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TRANSCRIPT
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.