modificaton and validation of the linear amplitude...

Hintz, Velasquez, Johnson, and Bahia 1

MODIFICATON AND VALIDATION OF THE LINEAR AMPLITUDE

SWEEP TEST FOR BINDER FATIGUE SPECIFICATION

Submission date: August 1, 2010

Word count 4952 plus 2 Tables and 8 Figures

Total number of words: 7452

Cassie Hintz (Corresponding Author)

Graduate Research Assistant

Department of Civil and Environmental Engineering

University of Wisconsin - Madison, 53706

Email: [email protected]

Ph: (608)-890-2566

Raul Velasquez, Ph.D.

Research Associate




Carl Johnson, Ph.D.

Stark Asphalt

A Division of Northwest Asphalt Products, Inc.

Milwaukee, WI 53225


Hussain Bahia, Ph.D.

Professor




Submitted for publication and presentation at the

Transportation Research Board Annual Meeting

January 23-27, 2011

Washington, D.C.

mailto:[email protected]





ABSTRACT

Current asphalt binder specifications lack the ability to characterize asphalt binder damage

resistance to fatigue loading. Multiple accelerated testing procedures that attempt to efficiently

and accurately characterize asphalt binder contribution to mixture fatigue are currently under

investigation. One of these tests that has received significant acceptance by experts and has been

submitted as a draft AASHTO standard is the Linear Amplitude Sweep test (LAS) which is

based on using viscoelastic continuum damage (VECD) mechanics to predict binder fatigue life

as a function of strain in pavement. The LAS test uses cyclic loading with systematically

increasing load amplitudes to accelerate damage and provides sufficient data for analysis in less

than 30 minutes. While results of the current linear amplitude sweep testing protocol are

promising, there has been some concerns regarding the time and complex numerical procedures

required for the analysis. In addition, there are concerns regarding the strain amplitudes proposed

for the LAS as they do not lead to sufficient damage accumulation for a range of polymer

modified binders. This paper presents simplifications of the current analysis procedures and

evaluates the influence of using extended strain levels to impose sufficient damage for better

calculation of the binder fatigue law parameters. To validate the effectiveness of the modified

procedure, the results were correlated to the fatigue performance recorded by the LTPP program

with consideration of the pavement structure. Fair correlations were found showing the potential

for effective use of the modified method in the binder specifications.

INTRODUCTION

The current PG specification to evaluate asphalt fatigue resistance is based on the linear

viscoelastic properties of the material (i.e., |G*|·sin). However, this approach lacks the ability to

characterize actual damage resistance (1-2). Furthermore, this specification does not account for

pavement structure or traffic loading as the measurement is made at a specific strain level, for a

very few cycles of loading. The developers of the PG fatigue parameter were aware of this

limitation, but they speculated that binder in pavements function mostly in the linear visco-

elastic range and thus strain is not likely to affect their properties. They also assumed that energy

estimated in this range can be a good indicator of binders’ resistance to fatigue. Since late

1990’s there has been increased focus on challenging the assumptions, particularly for modified

asphalts that have better fatigue resistance and show more non-linear response to loading.

Therefore, there is currently a considerable amount of effort placed on the development of an

asphalt binder test procedure that can accurately determine the binder's contribution to asphalt

mixture fatigue by means of damage characterization.

Multiple procedures, such as the time sweep, have been proposed to improve the current

fatigue specification. The time sweep is a test method that consists of applying repeated cyclic

loading at fixed load amplitude to a binder specimen using the Dynamic Shear Rheometer

(DSR). The time sweep was developed during NCHRP Project 9-10 (1) to solve the deficiencies

of the current specification. The test is based on the definition of fatigue damage: degradation of

material integrity under repeated loading. The procedure allows for selection of load amplitude,

thus allowing for consideration of pavement structure and traffic loading. However, time sweep

tests are time consuming and repeatability is often difficult to attain.

