Refinedhmabeamfatiguetestingconditions Astm
Refinedhmabeamfatiguetestingconditions Astm
Refinedhmabeamfatiguetestingconditions Astm
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ABSTRACT: The beam fatigue test of hot-mix asphalt (HMA) has been used for nearly a half
century. However, several conflicting results have been recently reported. This study attempts
to refine test conditions such as waveform type (haversine vs. sinusoidal), incorporating rest
periods between loading cycles, and the effect of rest period on the healing of the HMA to
minimize (eliminate) gross errors in the data analysis of the fatigue test results. In the deflection-
controlled haversine test (ASTM D-7460) permanent deformations lead to a new equilibrium
neutral position of the beam and the force output follows a sinusoidal waveform. This tends to
bend the beam in both directions similar to the deflection-controlled sinusoidal test. This would
produce erroneous fatigue results since the test assumptions do not match the actual test
consistent than the deflection-controlled haversine test (ASTM D-7460). When tests, with and
without rest periods, are compared for healing studies, it is even more important to use a
deflection-controlled sinusoidal test in order to obtain a fair comparison and accurate healing
results. Since neither the haversine waveform nor the sinusoidal waveform in the lab exactly
consistent results. It is recommended that ASTM changes the ASTM D-7460 designation and
Implementing the recommended test conditions is a crucial step in studying the concept of HMA
healing and, as a result, estimating the endurance limit which plays an important role in
Introduction
Beam fatigue (four point bending) testing of hot-mix asphalt (HMA) in the laboratory (Figure 1)
has been used for several decades by many researchers to simulate field conditions. It is
anticipated that the test will gain wider acceptance since it forms the foundation of the fatigue
analysis used in the Mechanistic-Empirical Pavement Design Guide [1]. In this test, a HMA
beam is subjected to repeated bending until it fails. The stiffness ratio is calculated by dividing
the current stiffness, at a given level of repetitions (cycles), by the initial stiffness. The number
of loading cycles at failure is recorded and plotted against the strain value. Normally 8 to 12
specimens are tested at different strain or stress levels to establish the fatigue relationship at a
specific temperature. Since the stiffness of HMA is largely affected by temperature, the test is
typically performed at several temperatures to evaluate the effect of stiffness on the fatigue life.
Historically, haversine and sinusoidal waveforms have been used in the beam fatigue test
on HMA. Most researchers [8, 10, 11, 12, 13, 14], especially in the U.S., have been applying a
haversine waveform under either controlled deflection (strain) or controlled force (stress) mode
for several decades. Also, the literature indicates that most researchers have run the beam
With the advanced computer and equipment technology that has been developed in recent
years, researchers have been able to examine the pulse shapes in more detail. Therefore, recent
literature has emerged to show erroneous results, such as inconsistent waveforms or unexpected
fatigue results. Pronk et al [1, 2] showed that beam fatigue tests with a constant haversine
deflection on HMA would immediately change into tests with constant sinusoidal deflections
performed on a bent beam. They even went one step further and concluded that it is not possible
to carry out fatigue bending tests where both a haversine stress (force) oscillating signal and a
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haversine strain (displacement) oscillating signal are maintained throughout the test because of
the viscoelastic (viscous part) character of asphalt. This implies that a haversine test in a HMA
beam would result in erroneous fatigue results since a haversine force does not have the same
effect on fatigue as a sinusoidal force with the same peak-to-peak value. The haversine force
results in tension at the bottom of the beam and compression at the top, whereas the sinusoidal
force results in reversible tension and compression at the top and bottom of the beam with half of
the stress magnitude as that produced by the haversine force. Also, tension reduces the fatigue
life of the beam, while compression may tend to heal fatigue cracks.
