Validating the Fatigue Endurance Limit for Hot Mix Asphalt (2010)

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7A review of the existing literature was conducted to answer the following specific questions: 1. What is an endurance limit? 2. What field or laboratory studies support the existence of an endurance limit? 3. What HMA material factors affect fatigue life and conse- quently might affect the endurance limit for different materials? 4. What are the best methods of measuring fatigue life in the laboratory? 5. What analysis methods should be used to analyze fatigue data in order to identify the endurance limit for a given mixture? A tremendous volume of literature was identified related to the factors affecting fatigue life, methods of measuring fatigue life, and analyzing fatigue data. Three very good summaries of this literature were identified, one by Epps and Monismith (1) produced in the early 1970s and two additional summaries produced as part of the Strategic Highway Research Program (SHRP) (2, 3). Therefore, an attempt was not made to sum- marize all of the references related to factors affecting fatigue life and fatigue measurement. Arguments for the Existence of the Endurance Limit Pavements have been designed primarily to resist rutting of the subgrade and bottom-up fatigue cracking. In classi- cal pavement design, as design load applications increase, pavement thickness must also increase. There is a growing belief that for thick pavements, bottom-up fatigue cracking does not occur. The concept of an endurance limit has been developed, representing a strain level resulting from a com- bination of HMA stiffness and thickness, below which bottom-up cracking will not initiate. Therefore, additional pavement thickness, greater than that required to keep strains below the endurance limit, would not provide addi- tional life. This concept has significant design and eco- nomic implications. The concept of the endurance limit was originally devel- oped for metals (4, 5). Barret et al. (5) describe the endurance limit for metals as being a stress below which, for uncracked materials, the plot of stress versus cycles to failure becomes essentially horizontal and fatigue does not occur. Figure 2.1 illustrates the theoretical concept of the endurance limit, as it would be applied to HMA. The concept of the endurance limit was first implemented for paving materials by the Portland Cement Association. An examination of fatigue tests conducted by various researchers on Portland cement concrete beams, discussed in Baladi and Snyder (6) and Huang (7), indicated that if the stress ratio is kept below 0.45, the concrete will have an essentially infinite fatigue life. The stress ratio was defined as the ratio of stress induced in the concrete pavement to the concrete’s modulus of rupture. A maximum of 10 million cycles to failure was used for the majority of this testing (one sample was tested to approximately 20 million cycles) (Fig- ure 2.2). Monismith and McLean (8) first proposed an endurance limit of 70 micro-strain (ms) for asphalt pavements. It was observed that the log-log relationship between strain and bending cycles converged below 70 ms at approximately 5 million cycles. Maupin and Freeman (9) noted a similar convergence. Using low-strain design principles, Monismith and McLean (8) designed a pavement structure that increased the fatigue life of the pavement from 12 to approximately 19-plus years. In the field, Nunn (10) in the United Kingdom (UK) and Nishizawa et al. (11) in Japan proposed concepts for long-life pavements for which classical bottom-up fatigue cracking would not occur. Nunn (10) defines long-life pavements as those that last at least 40 years without structural strengthen- C H A P T E R 2 State of Practice

81 10 100 1000 1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000 ,000,000 Number of Cycles to 50% Stiffness Ta rg et M ic ro S tra in Endurance Limit Figure 2.1. Idealized concept of the endurance limit. Source: Huang, Yang, H., Pavement Analysis and Design, 2nd ed., © 2004, p. 317. Reprinted by permission of Pearson Education, Inc. Upper Saddle River, NJ. Figure 2.2. Illustration of endurance limit for concrete pavements (7). ing. The UK’s pavement design system was based on experi- mental roads that had carried up to 20 million standard axles. When this study was conducted, these relationships were being extrapolated to more than 200 million standard axles. Nunn (10) evaluated the most heavily traveled pavements in the UK, most of which had carried in excess of 100 million standard axles to evaluate the then current design system. Nunn (10) concluded the following: • For pavements in excess of 7.1 in. (180 mm) thick, rutting tended to occur in the HMA layers. • Surface initiated cracking was common in high-traffic pavements, but there was little evidence of bottom-up fatigue. Surface initiated cracks tended to stop at a depth of 4 in. (100 mm). • It was observed that the stiffness of thick pavements was increasing with time, most likely due to binder aging. This would not tend to occur if the pavement was weakening due to accumulated damage. • A minimum thickness for a long-life pavement was recom- mended as 7.9 in. with a maximum thickness of 15.4 in. This range is based on a variety of factors such as binder stiffness.