Recently, an effort has been placed on developing an accelerated asphalt binder fatigue

test to replace the time sweep. Accelerated procedures that systematically increase the load


amplitude have shown great potential for fatigue resistance characterization (3). The focus of

this paper is to modify the test procedure originally developed by Johnson and Bahia (4) as a

surrogate to the time sweep test. This accelerated method, called the linear amplitude sweep

(LAS), consists of a series of cyclic loads at systematically linearly increasing strain amplitudes

at a constant frequency of 10 Hz. Similarly to the time sweep, the LAS test is run in the DSR and

uses standard 8 mm parallel plate geometry. The loading schematic applied to the asphalt binder

is shown in Figure 1. Loading begins with 100 cycles of sinusoidal loading at 0.1% strain to

obtain an undamaged response. Next, each load step consists of 100 cycles at a rate of increase

of 1% applied strain. Johnson and Bahia (4) recommended using loads steps between 1% and

20% applied strain to evaluate damage evolution. The test also includes a frequency sweep test

using a very low strain amplitude of 0.1% to obtain undamaged material properties. The

amplitude sweep can be run directly following the frequency sweep as the frequency sweep does

not damage the material. Note that the combination of the frequency and amplitude sweeps tests

takes approximately 10 minutes.

FIGURE 1 Strain sweep loading scheme proposed by Johnson and Bahia. (4).

Linear amplitude sweep test results can be analyzed using viscoelastic continuum damage

(VECD), which has been used extensively to model the complex fatigue behavior of asphalt

binders and mixtures (5-8). The primary benefit of using continuum damage mechanics is that

results from a single test run at a specific set of conditions can be used to predict the behavior of

that material under any variety of alternate conditions. Application of VECD follows Schapery’s

theory of work potential to model damage growth (9). Work is related to damage using

Schapery’s work potential theory by:

(1)

where W is the work performed, D is the damage intensity, and is a material constant

that is related to the rate at which damage progresses.


The parameter α is taken to be 1 + 1/-m, where m is the slope a log-log plot of relaxation

modulus versus time. Johnson and Bahia. (4) proposed calculating m by converting frequency

sweep data to relaxation modulus using approximate inter-conversions presented by Schapery

and Park (10).

Quantification of work performed using dissipated energy follows Kim et al. (11).

Dissipated energy under strain controlled loading is calculated with:

(2)

where, W is dissipated energy, γ0 is shear strain, |G*| is the complex modulus, and is the

phase angle. Equation 2 can then be substituted in Equation 1 and numerically integrated to

arrive at the following equation to allow for calculation of damage intensity (D):

(3)

where ID is the initial un-damaged value of |G*|. Johnson and Bahia (4) proposed fitting

|G*|·sinversus damage to the following power law:

(4)

where C0, C1, and C2 are model coefficients. C0 can be taken as the average value of

|G*|·sinduring the 0.1% strain amplitude load step and C1 and C2 must be derived to best fit

experimental data. Determination of model coefficients using Equation 4 requires use of an

optimization tool such as Microsoft Excel's Solver to best match experimental data. After the

parameters C1 and C2 are known, the derivative of Equation 4 with respect to D can be

determined and substituted into Equation 1. Equation 1 can then be integrated to obtain the

following closed-form relation between number of cycles to failure and strain amplitude for a

defined failure criteria (3).

(5)

where k = 1 + (1 – C2);

f = loading frequency, Hz;

|G*| = undamaged complex shear modulus;

Df = damage accumulation at failure.

Simplification of Equation 5 can be accomplished to arrive at the basic form shown

below:

(6)


where,

(7) and

B = -2

The number of cycles to a given damage intensity can be calculated at any strain level

using (6). Thus, one can account for pavement structure and traffic loading by adjusting the

strain level in Equation (6).

While results of the linear amplitude sweep test are promising, there are important

concerns about the current testing and analysis protocols. In the proposed procedure, strains

amplitudes ranging from 0.1% to 20% are used. However, some asphalt binders exhibit little

damage under this procedure. A typical plot of shear stress versus strain for four binders tested

at the intermediate performance grade (PG) temperature is presented in Figure 2. The PG 76-10

binder exhibits significant damage as evident by significant decreases in stress response at high

strains. However, the PG 52-40 and PG 58-34 binders demonstrate minimal damage as the shear

stress response does not degrade significantly even at 20% strain. It is unknown whether or not

VECD is able to accurately characterize the damage resistance of these materials under the

current testing protocol.

FIGURE 2 Stress vs. strain curve from LAS test.

