Researching on Fatigue Model of Asphalt Mixtures

Journal of Highway and Transportation Research and Development Vol.2,No.2(2007)25

Researching on Fatigue Model of Asphalt Mixtures

XIE Jun (M^Y'2' ,GUO Zhong-yin (H$&£p)2

(1.School of Highway Engineering.Changsha University of Science & Technology,Changsha Hunan 410076,China;

2. Road and Traffic Engineering Key Laboratory of Ministry of Education,Tongji University,Shanghai 200092,China)

Abstract: Firstly different fatigue testing methods of HMA were summarized, the scope of applicability of two kinds of control mode were

analyzed,it is recommended that indirect tensile fatigue test with stress control mode to be used.Then effect of different testing factors

were analyzed, the scope of the loading wave,stress ratio,frequency and temperature were selected.Three kinds of HMA specimens were

compacted by gyratory compactor. Indirect tensile fatigue tests were carried by uniform test design method under different temperatures,

frequencies and loadings, including three void ratios of asphalt mixes. Significance of the testing results was analyzed.The fatigue models

were brought forward through multiple linear regression methods based on VFA, temperature, frequency, initial strain and initial modulus

for general and heavy-duty loading. Comparative study of the fatigue models was made at home and abroad, it is shown that the fatigue

models are comparable.They could be used for the fatigue prediction of asphalt mixtures.

Key words: road engineering; asphalt pavement; linear regression;fatigue model; indirect tensile fatigue test; HMA;uniform design

In order to study the mechanism of fatigue cracking and

reduce the fatigue failure of the pavement, researchers of dif-

ferent countries used different methods and proposed differ-

ent fatigue models of asphalt mixtures . But these models

were obtained by different experimental methods, different

experimental conditions and different parameters, each of

them has its specific application scope.

In order to understand and master the fatigue law of as-

phalt mixtures, three kinds of asphalt mixtures including AO

25I,AO20I and AK-16A were used,and fatigue testing was

conducted under different conditions, then the fatigue model

of asphalt mixtures was obtained.

1 Fatigue testing program

1.1 Fatigue test methods

At present there are mainly four kinds of testing meth-

ods about the fatigue properties. The first is the fatigue dam-

age test of the actual pavement under the real traffic load,

such as AASHTO roads and so on. It costs the time so longer

and also is influenced under the climatic conditions. The sec-

ond is the full-scale pavement structure of fatigue test under

simulated traffic load, including circular road test, straight

road test and accelerated loading test, etc. The third is the

testing plate method which including pulse pressure head

type, tire pressure type, motor wheel rut type and moving

plate rut type, etc.The fourth is the fatigue test of small

specimens in laboratory.

Because the first three kinds of test methods expend

more fund and time, most of the test choices are small speci-

mens of laboratory fatigue test which is of short cycle time

and cost less. Laboratory fatigue characteristics of the speci-

men can be obtained by repeated bending or shear test, ma-

inly including uniaxial tensile text, indirect tensile text, sim-

ple bending text and so on.But so far,most of countries have

not take the fatigue test as test method regularization, North

America mainly uses the repeatedly bending fatigue test of

the beam specimens and the Europe mainly uses the fatigue

test of cantilever beam trapezoidal specimens.

At present in multitudinous laboratory small-scale fa-

tigue tests, indirect tensile fatigue tests capture more and

more eyes. Although the indirect tensile test used for so many

years, researchers such as A. S. Adedimila and Kennedy ,

John M Read and Said thought that it has good repeat-

ability , more reasonable than other methods, and it has more

efficient accuracy in judging asphalt mixture fatigue charac-

teristics. XU Zhi-Hong found a certain relevance between

indirect tensile fatigue test and flexural fatigue test results

through research and comparative analysis of the results. Fle-

xural specimens preparation are more difficulty, the accuracy

of the cutting is higher, the test specimens is easy to break,

Manuscript received December 21,2006

E- mail address : howardxj @ 126. com

J. Highway Transp. Res. Dev. (English Ed.) 2007.2:25-29.

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26 Journal of Highway and Transportation Research and Development

testing lasted longer, and the data are more dispersible. On

the contrary, indirect tensile test is convenient, the data is

centralized. Therefore, under the existing conditions using in-

direct tensile test as a method of laboratory fatigue test is

recommended.

