on a review of the published work in the area of fracture mechanics with special attention to the use of the semi circular samples in the fracture analysis for the asphalt mixes. Extensive review was reported in the May progress report. Additional review is also conducted during this quarter. It is presented in Appendix B. Task B2 – Finite Element Analysis The work in this task did not commence with respect to conducting analysis on the mixes. However, a license to the Finite Element package ABAQUS has been purchased and the package is installed. Training of the graduate student is in progress to learn how to use the software package. The effort spent in this regard is estimated to be about 5% of the work level in this task. Task B3 – Development of the Fracture Test Procedure Since none of the mixes are prepared yet, no fracture testing has been conducted on the designated mixes for this project. However, we have used other mixes from old projects to conduct a pilot study on the validity of the proposed test procedure using the semi-circular notched sample. A summary of that pilot study is presented in Appendix C. This pilot study was also part of independent research that has been submitted for presentation and publication at the TRB 2008 annual meeting. Paper review is pending. Tasks B4, B5, B6 and Phases C and D Work in these tasks and phases did not commence yet.

3. Equipment Requisition A new Superpave Performance Tester (SPT) has been purchased from IPC Global (Australia) through InstroTech, Inc of North Carolina. The equipment will be used for the dynamic modulus test and Flow Number tests in accordance to the NCHRP project 9-29. The SPT has been installed in the asphalt mix lab and is in operation (Figure 2). The research team had a brief training session with the InstroTech specialist. There are still a few items related to the software for various tests. For example, for the dynamic modulus test, various frequencies can be applied while in the flow number test, we have no control on the applied load function. The team is working on resolving these issues with IPC Global.

7

In addition, work on developing a temperature control room for low temperature fracture testing is in progress. An effort to build such system in the lab is in progress. A new cooling coil has been installed in an old cooler and being tested for operation. (Figure 3)

Figure 2 SPT System

Figure 3 Cooling System (Under Development)

8

Summary The main outcomes that have been achieved during this quarter can be summarized as follows:

1. Installing the SPT testing system 2. Progress in building a cooling system for fracture testing at low temperature. 3. Procuring all required binders 4. Procuring all raw aggregates for lab mixes. 5. Identifying six field mixes 6. Continued literature review 7. Conducting a pilot study for fracture testing using both semi-circular and beam, samples,

and 8. Hiring two new graduate students

Appendices Appendix A: Review of Literature for Constitutive Models in Asphalt Mixes Appendix B: Literature Review on Fracture of Asphalt Concrete Appendix C: Pilot Study on HMA Fracture

APPENDIX A REVIEW OF LITERATURE FOR CONSTITUTIVE MODELS IN ASPHALT MIXES BY: THOMAS WEAVER 

1 Numerical Modeling of Asphalt Concrete Numerical models are being used increasingly in research and practice to predict the performance of asphalt concrete pavement performance.  Numerical models able to account for many parameters that impact asphalt concrete pavement behavior are: discrete element models and constitutive models.   

The discrete element methodology models each individual particle within a material and uses contact laws to govern the interaction of the particles.  This procedure was initially developed by Cundall (1971).  Application of the discrete element method may lead to better understanding of the physics governing asphalt concrete behavior and is a valuable research tool.  However, use of this method is not likely in the near future by engineering practitioners to model asphalt concrete pavement performance.   

Constitutive modeling is another method useful for modeling asphalt concrete behavior and models material response on a more global level.  This methodology is more developed than the discrete element methodology and with more research, may be useful for engineering practitioners to assess long term asphalt concrete pavement performance. 

The following section presents background information on constitutive models, in particular, models that have been implemented in finite element programs (Note, more work is required to complete this literature review). 

1.1 Constitutive Models Constitutive models are relationships correlating stress with strain.  The simplest constitutive model is Hooke’s law which states: 

 

where σ is stress, E is the modulus of elasticity, and ε is strain.  More complex models are required to capture non‐linear response of materials due to yielding, fracture, and other variables impacting material behavior.  Two constitutive models that have been implemented in finite element programs are the disturbed state concept (DSC) constitutive model and an elastoviscoplastic model.  These models are described below. 

1.1.1 Disturbed State Concept The disturbed State concept (DSC) constitutive model was developed by Desai (2001) and has been used to model asphalt concrete pavement (Desai 2007).  This model is capable of including the effect of elasticity, plasticity, creep, microcracking, and fracture under mechanical and environmental loading.   

