Development and Evaluation of Performance Tests to Enhance …€¦ · Development and Evaluation...

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 – QR4 For the period

April1to June 30, 2008

Submitted to

U.S. Department of Transportation

Ed Weiner, COTR

And

Idaho Transportation Department Ned Parrish, Research Manager

Michael J. Santi, PE, Assistant Material Engineer

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 University of Idaho (UI) National Institute for Advanced Transportation Technology (NIATT) Center for Transportation Infrastructure (CTI)

July 9, 2008

1. Introduction

This is the fourth quarter report of the project which summarizes progress during the period April to June 2008. The focus during this period addressed several tasks as will be discussed in the report. In previous reports, a description of the project objectives and work plan has been presented. These reports are posted on the designated project reports web page at: http://www.webs1.uidaho.edu/bayomy/KLK479-483/QReports.htm. This QR4 report focuses on progress during the 4th quarter of the project. Description of work progress is presented on task by task basis.

2. Progress by Task

The chart in Table 1 summarizes the progress as % work completed as of June 30, 2008. Table 1 Approximate Level of Work Completed by Task at the end of Quarter 4

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% 2% 0% 2% 6% 0% 10% 10% 20% 70%

Task A2 – Analytical Analysis 12% 2% 4% 0% 7% 0% 5% 5% 15% 50%Task A3 – Experimental Design, Binder and Agg. Eval. 15% 15% 10% 5% 15% 0% 5% 10% 10% 85%

Task A4 – Prep and Evaluation of Asphalt Mixtures 5% 5% 10% 15% 20% 15% 15% 0% 0% 85%

Task A5 – Data Analysis 10% 0% 5% 10% 10% 20% 55%

Task B1 – Literature Review 10% 15% 5% 5% 5% 5% 0% 5% 0% 50%

Task B2 – Finite Element Analysis 5% 5% 5% 5% 15% 5% 2% 3% 5% 50%Task B3 – Development of the Fracture Test Procedure 12% 2% 5% 16% 5% 5% 10% 55%

Task B4 – Prep and Evaluation of Asphalt Mixtures 0% 15% 10% 15% 20% 60%

Task B5 – Data Analysis 0%

Task B6 – Reliability Analysis 5% 3% 5% 13%

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%

Tot

al %

Tas

k C

ompl

etedQ1 Q2 Q3 Q4 Q1

Calendar Yr 2008 Calendar Yr 2009

Year 1 Year 2 Year 3

Phase A: Evaluation of Mix Resistance to Deformation

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

Phase C: Implementation of Research Products and Training

Reporting

Phase D: Final Report Review and Submittal

Q2 Q3 Q4

Calendar Yr 2007

Work performed during the report period in the various project tasks is described below:

1

http://www.webs1.uidaho.edu/bayomy/KLK479-483/QReports.htm

Phase A: Evaluation of Mix Resistance to Deformation Task A1 – Review of previous studies and available data During this quarter, literature review continued to address the various models of the asphalt pavement permanent deformation, and its interaction with the dynamic modulus of the mix. Method of predicting permanent deformation in the new MEPDG guide is also addressed. A summary of work performed under this task is presented in Appendix A. The work completed in this task is estimated by about 70%. 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. Research efforts during this quarter focused on reviewing work related to viscoplastic models. An initial analysis using ABAQUS software is performed to develop a predictive model for the dynamic modulus of the asphalt mixtures. A brief summary of this analysis is presented in Appendix B. The work completed in this task (so far) is estimated by about 50% Task A3 – Experimental Design, Binder and Aggregate Evaluation Binder testing: All binder testing is now completed, and has been reported in previous quarter reports. During this quarter, independent binder grade verification is conducted by ITD, and all binders were verified. Aggregate testing: Other than the aggregate gradations that have been identified in QR1 report, no further evaluation on aggregates have been made in this period. Aggregates Imaging System (AIMS) Testing is still pending. The work completed in this task is estimated to be about 85%. Task A4 – Preparation and Evaluation of Asphalt Mixtures Work in this task focused on the preparation of lab samples for E* testing. Simultaneously, samples for Jc and triaxial testing are also being prepared for the designated mixes. All required samples for various tests have been prepared except for those tests that are pending as listed below: Gyratory Stability Testing: 100% completed.

E-star and Flow number Testing: 100% completed. APA test: Completed at ITD lab in Boise. Image Analysis: pending. MnRoad samples preparation: pending Samples for Jc (Fatigue fracture testing are being prepared under Task B4.

Work completed in this task is still estimated by about 85%

2

Task A5 – Data Analysis During this quarter, extensive analysis is conducted of the data developed under E* test and the Gyratory stability (GS) to determine the relationship between the GS and other mix properties including (aggregate structure, asphalt content, and mix density). The data analysis progress is as follows: GS, E*, and FN: 100% completed Model Development: 100% completed MEPDG Runs: In progress

APA: In progress MnRoad samples testing: pending

The analysis is presented in Appendix C of this report. Work completed in this task is estimated by about 55% Phase B: Evaluation of Mix Resistance to Fracture and Fatigue Cracking Task B1 – Literature Review on Fracture The reviewed literature was presented in QR2 and QR. No further review was conducted in this quarter. The work completed in this task is still estimated to be about 50%. Task B2 – Finite Element Analysis Work in this task overlaps two phases (Task A2 and Task B2). Use of FE under task A2 focuses on the constitutive modeling under the numerical analysis. The work developed using the ABAQUS software package is reported under task A2 and is presented in Appendix B. Under task B2, the use of FE analysis addresses the simplified fatigue model. In this regard, a DEM model is sought. Details f this analysis is developed along with Task B3 and presented in Appendix D. The effort spent in this task, so far, is estimated by about 50% of the work level in this task. Task B3 – Development of the Fracture Test Procedure The focus of this task is on the development of a simple test to predict fatigue cracking from a simple fracture test under static loading condition. The goal is to link a simple static fracture test to a dynamic fracture test, and develop correlations from which the fatigue can be estimated from the simple fracture test. The work completed in this task so far is estimated by about 55%. Task B4 – Prep and Evaluation of Asphalt Mixtures During this quarter, more than 90 samples were prepared. Dynamic testing is being performed on these samples. Details of the developed work are presented in Appendix D.