Meanwhile in indirect tensile test, specimens were the

role of horizontal tensile stress, from the analysis of the linear

elasticity theory, it is similar with the stressful condition of

actual pavement ; the tensile stress which in the region of

the specimens cracking damage are relatively uniform; the

test results and the actual pavement performance has some

relevance, so the indirect tensile method was used for fatigue

tests.

1.2 Test control models There are mainly two test control models in asphalt

mixtures fatigue test which are stress controlled and strain

controlled, and usually the strain controlled model is more

suitable for the thinner pavement, the stress controlled model

suitable for the thicker pavement. According to experience,

the pavement critical thickness usually is 5 in(12.7 cm)

.The stress controlled model is usually used for its operation

and convenience. When using strain controlled model, gener-

ally takes its stiffness decreased to 50% of its initial stiffness

as the damage criteria and it has certain randomness, usually

the test specimens can t appear obvious fracture, and it has

certain difficulty in technology applications.

Considering the present thickness of highway pavement

is generally thicker than 12.7 cm, the effect of load repeti-

tion makes the surface strain growing faster, it more accords

with stress controlled model, and closer to the fatigue charac-

teristics of the actual structure of the pavement. When using

the stress controlled model, its reappearance ability is better

and test time is relatively short, the definition to judge the

fatigue test failure is quite clear, which means that the speci-

mens fracture completely is the damage state.Moreover, the

quantity of the specimens is fewer needed in the test, and the

precision controlling is reliable, and the degree of the data

dispersion is small, so the stress controlled model was used

for the fatigue test.

1.3 Test factors

There are numerous factors which affect the fatigue

properties of the asphalt mixtures, including the influence of

external factors, such as loading frequency, wave form, load-

ing level and test temperature, etc. , and also including the

factors of the material itself, such as types of asphalt, ag-

gregate, grades, types of mixtures' structure and so on. In or-

der to enable the test results have a certain representation

and applicability, all the factors above in the test design need

to be considered.

For loading wave, it is usually thought that it has little

effect on fatigue properties, research results indicate that the

moving wheel load produces a stress strain effect to the pave-

ment which is close to the sine curve, so using the sine load-

ing wave, as shown in Fig. 1. As it is all in the pressure

side, i.e., haversine wave, in order to accelerate the test

speed, we do not insert intervals between neighboring waves.

Initial

Peak value

Fig.l Loading wave

According to the typical pavement structure' s scope of

stress ratio under different loadings, three stress ratios

(such as 0.3,0.5,0.7)of the loading level were used from

low value to high value, which represents the effect of differ-

ent traffic axle loads separately such as ordinary load and the

heavy-duty load and so on.

Regard to the actual pavement, loading time is directly

related to riding speed. When the loading frequency is 10 Hz

the loading time is 0.016 s,and it is equivalent to the speed

of 60 ~ 65 km/h for the asphalt pavement which is quite

close to the range of the driving speed specified in the as-

phalt pavement design specifications of China.So 5, 10, 15

Hz corresponds to low, medium and high frequencies respec-

tively were used which can reflect the difference of the actual

traffic speeds on pavement.

With regard to the test temperature, in accordance with

relevant research results, the fatigue damage of asphalt mix-

tures occurring mainly concentrates in 13 ~ 15 °C, corre-

sponds to the spring thawing period in the north of China and

the temperature of rainy season in the south of China. It is

usually considered 15 °C for the most severe situation, and

also in the asphalt pavement design specifications of China

the temperature of 15 °C is used as parameter values for ten-

sile stress. Meanwhile the difference of temperature could


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XIE Jun, et al; Researching on Fatigue Model of Asphalt Mixtures 27

cause the changing of the asphalt mixture stiffness modulus

and directly affect the fatigue life, So 15 X. was chosen as

the test temperature, and 5 t and 25 tl are considered to

represent the low and high levels of temperature, which is

better to cover the differences of fatigue equivalent tempera-

ture in all regions of our country.