procedure (ASTM D-7460) that has been used by many researchers throughout the last five
decades. Although not explicitly discussed in their papers, the results of other researchers [3, 4]
imply that when a haversine deflection-controlled test is run on a HMA beam the wave pulse
changes to sinusoidal, which support Pronk’s claim. Therefore, it is important to verify Pronk’s
claim under different conditions. Also, it is important to verify this claim for tests with and
without rest periods between loading cycles and investigate the effect of the waveform on
healing. Proper test conditions for the beam fatigue test are needed that would ensure accurate
fatigue results and confirm the healing that could happen to the HMA during the rest periods,
Objective
The objective of this paper is to enhance conditions for deflection-controlled beam fatigue
testing of HMA. Issues studied include the applied pulse shape (haversine versus sinusoidal), the
incorporation of rest periods between loading cycles, and the effect of rest period on the healing
of the HMA.
5
Background
Deflection-controlled beam fatigue tests can be performed using either a haversine waveform
(ASTM D-7460) or a sinusoidal waveform (AASHTO T-321). Figure 2 shows the input
haversine and sinusoidal waveforms in the beam fatigue test without rest periods. The haversine
waveform tends to bend the beam downward in one direction, whereas the sinusoidal waveform
tends to bend the beam upward and downward with half of the magnitude of the haversine in
each direction. In the last several years, researchers have also started performing the beam
fatigue test with rest periods between loading applications to evaluate the healing effect that may
occur during the rest period. From this, estimates of the presence of an endurance limit have
Although the continuous loading cycles without rest periods do not accurately simulate actual
traffic loading, it has been the most dominant procedure due to testing time constraints. Some
researchers, however, introduce a rest period after each loading cycle in order to simulate traffic
loading in the field [8, 9, 10]. A typical loading pulse is 0.1 second and typical rest periods
range from 0.1 – 19 seconds. Introducing rest periods during the fatigue test allows the HMA
material to heal some of micro cracks caused by the load due to the viscous nature of the
material. Figure 3 shows a schematic of the stiffness ratio (current stiffness/initial stiffness)
versus loading cycles with and without rest period. The difference between the two curves can
Several researchers have studied the significance of rest periods between load
applications during fatigue testing of HMA. Researchers showed a general enhancement of the
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fatigue life when introducing rest periods [8, 10, 11, 12, 13, 14]. Some researchers reported an
increase in fatigue life as much as 25 times [15]. The optimum rest period would be different
based on mixture properties (aggregate gradation, binder content, binder grade, mixture
volumetric, etc.) and test conditions (mode of loading, temperature, frequency, stress or strain
levels, etc). Other researchers [19] stated that fatigue life can be explained by other phenomena:
nonlinearity, heating, thixotropy and fatigue. Analysis reported by Benedetto [19] showed that
the two reversible effects (heating and thixotropy) are very important and can not be ignored
when interpreting fatigue tests. Nonlinearity was also shown to be reversible. Heating is due to
Experimental Tests
Deflection-controlled haversine and sinusoidal flexural fatigue tests were performed on HMA
beams according to ASTM D-7460 and AASHTO T-321, respectively, using two IPC machines
(Figure 1). Tests with and without rest periods were performed on a densely-graded base mix
with a nominal maximum size aggregate of 3/4 inch and a PG 64-22 binder [16]. The haversine
and sinusoidal waveforms had the same strain pulse of 0.1 seconds. Two strain levels of 400 and
800 microstrains and three test temperatures of 4, 21 and 38oC (40, 70 and 100F) were used.
In this part of the study, deflection-controlled haversine (ASTM D-7460) and sinusoidal
(AASHTO T-321) flexural fatigue tests were performed. The shape of the force pulses was
examined for both haversine and sinusoidal waveforms during the test. Figure 4 shows an
example of several cycles of input deflection and the resulting force response during the test
without rest period. For the sinusoidal test, both the deformation input and the resulting force
follow sinusoidal waveforms. For the haversine test, however, the deflection input remains as
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haversine, while the force output follows a sine waveform. This means that although the input
deflection tries to bend the beam in one direction, the beam actually bends in both directions.