3

The work completed in this task so far is estimated by about 60%. Task B6 – Reliability Analysis A sufficient number of asphalt samples have been tested to determine the statistical parameters and probability distributions of key parameters for the permanent deformation model, including the gyratory stability GS, the maximum specific gravity Gmm, the binder content Pb%, and the air voids, AV%, the dynamic modulus, E*, and the dynamic shear modulus, G*. The statistical parameters and probability distributions for the permanent deformation model were used to develop a simulation model for permanent deformations. The simulations compare the permanent deformations from the E* model to the deformations predicted by the Mechanistic-Empirical Design Guide. One hundred thousand simulations were run at various temperature levels to determine the probability that the deformations predicted by the E* model exceed those allowed by the Mechanistic-Empirical Design Guide. Tasks B5 and Phases C and D Work in these tasks and phases did not commence yet.

3. Equipment Development and Troubleshooting

During this quarter research team focused on the upgrade of the MTS machine. 1. A new controller has been acquired. Training of the team is conducted and the test set-up

has been modeled. Preliminary testing is underway. 2. An in-house system for sample coring, slicing and notching have been developed and

used for sample preparation for fracture tests. 3. Work is still in progress on developing a temperature control room for low temperature

fracture testing.

4. Summary

The main outcomes that have been achieved during this quarter can be summarized as follows: 1. Further review of the permanent deformation models, especially those used in the

MEPDG were prepared. 2. Analysis of the E* data and GS data led to a statistical relationship between E* and GS.

Dimensional analysis was sued to reach at an E* model that proved to be statistically significant.

3. APA testing of mixes was completed. 4. Binder grades were independently verified at the ITD lab in Boise. 5. MTS testing system controller is now in operation. 6. Coring and notching jigs for preparation Jc samples are complete and operational. 7. Progress in building a cooling system for fracture testing at low temperature. 8. Samples for fatigue fracture testing are being prepared 9. The model of PFC2D (discrete element program) was generated and examined with test

condition to compare the specimen test results. 10. Continued literature review

4

5

Appendices Appendix A: Prediction of HMA Permanent Deformation (Task A1) Appendix B: Viscoplastic Analyses of Asphalt Pavements (Task A2) Appendix C: Data Analysis (EStar, GS, FN, APA) (Task A5) Appendix D: Simplification of Fatigue Test (Tasks B3 and B4)

Appendix A Prediction of HMA Permanent Deformation (Prepared by: A. Abu Abdo and F. Bayomy)

This appendix describes further literature review of permanent deformation models for asphalt pavements, which is performed under Task A1 – Review of previous studies and available data.

Prediction of HMA Permanent Deformation Permanent deformation or rutting is one of the major stresses in flexible pavements, which is caused by the densification and movement of materials under repeated loads, and also might results from lateral plastic flow under the wheel track (NCAT 2000). When the new Superpave binder grade system was developed under SHRP (Strategic Highway Research Program), it was suggested that choosing the right upper binder grade could extend the life of flexible pavements with regards to permanent deformation; unfortunately that is not the case.

Many approaches have been used to predict permanent deformation in HMA. Most of the widely used approaches are based on the classic power relationship between the permanent strain and number of load cycles as shown in Eq. 1.

(Eq. 1)

where,

εp: Accumulated Permanent Strain at N cycle,

N: Number of Load Repetitions, and

a,b: Non‐linear Regression Coefficients.

This classic power equation is derived from the secondary stage in a typical behavior of HMA tested sample under repetitive loads as shown in Figure 1, where “a” is the intercept at N = 1 cycle and “b” is the slope of the line.

The widely used approaches to predict permanent deformation in flexible pavements includes; Layered Vertical Permanent Strain Approach, Plastic‐Elastic Vertical Strain Ratio Approach, Permanent Strain Rate Approach, and Rutting Rate Approach.

QR4_Appendix A: Prediction of HMA Permanent Deformation - Page 1


Figure 1 Typical Permanent Deformation Behavior for HMA under Repetitive Loading (After NCHRP 1‐37A)

Layered Vertical Permanent Strain Approach Layered Vertical Permanent Strain Approach is based on determining the permanent strain in each layer as a function of repeated load applications. Then the total deformation is computed by summing up permanent deformation in each layer. Two famous models used this approach; Allen and Dean Models (Allen and Dean 1986) and Asphalt Institute Model (May and Witczak 1992).

Allen and Dean Models were developed for all pavement layers. These models are incorporated in software called PAVRUT. In addition to permanent deformation models, traffic and temperatures models were added to the software (Allen and Dean 1986). This software can be used to estimate the permanent deformation for any flexible pavement. The permanent deformation model for HMA is as follow,

(Eq. 2)

where,

εp: Permanent Axial Strain,

N: Number of Stress or Wheel Load Repetitions,

Co = ‐0.000663.T2 + 0.1521.T – 13.304 + (1.46 – 0.00572.T).Log (σ1),

σ1: Deviator Stress, psi,

T: Temperature, °F,

C1 = 0.63974,

C2 = ‐0.10392, and

C3 = 0.00938.

Based on triaxial tests on 251 samples, the Asphalt Institute has developed a model that determines the permanent deformation of HMA by including the effects of mix design properties. Thus, Eq. 3 was developed. Users need to take into consideration that this model cannot be used for mixes with less than 3% air voids or for deviator stresses larger than 90 psi (May and Witczak 1992).

14.97 1.4808 6.865 1.107 log0.117 1.908 0.971

(Eq. 3)

where,

εp: Permanent Axial Strain,

N: Number of load repetitions to failure,


Sd: Deviator Stress, psi,

V: Viscosity at 70 °F, Ps x106,

Peff: Percent by volume of effective asphalt content, and

Vv: Percent by volume of air voids.