Additionally, calculation of the α parameter using frequency sweep results is difficult. A

model is fit to the frequency sweep data and that model is used to convert relaxation modulus

from the frequency domain to the time domain. Furthermore, fitting of the model parameters in

(4) using an optimization tool such as Excel Solver is highly dependent on initial guesses for C1

and C2. A poor initial guess can lead to a very poor model fit compared to that of a good initial


condition as illustrated in Figure 3. Thus, it is desirable to have a method to determine model

coefficients that is independent of priori knowledge of typical values for C1 and C2.

FIGURE 3 Example of the effect of initial guess on model fit.

OBJECTIVES

The goal of this study is to address the concerns raised about the current LAS testing and

analysis methods. The following points summarize the main achievements of this study:

1. A simplified method for determining the parameter α is presented.

2. A method that allows for elimination of the use of standard least squares optimization to

determine the model parameters in Equation 6 has been developed.

3. An evaluation of the effect of extending the strain amplitudes up to 30% rather than 20%

on LAS results has been conducted to determine if higher strains are necessary to fully

characterize binder fatigue resistance.

4. A comparison of applying the modified method to a number of modified binders used in

the Long Term Pavement Performance (LTPP) program is presented. Also a first look at

validation of the test method by correlation to field performance is presented.

MATERIALS AND TESTING

Eight Long-Term Pavement Performance (LTPP) binders were used in this study. The LTPP

program monitors selected pavement sections for various distresses. The asphalt binder testing

was conducted with an Anton Paar Smart Pave DSR with standard specimen geometry of 8-mm

diameter and 2-mm thickness. All tests were conducted at the intermediate temperature

performance grade (PG Grade) of the asphalt binder after rolling thin film oven (RTFO) aging.

Evaluation of the effect of long-term aging, using pressure aging vessel (PAV) material, will be

investigated in future work. Table 1 provides a summary of the asphalt binders used in this

paper. Determination of the undamaged properties of the binders was obtained by means of

frequency sweep tests. Frequency sweep tests were conducted at the intermediate PG grade

using 0.1% strain to avoid damage. Frequencies ranged from 0.1 to 30 Hz. After the frequency

sweep test, the binders were tested using the linear amplitude sweep. In the amplitude sweep,

initially 100 cycles are applied at 0.1% strain. After this step, each successive load step consisted


of 100 cycles at a rate of increase of 1% applied strain per step for 30 steps, starting at 1% and

ending at 30% applied strain. Generally, two replicates were run for each binder. However, if

results varied by more than 15%, a third replicate was run. Analysis of the results was used to

evaluate the proposed simplifications and changes to the LAS test.

TABLE 1 LTPP Binder Summary

*Measured distress is zero, but is listed as 0.01 for inclusion on logarithmic plot

SIMPLIFIED METHOD TO CALCULATE α As discussed previously, the damage exponent is calculated from undamaged rheological

properties using the slope of a log-log plot of relaxation modulus, G(t), versus time. This can be

accomplished in two ways: (a) by direct measurement of relaxation modulus from a stress

relaxation test or (b) by converting frequency sweep test data to the relaxation using approximate

methods developed by Schapery and Park (10). Note that all standard dynamic shear rheometers

are capable of conducting frequency sweep tests. This paper proposes a method to obtain from

frequency sweep test data.

The original method converts the data from the frequency to the time domain. Storage

moduli (G'(ω)) at each angular frequency (ω) must be calculated using complex modulus and

phase angle as follows:

(8)

The slope (n) of a log-log plot of G’() versus plot must be calculated at each

frequency as follows:

(9)

The parameter ’ can be calculated for each value n using:

(10)

Sample PG Test Temperature

(°C)

Pavement

Thickness (in)

Fatigue

Cracking (m2)

04-B901 76-10 37 10.7 328.0

09-0902 64-28 22 7.2 0.01*

34-0961 78-28 28 6.4 178.8

37-0962 76-22 31 8.5 0.01*

09-0961 58-34 16 6.9 2.1

34-0901 64-22 25 5.6 49.5

89-A902 52-40 10 4.9 6.7

35-0902 64-22 25 10.8 32.0


where is the gamma function, Γ(x) = (x − 1)!. After ’ is calculated for each frequency,

complex moduli as a function of frequency can be converted to relaxation moduli as a function

of time using Equation 11. The time corresponding to a given frequency are calculated as 1/ω.