This also implies that the stress output, and the resulting strain, are sinusoidal. In other words,
the deformation input follows a haversine waveform, while the strain follows a sinusoidal
waveform.
Figure 5 shows an example of the force output versus time for haversine and sinusoidal
tests with the same input peak-to-peak deflection using the same strain level and test
temperature. The figure shows that although the input waveforms are different, the force outputs
are almost the same for the two tests. This also definitely confirms Pronk’s claim that it is not
possible to carry out fatigue bending tests where both a haversine stress (force) oscillating signal
and a haversine strain (displacement) oscillating signal are maintained throughout the test.
Figure 6 illustrates what happens (hypothetically) to the HMA beam during the sinusoidal
deflection-controlled test and the haversine deflection-controlled test. In the sinusoidal test
(Figure 6 (a)), the deflection input is sinusoidal, which bends the beam in both directions. The
neutral position of the beam does not change during the test and remains in the original position
half way between the two extreme positions. In the haversine test (Figure 6 (b)), the deflection
input is haversine, which bends the beam with the same peak-to-peak mgnitude as the sinusoidal
test except in one direction only. Because of the viscous response of the material, creep
(permanent deformation) occurs in the beam and the neutral position of the beam shifts dowward
after a few loading cycles. The neutral position is located half way between the extreme
positions and the haversine deflection is changed to a sinusoidal deflection performed on a bent
beam.
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Figure 7 illustrates the deflection input and the stress and strain outputs that occur in the
HMA beam during the tset. Since the neutral position of the beam does not change in the
sinusoidal test, both strain and stress developed are sinusoidal causing alternating tension and
compression in the beam as shown in Figure 7 (a). In the haversine test, the deflection input
remains haversine throughout the test. The developed strain and stress pulses start as haversine
causing strain and stress in one direction (compression at the top of the beam and tension at the
bottom without reversal). Because of the shifted posion of the beam, the developed strain and
stress pulses immediately change to sinusoidal causing alternating tension and compression with
half of the magnitude of the stress applied at the beginning of the test as shown in Figure 7 (b).
At the end of the test, when the load is removed, the beam remains in the bent position showing
permanenet deformation. This observation also confirms the conclusions of Pronk’s et. al [1, 2].
Note that the strain always lags behind the stress in both the sinusoidal and haversine tests.
Currently, the literature incorrectly uses the terms “strain-controlled” and “deflection-
controlled” for beam fatigue tests on HMA interchangeably. Since the loading machine controls
the deflection, not the strain, the so-called haversine strain-controlled test is technically a
material such as HMA, since the deflection remains haversine while the strain changes to
sinusoidal. If the test is run on an elastic material such as a portland cement concrete, a
deflection-controlled test would be the same as a strain-controlled test because the deflection
In this part of the study, deflection-controlled haversine and sinusoidal flexure fatigue tests were
performed with rest periods of either 5 or 10 seconds using the same HMA materials and other
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conditions as the test without rest period. The shapes of the force and deflection pulses were
examined for both haversine and sinusoidal waveforms during the test. Figure 8 shows an
example of several cycles of input deflection and the resulting force response during the
sinusoidal and haversine tests with rest period. For the sinusoidal test, both the deflection input
and resulting force output are sinusoidal. For the haversine test, the force reverses direction at
the end of the pulse for a short period of time because of the creep. During the rest period,
however, the forces (stresses) are mostly recovered and force (stresses) waveform changes to be
close to haversine with a small negative value depending on the duration of the rest period.