PlasticElastic Vertical Strain Ratio Approach Plastic‐Elastic Vertical Strain Ratio Approach was based on the constitutive relationship developed from the statistical analysis of repeated load permanent deformation lab tests. This model is in a form of the classical power model, but determines the ratio of the permanent strain to the elastic (resilient) strain as in Eq. 4,

(Eq. 4)

where,


εr: Resilient Strain as a function of asphalt mixes properties,

N: Number of load repetitions,

a,

r: Field adjustment factor.

b: Non‐linear regression coefficients, and

Many studies have been conducted to determine the regression factors by relating these factors to different mixes properties. Leahy (1989) argued that temperature was the most important factor. Leahy’s model was less sensitive to loading condition and mix properties as seen in Eq. 5.

6.631 0.435 2.767 0.110 log

0.118 0.930 0.5011

where,

(Eq. 5)



s properties,

si,

poise,

tive asphalt content, and

oach, Kaloush and Witczak (1999) developed two models that have fewer

εr: Resilient Strain as a function of asphalt mixe



σd: Deviator stress, p

η: Viscosity at 70 °F, 106

Vbeff: Percent by volume of effec

Va: Air voids, percent.

Similar to Leahy’s apprparameters, but with approximately the same accuracy. These models are,

3.74938 2.02755 0.4262 (Eq. 6)

and,

0.1981 0.404 (Eq. 7)

where,

mulated Permanent Strain at N cycle,

s properties,

under predict the εp/εr ratio at higher number of load repetitions, mainly due to determination of the regression coefficients from steady‐state zone of creep or repeated load tests. To

. . (Eq. 8)

where,

ber of load repetitions to failure,

i,

6 poise,

tive asphalt content, and

Va: Air voids, percent.

εp: Accu

εr: Resilient Strain as a function of asphalt mixe

N: Number of load repetitions, and


These models tend to

obtain better results, Kaloush and Witczak (1999) presented another model that predict the number of cycle at failure based on the asphalt mix volumetric properties, binder viscosity, temperature and stresslevel. The model is expressed as follow,

1.00788 5 . . .

Nf: Num


S: Deviator stress, ps

η: Viscosity at 70 °F, 10

Vbeff: Percent by volume of effec


Permanent Strain Rate Approach Permanent Strain Rate Approach is based on modifying the classical power model (Eq. 1) and determining the rate of permanent strain with changes per cycle as shown in Eq. 9,

(Eq. 9)

Divide by the resilient strain (εr),

(Eq. 10)

By letting, and 1 . The final model form is similar to the classic power form as shown in

Eq. 11.

(Eq. 11)

The term

“μ” is the permanent deformation parameter representing the constant proportionality between εp and ε . The term “ ” is the permanent deformation parameter that indicates the decrease in permanent

pavement layers. The permanent strain in follows,

r

deformation as the number of cycles increases.

Rutting Rate Approach The most famous model under Rutting Rate Approach is the Ohio State University Model (Majidzadeh et al. 1981); the model describes the progression of rutting in allany layer is determined as

(Eq. 12)

where,

ε Strain, p: Permanent

N: Number of allowable load applications, and

erimental constants.

and Thompson 1990) that values of “m” does not vary significantly (0.83 – 38x10‐4) as per the material type, the stress level and the

s the Layered Vertical Permanent Strain Approach to determine the permanent

A, m: Exp

It was found (Barenberg0.86). However, “A” varies widely (12.4x10‐4 – 1environment.

Role of E* in the Prediction of Permanent Deformation in the 2002 AASHTOMEPDG (NCHRP 137A) MEPDG utilizedeformation for HMA layers. Where the general form is,

(Eq. 13)

εp: Accumulated

where,

Permanent Strain at N cycle,


εr: Resilient Strain as a function of asphalt mixes properties,

ients.

es adequate results, field shift factors ( ri) were introduced to provide more own in Eq. 14,


T: Temperature, °F, and

ai : Non‐linear regression coeffic

While this relation providaccurate predictions of this model, as sh

(Eq. 14)

Based on 88 Long Term Pavement Performance (LTPP) sites ted loca in 28 states, Eq. 2.29 was calibrated and modified using 38 . Later, a depth parameter “k1” was introduced based on MnRoad test site (Stroup‐Gardiner and Newcomb 1997), to

7 observations to obtain better predictions than the original model

increase the accuracy of this model as follows,

10 . . . (Eq. 15)

where,

0.328196 .

epth to computational point, in,

0.1039 2.4868 17

and

hac: Total Asphalt Layer thickness, in.

The resilient (elastic) strain is determined the general Hooke’s Law (Eq. 16), where the asphalt dynamic modulus is incorporated. There determined resilient modulus is a function of materials

uency.

,

.342 ,

depth: D

0.0172 1.7331 27.428 ,

usingfore, the

properties, temperature and load freq

(Eq. 16)

where,

εrz: Resilient Strain in the v

E*: Dynamic Modulus of HMA,

σz, σx, and σy: Stresses in the z, x, and y directions, and

ν Poison’s Ratio of HMA.

Finally, the determined permanent strain in any layer is used to determine the permanent deformation

(Eq. 17)

ertical direction,

:

by,

∑ . Δ

where,



D: Total Permanent

mber,

in layer i, and

n. A Computerized Analysis of Rutting Behavior of Flexible Pavement. Transportation Research Record 1095, Washington D.C., 2005.

Consultants Division. Guide for Mechanistic‐Empirical Design of New and

Barenb Analysis Procedures for ch

ersity of Maryland, College Park, Maryland,

Leahy, tion,

Majidza ., et al. Implementation of a Pavement Design System ‐ Volumes 1 and 2. Final

May, R Mix Analysis System. Proceeding

NCAT. H tional Center for Asphalt

Stroup‐ .