(11)

Adding to the complexity of the conversion to relaxation, typically a model must be fit to

frequency sweep data prior to conversion to allow for prediction of the response at frequencies

outside of the testing range. Frequencies in the range of 0.1 Hz to 30 Hz correspond to relaxation

times ranging from approximately 0.005 to 1.59 sec using the presented inter-conversion

method. Hence, direct measurements only allow for calculation of a small range of relaxation

times, and therefore predictions of complex moduli and phase angles at additional frequencies

are advantageous in order to obtain relaxation moduli over a reasonable time span.

The conversion of frequency sweep data relaxation is largely based on the relationship

between storage modulus and frequency. Johnson (12) demonstrated that the slope of a log-log

plot of storage modulus versus frequency can be used to calculate α. Unlike the slope of the log

of relaxation modulus and log of time, the slope of a log-log plot of storage modulus versus

frequency is positive. However, the magnitude of this slope is nearly identical to the log-log plot

of the relaxation modulus versus time. Thus, α can be calculated as 1+1/m where m is the slope

of the log storage modulus versus log frequency curve. Johnson (12) concluded that for four

binders, the method for calculating α was insignificant on the resulting fatigue law parameter A

in (6) based on an analysis of variance (ANOVA). In this study, a different approach was taken

to determine if the α's calculated from relaxation modulus versus time and storage modulus

versus frequency are statistically equivalent.

For the eight binders tested, α was determined using both methods. Two tests were run on

each binder. The α values calculated using log (relaxation modulus) versus log (time) and log

(storage modulus) versus log (frequency) are shown in Table 2. The maximum discrepancy in α

between the two methods is 2.24%. Thus, observation of individual values provides evidence

that the two calculation methods result in very similar α values.

To further evaluate if the two methods result in the same α values, a test of hypothesis of

the means of α estimated using the two methods was conducted. A t-statistic was used to test the

hypothesis that the two -means are statistically equal. That is, H0: µ1 = µ2 against H1: µ1≠µ2.

The underlying assumption of conducting the hypothesis test is that the samples are normally

distributed. Normality plots of α for both computation methods indicated that the samples are

normally distributed. The resulting test statistic, t0, computed using the two sample distributions

was 0.195 and the t-statistic using a significance level of 95% was 2.042. Since the test statistic

is in the acceptance region. The null hypothesis can not be rejected and therefore the α's

computed using the two methods are equivalent.


Table 2. Comparison of α values calculated using log(relaxation modulus) vs. log(time) and

log(storage modulus) vs. log(frequency).

Sample PG α - Relaxation

modulus vs. Time

α - Storage Modulus

vs. Frequency

Percent

Difference 04-B901_1 76-10 2.291 2.240 2.24%

04-B901_2 76-10 2.293 2.247 2.02%

09-0902_1 64-28 2.443 2.405 1.57%

09-0902_2 64-28 2.444 2.399 1.82%

34-0961_1 78-28 2.609 2.572 1.42%

34-0961_2 78-28 2.619 2.561 2.21%

37-0962_1 76-22 2.391 2.345 1.91%

37-0962_2 76-22 2.368 2.340 1.17%

09-0961_1 58-34 2.741 2.689 1.91%

09-0961_2 58-34 2.729 2.701 1.03%

34-0901_1 64-22 2.399 2.356 1.81%

34-0901_2 64-22 2.404 2.353 2.13%

89-A902_1 52-40 2.809 2.818 0.33%

89-A902_2 52-40 2.926 2.882 1.51%

35-0902_1 64-22 2.609 2.580 1.13%

35-0902_2 64-22 2.618 2.585 1.29%

ELIMINATION OF THE NEED TO USE STANDARD OPTIMIZATION TOOLS

Use of optimization tools to solve for best fit model parameters is problematic if one does not

have a reasonable initial guess for these parameters. Optimization tools use an iterative approach

to find best possible values to minimize the error of a model fit. That is, the initial values entered

by a user are altered iteratively until the values which provide the smallest error between the

measurements and model predicted values is reached. However, if the initial guesses for model

coefficients are highly erroneous, the best model parameters will most likely not be the values

the optimization tool predicts. Initial guesses are especially critical when multiple model

coefficients are being determined as in the case of Equation 4. Thus, it is desirable to have a

means to solve the model coefficients without initial guessing.