Nishizawa et al. (11) reported an endurance limit of 200 ms based on the analysis of in-service pavements in Japan. Simi- larly, strain levels at the bottom of the asphalt layer of between 96 and 158 ms were calculated based on back-calculated stiff- ness data from the falling-weight deflectometer for a long-life pavement in Kansas (12). Others (13, 14) report similar find- ings, particularly, the absence of bottom-up fatigue cracking in thick pavements and the common occurrence of top-down cracking. Factors Affecting Fatigue Life A significant amount of fatigue research was conducted in the 1960s and 1970s. Epps and Monismith (1) provide a summary of the effects resulting from binder stiffness, asphalt content, aggregate type, aggregate gradation, and air void content. Table 2.1 indicates the relative affects of these components. The authors conclude that binder stiffness and air void content have a larger influence on fatigue life than aggregate type and gradation. The SHRP A-404 research (3) noted that angular aggregates tended to produce both stiffer mixes and longer fatigue lives. Harvey and Tsai (15) evaluated the effect of air voids and asphalt content on fatigue life. In most previous evaluations, a constant com- paction effort was used to produce samples. This results in air voids being highly correlated with the asphalt content of a given mix in which case there is little relationship between asphalt content and fatigue life. In this instance, specific air void levels were targeted, resulting in relationships between fatigue life and both air void content and asphalt content. Voids filled with binder (VFB) have been a typical parame- ter used in fatigue life prediction equations. Harvey and Tsai (15) caution against the use of VFB since various combina- tions of air voids and asphalt content will produce the same VFB. Maupin and Freeman (9) note that there was little increase in fatigue life resulting from an increase of 0.5% binder, but significant increases were seen with an increase of 1.0% binder. Strategies to Produce Long-Life Pavements A number of strategies have been put forth to promote the likelihood of constructing a long-life pavement, including: polymer modification, rich bottom layers, and high-modulus asphalt bases. Polymer Modification Fatigue testing and analyses of asphalt mixtures made with modified asphalt binders has been performed in sev- eral studies. In 1988, Goodrich presented an early study on the fatigue performance of polymer modified mixes (17). In this study, three unmodified asphalt binders with different tem- perature susceptibilities and two modified asphalt binders— produced using one base asphalt and two levels of modification 9 Effect of Change in Factor Factor Change in Factor On Stiffness On Fatigue Life in Controlled Stress Mode of Test On Fatigue Life in Controlled Strain Mode of Test Asphalt Penetration decrease increase increase decrease Asphalt Content increase increasea increasea increaseb Aggregate Type increase in rough texture and angularity increase increase decrease Aggregate Gradation open to dense increase increase decreased Air Void Content decrease increase increase increased Temperature decrease increasec increase decrease Notes: aReaches optimum level above that required by stability considerations. bNo significant amount of data; conflicting considerations of increase in stiffness and reduction of strain in asphalt make this speculative. cApproaches upper limit at temperature below freezing. dNo significant amount of data. Table 2.1. Factors affecting the stiffness and fatigue behavior of hot mix asphalt (16 in 1).

