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APPENDIX B
Proposed Standard Practice for
Predicting the Endurance Limit of Hot Mix
Asphalt (HMA) by Pseudo Strain Approach
AASHTO Designation: PP XX-XX
1. Scope
1.1 This practice describes methodology for predicting the endurance limit for hot mix
asphalt for long-life pavement design by pseudo strain approach.
1.2 This standard may involve hazardous materials, operations, and equipment. This standard
does not purport to address all of the safety problems associated with its use. It is the
responsibility of the user of this procedure to establish appropriate safety and health practices
and to determine the applicability of regulatory limitations prior to its use.
2. Referenced Documents
2.1 AASHTO Standards
· PP XX-XX, Preparation of Cylindrical Performance Test Specimens Using the Super-
pave Gyratory Compactor
· PP XX-XX, Determining the Dynamic Modulus and Flow Number for Hot Mix
Asphalt (HMA) Using the Simple Performance Test System
· PP XX-XX, Developing Dynamic Modulus Master Curves for Hot-Mix Asphalt
Concrete Using the Simple Performance Test System
2.2 Other Publications
· Equipment Specification for the Simple Performance Test System, Version 2.0,
Prepared for National Cooperative Highway Research Program (NCHRP), March
26, 2004.
3. Terminology
3.1 Dynamic Modulus |E|, the absolute value of the complex modulus calculated by
dividing the peak-to-peak stress by the peak-to-peak strain for a material subjected to
a sinusoidal loading.
3.2 Phase Angle , the angle in degrees between a sinusoidally applied stress and the
resulting strain in a controlled-stress test.
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3.3 Endurance limit the strain level, at a given temperature, below which no fatigue dam-
age occurs in the HMA.
4. Summary of Practice
4.1 This practice describes the analysis needed to determine the endurance limit for hot-
mix asphalt concrete mixtures by pseudo strain approach. It involves testing
continuous cyclic fatigue test data of cylindrical asphalt concrete.
5. Significance and Use
5.1 The endurance limit can be used during pavement design to determine a pavement
thickness which will prevent fatigue cracking.
6. Apparatus
Specimen Fabrication Equipment Equipment for fabricating cylindrical test specimens
as described in AASHTO PP XX-XX, Preparation of Cylindrical Performance Test
Specimens Using the Superpave Gyratory Compactor.
6.1 Specimen Fabrication Equipment Equipment for fabricating cylindrical test speci-
mens as described in PP XX-XX, Preparation of Cylindrical Performance Test Speci-
mens Using the Superpave Gyratory Compactor.
6.2 Dynamic Modulus Test System A dynamic test system meeting the requirements of
Equipment Specification for the Simple Performance Test System, Version 2.0
6.3 Conditioning Chamber An environmental chamber for conditioning the test spec-
imens to the desired testing temperature. The environmental chamber shall be capa-
ble of controlling the temperature of the specimen over a temperature range from
4 to 60°C (39 to 140°F) to an accuracy of ± 0.5°C (1°F). The chamber shall be large
enough to accommodate the number of specimens to be tested plus a dummy spec-
imen with a temperature sensor mounted at the center for temperature verification.
6.4 Analysis Software Software capable of handling numerical approaches like numeri-
cal integration and nonlinear optimization. Data analysis can be conducted using a
spreadsheet program, or a variety of scientific computation packages like MATLAB,
Lab View.
7. Hazards
7.1 This practice and associated standards involve handling of hot asphalt binder,
aggregates and asphalt mixtures. It also includes the use of sawing and coring
machinery and servo-hydraulic or pneumatic testing equipment. Use standard safety
precautions, equipment, and clothing when handling hot materials and operating
machinery.
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8. Standardization
8.1 Items associated with this practice that require calibration are included in the
documents referenced in Section 2. Refer to the pertinent section of the referenced
documents for information concerning calibration.
9. Test Specimen
9.1 Compaction Prepare at least three test specimens to the target air void content and
aging condition in accordance with AASHTO PP XX-XX, Preparation of Cylindri-
cal Performance Test Specimens Using the Superpave Gyratory Compactor (SGC).
The target air void content should be representative of that expected to be obtained
in the field.
Note 1 A reasonable air void tolerance for test specimen fabrication is ± 0.5 %.
Note 2 The coefficient of variation for properly conducted fatigue tests has not yet
been determined
9.2 Preparation Core the cylinders from gyratory compacted specimens and cut the ends
of cylinders thus obtained to ensure uniform air void content. Check the cylinder for
its geometry and axis alignment.
Note 3 A reasonable diameter tolerance for test specimen is ± 1 mm.
9.3 Gluing Clean the cored sample using compressed air and modified alcohol so that
the dust particles over the surface are totally removed. Apply glue on the ends of the
cleaned specimen. Place end plate over the specimen end and press against one
another by hand. Repeat same procedure for another end also. Mount the specimen
along with end plates on gluing jig and make adjustments such that cylinder axis is
aligned with that of end plates. Place dead weight on gluing jig so that endplates are
pressed against specimen. Remove the excess glue (if any) and leave the specimen for
sufficient curing.