To eliminate the need for optimization tools, Equation 4 can be linearized to allow for

easy calculation of model coefficients C1 and C2. Linearization is accomplished by performing a

logarithmic transformation of Equation 4 as shown in Equation 12. Recall that C0 is taken to be

the average value of |G*|·sinmeasured in the 0.1% strain step of the amplitude sweep. In other

words, C0 represents the un-damaged |G*|·sin and does not need to be determined through

model fitting.

(12)

Equation 12 is the common form of a linear equation, y = b + m·x, where m is the slope

and b is intercept. Hence, C1 is the intercept a line formed as log(C0 - |G*|·sin) versus log(D)

and C2 is the slope of this line. Solving for the slope and intercept is easily accomplished and

independent of initial guesses for C1 and C2.

If Equation 4 is a perfect representation of experimental data, the plot of log(C0 -

|G*|·sin) versus log(D) should be perfectly linear. However, at very low damage levels,


experimental data exhibits nonlinear trend. The plot of log(C0 - |G*|·sin) versus log(D) for a

typical binder is shown in Figure 4. If data at damages below 100 are ignored, the linear fit is

greatly improved as evidence by Figure 5. Thus, if C1 and C2 are determined using data

corresponding to damage levels above 100, an adequate model fit is attained.

FIGURE 4 Linear fit of log(C0 - |G*|·sin) versus log(D) including all experimental data.

FIGURE 5 Linear fit of log(C0 - |G*|·sin) versus log(D) excluding damages below 100.

Both Excel Solver and the linearization method were used to determine C1 and C2 for the

eight asphalt binders tested using all strains, (i.e. up to 30%). The fatigue law parameter A in


Equation (6) obtained using the two methods were compared. For this analysis, A was chosen to

be defined using the damage intensity corresponding to a 35% decrease from the initial |G*|·sin

as recommended by Johnson and Bahia. (4). Therefore, in the proceeding analyses, A will be

noted as A35. The fatigue law parameter B only depends on α and therefore is independent of the

amplitude sweep results. The values of A35 computed using optimization and linearization for all

16 tests completed, (e.g., two tests for each binder), are shown in Table 3. The results in Table 3

show that A35 computed using the two methods are very similar.

A plot of A35 computed using linearization and optimization methods is provided in

Figure 6. A line of equality on the plot reveals the results from optimization and linearization are

similar for all binders with the exception of binder 89-A902, which is a heavily modified binder

of a the PG 52-40 grade. An R2 of 0.97 is achieved when comparing the A35 values determined

from the two methods, when this binder is excluded from the analysis. While there is no strong

justification to exclude this binder, other than it is a very soft and highly elastic binder, the

simplified method give the same ranking of this binder as the optimization method. The results

therefore indicates that the simplified linearization procedure can be used in place of

optimization to solve for the coefficients C1 and C2 in Equation 4.

TABLE 3 A35 Computed Using Optimization and Linearization

Sample PG A35 -

Optimization A35 -

Linearization

04-B901_1 76-10 7.43E+06 8.44E+06

04-B901_2 76-10 6.95E+06 7.57E+06

09-0902_1 64-28 9.27E+06 1.04E+07

09-0902_2 64-28 8.28E+06 9.50E+06

34-0961_1 78-28 2.78E+07 3.33E+07

34-0961_2 78-28 2.93E+07 3.47E+07

37-0962_1 76-22 5.58E+07 6.29E+07

37-0962_2 76-22 5.31E+07 5.97E+07

09-0961_1 58-34 3.62E+07 4.01E+07

09-0961_2 58-34 3.64E+07 4.08E+07

34-0901_1 64-22 8.81E+06 9.77E+06

34-0901_2 64-22 8.15E+06 9.37E+06

89-A902_1 52-40 6.26E+07 8.80E+07

89-A902_2 52-40 7.29E+07 9.70E+07

35-0902_1 64-22 4.86E+07 4.41E+07

35-0902_2 64-22 4.69E+07 4.30E+07


FIGURE 6 Comparison of A35 computed using different methods to derive power law

coefficients to model |G*|·sinversus D curve.

EFFECT OF USING HIGHER STRAINS ON LAS RESULTS

Figure 7 shows stress-strain curves for the binders tested using the linear amplitude sweep

procedure. It can be observed in Figure 7 that some of the binders (09-0961, 37-0962, and 35-

0902), do not exhibit significant decreases in stress at 20% strain in the LAS test which could

result in poor prediction of damage. However, all binders display a considerable reduction in

stress when additional higher strain amplitudes are applied. The following analysis determines if

strains in excess of 20% are needed better characterization of damage behavior .