Choose AC, AK as mixtures structure types, their grada-

tion is AC-20I, AC-25I and AK-16A, which are types of do-

mestic common gradation, and their nominal maximum ag-

gregate size is 19 mm, 26.5 mm, and 16 mm respectively,

which has the better representation. The asphalts are Zhong-

hai heavy traffic asphalt and Luante modified asphalt, amount

of the asphalt are optimum asphalt content and diabase stone

is used as the aggregate.

Takes low, medium and high levels of voids ratio(0%

~ 3% , 3% ~ 6% , 6% ~ 9%) for each kind of mixtures,

which is basically covers the design porosity of current conv-

entional mixtures.

1.4 Specimen molding

There are some methods of specimen molding such as

static pressure molding, compaction molding, gyratory mold-

ing, kneading molding and the wheel compaction molding,

etc. A. M. Hartman discussed the effect of the fatigue prop-

erties using different compaction methods, and thought that

the arrangement of the specimen aggregate which is obtained

through the static pressure molding method is inconsistent

with the status of the field s; it is easy to cause the aggregate

damaged through the compaction molding method in the

molding process, also has no way to simulate the compaction

effect of rubber tire to the asphalt pavement, simultaneously

the high-energy of the compaction release is easy to make the

asphalt membrane rupture which is making structural perfor-

mance different from that of mixtures of asphalt concrete at

the field compaction; and the specimen which is made by the

latter three kinds of molding methods can better represent the

properties of the asphalt concrete at the field compaction.

Synthesized all mentioned above,the rotational compac-

tion molding method was considered to prepare specimens,

and their diameter is 100 mm and high is 63.5 mm.

2 Fatigue test design

Considering the main factors which influence the fatigue

test scheme, test parameters of indirect tensile fatigue test are

show in Tab. 1.

Tab.l Parameters of indirect tensile fatigue test

Parameter type Parameter level

AC-25I

Mixture structure type AC-20I

AK-16A( modified asphalt)

VA Test factor

Load wave

0% ~ 3% ,3% - 6% ,6% ~ 9%

Haversine wave,without intervals

Load level 0.3,0.5,0.7

Temperature 5 T,15 t,25 X.

Frequency 5 Hz,10Hz,15Hz

Because there are so many variables in test, if we con-

duct a full - factor test, the fatigue test number is 972

times. Due to the restriction of time, materials and test equip-

ment, it is unrealistic to conduct all-factor of fatigue test, so

we use the uniform method of test design to carry on the ex-

perimental design to reduce the number of test and enable

the test to have a better representation result.

Uniform method of test design is a brand-new partial

factor experimental design method which is suitable for multi

-factor, mufti- level experimental design situation.Through

uniform design we can make the selected test points uniform

distributed in the multidimensional test space and enable the

limited test points to have a good representation to the

whole, thus we can reduce the number of experimental great-

ly and save the experimental workload. Uniformity only con-

siders the uniform dispersion of the test points, i. e., to let

the test points balanced distributed in the experimental space

and each test point has full representation.In uniform design

method each level of each factor is tested only once, when

the number of level increases, the experimental number is

only increased along with level number increases, it is called

the continuity of test number of times increment with the lev- -

el increment.

Using uniform design table of U6(64) ,the combination

of test is shown in Tab. 2.