(not identified)—were evaluated using mixture fatigue tests. The intent was to correlate binder properties with mixture fatigue performance. Laboratory testing was conducted using flexural beam fatigue at 25°C and 1.67 Hz loading frequency in controlled stress mode. Tests were conducted at an initial strain level of 400 ms, and findings indicated that the fatigue lives of the two modified asphalt binders were an order of magnitude greater than the fatigue life of one of the unmod- ified asphalt binders (produced from the same source as the base asphalt used to create the modified asphalt binders). The base asphalt properties appear to be important in the perform- ance of the modified asphalt binders. Mixtures made with one unmodified asphalt binder with low temperature susceptibil- ity, had approximately two to three times the fatigue life of the polymer modified mixtures. During the Strategic Highway Research Program (SHRP), the A-003A contractor evaluated the use of the flexural beam fatigue test as a mixture performance test for fatigue. The modified asphalt mixtures experiment (MAME), described in SHRP Report A-404, was performed to determine if the fatigue characteristics of modified mixtures could be evalu- ated using the flexural beam fatigue test (18). Asphalt mixtures were made using one aggregate source, three asphalt binders (AAF-1, AAG-1, and AAK-1), and three modifiers (identified as M-405, M-415, and M-416). Test results indicated that the addition of modifier M-405 to each of the three asphalt binders decreased the fatigue life compared to the unmod- ified asphalt mixes. The addition of modifiers M-415 and M-416 had a negative effect on the fatigue life of mixes made with AAG-1, but substantially increased the fatigue life (by approximately three to five times) of mixtures made with AAK-1 compared to the unmodified mixtures. A validation study was performed using slab wheel track tests on mixtures made with AAG-1 and the three modifiers. Although the results were similar for the M-405 modifier (decrease in fatigue life), the M-415 and M-416 modifiers resulted in an increase in fatigue life from the slab wheel track test. This was contrary to the findings of the flexural beam fatigue tests. Shortly after the implementation of the Superpave performance-graded asphalt binder tests and specification, users recognized that the properties of modified asphalt binders may not be characterized properly using the Super- pave binder tests. This led to the funding of NCHRP Project 9-10, “Superpave Protocols for Modified Asphalt Binders,” in 1996. The research (19) was conducted by the University of Wisconsin-Madison, Asphalt Institute, and NCAT, under the direction of Hussain Bahia. The NCHRP 9-10 research evaluated the effectiveness of the intermediate temperature stiffness requirement (G*sin δ ≤ 5000 kPa) by performing flexural beam fatigue tests on four aggregate structures (gravel and limestone, coarse and fine gradation) using nine different modified asphalt binders. Testing was conducted on mixtures using 10 Hz sinusoidal loading with a peak-to-peak strain of 800 ms. The test tem- perature was selected for each mixture as the temperature where the intermediate temperature requirement was met (G*sin δ = 5000 kPa). So, unlike other studies in which the temperature was fixed (usually at 20°C), the viscous compo- nent of the shear modulus was fixed. A brief examination of the data in the report indicates that the fatigue lives of the modified mixtures could be signifi- cantly different. Mixtures made with a PG 82-22 asphalt binder produced using a radial styrene-butadiene-styrene (SBS) modifier had fatigue lives at 24°C that were two to five times the fatigue lives (tested at 32°C) of mixtures made with an unmodified (oxidized) PG 82-22 asphalt binder. Since the G*sin δ value was the same for each of these mixtures at their respective test temperatures, the researchers considered the intermediate temperature criterion in the PG binder specifi- cation to be inadequate for assessing the fatigue characteris- tics of asphalt binders. A temperature equivalency experiment conducted during SHRP (18) indicated a strong relationship between temper- ature and fatigue life at a given strain level, with fatigue life decreasing as the temperature decreased. Thus, it could be hypothesized that the difference in fatigue life between the SBS-radial modified PG 82-22 mixtures and the oxidized PG 82-22 mixtures would be greater if the test temperatures had been equal. Monismith et al. (20) reported on the development of the design and specifications for the California I-710 rehabilita- tion. In the study, AR-8000 (roughly equivalent to a PG 64-10 or PG 64-16) and PBA-6a (PG 64-40) asphalt binders were used to prepare mixtures for testing. When tested at 20°C using the procedure described in AASHTO T321, the mea- sured fatigue life of the PBA-6a mixtures was approximately an order of magnitude (10 times) greater than the fatigue life of the AR-8000 mixtures. This relationship seemed to be affected by the applied strain resulting in an increased