The DSC considers a material to exist in two states,  a relatively intact state (RI) or a microcracked state/fully adjusted (FA) state.  As the material is loaded, the material transforms from RI to FA.  The DSC 

relates these two states and the transformation from RI to the FA state through a disturbance value.  The disturbance value ranges from 0 to 1 corresponding to relatively intact to significantly damaged material, respectively.  The disturbance value controls the softening that occurs in a material after yielding has occurred.   

The relatively intact state is modeled as an elastic‐plastic material using a yield function and elastic material properties.  The parameters used to define material response can be defined as functions of temperature and loading rate.  Creep can also be included. 

The fully adjusted state may be defined as a critical state where no volume changes occur during yielding under a constant shear. 

The disturbance value is obtained using the equation: 

1  

Where D is the disturbance, εD is the acculuative deviatoric platic strain, and the values Du, A, and Z are disturbance parameters. 

1.1.1.1 Determination of DSC Paramters The DSC model requires elastic parameters, plasticity parameters, creep parameters, disturbance parameters, and thermal effects.  Not all parameters are needed if a certain aspect of the model is neglected.  The model parameters and methods for obtaining these parameters as provided by Desai (2007) and are summarized below. 

The elastic parameters are Young’s modulus, E, and Poisson’s ratio, ν.  The modulus value can be obtained from a stress‐strain curve and is a function of mean pressure. 

The hierarchical single yield surface developed by (Desai et al. 1986) is used for the plasticity model.  

Parameters needed to define this yield surface are γ, β, n, a1, η1, and R.  The value of γ is determined from the plot of the ultimate envelope based on the asymptotic stress in the ultimate region.  The value n is determine from the stress condition at which transition from compaction to dilation occurs.  Hardening parameters a1 and h1 are determined by computing the accumulated plastic strain from the incremental stress‐strain curve, and the cohesive intercept, c, is used to find the value R. 

Other parameters associated with creep, disturbance, and thermal effects are presented below.  Creep parameters may be obtained from a plot of strain versus time.  The disturbance parameters, A and Z, are found from a stress vs. strain curve where softening occurs.  The value Du is the residual response and can be assumed to be 0.9. Thermal effects can be determined by plots of the parameter of interest with temperature.   

The number of parameters and effort required to obtain these parameters will likely be cumbersome to most engineers. 

   

1.1.2 Elastoviscoplastic Model A number of researchers have developed elastoviscoplastic constitutive models for application to asphalt concrete (Abdulshafi and Majidsadeh 1985, Scarpas et al. 1997, Lu and Wright 1998, Seibi et al. 2001, Collop et al. 2003, and Masad et al. 2007).  Differences in these models include the yield surface employed (e.g. Drucker‐Prager, HISS, Mohr‐Coulomb) and whether the model accounts for microstructure behavior that influences anisotropy and damage.  In general, these models decompose the total strain rate into a viscoelastic strain rate and a viscoplastic strain rate.  The constitutive model proposed by Masad et al. (2007) is discussed in more detail below since this model accounts or material anisotropy associated with the aggregate and damage associated with material cracking. 

1.1.2.1 Anisotropy and Damage Material anisotropy is a result of the anisotropy associated with granular material in the asphalt concrete mix.  Masad et al. (2007) have proposed using image analysis of an asphalt concrete cross section to determine the orientation of aggregates within the material.  Based on the orientation of the 

aggregates, a vector magnitude Δ is computed.  The vector magnitude D is used to modify the stresses in the material computed using a viscoplastic model.   

The concept of modifying the effective stress in the material as a result of crack growth as proposed by Kachanov (1958) has been implemented within the model proposed by Masad et al. (2007).  When computing the stress as implemented in the viscoplastic model, the effective stress is multiplied by a factor that increases the effective stress in the material.  In this model, the variable controlling damage ranges from 0 for undamaged to 1 for a completely damaged material. 

1.1.2.2 Material Parameters The material parameters required for the constitutive model proposed by Masad et al. (2007) are listed in Table 1 below.  Similar to the DSC model, many parameters are needed to define the material behavior with an elastoviscoplastic model that can account for anisotropy and damage.  However, based on results presented by Masad et al. (2007), some parameters do not change significantly from one material to another.  For example, the anisotropy vector magnitude for granite and general gravel aggregates were 28.6 and 26.1, respectively.  As long as typical aggregates are consistently utilized, image analysis tests may be eliminated from the required testing sequence for determining this parameter.  Correlations with other simplistic tests may also be possible for estimating appropriate material parameters for this model.   