Comparing the sinusoidal test without rest period (Figure 4 (a)) to the sinusoidal test with
rest period (Figure 8 (a)), the deflection and force (stress) waveforms maintain a sinusoidal
pattern. This means that the stress and strain conditions will be the same in both tests with and
without rest period. This condition would produce a fair comparison in the fatigue and healing
analysis. On the other hand, comparing the haversine test without rest period (Figure 4 (b)) to
the haversine test with rest period (Figure 8 (b)) shows that the haversine test does not produce
consistent results. The test without rest period produces sinusoidal forces (stresses), whereas the
test with rest period produces almost haversine forces (stresses). As discussed earlier, haversine
forces result in tension at the bottom of the beam and compression at the top, whereas sinusoidal
forces result in reversible tension and compression at the top and bottom of the beam. Also,
alternating tensile and compressive stresses are equal to about half of the stress magnitude
produced by haversine forces even though both tests run under the same deformation waveform
and peak-to-peak value. Moreover, tensile stresses reduce the fatigue life of the beam, while
compressive stresses may actually heal micro cracks and prolong the fatigue life of the specimen.
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This implies that the haversine test with a rest period is more harmful to the beam than
the haversine test without rest period. Although the rest period helps in the healing process, the
haversine force bends the beam in one direction with almost double the magnitude of the case
without rest period. This produces too much tension at the bottom of the beam. Therefore, a
totally unfair comparison could result when comparing the tests with and without rest period in
As discussed earlier, the use of a haversine deflection-controlled fatigue test without rest period
(ASTM D-7460) produces inconsistent waveforms, which might produce erroneous fatigue
results. A more serious effect happens during the healing analysis when the results of the test
with rest period are compared to those of tests without rest period. Figure 9 shows examples of
fatigue test results using haversine deflection control with and without rest periods. Figure 9 (a)
shows that the test with a rest period, in some cases, resulted in faster damage (smaller stress
ratios) and lower fatigue life than the test without rest period, producing “negative healing.”
This, of course, is completely opposite to the main hypothesis of healing, which is based on the
premise that it is the rest period that “heals” the damage in the HMA and extends its fatigue life.
In other cases, beams subjected to rest periods started in the proper trend, where they had less
damage than beams without rest periods. However, these beams failed during the test as shown
Figure 10 shows examples of fatigue test results using sinusoidal deflection control.
Unlike the case of haversine waveforms, the figure shows that there is always less damage for
the test with a rest period as compared to the test without a rest period (positive healing). The
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figure also shows that the test with rest period results in a longer fatigue life than the test without
In the field, strain signals at the bottom of the asphalt layer may appear to look more like a
haversine than sinusoidal when a wheel load passes [17, 18]. Therefore, using a haversine
waveform in lab tests may initially appear to be more realistic. Based on the results of this study,
however, it is hard to simulate the field condition in the lab since the beam fatigue test with a
constant haversine deformation waveform will immediately change into a test with a sinusoidal
stress waveform. It is also important to note that only the asphalt mixture is tested in the lab
without consideration of the bottom foundation layers (base, subbase or subgrade). Hot-mix
asphalt is a viscoelastic material and in contrast with the road there is no ‘elastic’ foundation
support layer in the lab fatigue test to push the specimen back to its original position after the
load is removed [2]. Since neither the haversine waveform nor the sinusoidal waveform exactly
simulates the field condition, it is important to use sinusoidal waveforms to obtain consistent and
Deflection-controlled haversine and sinusoidal flexure beam fatigue test protocols are defined in
ASTM D-7460 and AASHTO T-321, respectively. This study attempts to optimize the test
conditions such as waveform type (haversine vs. sinusoidal), incorporating rest periods between
loading cycles, and the effect of rest period on the healing of the HMA. The following
to a new equilibrium neutral position of the beam after only a few cycles due to the
12
viscoelastic character of asphalt. Although the deflection input remains haversine, the
resulting stresses and strains follow a sinusoidal waveform, which bends the beam in both
2. The deflection-controlled haversine test produces erroneous fatigue results since the test
assumptions do not match the actual test conditions. The test calculations assume tension
at the bottom of the beam and compression at the top, while actually alternating tension
and compression at the top and bottom of the beam are developed with only half of the
stress magnitude. In addition to the incorrect stress magnitude, tension and compression
do not have the same effect on fatigue since tension reduces fatigue life and compression
3. The deflection-controlled sinusoidal test (AASHTO T-321) is more consistent than the
deflection-controlled haversine test (ASTM D-7460) since it produces the intended stress
4. For studies dealing with healing and endurance limit of HMA, when tests with and
without rest periods are compared, it is even more important to use a deflection-
controlled sinusoidal test (AASHTO T-321) in order to obtain a fair comparison and
5. Since neither the haversine waveform nor the sinusoidal waveform in the lab exactly
consistent results.