dif- ference between the two sets of fatigue lives at higher strain levels. Lee et al. (21) reported on a laboratory evaluation of the effects of aggregate gradation and binder type on mixture fatigue life. Using uniaxial tension fatigue test results (con- ducted at 25°C) and a viscoelastic fatigue model, the authors calculated that mixtures made with an SBS-modified PG 76-22 asphalt binder had 10 times greater fatigue life than mixtures made with an unmodified asphalt binder, regardless of aggre- gate gradation. Research performed in 2002 by the Asphalt Institute for the Asphalt Pavement Alliance evaluated the possibility of a fatigue endurance limit by testing mixtures made with two asphalt binders (PG 64-22 and PG 76-22) and two asphalt binder contents at various strain levels. The results, shown in 10

Figure 2.3, indicate that the mixtures made with the PG 76-22 asphalt binder have approximately an order of magnitude (i.e., 10 times) greater fatigue life than the mixtures made with the PG 64-22 asphalt binder. Von Quintus (23) conducted a study to quantify the effects of polymer modified asphalts. Based on a literature review, Von Quintus reported that PMA mixtures generally last about 25% longer than conventional mixtures. Some premature failures caused concern. However, most of the failures were “ . . . found to occur prior to the adoption of the Performance Graded (PG) binder specification and can be traced back to inferior con- struction (for example, high air voids), inferior materials, and/or inadequate design thickness.” The study also notes “One of the more important findings from the recent field experiments is that many of the PMA pavements are not exhibiting fatigue cracking or have less load-related crack- ing than the control sections (unmodified mixtures).” In summary, there appears to be significant historical data indicating that the laboratory fatigue performance of modi- fied asphalt mixtures is greater than mixtures made with unmodified asphalt binders. In some reported cases, modi- fied asphalt mixtures have exhibited an order of magnitude greater fatigue life compared to unmodified asphalt mix- tures. The fatigue characteristics appear to be dependent on the base asphalt binder used for modification. Rich Bottom Layers The concept of a rich bottom layer originated from the Australian experience (24) and was explored during SHRP experiments. Two potential benefits are created through the use of a rich bottom layer: increased asphalt binder con- tent and decreased air voids in the bottom layer (as a result of easier compaction created by the additional asphalt binder). Several known literature sources confirm the rationale for these concepts. In the mix design fatigue experiment reported in SHRP Report A-404, one asphalt-aggregate mixture (RB aggregate and AAG-1 asphalt binder) was used to prepare specimens at three different levels of air voids and two different levels of asphalt binder content (4.5 and 6.0%). The effect of asphalt binder content on fatigue life was a primary focus of this study since the 8 × 2 expanded test program experiment did not evaluate asphalt binder content as a variable. A separate 2 × 2 pilot test program used two asphalt binder contents defined as optimum and high—with the high asphalt binder content established as 0.6% higher than the optimum asphalt binder content. For the 2 × 2 pilot test program, a statistical analysis of results from flex- ural beam fatigue (controlled stress and controlled strain) and other tests indicated that asphalt content did not signifi- cantly affect fatigue life (18). The results of the mix design fatigue experiment indicate that asphalt binder content significantly affected flexural stiff- ness (decreasing by 8% as asphalt binder content increased) and fatigue life—increasing the fatigue life by 67% as the asphalt binder content increased from 4.5% to 6%. As in other experiments, increasing the air void content resulted in a decrease in flexural stiffness of 33% and a decrease in fatigue life by 45% as air voids increased from 4% to 8% (18). Harvey and Tsai (25) conducted a study on the effects of asphalt content and air void content on mixture fatigue and stiffness. Samples were produced at five asphalt contents: 4.0%, 4.5%, 5.0%, 5.5%, and 6.0% by weight of aggregate and three ranges of air voids: 1% to 3%, 4% to 6%, and 7% to 9%. In this experiment, a constant compaction effort was not used, so air voids were independent of asphalt content. Con- stant strain tests were performed at two strain levels: 300 and 150 ms. Analysis of the data indicated that higher asphalt con- tent and lower air voids resulted in longer fatigue lives. Lower asphalt content and lower air voids resulted in higher initial stiffness. Instead of using stiffness in mixture fatigue life pre- diction models, the authors recommended evaluating the 11 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 10 100 Strain (x10-6) Cy cl es to F ai lu re 64-22 Opt 64-22 Opt+ 76-22 Opt 76-22 Opt+ 1,000 Figure 2.3. Fatigue life comparison for modified and unmodified mixes (22).