R Deformation,

i: Layer nu

n: Total number of layers,

εpi: Permanent Strain

∆hi: Thickness of layer i.

References Allen, D.L. and R.C. Dee

ARA, Inc., ERESRehabilitated Pavement Structures. NCHRP Final Report 1‐37A, Illinois. erg, E.J. and M. R. Thompson. Calibrated Mechanistic StructuralPavements, Phase 2 of NCHRP Project 1‐26. National Cooperative Highway ResearProgram. TRB. Washington, DC., 1990.

Kaloush, K., and Witczak, M.W.. Development of Permanent to Elastic Strain Ratio Model for Asphalt Mixtures. Development of the 2002 Guide for the Design of New and Rehabilitated Pavement Structure, Univ1999. R.B.. Permanent Deformation Characteristics of Asphalt Concrete. PhD DissertaUniversity of Maryland, College Park, Maryland, 1989. deh, KReport, Research Project EES 579, Ohio State University. 1981. .W. and M.W. Witczak. An Automated Asphalt Concreteof the Association of Asphalt Paving Technologists, Volume 61. South Carolina, 1992. ot Mix Asphalt Materials, Mixture Design and Construction. NaTechnology. NAPA Research and Education Foundation, 2nd Edition, Maryland, 2000. Gardiner, M. and D. Newcomb. Investigation of Hot Mix Asphalt Mixtures at Mn/RoadMinnesota Department of Transportation, Office of Research Administration, Final Report, Minnesota, 1997.

Appendix B Viscoplastic Analyses of Asphalt Pavements (Prepared by: Thomas Weaver)

1 Numerical Analyses In previous reports, we have presented background information on constitutive models that can be used to predict the stress-strain response of asphalt pavements under physical and environmental loads. After reviewing the literature, we identified two simple constitutive models which may be used for numerical modeling of asphalt pavement response. These constitutive models are available for use in the finite element analysis software ABAQUS (2003). Over the past quarter, we have learned how to use the viscoplastic model in ABAQUS and we have begun to model E* tests from the current project. Results from an analysis of an E* test are presented below.

1.1 Viscoplastic Analyses The constitutive relationship used in our viscoplastic analyses is presented in Equation 1.

( )[ ]( ) 11

1 ++= mmvpnvp mAq εε& (Eq. 1)

The viscoplastic strain rate ( ) is a function of deviatoric stress (q), viscoplastic strain ( ), and three constants (A, m, and n). To use this model, the three constants must be specified. In addition to the three model constants the material Young’s modulus (E) and Poisson’s ratio (ν) must be specified.

Analyses have been performed to determine the model parameters for a test designated as 1EC2_21°_25Hz. This was a sample prepared in the laboratory using a course aggregate. The E* test temperature was 21 °C, and the cyclic stress was applied at a rate of 25 Hz. The values for the model constants that produced a reasonable match between the analysis and measured test results are provided in Table 1. The stress applied to the asphalt sample in the E* test is shown in Figure 1. This same stress time history was applied to the asphalt sample in the numerical analysis. The strain as a function of time resulting from the applied stress is shown in Figure 2. The strain vs. time from the E* test and analysis compare well. However, the comparison of measured and computed stress vs. strain as shown in Figure 3 do not compare as well. A closer look at the strain vs. time results show that the measured and computed strain data are not perfectly in phase. This difference in phase is likely the cause of the difference in the stress-strain loops. Additional analyses will be performed to improve the comparison between the measured and computed stress-strain loops. We are also in the process of modeling additional E* test results in an effort to determine the model input values for samples with differing properties.

Table 1 Viscoplastic Model Input Values for Finite Element Analysis of E* Test 1EC2_21°_25Hz

Young’s Modulus, E Poisson’s Ratio, n A m n 4000 MPa 0.3 0.0003 -0.045 0.008

QR4_Appendix B: Viscoplastic Analyses of Asphalt Pavements - Page 1

0

50

100

150

200

250

300

350

0 0.1 0.2 0.3 0.4 0.5

Stress (k

Pa)

Time (sec)

Figure 1 Stress vs Time for E* Test 1EC2_21°_25Hz

0.0E+00

5.0E‐05

1.0E‐04

1.5E‐04

2.0E‐04

2.5E‐04

0 0.1 0.2 0.3 0.4 0.5

Strain

Time (sec)

Measured Analysis

Figure 2 Strain vs Time for E* Test 1EC2_21°_25Hz


0

50

100

150

200

250

300

350

0.00E+00 5.00E‐05 1.00E‐04 1.50E‐04 2.00E‐04 2.50E‐04

Stress (k

Pa)

Strain

Analysis Measured

Figure 3 Stress vs Strain for E* Test 1EC2_21°_25Hz

2 References

ABAQUS/Theory Manual (2003). Version 6.4, Hibbit, Karlson & Soren

Pirabarooban, S., Zaman, M., and Tarefder, R.A. (2003). “Evaluation of rutting potential in asphalt mixes using finite element modeling,” 2003 Annual Conference of the Transportation Association of Canada, 16p.


Appendix C Data Analysis: E*, GS, FN and APA (Prepared by: A. Abu Abdo and F. Bayomy)

This appendix describes further analysis of test data that were developed during this quarter. The data includes dynamic modulus (E*), Gyratory Stability (GS), Flow Number (FN) and the Asphalt Pavement Analyzer (APA).

The analysis is performed under Task A5 – Data Analysis

E*Master Curves Dynamic modulus test data was compiled and analyzed. Master curves were constructed at a reference temperature of 21.1 °C. A sigmoidal curve fitting equation (Eq. 1) was used. The sigmoidal function shape parameters were determined using the minimum square error method. These parameters are

in 1. listed Table

(Eq. 1)

where,

E

mum value of E*,

*: Dynamic Modulus,

: Log mini

aximum value of E*, δ α: Log m

β, γ: Shape Parameters of the Sigmoidal Function, and

fshifted: Shifted Frequencies.