 

   

Table 1 Material Parameters for Elastoviscoplastic Model (Masad 2007) 

Parameter Test for Determining Parameter 

Anisotropy, Δ Image analysis 

Viscoelastic stiffness, E1  Uniaxial compression 

Viscoelastic stiffness, E2  Uniaxial compression 

Poisson’s ratio, ν Triaxial shear 

Drucker‐Prager friction angle, α Triaxial shear 

Drucker‐Prager cohesion, κ0  Triaxial shear 

Perzyna’s viscoplastic parameter, Γ Triaxial shear 

Perzyna’s viscoplastic parameter, N  Triaxial shear 

Dilation Parameter, β  

Damage Parameter, ξ1  Triaxial shear 

Damage Parameter, ξ1  Triaxial shear 

Damage Parameter,ξ1  Triaxial shear 

Hardening Parameter, κ1  Triaxial shear 

Hardening Parameter, κ2  Triaxial shear 

 

1.2 Summary Numerical models have been developed for modeling asphalt concrete behavior.  Two types of constitutive models were described above: the disturbed state concept and the elastoviscoplastic models.  The challenge associated with using constitutive models is the number of parameters that must be defined for using the model.  Results of some laboratory testing by Masad et al. (2007) indicate that it may be possible to reduce the amount of testing required to determine all of the material parameters for the elastoviscoplastic model.  If the amount of laboratory testing can be reduced or more simple tests can be substituted for some of the triaxial shear tests, this model may become useful for engineers in assessing long‐term asphalt concrete pavement performance. 

 

   

2 References  

Abdulshafi, A., and Majidzadeh, K. (1985). “Combo viscoelastic‐plastic modeling and rutting of asphaltic mixtures.” Transportation Research Record 968, Transportation Research Board, Washington, D.C., 19‐31. 

Collop, C., Scarpas, A.T., Kasbergen, C., and de Bondt, A. (2003). “Development and finite element implementation of a stress dependent elasto‐visco‐plastic constitutive model with damage for asphalt.” Transportation Research Record 1832, Transportation Research Board, Washington, D.C., 96‐104. 

Desai, C.S., (2001). Mechanics of materials and interfaces: The disturbed state concept, CRC, Boca Raton, FL. 

Desai, C.S. (2007). “Unified DSC constitutive model for pavement materials with numerical implementation,” International Journal of Geomechanics, ASCE, Vol. 7, No. 2, 83 – 101. 

Desai, C.S., Somasundaram, S., and Frantiziskonis, G. (1986). “A hierarchical approach for constitutive modeling of geologic materials.” Internation Journal for Numerical and Analytical Methods in Geomechanics, 10(3), 225‐257. 

Lu, Y., and Wright, P.J. (1988). “Numerical approach of viscoelastoplastic analysis for asphalt mixtures.” Computers & Structures, 69, 139‐157. 

Masad, E., Dessouky, S., Little, D. (2007). “Development of an elastoviscoplastic microstructural‐based continuum model to predict permanent deformation in hot mix asphalt,” International Journal of Geomechanics, ASCE, Vol. 7, No. 2, 119 – 130. 

Scarpas, A., Al‐Khoury, R., Van Gurp, C., and Erkens, S.M. (1997). “Finite element simulation of damage development in asphalt concrete pavements.” Proc., 8th Int. Conf. on Asphalt Pavements, Univ. of Washington, Seattle, 673‐692. 

Seibi, A.C., Sharma, M.G., Ali, G.A., and Kenis, W.J. (2001). “Constitutive relations for asphalt concrete under high rates of loading.” Transportation Research Record 1767, Transportation Research Board, Washington, D.C., 111‐119. 

APPENDIX B LITERATURE REVIEW ON FRACTURE OF ASPHALT CONCRETE BY: SJ JUNG 

1

Page1 

Simplification of Fatigue Test To improve the pavement design, a simple and dependable testing and validating procedure is needed to enhance the material design and prediction of pavement life. Currently, fatigue test is one that are using to estimate pavement life and material design. However, a fatigue test is expensive and time consuming work to applicable on the each project. It is a very important to develop an effective method that can estimate fatigue characteristic of pavement indirectly. Lundstrom(2003) reviewed Daniel(2002)’s work whether the monotonic tests are able to predict fatigue characteristics of asphalt concrete mixtures. The work potential theory is a relatively simple approach for modeling material experiencing growth of damage but the results of the study show that monotonic tests do not support the characterizing fatigue behavior generally. One of possibilities of differences between monotonic and cyclic tests is that samples undergo short fatigue lives (i.e. low number of cycles is needed to failure). It is similar pattern of monotonic test which can be compared to the long fatigue lives. Another possibility is that a loading level is not enough to cause significant damage growth. And some amount of work is used to converting heat when a viscoelastic material is subjected to multiple load cycles. More efforts (i.e. modification) need to predict fatigue characteristic of asphalt concrete mixtures using monotonic tests generally. Our approach will be that results from other researcher can be used to develop for a new prediction model. After literature review, fatigue characteristics of asphalt mixtures using existing model will be examined for verifying model study. Existing data were compared, table 1 which shows parameters used in each method shows what parameter can be affected in each model. Table 2 which shows composition of mixture and other parameters can be used the condition of the model without verification.

