Application of four-point bending beam

fatigue test for the design and construction

of a long-life asphalt concrete rehabilitation

project in Northern California

V. Mandapaka, I. Basheer, K. Sahasi & P. VacuraCalTrans, Sacramento, CA

B.W. Tsai, C. L. Monismith, J. Harvey & P. UllidtzUCPRC, UC-Davis, CA

Introduction

• Caltrans adopted Mechanistic Empirical design

method (CalME) to design long-life flexible

pavements.

• Rutting and Fatigue are the main modes of failure.

(Fatigue being the scope of this paper)

• 4 Point Bending Beam Fatigue test (LLP AC1) based

on AASHTO T321 has been adopted by Caltrans to

determine fatigue properties of HMA materials.

Introduction contd.

A pavement section on I-5 in Tehama County has been used to illustrate the use of fatigue data to develop fatigue performance specifications

Project location:

I-5 Tehama County, PM 37.5/41.5

• Structural section and material details.

OGFC 0.1 ft

PG 64-28 PM 0.3 ft

Old CTB 0.5 ft

PG 64-10 (25% RAP) 0.2-0.5 ft

PG 64-10 Rich Bottom 0.2 ft

Aggregate Subbase+ Subgrade

Objective

The objective of this paper is to present the

methodology for utilizing the four-point bending (4PB)

beam fatigue test (AASHTO 321) to:

• Obtain the stiffness master curves required for

determining the fatigue damage model parameters

necessary for CalME, and

• Determine the fatigue performance specifications

for the three HMA materials proposed for use on the

project.

4PB testing equipment

4 PB beam testing setup

• Testing can be

performed under

different:

• Frequencies (To

simulate traffic speed)

• Temperatures (to

consider climatic effect)

• Strain levels

HMA stiffness master curves

• HMA stiffness master curve is developed using 4PB

beam fatigue frequency sweep test.

• Several tests were performed at 11 frequencies: 15,

10, 5, 2, 1, 0.5, 0.2, 0.1, 0.05, 0.02, 0.01 Hz

• Three temperatures: 10C, 20C and 30C

• Two strain levels : 200 and 400 micro strain

• Note: The test was performed for each HMA material

that was used on this project.

HMA master curve equation

• Ei= the intact modulus; α2, β1, γ1, δ1 αT=model parameters,;

tr = reduced time; viscref = reference viscosity;

A and VTS =constants, T is temperature.

( ) ( )( )trEi log1exp1

log1

21 γβ

αδ++

+=

aT

ref

visc

visclttr

×=

TVTSAvisc 101010 log)(loglog ⋅+=

Fatigue Model

• In CalME, it is assumed that fatigue damage causes

the HMA modulus to decrease.

• HMA fatigue curve is developed using 4PB beam

fatigue test.

• The data obtained from the Frequency Sweep test

was used to determine fatigue model parameters.

• 1 temperature (20C); 2 strains (200 and 400

microstrain); 4 frequencies data was considered for

the analysis.

Fatigue model equations

ω = damage( ) ( )( )( )tr

Elogexp1

1log

γβωαδ

++−×+=

α

ω

=

pMN

MN

×+=C

To1

exp 10 αααδγβ

µεµε

×

×

×=

ref

i

refrefp E

E

E

EAMN

MN= No. load repetitions; MNp = Permissible # load repetitions;

T= HMA average temperature; A, α0, α1, β, γ, δ = model

parameters (β= 2*γ ), µε= tensile strain at the bottom of HMA;

E= current damaged modulus; Ei= intact modulus;

µεref and Eref = reference strain and modulus.

Comparison between measured E/Ei and

calculated E/Ei (PG64-28PM)

Comparison between measured E/Ei and

calculated E/Ei (PG64-10RAP)

Comparison between measured E/Ei and

calculated E/Ei (PG64-10RB)

Fatigue damage model parameters

Material type A α0 α1 εref β Eref γ δ RMS

PG64-28PM 4887.23 -1.4535 0 200 -7.6899 3000 -3.845 0 3.1343

PG64-10RAP 151.216

-0.35766 0 200 -5.9161 3000 -2.9581 0 7.3679

PG64-10RB 2491.20

-0.74099 0 200 -6.4907 3000 -3.2454 0 7.6002

•Nonlinear model optimization was used to

calculate model parameters.

•All parameters were uploaded into the CalME

software with other material parameters.