QR4_Appendix C: Data Analysis (E*, GS, FN, APA) - Page 1

Tabl 1 E* Mas r Cu ve Fitting Parameters e te r

Mix Condition lo E* = + / +exp( + (log(fshifted )] g [1 )) Shift Factor @

4.4°C 21.1°C 37.8°C 54.4°C1 Opt 1.82315 2.37408 ‐0.8773 ‐0.5985 120 1 0.0306 0.00351 ‐0.5% AC 1.96638 2.31606 ‐0.8783 ‐0.5979 120 1 0.02 0.00151 +0.5% AC 1.62788 2.57484 ‐0.8783 ‐0.5979 110 1 0.03123 0.00251 PG 58‐28 1.29003 2.88701 ‐0.8422 ‐0.8203 120 1 0.015 0.00111 PG 64‐28 1.46992 2.76558 ‐0.87 ‐0.9937 120 1 0.01875 0.0011 PG 70‐22 1.95472 2.34749 ‐0.8022 ‐1.0907 120 1 0.01137 0.000931 PG 70‐34 1.60584 2.48665 ‐0.8773 ‐0.5985 120 1 0.01606 0.0009FA Fine Mix 1.6994 2.46575 ‐0.7798 ‐0.8923 150 1 0.01307 0.00105CA Coarse Mix 1.51455 2.53525 ‐0.8241 ‐0.8981 110 1 0.0152 0.001552 Opt 1.72997 2.26722 ‐0.7773 ‐0.9285 150 1 0.0106 0.00062 ‐0.5% AC 1.8806 2.2083 ‐0.7773 ‐0.8985 170 1 0.0106 0.00062 +0.5% AC 1.92063 2.04252 ‐0.8773 ‐0.2985 140 1 0.0126 0.0022 PG 58‐34 1.29383 2.64414 ‐0.7773 ‐0.5985 150 1 0.0176 0.0022 PG 70‐34 2.06985 1.96893 ‐0.7773 ‐0.9985 150 1 0.0106 0.00062 PG 70‐28 1.70219 2.36354 ‐0.7773 ‐0.8985 170 1 0.0106 0.00082 PG 64‐22 1.63599 2.54099 ‐0.6277 ‐0.9985 190 1 0.00998 0.000452 PG 64‐28 1.89209 2.22777 ‐0.5773 ‐0.8985 170 1 0.0106 0.00041 Field Mix 1.95134 2.32682 ‐0.6973 ‐0.8985 180 1 0.0106 0.00052 Field Mix 1.45939 2.49869 ‐0.8773 ‐0.5985 150 1 0.0186 0.00123 Field Mix 1.71349 2.34622 ‐0.6773 ‐0.7889 150 1 0.01298 0.00084 Field Mix 1.38751 2.60745 ‐0.8273 ‐1.0999 200 1 0.01306 0.00065 Field Mix 1.81837 2.26658 ‐0.7773 ‐0.9985 150 1 0.01598 0.00086 Field Mix 1.83155 2.26015 ‐0.7773 ‐0.9985 200 1 0.01306 0.00057 Field Mix 1.5832 2.36387 ‐0.8973 ‐0.9985 130 1 0.01306 0.0004

Data Analysis for E*, FN, and APA

Aggregates Structure Effects To study the effect of changes in aggregates structures on the E* prediction model parameters, four different aggregate structures were evaluated; Mix 1 (25mm mix), Mix 2 (19mm mix), very coarse mix (25mm mix), and fine mix (4.75mm mix). To ensure that only the change in aggregate structure is evaluated, these mixes were designed using the same asphalt binder grade (PG 70‐28) and content (4.9%). E* Master Curves (Figure 1) for these mixes showed the finer the mix the lower stiffness would be, especially at higher temperature, thus the mix stability is lower, until a point is reached where the lack of fine materials causes the mix to become less stable, due to the decrease of friction between aggregate particles which is necessary for aggregate interlocking. FN and APA results for these mixes (Figure 2 and Figure 3) showed the same trend, where Mix 1 yielded higher FN and lower rut depth results than Mix 2, which lead to the conclusion that Mix 1 shall perform better than Mix 2 under the same loading conditions.


10

100

1000

10000

100000

0.0001 0.01 1 100

E*, M

Pa

Frequency, Hz

Coarse Mix

Mix 1 (Opt)

Mix 2 (Opt)

Fine Mix

Figure 1 E* Masters Curve for Four Different Aggregates Structures

0

1000

2000

3000

4000

5000

6000

7000

8000

Fine Mix Mix 2 Mix 1 Coarse Mix

FN, cycle

Lab Mixes

Figure 2 Effect of Aggregate Structure on FN

0

1

1

2

2

3

3

Fine Mix Mix 2 Mix 1 Coarse Mix

Rut D

epth,m

m

Lab Mixes

Figure 3 Evaluation of Different Aggregates Structures Using APA Test Results


Binder Content Effects Dynamic modulus test was conducted for Mix 1 and Mix 2 at different asphalt contents; optimum and ±0.5 AC% from optimum, all these mixes were designed to achieve four percent air voids. As per Superpave Mix Design, these mixes should perform best at the optimum asphalt content, at which the air voids of the compacted specimen at N‐design is four percent. E* Master Curves (Figure 4) showed that E* values for ‐0.5% asphalt content from optimum is higher than optimum asphalt content and +0.5% asphalt content for the same mix. FN and APA results (Figure 5 and Figure 6) followed similar pattern, where Mix 1 and Mix 2 yielded higher FN and lower rut depth results at a ‐0.5% asphalt content that at optimum. Therefore, it is expected that for Mix 1 and Mix 2 that with a ‐0.5% asphalt content from optimum these mixes will perform better than optimum.