Tab.2 Results of uniform text design

Temperature (t) Frequency (Hz) Stress

1 5(1) 10(2) 0.7(3)

2 15(2) 5(4) 0.7(6)

3 25(3) 15(6) 0.5(2)

4 5(4) 5(1) 0.5(5)

5 15(5) 15(3) 0.3(1)

6 25(6) 10(5) 0.3(4)

To ensure the reliability of test data and to meet the

need of statistical analysis, the number of each combination

of the test level is tested at least four times, therefore, the

specimen number of fatigue test is 216, which greatly reduces


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2X Journal of Highway and Transportation Research and Development

the workload of test.

3 Fatigue test

According to results of uniform design conduct indirect

tensile fatigue test, before the test first conduct splitting

strength test to determine the splitting strength of the mix-

tures for the load level determination of the fatigue test.

Use specimens formed by gyratory compaction instru-

ment and test their air voids. After testing, it was found that

there is a 2% - 3% difference between objective air voids

and design air voids,and the specimens were formed accord-

ingly. After testing specimens' density and air void, the

specimens conforming to the requirement were we chosen to

conduct test.Voids error in the test results is within the ±

l%,it conforms to the requirement. Before the test, speci-

mens were put in temperature environment box at least 6h

under constant temperature to ensure that the specimens

reach temperature requirement before fatigue test.

Through computer-controlled regulating pressure head,

well-prepared specimens were sent into indirect tensile fa-

tigue test fixture of MTS test system to make the pressure

head close contacts to specimen surface and guarantee layer

is vertical to the test specimen.The control software test pa-

rameters include stress, test frequency, test wave ( havers-

ine), loading speed, test end criterion, data acquisition and

data density and so on. In order to avoid the possible pro-

longed specimen disengaging which would impact on speci-

men , when setting the test load, set the minimum value of

sine load equal to 2% of the maximum value.

Before the test begin, conduct the pre-loading by the

minimum load to the test specimens to make them well con-

tact with the loading equipment.

After test parameters setting completed, through com-

puter control fatigue test can be conducted. In the test pro-

cess, the test data were collected and preserved in accor-

dance with the timing.

4 Analysis of test results

The specimen deformation curve of fatigue test is shown

in Fig. 2.

From Fig. 2 it is shown that the specimen deformation

can be divided into three stages with time increasing.In the

first stage,the specimen deformation increased rapidly;in the

second stages, the specimen deformation has gone through a

Ms)

Fig.2 Typical fatigue curve

period of steady growth; in the third stages, the specimen was

nearly destroyed with a sharp increase of deformation, and it

was completely destroyed at last.

Taking the corresponding time of the total destruction of

specimens as the fatigue life of the specimen, the fatigue life

of each can be determined from the specimen deformation

curves, and the strain and stiffness modulus of initial state of

the specimen(200 loading cycle)can be calculated.

The significance test result of parameters and fatigue

life is shown in Tab.3.

Tab.3 Results of significance test

Factors Temperature VFA Frequency Stress Initial Initial stiffness

strain Ine modulus lnS„

In/V,

Note: * * * is high significant, * * is significant.

From Tab.3, in the test parameters change range, the

effect of stress on fatigue life is the most significant, and the

impact of test temperature, test frequency, void ratio, VFA

(voids filled with asphalt) , the initial strain and initial stiff-

ness modulus on fatigue life is also very significant. The

greater the stress, the shorter the fatigue life is, fatigue life

increases with test temperature increases, and the fatigue life

decrease with void ratio of asphalt mixture increases.

For comparison, using different models with different

parameters for regressing, namely: stress for model I; VFA,

temperature, frequency, stress for model II; VFA, tempera-

ture, frequency, the initial strain and stiffness modulus for

model III; VFA, strain and stiffness modulus for model rV.

The uniform design method results are regression ana-

lyzed by using multiple linear regression method. Because the

fatigue law of heavy traffic asphalt is different from that of

modified asphalt, so AC-25 and AC-201 mixtures are re-

gressed unitary,AK-16A is regressed independently,consid-

ering 50%, 90% and 95% of the guaranteed rate respec-

tively .