6. In the beam fatigue test on a viscoelstic material such as HMA, the loading machine
controls the deflection, not the strain. Because of the permanent deformation that occurs
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in the material, the strain does not match the deflection. Therefore, care should be taken
when referring to tests on viscoelastic materials. For example, the so-called haversine
Consideration of all of these conclusions leads the authors to strongly recommend that
the American Society of Testing and Materials (ASTM) changes the ASTM D-7460 designation
and test procedure to eliminate the deflection-controlled haversine waveform and replace it with
the deflection-controlled sinusoidal waveform. This change would ensure consistent and more
accurate fatigue test results which will have a considerable impact upon designing more
sustainable pavements.
Acknowledgement
The paper was prepared as a part of the NCHRP Project 9-44A, which is funded by the National
Cooperative Highway Research Program (NCHRP). Dr. Matthew Witczak’s general overview
guidance and valuable input to the manuscript are acknowledged and greatly appreciated.
References
1. Pronk A.C. Comparison of 2 and 4 point fatigue tests and healing in 4 point dynamic
bending test based on the dissipated energy concept”, 8th International Conference on
3. Al-Khateeb, G., and Shenoy, A. A Distinctive Fatigue Failure Criterion, Journal of the
Association of Asphalt Paving Technologists (AAPT), Vol. 73, 2004, pp. 585-622.
14
5. NCHRP Project 944-A, Validating an Endurance Limit for HMA Pavements: Laboratory
6. Carpenter, S.H., and Shen, S., Application of the Dissipated Energy Concept in Fatigue
Endurance Limit for Hot Mix Asphalt, Final NCHRP Report 646, NCHRP 9-38 Project,
8. Castro, M. and Sanchez, J.A., Fatigue and healing of asphalt mixtures: Discriminate
analysis of fatigue curves. Journal of Transportation Engineering, ASCE, Vol. 132, No.
pp.188-222.
10. Bonnaure, F., Huibers, A., and Boonders, A. A Laboratory Investigation of the Influence
pp.104-128.
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11. Bazin, P., and Saunier, J. Deformability, Fatigue and Healing Properties of Asphalt
12. Raithby, K.D. and A.B. Sterling, The Effect of Rest Periods on the Fatigue Performance
13. Kim, Y. R., Little, D. N., and Benson, F., Chemical and Mechanical Evaluation on
14. Jacobs, M. M. J., Crack Growth in Asphaltic Mixes. Ph.D. Thesis, Delft University of
15. Raithby, K.D. and A.B. Sterling., Some effects of loading history on the fatigue
performance of rolled asphalt. Transport and Road Research Laboratory (TRRL), Report
16. Abojaradeh, M. A., “Predictive Fatigue Models for Arizona Asphalt Concrete Mixtures,”
17. Al-Qadi, I.L., Yoo, P.J., Elseifi, M.A., and Janajreh, I., Effects of tire configurations on
18. Priest, A. L., Timm, D. H., Solaimanian, M., Gibson, N., and Marasteanu, M., A full-
19. H.Di Benedetto, Q.Nguyen, C.Sauzéat Nonlinearity, Heating, Fatigue and Thixotropy
during Cyclic Loading of Asphalt Mixtures, Road Materials and Pavement Design, VOL
Fig. 3. Number of Cycles vs. Stiffness Ratio with and without Rest Periods.
