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The direct tension test was eliminated early in the SHRP fatigue lives in excess of 11 million cycles (37). Tests were also
A003-A research due to difficulties aligning and gripping the conducted that indicated that periodic overloads (loads cre-
specimens (2). However, research under the direction of Kim ating strain levels in excess of the endurance limit) would not
appears to have improved this technique (3133). Previous substantially reduce the fatigue life where the majority of
researchers noted that only a portion of a sample's dissipated the load cycles were less than the endurance limit (37). The
energy is most likely causing damage (34, 35). Daniel and Asphalt Institute conducted a study to identify the endurance
Kim (32) developed a method using a characteristic curve limit for the Asphalt Pavement Alliance (38, 39). Beam samples
from which fatigue life can be predicted rapidly from monot- were tested to a maximum of 4 million cycles. Extrapolations
onic uniaxial tension tests. A characteristic curve is generated support the presence of an endurance limit between 70 and
by modeling viscoelastic material behavior using Schapery's 100 ms.
correspondence principle, continuum damage mechanics, Shen and Carpenter (40) developed a new method for
and work potential theory. This method may be used to more determining/predicting the endurance limit. Their research
rapidly determine the endurance limit of a mixture. Uniaxial indicated a linear relationship between the log of the plateau
tension testing would not require the production of an HMA value of the ratio of dissipated energy curve (previously called
beam and instead would use a sample more closely related to DER) and the log of cycles to 50% initial stiffness for both
those being contemplated for simple performance tests related normal and low (below the endurance limit) strain levels.
to rutting. Further, they believe this methodology can be used to ex-
Maupin and Freeman (9) evaluated five simple tests to pre- trapolate the failure point for tests conducted in as little as
dict fatigue life. Indirect tensile test results were found to be 500,000 cycles. A tentative plateau value of 8.57E-9 was iden-
correlated to the coefficients used in standard equations to tified as indicating the endurance limit. This appears to be a
predict fatigue life in both constant stress and constant strain promising technique for analyzing the endurance limit.
modes of testing. Von Quintus has indicated that a long-life
pavement may be designed where the strain at the bottom
Modeling Fatigue and Relationship
of the asphalt layer is less than 1.0% of the indirect tensile
to Field Performance
strength failure strain. Thus, indirect tensile strength may
also provide a rapid screening tool to evaluate the endurance The NCHRP 1-37A Design Guide has instituted an
limit of a given mixture. enhanced version of the Asphalt Institute Model for fatigue
life (41). The enhancements were developed to better predict
the performance of thin pavements in a constant strain mode
Laboratory Studies to Quantify
of loading. With this model, pavement thickness will contin-
the Endurance Limit
ually increase with increasing design traffic loads. The litera-
As interest in long-life pavements grew, laboratory studies ture indicates a number of factors that must be accounted for
began to try to validate the existence of the endurance limit if an alternate approach for fatigue life determination, which
and develop methods of determining it for a given mixture. incorporates the endurance limit, is developed.
Ghuzlan and Carpenter (34) proposed the use of the dissipated Previous studies indicate a coefficient of variation of
energy ratio (DER) to define the existence of an endurance approximately 40% for beam fatigue tests (3, 30). This vari-
limit. The dissipated energy for a given fatigue cycle is calcu- ability must be accounted for when making fatigue life pre-
lated as the area of the stress-strain hysteresis loop (3, 35). DER dictions and extrapolations. Several methods for accounting
is simply the ratio of dissipated energy from one cycle to the for this variability have been proposed (30, 4244). For
next. During the course of a fatigue test, three regions of the fatigue-life predictions below the endurance limit, varia-
DER curve versus loading cycles may be identified: an ini- bility of design traffic estimates should also be considered
tial downward trend, a plateau with a nearly constant energy (30, 43). However, if a truly infinite fatigue life is estimated
input, and a failure region where the dissipated energy rapidly by the endurance limit, design traffic reliability may be of
increases which occurs at approximately 40% of the initial lesser importance. Harvey et al. (43) developed a method
stiffness (34, 35). Carpenter et al. (36) conducted additional that incorporates the variability from laboratory fatigue
beam fatigue tests in the range of 70 to 100 ms with samples tests, materials production, and construction. Material pro-
being tested to between 38 and 46 million cycles. They con- duction variability includes asphalt content and in-place air
cluded that low strain testing in the range of 70 ms resulted in voids. Construction variation is represented by variation in
"extraordinarily long fatigue life." Researchers at the Univer- pavement thickness and subgrade support. Monte Carlo sim-
sity of Illinois, under the direction of Carpenter, have con- ulation is used to estimate the combined affect of material
ducted a number of low strain beam fatigue tests that and construction variation. Savard et al. (44) report on a
indicated a break in fatigue life behavior for samples with French methodology to determine an acceptable strain limit
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based on variability in the fatigue tests and subgrade sup- Finally, in-service pavements tend to have longer fatigue
port. This methodology could be used to shift the measured lives than those indicated by laboratory tests. Thus, a shift
endurance limit for a mixture from a 50% reliability of the factor is applied to laboratory fatigue life to predict field
laboratory test data to an acceptable level of reliability for fatigue life (41, 4344, 4647). The shift factor is believed
the constructed pavement. to account for such things as the affect of rest periods and
Fatigue tests are typically conducted at 20°C. However, healing. Shift factors may range from 10 to 100 (43). Leahy
pavement damage varies with temperature and the result- et al. (46) recommended a shift factor of 10 for up to 10%
ing changes in stiffness of the HMA layers. Methodologies fatigue cracking in the wheel path. Harvey et al. (43) cali-
have been developed to shift fatigue life results at 20°C to brated shift factors for California conditions. The shift fac-
an equivalent annual or monthly temperature (30, 4345). tor calculated with their equation increases with decreasing
Overloads, or strain levels exceeding the endurance limit, are strain levels. A shift factor of 16.6 would be calculated for
most likely to occur either in the warmest summer months 70 ms. Pierce and Mahoney (47) note that Washington
(37) or when the spring thaw occurs, depending on environ- State uses shift factors between 4 and 10. Smaller shift fac-
mental conditions. tors are used for thicker pavements.