10

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0.0001 0.01 1 100

E*, MPa

Frequency, Hz

Mix 1 (Opt)

Mix 1 (‐0.5% AC)

Mix 1 (+0.5% AC)10

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1000

10000

100000

0.00001 0.001 0.1 10 1000

E*, MPa

Frequency, Hz

Mix 2 (PG Opt)

Mix 2 (‐0.5% AC)

Mix 2 (+0.5% AC)

Figure 4 E* Master Curve for Mix 1 and Mix 2 at Different Binder Contents

0

2000

4000

6000

8000

10000

12000

‐0.5% Opt +0.5%

FN, cycle

Asphalt Content

Mix 1

Mix 2

Figure 5 E* FN Results for Mix 1 and Mix 2 at Different Binder Contents


0

1

1

2

2

3

3

‐0.5% Opt +0.5%

Rut D

epth, m

m

Asphalt Content

Mix 1

Mix 2

Figure 6 APA Test Results for Mix 1 and Mix 2 at Different Binder Contents

Binder Grade Effects To evaluate changes of binder grades on E*, the upper and lower grades of the binder grades were changed. The upper grade represents the highest temperature the binder can operate, and it is mainly considered for permanent deformation. On the other hand, the lower grade represents the lowest temperature, and it is mainly considered for thermal cracking. Therefore, it expected that the stiffness of higher grade should be higher than a lower grade. E* results for Mix 1 and 2, as presented in Figure 7‐a, show that at high temperatures the higher binder grade (70, 64, and 58) yielded higher E* values and nearly the same values at low temperatures.

Figure 7‐b presents E* results for mixes with low temperature binder grades (‐34, ‐28, and ‐22). It was speculated that at higher temperatures, E* values would be similar since upper grade is the same, and E* values would vary at low temperatures. At lower binder grade (e.g PG 64‐34) it is expected to have low stiffness (lower E* values) than a binder with a higher binder grade (e.g PG 64‐22) to resist thermal cracking. Results showed that both mixes did not follow that trend at high temperatures, but followed the trend at lower temperatures.


10

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100000

0.0001 0.01 1 100

E*, MPa

Frequency, Hz

Mix 1 (PG 70‐28)

Mix 1 (PG 64‐28)

Mix 1 (PG 58‐28)10

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10000

100000

0.00001 0.001 0.1 10 1000

E*, MPa

Frequency, Hz

Mix 1 (PG 70‐28)

Mix 1 (PG 70‐34)

Mix 1 (PG 70‐22)

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0.00001 0.001 0.1 10 1000

E*, MPa

Frequency, Hz

Mix 2 (PG 64‐34)

Mix 2 (PG 70‐34)

Mix 2 (PG 58‐34)10

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0.00001 0.001 0.1 10 1000

E*, MPa

Frequency, Hz

Mix 2 (PG 64‐34)

Mix 2 (PG 64‐28)

Mix 2 (PG 64‐22)

a) Changes in Upper Binder Grade b) Changes in Lower Binder Grade

Figure 7 E* Master Curve for Mix 1 and Mix 2 with Different Binder Grades

Quality Control Measurements To evaluate the possibility of utilizing Gyratory Stability (GS) as a quality control tool in the field, GS, FN, and rut depth measured by APA were determined for seven field mixes. As shown in Figure 8 and Figure 9 GS results correlated well with FN and APA results. The higher GS is the higher FN and the lower rut depth will be. In addition, a trend has been observed, the lower the asphalt content the higher the GS values (Figure 10), due to the increase of friction and interlocking between aggregate particles.


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12000

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6

8

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14

16

18

Mix 4 Mix 7 Mix 6 Mix 2 Mix 3 Mix 5 Mix 1

FN, cycle

GS, kN.m

GS, kN.m

FN, cycle

Figure 8 Relation between GS vs. FN for All Field Mixes

0

0.5

1

1.5

2

2.5

3

0

2

4

6

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14

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18

Mix 1 Mix 3 Mix 5 Mix 6 Mix 7Ru

t Dep

th, m

m

GS, kN.m

GS, kN.m

Rut Depth, mm

Figure 9 Relation between GS vs. FN for Field Mixes

0%

1%

2%

3%

4%

5%

6%

7%

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6

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14

16

18

Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6 Mix 7

AC%

GS, kN.m

GS, kN.m

AC%

Figure 10 GS vs. AC% for Field Mixes


Dynamic Modulus (E*) Proposed Model Using the Dimensional analysis (Bridgman 1963, Buckingham 1914 & Curtis et al. 1982),

E* was found to be a function of binder dynamic shear modulus (G*), Gyratory Stability (GS), percent maximum specific gravity (%Gmm), and binder content (Pb). Where the binder effects are measured by G*, %Gmm, and Pb, aggregates effects are measured by GS, %Gmm, and (1‐Pb), and finally air voids are measured by %Gmm. Further, it was found that the model consists of two sets of parameters; (G*/Pb) and (GS.%Gmm/(1‐ Pb)). To determined the relation between these parameters and E*, the sensitivity of E* versus (G*/Pb) and (GS.%Gmm/(1‐ Pb)) were investigated and a model was developed as shown in Eq. 2.

( )

568.0

1.%.*46210 ⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=bb

mm

PPGGSG.E* (Eq. 2)

where,

E*: Dynamic Modulus for Asphalt Mix, MPa,

G*: Dynamic Shear Modulus for RTFO Aged Binder, MPa,

Pb: Binder Content,

GS: Gyratory Stability, kN.m,

%Gmm = Gmb/Gmm = Gmm (1‐AV%),

Gmb: Bulk Specific gravity of Mix,

Gmm: Maximum Specific gravity of Mix, and

AV%: Air Voids.

Using the two tail statistical t‐Test with α equal to 0.01 (99% reliability), it was found that there was no significant difference between the actual and predicted E* mean values. As shown in Figure 11‐a, it was found that the developed model had a correlation of R‐square of 0.962 and an upper and lower bounds of 12%. To verify the ability of the model to predict E* for mixes other than the ones used in the model development, the predicted E* with actual E* data for other tested mixes (field mixes) were compared. It was found as shown in Figure 11‐b that the proposed model could predict E* for these different mixes with correlation of R‐square of 0.9469. When using the two tail statistical t‐Test with α equal to 0.01 (99% reliability), it was found that there was also no significant difference between the actual and predicted E* mean values.