20
0.6 0.15
Force-
0.4 0.1
Output
Deflection, mm
0.2 0.05
Force, kN
0 0
-0.2 -0.05
-0.4 Deflection- -0.1
Input
-0.6 -0.15
1498.9 1499 1499.1 1499.2 1499.3 1499.4
Time
(a) Sinusoidal
(70F, 800 ms, 0 sec RP, Strain Controlled)
0.6 0.3
Deflection-
0.4 Input 0.2
Deflection, mm
0.2 0.1
Force, kN
0 0
-0.6 -0.3
1498.8 1499 1499.2 1499.4 1499.6 1499.8
Time, sec
(b) Haversine
Fig. 4. Force and Deflection vs. Time for Sinusoidal and Haversine Deflection Controlled Tests
without Rest Periods (800 microstrains, 21oC).
21
Force vs. Time (3 consecutive cycles)
(70F, 400 ms, 0 sec RP, Strain-Controlled, Haversine vs Sinusoidal)
0.8
0.4
Force, kN
Haversine
0
-0.4
Sinusidal
-0.8
1498.9 1499 1499.1 1499.2 1499.3 1499.4
Time
Fig. 5. Force vs. Time for Haversine and Sinusoidal Deflection-Controlled Tests without Rest
Periods (400 microstrains, 21oC).
22
Fig. 6. Neutral and Extreme Positions Using Sinusoidal and Haversine Waveform Deflection-
Controlled Test on HMA.
23
Fig. 7. Stresses, Strains and Deflections versus Time for Sinusoidal and Haversine Deflection-
Controlled Tests.
Force and Deflection vs. Time (3 consecutive cycles) 24
(70F, 800 ms, 5 sec RP, Strain-Controlled, Sinusoidal)
1.2 0.15
Force-
Deflection-
0.8 Output 0.1
Input
Deflection, mm
0.4 0.05
Force, kN
0 0
-0.4 -0.05
-0.8 -0.1
-1.2 -0.15
1499.0 1499.1 1504.1 1504.2 1509.2 1509.3
Deflection, mm
0.4
0.1
Force, kN
0.2
0 0
-0.2
Deflection- -0.1
-0.4
Input
-0.6
Force- -0.2
-0.8 Output
-1 -0.3
1498.8 1499.1 1499.4 1499.7 1500 1500.3
Time, sec
(b) Haversine
Fig. 8. Force and Deflection vs. Time for a Deflection Controlled Test with Sinusoidal and
Haversine Pulses with Rest Periods (800 microstrains, 21oC, 5 sec. Rest period).
25
Two Rest Period Levels Comparison
(at 400 ms, 40F)
0.8
Stiffness Ratio
0.6
Without rest period, 2 replicates
0.4
0.2
With 10 sec. rest period, 2 replicates
0
0 5000 10000 15000 20000 25000 30000
Cycles
Two Rest Period Levels Comparison
(a) 400 microstrains, 4C
(800 ms, 70F)
1
0.8
Stiffness Ratio
0.4
0.2
With 10 sec. rest period, 2 replicates
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
Cycles
Two Rest Period Levels Comparison
(b) 800 microstrains,
(800 ms, 100F)21C
1.2
0.8
0.6
0.4
0.2
With 10 sec. rest period, 2 replicates
0
0 5000 10000 15000 20000 25000 30000
Cycles
0.8
Stiffness Ratio
0.6 With 5 sec. rest period
0.4
0
0 5000 10000 15000
Cycles
Two (a)
Rest
800Perod Comparison
microstrains, 21C
(800 ms, 100F, Strain-Controlled, Sinusoidal)
1.2
With 5 sec. rest period
1
Stiffness Ratio
0.8
0.6
0.4
Without rest period
0.2
0
0 5000 10000 15000 20000 25000
Cycles
(b) 800 microstrains, 38C
Fig. 10. Examples of Beam Fatigue Test Results Using Sinusoidal Deflection-Control with and
without Rest Periods.