The results of regression are shown in Tab.4 according


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XIE Jun, et al: Researching on Fatigue Model of Asphalt Mixtures 29

to 50 % guaranteed rate.

Tab,4 Results of fatigue model regression

Model Mixture Regression model

AC Nr = 1. 96 X lOS X € - 1.887

AK-16A Nr=2.416x lOll X €-2.8967

AC Nr = 5.2 X lQ2 X exp( - 0.0291 VFA-

0.069 5 T + 0.106 21) (a/ 17o) -3.8199 II

Nr = 3.72x lQ2 X exp( - 0.031 VFA-AK-16A

0.017 3T+0.lOl 71)(17/170)-4.2857

AC Nr = 8.181 X lO17 X exp( - 0.013 4 WA -

0.205 4T + 0.0361)0 -4.053 2 S,;;0.8392 III

Nr = 3.7 X lQ28 x exp(0.045 2VFA-AK-16A

0.2112T+0.06521)€-4.3625 S,;;3.9078

AC Nr = 5.633 x lO-7 x exp( - 0.025 4 VFA)€ -2.t;1t; 5 S~0l22 IV

Nr = 1.33 x lO x exp( - O.OlO 3 VFA)o -3.75932 S~7791 AK-16A

The results of variance analysis of regression models are

shown in Tab. 5 .

Tab.S Results of variance analysis

Model Mixture Correlation coefficient F Significance level

AC 0.730932 37.1745 0.001

AK-16A 0.898 129 66.6989 0.001

AC 0.969 801 141.5639 0.001 II

AK-16A 0.988647 126.7192 0.001

AC 0.964705 74.916 0.001 III

AK-16A 0.993475 178.369 0.001

AC 0.79165 17.916 0.001 IV

AK-16A 0.934593 32.212 0.001

( 1 ) From the correlation coefficient of regression mode

s ,model II and III model have highest coefficient, which

reaches over 95 % ; while the correlation coefficient of model

I and model III are above 73 % . When the significant level is

0.01 ,the correlation coefficients of all regression models are

greater than the critical value, which indicates it is meaning

ful for the regression models.

(2) From the variance analysis of three kinds of models

and through F test, the significant level of regression model is

0.001 and with a higher significantly level. It shows that the

regression model fits with high accuracy and regression mod

el is also meaningful.

( 3) Model I is the classic regression of fatigue life, from

the relevance of regression model, its correlation coefficient is

poor. It shows that there is a big error only considering strain

to substitute other factors affecting the fatigue life prediction.

(4) Model II, III and IV comprise VFA parameters,

VFA directly reflects the different asphalt contents in differ

ent asphalt mixtures, it can reflect the difference of internal

structures.

(5 ) Model II comprises such parameters which have

significant influence on the fatigue life, including VF A, tem

perature, loading frequency, and stress. Its relevance is bet

ter, and it also shows that the fatigue life is directly influ

enced by the above parameters.

( 6) Compare model III with model II, it not only com

prises VF A , temperature, frequency, etc. but also comprises

initial strain and the initial stiffness modulus. It not only re

flects the impact of parameters on the fatigue life, but also

facilitates comparison with other models.

(7)Model N omitted the temperature and loading fre

quency, while considered initial strain and stiffness modulus

which affected by temperature significantly. Although it

makes easy for model simplification, but from the results of

the regression, the power of stiffness modulus is positive and

anomaly. It shows that there is quite an error using stiffness

modulus to simply substitute other factors which affect the

fatigue life prediction.

Based on the above analysis and comparison, it is rec

ommended to use model III as the fatigue model.

5 Comparison of fatigue models

In some fatigue life models of home and abroad, AI

model, Shell model and SHRP model are the most famous

and have wider application, as shown in Pig. 6 . SHRP model

is used in the guide 2002 version, which is based on the AI

model. AI model is of stress controlled mode, Shell model is

of strain controlled mode.