The next step in the model validation process was to compare the proposed model prediction for all mixes with other models. Actual E* values were compared to predicted values by Witczak model (Witczak and Fonesca 1996) that was incorporated in the 2002 AASHTO MEPDG. Further, E* values were compared to the newly revised model by Witczak (Bari and


Witczak 2006); it has been the suggested that Witczak new model has better prediction when compared to the earlier model.

Results from both Witczak models did not predict the actual E* values as well when compared to the proposed model as presented in Figure 11‐c & Figure 11‐d. It was observed that the second Witczak model results were less scattered than the first model and unlike the proposed model, both Witczak models seemed to over predict E* values.

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E*, MPa

E*Est, MPa

Equality Line

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E*, MPa

E*Est, MPa

Equality Line

a) Developed Model (Lab Mixes) b) Developed Model (Field Mixes)

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E*, MPa

E*Est, MPa

Equality Line

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E*, MPa

E*Est, MPa

Equality Line

c) Witczak Model (1996) d) Witczak Revised Model (2006)

Figure 11. Results of Predicted E* Using Proposed and Witczak Models

To verify if predicted E* by the proposed model can be used in the MEPDG instead of actual E* test data, reliability and probabilistic analysis has been carried out to determine how


reliable the proposed model was in predicting permanent deformation determined by MEPDG (NCHRP 1‐37A) when compared to actual E* test results.

The analysis is based on simulation techniques, where some phenomena are numerically simulated and then determine the number of times some events happen such as failure. Utilizing variables probability distributions, random variables are generated and then used in the analysis. Thus, making sure that the wide range of inputs and variables that might occur is taken into account in the design. One of the widely used simulations is the Latin Hypercube Sampling Method. The main advantage of this method is the lower number of random variables needed to obtain good results. The range of random variables is divided into sections and a value from each section is used only once in the simulation. This prevents any variable clusters and selection from one section (Nowak and Collins 2000).

The first step of any reliability and probabilistic analysis is to determine the probability distributions of variables. The distributions of the variables used in this study were determined; Pb, %Gmm, and GS were found to be normal random variables since their probability distributions were normally distributed. On the other hand, G* and E* were considered as a lognormal random variables.

Using Latin Hypercube Sampling, 100,000 random variables have been generated. These variables were used to determine permanent deformation exerted by standard axle load over a 200mm HMA layer, stresses were determined using KENPAVE software (Huang 2004). The overall reliability of the proposed model was found to be 95% for all cases, which is better than the recommended reliability used in MEPDG of 90%. Reliability results for different temperatures are summarized in Table 2.

Table 2. Reliability Analysis Results for Proposed Model

Temperature (°C) Reliability

4.4 99%

21.1 96%

37.8 93%

54.4 92%

Overall 95%

Summary and Conclusions

Based on the test results and data analysis presented in this study, the following conclusions and observations are made:



• E* was found to be a function of binder grade and content, and aggregates properties and structures.

• Dimensional analysis was used effectively in determining the dynamic modulus (E*) model parameters. It was found that E* is a function of binder dynamic shear modulus (G*), Gyratory Stability (GS), Percent of maximum specific gravity of the mix (%Gmm) and binder content (Pb).

• Based on Dimensional Analysis and by using a regression analysis an E* prediction model has been developed, with an R‐square of 0.962. When using a two tail t‐Test, it was found there is no significant difference between the means of the actual and predicted E* values with a reliability of 99%.

• Using seven field mixes, the model was validated by using a two tail t‐Test, it was found there is also no significant difference between the means of the actual and predicted E* values with a reliability of 99% and an R‐square of 0.9469.

• The proposed model results were compared to the two recent Witczak’s models (1996 and 2006); it was found that the proposed model has better predictions.

• Using the reliability and probabilistic analysis, the overall reliability of the developed model was found to be 95%, when used to determine the permanent deformation using the 2002 AASHTO Mechanistic Empirical Pavement Design Guise (MEPDG) prediction models versus using actual E* test results.

References 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.

Bridgman, P.W.. Dimensional Analysis. Yale University Press, 1963. Buckingham, E.. On Physically Similar Systems; Illustrations of the Use of Dimensional

Equations. Physical Review 4, 1914. Curtis, W.D., J.D. Logan and W.A. Parker. Dimensional Analysis and Pi Theorem. Linear Algebra

And Its Applications 47, 1982. 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. Nowak, A.S. and K.R. Collins. Reliability of Structures. Mc Graw Hill Higher Education, Boston,

2000.

QR4_Appendix D: Simplified Fatigue Test ‐ Page 1

Appendix D Simplification of Fatigue Test (Prepared by: S. Jung and Seung Baek)

The proposed experimental study is focused on developing a procedure of simplification of Fatigue Test by using a semi circular notched sample (hereafter SCNS). SCNS has been proven[1] that it is easy to prepare and simple to test. Total 92 semi circular samples for preliminary experimental test were prepared from 23 cylindrical samples with field mixes. Preliminary mix (first group) was used to verify the study parameters including frequency, temperature, and strain rate. Table 1 illustrated the study parameters, which were used by other researchers, to improve the understanding of fatigue behavior under different study parameters. Sample testing was conducted with upgraded MTS control system to verify between input control and output result. Based on the previously studied parameter by other researcher, sample tests based on parameters in table 1 were also conducted with the following conditions: displacement rate of 100*10-6, 500*10-6, and 1000*10-6 in/sec and cyclic loading at 0.1, 0.5 and 1 Hz, with MTS system. The cyclic test was controlled with force ranges (10-30%, 10-50%, 30-50% and 30-70% of maximum stress) to understand the correlation between static and fatigue test. Based on the outcome of preliminary test, the second group of test samples will be conducted with different combination of several PG grade and asphalt contents (Table 2). Four SCNS, which were prepared from one cylindrical sample, were tested with one static test and three fatigue tests. To determine the test procedure, simple displacement control for loading rate was used including 100*10-6, 500*10-6 and 1000*10-6 in/sec (Table 3). Table 3 illustrated maximum displacements at the failure and higher loading rate illustrated higher strain energy. Displacement with different rates indicates that level of max. displacement during the failure tends to be smaller displacement (Table 3). It means that sample does not have enough time to deform against faster loading rate. The static test was conducted with displacement control on different samples to compare result of strain energy data between static test results and cyclic test. The strain energy for static test was determined at the area under the curve (Figure 1). The fatigue test was