laboratory fatigue life and then predicting pavement perform- ance by incorporating the effect of mixture stiffness on the predicted pavement strains resulting from layered elastic analysis. Using this methodology, the authors show the poten- tial benefits of a rich bottom layer. It is also important to rec- ognize that lower in-place air voids increase stiffness while resulting in longer fatigue lives, opposite conventional wis- dom that suggests that stiffer mixes have shorter fatigue lives. Monismith et al. (20) reported on the development of the design and specifications for the California I-710 reha- bilitation. In their study, AR-8000 (roughly equivalent to a PG 64-10 or PG 64-16) and PBA-6a (PG 64-40) asphalt binders were used to prepare mixtures for testing at two com- binations of asphalt binder content and air void content. Mixes were prepared with 0.5% higher asphalt binder content and 3% lower air voids. When tested at 20°C using the proce- dure described in AASHTO T321, the measured fatigue life of the mixes with 0.5% higher asphalt binder content (and lower air void contents) was approximately two times the fatigue life of mixes prepared at lower asphalt binder content. Anderson and Bentsen (26) reported on a study evaluating the influence of voids in mineral aggregate (VMA) on mix- ture performance. Since VMA is related to asphalt binder content, mixtures with high VMA had asphalt binder con- tents that were approximately 1.0% higher than the low VMA mixtures. Flexural beam fatigue testing conducted at 20°C and 500 ms indicated that the mixes with the higher asphalt binder contents had two times greater laboratory fatigue life than the low asphalt binder content mixes. Harvey et al. (24) reported on California’s experiences with the design and construction of long-life asphalt pavements. The authors reported that most full-depth asphalt long-life designs will include a stiff, fatigue-resistant bottom layer. This layer, termed a rich bottom layer, is designed to have a very low air void content (approximately 0% to 3%). Stiffness of the layer is a consideration since it is intended to reduce the over- all thickness of the HMA layers. The low air void content also reduces permeability and improves moisture resistance. The benefit of rich bottom layers is maximized with a thickness range of 50 mm to 75 mm. Illinois has also adopted this concept (14). Generally the stiffness of a mix can be increased with increased compaction. Further, increased compaction gen- erally increases fatigue life at the same strain level. Thus, increased compaction specifications for lower lifts result in both lower strains due to increased stiffness and also increased fatigue life for a given strain level, producing a more eco- nomical pavement. The unbound layers must be sufficiently stiff to allow a high degree of compaction in the bottom HMA layers. A study conducted by Maupin (27) examined the impact of asphalt content on durability of Virginia surface mixtures. Testing was conducted on 9.5-mm and 12.5-mm nominal maximum aggregate size (NMAS) mixtures to examine the effect of increasing asphalt binder content. Flexural beam fatigue tests conducted at 600 ms indicated a slight increase in fatigue life with the 0.5% higher asphalt content. A sub- stantial increase in fatigue life was noted with 1.0% higher asphalt content. High Modulus Base Europeans have used stiff binders to produce high modu- lus base layers (10, 14, 28, 29). Corte (28) reported on the use of high modulus asphalt mixtures in France. The first use of high-modulus asphalt concrete (HMAC) occurred around 1980. Initially, these mixtures were used for strengthening or rehabilitation where pavement thickness was constrained (for instance by bridge clearance). The use increased in 1985. It was found that locally available weak aggregates could be used with stiff binders. These mixtures were designed with relatively high asphalt binder content and low voids (less than 6%). Constant strain fatigue tests indicate that HMAC mixes are more fatigue