Table 1 Parameters used in each method

2

Page2 

Va Vb Sm ε PI δ(Sm) TR&B n f(frequency) a, b

E* VB TRB ε t

SPDM X X X Bonnaure X X X X

SHRP X X X X X Medani X

X

X X X X

H.J. Lee X X X X X Pell X X XShell X X XThickness Design

X X X X

Table 2 Composition of mixture and other parameters

Va (%)

Vb (%)

Vg (%)

PI T (°C)

TR&B (°C)

F (Hz)

Load (kN)

Total mixture

Time

Medani (2000)

1.9-30.9

6.1-19.3%

6.9-88.10

-1.5-2.0

-10-+35

43-78 10-50 10

H.J. Lee(2002)

3.0 - 4.0%

4.1 – 6.9%

25 10 0.2-0.3 6 0.1

Daniel (2002)

8% 4%

low, optimum,high optimum

-10C, 0C, 5C, 12C, and 20C

20, 10, 3, 1, 0.3, and 0.1 Hz

8.9 kN or 89 kN

8

3

Page3 

Reference: Bonnaure, F. P., Gravois, A. and Udron, J. (1980). A New Method for Predicting the

Fatigue Life Characteristics of Bituminous Mixes. Proceedings of Association of Asphalt Paving Technology.

Daniel, J. S., and Y.R. Kim (2002). "Development of a Simplified Fatigue Test and Analysis Procedure using a Viscoelastic Continuum Damage Model." Journal of the Association of Asphalt Pavement Technologists Vol. 71: pp. 619-650.

Lee, H.J., J. S. D., and Y. Richard Kim (2000). "Continuum Damage Mechanics-Based Fatigue Model of Asphalt Concrete." Journal of Materials in Civil Engineering Vol. 12(No. 2): pp. 105-112.

Medani, T.O., A. A. A. M. (2000). "Estimation of fatigue characteristics of asphaltic mixes using simple tests." Heron Vol. 45(No. 3): pp. 155-166.

Schapery, R. A. (1984). "Correspondence principles and a generalized J-integral for large deformation and fracture analysis of viscoelastic media." Int. J. Fract. Vol. 25: pp.195-223.

Schapery, R. A. (1990). "A theory of mechanical behavior of elastic media with growing damage and other changes in structure." Journal of the mechanics and physics of solids.Journal vol. 38.

Shell Int. Petroleum Co., L. (1987). Shellpavement design manual. London, U.K. SPDM (1978). Shell Pavement Design Manual. London, Shell International Petroleum

Company Ltd.

1  

APPENDIX C PILOT STUDY ON HMA FRACTURE BY: AHMAD ABU ABDO AND SJ JUNG 

   To determine the validity of our approach in HMA fracture, a pilot study was conducted on different mixes. The goals of this study were the evaluation of fracture toughness of asphalt mixes by determining the stress intensity factor (KIC) parameter by two methods; the semi‐circular notched bending fracture (SCNBF) test and the single edge notched beam (SENB) test, as shown in Figure 1. Furthermore, the study included the development of a temperature shift factor (αT) that enables the determination of the KIC parameters at different temperatures from a reference value at a reference temperature. 

 

 a) SCNBF Test            b) SENB Test 

Figure 1: Fracture Tests Setup 

Materials Available raw materials from previous projects were used in this study. Raw materials for two 

different Superpave mixes (M1 and M2) were procured from two existing projects in the State of Idaho. These two mixes have different aggregate properties. To achieve the goals and objectives of this study, an experimental mix matrix was prepared (Table 1). 