conducted with different cyclic loading at 0.1, 0.5, 1 Hz and force rages of 30% to 50% and 30% to70% on different sample group for preliminary mix (Figure 2). Based on the displacement and time relationship for cyclic test, the failure point can be determined by changing the slope between elastic and plastic region (Figure 3). Figure 4 shows one of results for static and cyclic test to determine the strain energy. Stain energy was determined for static and cyclic with 0.1 Hz and 1 Hz (Table 4 to 5) from the test results with preliminary mix group 1 and group 3. Based on the preliminary test results, the condition of testing for the second group with different combination of several PG grade and asphalt contents is currently investing for valid test results. The following methods are considered to simplify fatigue test;

1. The amount of energy put into the material is the same as the strain energy which is the area under a stress-strain curve.[2]

2. The work potential theory and a continuum damage theory are used to making a uniaxial constitutive model for asphalt concrete.[3]

Table 1 Test conditions

Temperature (°C) Strain rate (10-6 units/s)

Frequency (Hz) Monotonic Cyclic

Daniel [3] 5, 20 5, 12, 20 10, 30, 500, 1500 1, 10 Lundstrom [4] 0,10,20 100, 200, 400, 800 10 Medani [5] 5, 15, 20, 25, 30 for n 10-50 H. J. Lee [6] 25 5


Table 2 PG Grade and Asphalt Content of samples

Mix PG AC%

1

70-28 4.90 70-28 5.40 70-28 4.40 64-28 4.90 58-28 4.90 70-22 4.90 70-34 4.90

2

64-34 4.35 64-34 4.85 64-34 3.85 70-34 4.35 58-34 4.35 64-22 4.35 64-28 4.35 70-28 4.90

Coarse Mix 70-28 4.90 Fine Mix 70-28 4.90

Figure 1 The stress response to preliminary mix group 3 (100*10-6 in/sec)


Figure 2 Cyclic test (0.1 Hz) with 30-70% of maximum stress

Figure 3 Failure of cyclic test


Figure 4 Comparison of strain energy for static and cyclic test result

Table 3 Static test results with different rate Rate

Sample # Displacement Max. load Strain energy

10-6 in/sec in lb lb-in

1000

F5S4 2 0.0626 859.32 34.26 F5S14 1 0.0550 697.88 20.98 F5S16 2 0.0467 693.19 19.58 F5S19 2 0.0534 803.06 23.39

500

F5S4 3 0.0947 692.27 22.62 F5S14 3 0.0562 713.81 22.32 F5S16 3 0.0601 726.01 26.88 F5S19 3 0.0585 667.66 22.82

100

F5S4 1 0.0557 338.01 10.61 F5S14 2 0.0559 349.19 11.36 F5S16 1 0.0629 438.00 19.48 F5S19 1 0.0608 443.64 15.34

#: sample number from the same cylinder



Table 4 Test results for preliminary mix group 1

Sample Test condition Sample # Strain energy (lb-in)

Displacement (in)

Failure (cycle)

Static 100*10-6 in/sec F5S7

1 12.89 0.080 -

F5S11 12.50 0.049 - F5S13 8.16 0.050 -

Cyclic (0.1 Hz)

30-50% of max. stress

F5S7 3

10.20 0.067 480 F5S11 12.73 0.062 400 F5S13 6.78 0.050 400

Cyclic (0.1 Hz)


F5S7 4

14.97 0.068 240 F5S11 14.75 0.053 145 F5S13 11.55 0.060 190

Table 5 Test results for preliminary mix group 3

Sample Test condition Sample # Strain energy (lb-in)

Displacement (in)

Failure (cycle)

Static 100*10-6 in/sec F5S3

1 13.59 0.060 -

F5S6 16.44 0.074 - F5S9 14.73 0.056 -

Cyclic (1 Hz)


F5S3 3

13.80 0.063 4300 F5S6 16.96 0.086 2070 F5S9 13.47 0.057 2700

Cyclic (1 Hz)


F5S3 4

20.48 0.065 1020 F5S6 24.78 0.084 2030 F5S9 19.32 0.061 540

The model of PFC2D (discrete element program) was generated and examined with test condition to compare the specimen test results (Figure 5) and the model is kept modifying.

Figure 5 Semi-circular notched model for PFC2D (0.5-inch)



Reference: 1. Mull M.A., S.K., Yehia A., Fracture resistance characterization of chemically

modified crumb rubber asphalt pavement Journal of Materials Science, 2002. Vol. 37: p. pp. 557-566.

2. Daniel, J.S., W. Bisirri, and Y.R. Kim, Fatigue Evaluation of Asphalt Mixtures Using Dissipated Energy and Viscoelastic Continuum Damage Approaches. Journal of Association of Asphalt Paving Technologists, 2004.

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

4. R. Lundstrom, a.U.I., Characterization of Asphalt Concrete Deterioration Using Monotonic and Cyclic Tests. International Journal of Pavement Engineering, 2003. Volume 4(Issue 3): p. 143 - 153

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

6. H. J. Lee, Y.R.K., and S. W. Lee, Fatigue Life Prediction of Asphalt Mixes Using Viscoelastic Material Properties. J. of Transportation Research Board, 2002.

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