•Pavement structure was analyzed using the

Incremental-Recursive (I-R) method.

Performance Specifications

Performance Specifications were developed to:

• provide the contractor a quantitative measure of the

quality of materials that can be used in each HMA

layer.

• have a quality assurance of HMA materials

“Confidence Band Concept” was used to statistically

determine the lower bound of fatigue life at specified

strain levels.

Confidence Band Concept

010 2ˆ:boundUpper

YSFy α−+

010 2ˆ:boundLower

YSFy α−−

0y = calculated LnNf= calculated Ln(strain)0x

α−1F

)()( strainbLnaNfLn +=

( )( )

−−

+=∑ 2

202

|2ˆ

10 xx

xx

nSS

i

xYY

( )2

ˆ2

2| −

−=∑

n

yyS ii

xY

square of residual standard error

of the regression equationVariance of Ln(Nf)

F1-α =(1-α)-percentile of F-distribution with 2 & n-2 degrees of

freedom

Lower bounds for 95% confidence band

for mixes at 200 C

Strain Ln(Strain) PG64-10RB w/Lime(LB) Ln(Nf)

PG64-10RAP w/Lime(LB) Ln(Nf)

PG64-28PM w/Lime Lower Bound(LB)

Ln(Nf)

0.0001 -9.21034 15.81985 15.63268 20.20609

0.000164 -8.7139 15.21146 14.34777 19.86629

0.000229 -8.38366 14.52459 13.30796 19.45809

0.000293 -8.13583 13.45893 12.18087 18.78389

0.000357 -7.93738 12.04937 10.98033 17.74516

0.000421 -7.77186 10.61595 9.8585 16.56064

0.000486 -7.62989 9.29322 8.85378 15.41701

0.00055 -7.50559 8.09695 7.95648 14.36458

0.000614 -7.39505 7.0147 7.14983 13.40497

0.000679 -7.29552 6.03023 6.41876 12.5285

0.000743 -7.20501 5.12893 5.751 11.72418

0.000807 -7.12201 4.29864 5.13683 10.98212

95% confidence band for PG64-28PM HMA

(with 1.2% lime added, AC = 5.2%, AV = 6.0%)

tested at 200 C

0

10

20

30

40

50

-9 -8.5 -8 -7.5 -7

Ln(strain)

Ln

(Nf)

95 % Confidence Band: PG64-28PM w/Lime

400 microstrain(mean = 1.55E+08)

200 microstrain(mean = 4.64E+10)

Lower Bound

Upper Bound

18.10359(Nf = 72,826,467)

12.91058(Nf = 404,570)

95% confidence band for PG64-10RAP HMA

(with 1.2% lime added, AC= 5.38%, AV= 6.0%)

tested at 200 C

4

8

12

16

20

24

28

-9 -8.5 -8 -7.5 -7

Ln(strain)

Ln

(Nf)

95 % Confidence Band: PG64-10RAP w/Lime

400 microstrain(mean = 103,672)

200 microstrain(mean = 3,169,823)

Lower Bound

Upper Bound

13.74855(Nf = 935,232)

10.12395(Nf = 24,933)

95% confidence band for PG64-10RB HMA

(with 1.2% lime added, AC = 5.5%, AV = 3%)

tested at 200 C

4

8

12

16

20

24

28

-9 -8.5 -8 -7.5 -7

Ln(strain)

Ln

(Nf)

95 % Confidence Band: PG64-10RB w/Lime

400 microstrain(mean = 629,332)

200 microstrain(mean = 29,246,517)

Lower Bound

Upper Bound

14.85981(Nf = 2,841,407) 11.08419

(Nf = 65,133)

Lower bound fatigue life at 400 and

200 microstrain levels

HMA type Fatigue life at 400

microstrain

Fatigue life at 200

microstrain

PG 64-28 PM 15% RAP 404,570 72,826,467

PG 64-10 25% RAP 24,933 935,232

PG 64-10 Rich Bottom 65,133 2,841,407

Conclusions

• The 4PB tests were used to determine the fatigue

model parameters and master curves as they are

necessary inputs to the California M-E design

software, CalME.

• The 4PB fatigue test has enabled the integration of

construction quality requirements (performance

specifications) with the ME design of flexible

pavement

• The minimum fatigue life at a given strain level for

each material for a 95% confidence level was

specified as the performance criteria for each

material.