Table1: Selected Mixtures for Pilot Study on Fracture 

Mix PG AC%

-1.0% -0.5% Optimum +0.5% +1%

M1 64-34 √ 5.5% √ √

M2 64-28 √ 5.9% √

64-22 √  

2  

Sample Preparation and Tests Setup All specimens were mixed and compacted under controlled lab conditions. Specimens were 

compacted using the Servopac Gyratory Compactor to a number of gyrations to produce specimens with 4% air voids. For the optimum asphalt content for both mixes, the number of gyration coincided with their set N‐design. Specimens used in a dynamic modulus test were compacted to achieve 170mm high specimens with a total of 9% air voids. Different samples were used for each test. Two replicates were prepared for each mix condition. 

Semi­Circular Notched Bending Fracture (SCNBF) Test  Compacted cylindrical specimens were sliced into 4‐quarter semi‐circle specimens. One quarter 

is left un‐notched as a control specimen, and the other three quarters were notched with 12.7, 25.4 and 31.8mm notch depths. All specimens have the standard Superpave Gyratory diameter (150mm). Spacing between the two roller supports was 120mm. A ramp load with a constant vertical deformation rate of 0.5mm/minute was applied till fracture occurred. Testing was conducted at temperatures of 4.4, 24 and 54.4 °C. 

Single Edge Notched Beam (SENB) Test  Semi‐circular specimens were sawed into beam specimens with dimensions of 100mm wide and 

50mm high. Beams were notched with 12.7mm notch depth. Spacing between the two roller supports was 80mm. A ramp load with a constant vertical deformation rate of 0.5mm/minute was applied till fracture occurred. Testing was conducted at a room temperature of 24 °C. 

Dynamic Modulus |E*| Test  All Specimens were cored and sawed to obtain specimens with a 100mm diameter, 150mm high 

and 7% air voids. The dynamic modulus test was conducted as per AASHTO TP 62‐03 test protocol. Testing consists of applying a uniaxial sinusoidal compressive stress to an unconfined asphalt mix cylindrical test specimen under a series of loading frequencies (0.1, 1, 5, 10 and 25 Hz) at different temperatures (4.4, 21.1, 37.8 and 54.4 °C).  

Results and Analysis 

Geometry Effects  Prior to conducting experimental tests to study the effect of geometry on fracture toughness, a 

simple 2‐D Finite Element Analysis (FEA) was conducted for both geometries. Using the same material properties, loading and boundaries conditions, tensile stress at the tip of the notch was simulated. When loaded both test setups yielded approximately the same tensile stress at the tip of the notch; the stress at the tip of notch for SCNBF test setup was 8.07MPa (1170.67psi) and 7.53MPa (1092.12psi) for SENB test setup as shown in Figure 2. The difference is less than 7% of maximum tensile stress which can be caused by shape, size, and distribution of elements in the FEA model. Furthermore, KIC by SCNBF yielded 9.1MPa.m0.5 and 8.7MPa.m0.5 by SENB. The difference is less than 4.4%. Thus, with ideal conditions, there should be no significant difference in KIC by using either test setups. 

 

3  

a) SCNBF Test                 b) SENB Test 

Figure 2: Finite Element Analysis Results for three Point Loading Test Setup 

Next, to compare KIC determined by the two test setups, a statistical software package SAS was used. T‐tests were conducted, to determine if there is any significant difference between the mean values of KIC for each mix condition. With a level of confidence of 95% (α = 0.05), results for the tested mixes showed that there was no significant difference between KIC by either SCNBF or SENB test setups (Figure 3). However, results of SENB were more scattered than SCNBF results.  

 

Figure 3: SCNBF versus SENB Tests Results 

Temperature Shift Factor (αT)    Using the asphalt mix dynamic modulus |E*| test data; shift factors at 4.4 and 54.4 °C were 

developed for each mix conditions. KIC at room temperature were shifted to 4.4 and 54.4 °C temperatures. Using statistical t‐test with a level of confidence α = 0.05, there was no significant difference between the actual and the shifted KIC at 54.4 °C as shown in Figure 4‐a. On the other hand, 

0

0.05

0.1

0.15

0.2

0.25

0.3

M1(Opt-PG64-34)

M1(-0.5AC%) M2(Opt-PG64-28)

M2(+1AC%) M2(PG64-22)

K IC, M

Pa.m

0.5

SENBSCNBF

4  

at 4.4 °C (Figure 4‐b), there was no significant difference for Mix M1. The actual KIC values for Mix M2 were larger than the shifted KIC values.  