Note 4 Process of gluing end plates to test specimen shall be completed well within
initial setting time of glue.
10. Testing
10.1 Dynamic Modulus
10.1.1 Conduct dynamic modulus test in tension over a range of temperature and frequen-
cies using three specimens in accordance with AASHTO PP XX-XX, Determining the
Dynamic Modulus and Flow Number for Hot Mix Asphalt (HMA) Using the Simple
Performance Test System.
Note 5 Applied loads should be within linear elastic limits of asphalt concrete (this
can be guaranteed when observed strain is less than 75 microns).
Note 6 As flow number is not used in test practice described in this document, flow
number part of AASHTO PP XX-XX guidelines should be ignored.
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(a) Load History (b) Strain History
Figure 1. Typical stress/strain history for increasing amplitude uniaxial fatigue test.
10.2 Increasing Strain Amplitude Test
10.2.1 Conduct increasing strain amplitude fatigue test on other three specimens until fail-
ure starting from low strain amplitude at constant temperature (usually 20 C). A good
starting strain amplitude value is that at which dynamic modulus tests are conducted.
Around 10,000 cycles are applied at this amplitude to get steady state response.
Applied strain amplitude is then increased and 10,000 more cycles are applied. This
process shall be repeated at increasing strain amplitude level successively until speci-
men fails.
Note 7 Mounting of LVDT's and load cells shall be similar to that of dynamic mod-
ulus determination (refer 10.1).
Note 8 Temperature at which fatigue test is conducted shall be henceforth referred as
reference temperature.
Typical plots of load and strain histories for an increasing amplitude fatigue test are
given in Figure 1a and 1b respectively.
11. Calculations
11.1 Dynamic Modulus Mastercurve Construction
11.1.1 Using data previously obtained dynamic modulus data (refer 10.1), construct dynamic
modulus master curves at reference temperature for individual specimens. General
form of the dynamic modulus master curve is given in Equation 1.
log E = +
( Max - ) (1)
Ea 1 1
+ log + -
T
1+ e 19.14714 Tr
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where:
|E| = dynamic modulus, MPa
r = reduced frequency, Hz
Max = limiting maximum modulus, MPa
Tr = reference temperature, °K
T = test temperature, °K
Ea = activation energy (treated as a fitting parameter)
, , and = fitting parameters.
11.2 Relaxation Modulus Prediction
11.2.1 Using dynamic modulus (|E|) and phase angle (r) data (refer 10.1), obtain relaxation
modulus for each specimen using following relations.
E ( r ) = E ( r ) cos ( ( r ))
1 0.
.08
E (t r ) = E ( r ), r =
tr
n
= (1 - n ) cos
2
d log E ( )
n=
d log
where:
|E(r)| = storage modulus,
tr = reduced time,
= gamma function,
n = slope of log(E()) versus log() obtained at each point of reduced frequency.
11.2.2 Fit Prony series for relaxation modulus values obtained previously (refer 11.2.1). Gen-
eral expression for relaxation modulus as Prony series is given by Equation 2.
t
E ( t ) = E + En exp - (2)
n n
where:
E = Relaxation modulus as t,
En = Prony series coefficients,
n = Relaxation time.
11.3 Calculation of Pseudo Strain
11.3.1 Using time history of strain (using data obtained in 10.2) and predicted relaxation
modulus (refer 11.2), calculate pseudo strains for entire strain history for each speci-
men. Equation 2 shall be used for calculating pseudostrains at reference temperature.
1 t d
R (t ) = E ( t - ) d
ER
(3)
0 d
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Figure 2. Cross plot of Stress vs. Pseudo strain.
where:
ER = reference modulus (usually chosen as unity), MPa
E(t) = relaxation modulus, MPa
= measured strain
11.3.2 Crossplot stress vs. pseudo strain and check for formation of hysteretic loop. This shall
be started from lowest level of strain amplitude. Note down the strain level at which
hysteresis loop appears for first time. Also calculate average value of strain level at
which hysteresis loop forms. Typical plot comparing stress vs. pseudo strain before and
after damage is presented in Figure 2.
Note 6 The loop is observed in cross plot of stress vs. pseudo strain if the damage has
occurred.
12. Report
12.1 For each specimen, report the following
12.1.1 Sample air voids
12.2 For each mix, report the following
12.2.1 Reference Temperature
12.2.2 Dynamic modulus master curve coefficients
12.2.3 Strain level at which hysteresis loop appears for first time in cross plot of stress vs.
pseudo strain
12.2.4 Average strain level for loop formation
13. Keywords
13.1 Fatigue, Viscoelastic Continuum damage, Endurance limit