FIGURE 7 Linear amplitude sweep results.

A comparison between results using maximum strain amplitudes of 20% and 30% was

performed. This was conducted by comparing A35 values computed using all strains, ranging

from 0.1% to 30% with values computed using only the strain levels up to 20%. That is,

computations of A35 using a maximum strain of 20% was accomplished using the test data

excluding strain levels above 20%. A table comparing A35 values using maximum strain

amplitudes of 30% and 20% are shown in Table 4.

Overall, using strain amplitudes above 20% in the linear amplitude sweep test does not

drastically affect A35 values. With the exception of binder 09-0902_1, A35 values do not differ by

more than 20%. Furthermore, the three binders that exhibit little damage up to 20% strain,

binders 09-0961, 37-0962, and 35-0902, did not display large differences between A35 values

than the other samples.


TABLE 4 Comparison of A35 Values Computed using Maximum Strain Amplitudes of

20% and 30%

Sample PG A35 - 30% A35 - 20% %Difference

04-B901_1 76-10 8.44E+06 7.70E+06 8.73%

04-B901_2 76-10 7.57E+06 7.10E+06 6.20%

09-0902_1 64-28 1.04E+07 5.57E+06 46.62%

09-0902_2 64-28 9.50E+06 1.03E+07 8.17%

34-0961_1 78-28 3.33E+07 2.77E+07 16.84%

34-0961_2 78-28 3.47E+07 2.90E+07 16.40%

37-0962_1 76-22 6.29E+07 6.92E+07 10.02%

37-0962_2 76-22 5.97E+07 6.38E+07 6.94%

09-0961_1 58-34 4.01E+07 4.37E+07 8.93%

09-0961_2 58-34 4.08E+07 3.67E+07 10.07%

34-0901_1 64-22 9.77E+06 1.07E+07 9.74%

34-0901_2 64-22 9.37E+06 8.63E+06 7.84%

89-A902_1 52-40 8.80E+07 7.18E+07 18.38%

89-A902_2 52-40 9.70E+07 8.78E+07 9.49%

35-0902_1 64-22 4.41E+07 4.49E+07 1.98%

35-0902_2 64-22 4.69E+07 4.30E+07 8.30%

A best fit line was constructed using A35 values from tests with a maximum strain

amplitude of 30% versus values from tests with a maximum strain of 20% (Figure 9). The slope

of the best fit line is 1.056 with an R2 of 0.96, indicating that using a maximum strain of 30%

increases the computed A35 parameter by approximately 5.6%.

FIGURE 8 Correlation between A35 values using 30% and 20% maximum strain

amplitudes.

While using additional higher strains does not appear to substantially affect VECD

results, it is recommended that strains up to 30% are used in the LAS test. Increasing the

maximum strain used in the LAS test from 20% to 30% only requires 100 additional seconds.


Testing the binders up to a level of = 30% leads to a significant degradation of material integrity

and is thought to be the best representation of fatigue damage behavior.

Correlation of LAS Results with Fatigue Performance of LTPP Sections

The United States Long-Term Pavement Performance (LTPP) program maintains records of the

pavement distress on select sections of interstate highways. The asphalt binders used in this

study are included in several of these pavement sections. The pavement distress indicator used

by LTPP for fatigue cracking is cracked area per 500 meters of pavement length section. Linear

amplitude sweep results from this study were compared with measured fatigue cracking. Due to

the fact that pavement thickness greatly affects the strains at the bottom of the pavements where

fatigue cracking initiates, LTPP cracked area measurements were normalized by pavement

thicknesses. Cracked areas normalized by pavement thickness were plotted against number of

cycles to failure predictions at 4% strain using LAS results. With the exception of binder 09-

0902, the LAS results correlated well with field measurements as shown in Figure 9. This

provides promising evidence that the LAS test is capable of measuring asphalt binder

contribution to mixture fatigue.

FIGURE 9 Fatigue cracking from LTPP measurements compared to the LAS number of

cycles to failure.