By studying the fracture surface for both mixes, Figure 5 illustrated that the crack in Mix M1 specimens mostly propagated through the binder and around the aggregates (Figure 5‐a). In Mix M2, the crack has propagated through the binder and aggregates as shown in Figure 5‐b. For the same binder content (M1(+0.5AC%‐PG64‐34) and M2(Opt‐PG64‐28)), it was expected that Mix M1 would exhibit higher fracture resistance than Mix M2 due to better binder grade (PG64‐34).  Results showed that Mix M2 yielded larger KIC than Mix M1. Even when using a lower binder grade (PG64‐22) for Mix M2, Mix M2 still yielded higher KIC than Mix M1 (Figure 6). This might be rationalized by; at high temperature stiffness of binder is the controlling factor in asphalt mixes fracture resistance. At low temperatures, there are other factors (e.g. aggregate strength, shape, and texture) than binder stiffness that may affect fracture resistance, which may lead to higher KIC values. Further investigation is needed to adjust the shift factor to account for these factors for low temperatures.  

   

Figure 4: Actual versus Predicted SCNBF Results at Different Temperatures 

b) 4.4°C Te s t Te m pe rature

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

M 1(-0.5AC%) M 1(Opt-PG64-34)

M 1(+0.5AC%) M 2(-1AC%) M 2(Opt-PG64-28)

M 2(+1AC%)

K IC, M

Pa.m

0.5

Actual KICShifted KIC

a) 54.4°C Te s t Te m pe rature

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

M 1(-0.5AC%) M 1(Opt-PG64-34)

M 1(+0.5AC%) M 2(-1AC%) M 2(Opt-PG64-28)

M 2(+1AC%)

K IC, M

Pa.m

0.5

Actual KICShifted KIC

5  

 

a) Mix M1 (Opt‐PG64‐34)         b) Mix M2 (Opt‐PG64‐28)) 

Figure 5: Fracture Surface at 4.4°C 

According to the outcome of this study, and as expected, when evaluating KIC by SCNBF test at different temperatures, KIC was greater at low temperature of 4.4 °C and was lower at high temperature of 54.4 °C (Figure 6). For the tested mixes, it was found that KIC at any temperature ranked the tested mixes in the same pattern. KIC determined at room temperature of 24 °C followed almost the same trend of KIC at temperatures of 4.4 and 54.4 °C.  

 

 

Figure 6: Stress Intensity Factor KIC at Different Temperature 

Conclusions Based on the results of this pilot study, the following observations and conclusions are made: 

1. When comparing the semi‐circular notched bending fracture (SCNBF) test and the single edge notched beam (SENB) test, there was no significant difference at a level of confidence of 95% (α = 0.05) between results of the stress intensity factor (KIC) determined by both test setups. However, SENB test results were more scattered than SCNBF test results.  

0.000.020.040.060.080.100.120.140.160.180.20

M1(-0.5

AC%)

M1(Opt-

PG64-34

)

M1(+0.5A

C%)

M2(-1A

C%)

M2(Opt-

PG64-28

)

M2(+1AC%)

M2(PG64

-22)

K IC, M

Pa.m

0.5 (2

4 &

54.

4 °C

)

0.00.20.40.60.81.01.21.4

K IC, M

Pa.m

0.5 (4

.4°C

)

54.4°C24°C4.4°C

6  

2. Utilizing the dynamic elastic modulus |E*| test data, a shift factor (αT) was developed. For the tested mixes, there was no significant difference between actual and shifted KIC at higher temperature than the reference temperature. At lower temperatures there was no significant difference for Mix M1. Unlike Mix M1, actual KIC for Mix M2 was larger than shifted KIC. It is believed that stiffness of binder at high temperature could be the controlling factor. At low temperatures, there are other factors (e.g. aggregate properties) that might lead to higher KIC. Further investigation is required to account for these factors at low temperature. 

3. KIC by SCNBF test yielded as expected greater values at low temperature of 4.4 °C and low values at high temperature of 54.4 °C. Furthermore, it was observed that for the tested mixes KIC at room temperature (24 °C) followed the same trend of KIC determined at both temperatures 4.4 and 54.4 °C. KIC by SCNBF test at any temperature ranked the tested mixes in the same pattern.  

4. For the range of tested mixes, results showed that Mix M2 would exhibit higher fracture resistance than Mix M1. Thus, Mix M2 would perform better that Mix M1 under the same loading conditions. 

5. Overall, results suggested that semi‐circular notched bending fracture (SCNBF) test is beneficial in characterizing the fracture resistance of asphalt mixes. SCNBF test is also simple and repeatable, it can be used as a screening tool at the mix design stage to assess the fracture resistance of mixes, and help to eliminate weak mixes before conducting more sophisticated and time consuming tests.