Model

AI

SHRP

Shell

Tab.6 Contrast of fatigue models

Expression

Nr = SFx4.325x lO 3 x Cx €r 3.291 X S ,;;2.854,

SF= 18.4, C= lif·84(VFA-o.6875), VFA = Vb/( Va + Vb)

Nr =O.OO4 32K1' x lif·84(VFA-o.6875) X €r- 3.9492 X S .;;;1.281

Nr = (0.856Vb +€~.08)S';;0.36) -5

Typical materials parameters were selected. Assuming

that VA is 6.3 % , asphalt volume content Vb is 13. 1 % ,

stiffness modulus is 2 000 MPa, temperature is 15 "C, load

frequency is 1 0 Hz, and consider stain of ordinary and heavy

- duty load conditions, fatigue life of different models were

calculated under different strains, the fatigue curve was plot

ted as shown in Fig. 3 .

From Fig.3, the fatigue curve slopes of two fatigue

models (Model III) close to the


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XIE Jun, et ai: Researching on Fatigue Model of Asphalt Mixtures 29A

other three kinds of model' s slopes, the fatigue life is be

tween Shell model and AI model, which shows that the fa

tigue models are comparable.

1000

-+-AK ---AI -+-Shell ____ SHRP

i'- 1'- .......-AC

100 le+02 le+03 le+04 le+05 le+06 le+07 le+08

N(tims)

Fig.3 Contrast offatigue lives

6 Conclusion

Applying the unifonn experimental design methods,

through the indirect tensile fatigue tests at different tempera

tures, frequencies, levels of load for three kinds of asphalt

mixtures, and through relevance and variance analysis, the

asphalt mixture fatigue models which suitable for different

load conditions based on the temperature, frequency, VFA

and the initial strain and initial strain stiffness are ob

tained . It shows that fatigue models are comparable. They

could be used for the fatigue prediction of asphalt mixtures.

References

[1] XIE Jun, YANG Qun. Fatigue Models of Asphalt Mixtures [JJ.

Transportation Science & Technology ,2006(5) :93 - 96.

[2J ADEDlMILA A S, KENNEDY T W. Repeated-load Indirect Ten

sile Fatigue Characteristics of Asphalt Mixtures [J J . Transport

ation Research Board, 1976,595 : 25 - 33.

[3 J READ J M, COlLOP A C. Practical fatigue characterization of

bituminous paving mixtures [ J J . Association of Asphalt Paving

Technologists, 1997,66:74 - 108.

[ 4 J SAID SF. Variability in Roadbase layer Properties Conducting

Indirect Tensile Test [ C J /I Proceeding 8th International Confer

ence on Asphalt Pavements ( vol. II) . Seattle , Washington D. C. :

1997: 977 - 986.

[5J XU Zhi- hong, U Shu-ming, GAO Ying, et ai. Research on Fa

tigue Characteristic of Asphalt Mixture[JJ . Journal of Traffic and

Transportation Engineering, 2001 , 1 ( 1 ) : 20 - 24.

[6J WEN Hai-feng.Fatigue Performance Evaluation ofWestrack As

phalt Mixtures based on viscoelastic analysis of indirect tensile

test [D ] . Raleigh: North Carolina State University, 2001 .

[7 J XIE Jun. Research on Fatigue Response and Design Method of

Asphalt Mixture Pavement Under Heavy Duty Loading [D J .

Shanghai: Tongji University, 2006.

[8 J HARTMAN AM, GILCHRIST M D , WALSH G. Effect of Mixture

Compaction on Indirect Tensile Stiffness and Fatigue[JJ . Journal

of Transportation Engineering, 2001 , 127(5): 370 - 378.

[9 J FANG Kai-tai, MA Chang-xing. Orthogonal and Uniform Experi

ment Design [ MJ . Beijing: Science Press, 2001.

(Selected from Journal of Highway and Transportation

Research and Development, vol. 24 , no. 5 , pp . 21-25 , 2007 )


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Researching on Fatigue Model of Asphalt Mixtures