CONCLUSIONS

Based on the experimental results presented in this paper, the following conclusions can be

drawn:

A simplified method that avoids the use of inter-conversion methods for the calculation

of the α parameter needed in the VECD analysis was successfully implemented.

Viscoelastic Continuum Damage (VECD) coefficients can be easily obtained by applying

a logarithmic transformation to the damage curves. The use of this linearization technique


eliminates the need of optimization tools that required initial guesses for estimation of the

model coefficients.

It is recommended to modify the current Linear Amplitude Sweep procedure to include

strains ranging from 0.1% to 30% due to the fact that significant material degradation is

achieved for strain levels above 20%. Moreover, testing time only increases by 100

seconds with respect to the current procedure.

VECD analysis of LAS test results yields promising correlations between accelerated

binder fatigue life and measured cracking in actual pavements constructed as part of the

LTPP program. It is believed that method could be further improved by investigating a

method to separate non-linearity from damage accumulation to more accurately predict

fatigue lives will be investigated. Accounting for non-linearity could possibly delineate

results from tests using strain amplitudes ranging from 0.1% to 20% and tests including

strains exceeding 20%.

ACKNOWLEDGEMENTS

This research was sponsored by the Asphalt Research Consortium (ARC), which is funded by

the United States' Federal Highway Administration (FHWA). This support is greatly appreciated.

REFERENCES

1. Bahia, H. U., Hanson, D. I., Zeng, M., Zhai, H., Khatri, M. A., and R.M. Anderson.

Characterization of Modified Asphalt Binders in Superpave Mix Design, NCHRP Report

459, National Academy Press, Washington, D.C., 2001.

2. Bahia, H. U., Zhai, H., Zeng, M., Hu, Y., and P. Turner. Development of Binder

Specification Parameters Based on Characterization of Damage Behavior. Journal of the

Association of Asphalt Paving Technologists, Vol. 70, 2002, pp. 442-470.

3. Maratono, W. and H.U. Bahia. Developing a Surrogate Test for Fatigue of Asphalt

Binders. Proceedings from the 87th Annual Meeting of the Transportation Research

Board. (2008).

4. Johnson, C.M. and H.U. Bahia. Evaluation of an Accelerated Procedure for Fatigue

Characterization of Asphalt Binders. Submitted for publication in Road Materials and

Pavement Design. 2010.

5. Kim, Y.R., and D. N. Little. One-Dimensional Constitutive Modeling of Asphalt

Concrete. Journal of Engineering Mechanics, Vol. 116, No. 4, 1990, pp. 751--772.

6. Park, S. W., Y.R. Kim, and R.A. Schapery. A Viscoelastic Continuum Damage Model

and Its Application to the Uniaxial Behavior of Asphalt Concrete. Mechanics of

Materials, Vol. 24, 1996, pp. 195-223.


7. Chirstensen, D.W. and R.F. Bonaquist. Practical Application of Continuum Damage

Theory to Fatigue Phenomena in Asphalt Concrete Mixtures. Journal of the Association

of Asphalt Paving Technologists, Vol. 74, 2005, pp. 963-1002.

8. Kutay, M.E., N.H. Gibson, and J. Youtcheff. Conventional and Viscoelastic Continuum

Damage (VECD) Based Fatigue Analysis of Polymer Modified Asphalt Pavements.

Journal of the Association of Asphalt Paving Technologists, Vol. 77, 2008, pp. 395-434.

9. Schapery, R. A. Correspondence principles and a Generalized J Integral for Large

Deformation and Fracture Analysis of Viscoelasic Media. International Journal of

Fracture, Vol. 25, No. 3, 2984, pp. 195-223.

10. Schapery, R. A., and Park, S. W. Methods of Interconversion Between Linear

Viscoelastic Material Functions - Part II: An Approximate Analytical Method.

International Journal of Solids & Structures, Vol. 36, 1999, pp. 1677-1699.

11. Kim, Y., Lee, H. J., Little, D. N., and Y.R. Kim. A Simple Testing Method to Evaluate

Fatigue Fracture and Damage Performance of Asphalt Mixtures. Journal of the

Association of Asphalt Paving Technologists, Vol. 75, 2006, pp. 755-788.

12. Johnson, C.M. Estimating Asphalt Binder Fatigue Resistance using an Accelerated Test

Method. Ph.D Thesis. University of Wisconsin - Madison, Madison, 2010.

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