resistant than conventional base mixtures. This is believed to be due to the higher asphalt con- tent and lower voids found in the HMAC mixtures. Corte’s findings match the findings in similar studies where lower air voids increase stiffness, but also appear to increase fatigue life (20, 21). The stiffness of these layers reduce the strain at the bottom of the asphalt layer using less thickness than conventional asphalts. Cracking can be a problem with these mixes. Corte (28) discusses binder tests to minimize the like- lihood of cracking. Laboratory Fatigue Tests and Analysis Methods The SHRP A003-A project (2, 3) evaluated seven methods of measuring laboratory fatigue life. Repeated load flexure and direct tension tests received the highest rankings. A methodology was developed to evaluate fatigue life using flexural beam fatigue tests conducted in constant strain mode at 10 Hz. Thin pavements are generally subjected to a mode of loading best represented by constant strain. Thick pave- ments are generally represented by a mode of loading most closely represented by constant stress. However, the SHRP A003-A researchers recommended constant strain tests for all pavement loading conditions. This recommendation was based upon the fact that if fatigue evaluations are made in the context of the pavement structure (e.g. by calculating expected strains at the bottom of a given pavement structure), then constant stress and constant strain tests give similar rank- ings (3, 25, 30). AASHTO T321 is the current standard for beam fatigue tests. 12

The direct tension test was eliminated early in the SHRP A003-A research due to difficulties aligning and gripping the specimens (2). However, research under the direction of Kim appears to have improved this technique (31–33). Previous researchers noted that only a portion of a sample’s dissipated energy is most likely causing damage (34, 35). Daniel and Kim (32) developed a method using a characteristic curve from which fatigue life can be predicted rapidly from monot- onic uniaxial tension tests. A characteristic curve is generated by modeling viscoelastic material behavior using Schapery’s correspondence principle, continuum damage mechanics, and work potential theory. This method may be used to more rapidly determine the endurance limit of a mixture. Uniaxial tension testing would not require the production of an HMA beam and instead would use a sample more closely related to those being contemplated for simple performance tests related to rutting. Maupin and Freeman (9) evaluated five simple tests to pre- dict fatigue life. Indirect tensile test results were found to be correlated to the coefficients used in standard equations to predict fatigue life in both constant stress and constant strain modes of testing. Von Quintus has indicated that a long-life pavement may be designed where the strain at the bottom of the asphalt layer is less than 1.0% of the indirect tensile strength failure strain. Thus, indirect tensile strength may also provide a rapid screening tool to evaluate the endurance limit of a given mixture. Laboratory Studies to Quantify the Endurance Limit As interest in long-life pavements grew, laboratory studies began to try to validate the existence of the endurance limit and develop methods of determining it for a given mixture. Ghuzlan and Carpenter (34) proposed the use of the dissipated energy ratio (DER) to define the existence of an endurance limit. The dissipated energy for a given fatigue cycle is calcu- lated as the area of the stress-strain hysteresis loop (3, 35). DER is simply the ratio of dissipated energy from one cycle to the next. During the course of a fatigue test, three regions of the DER curve versus loading cycles may be identified: an ini- tial downward trend, a plateau with a nearly constant energy input, and a failure region where the dissipated energy rapidly increases which occurs at approximately 40% of the initial stiffness (34, 35). Carpenter et al. (36) conducted additional beam fatigue tests in the range of 70 to 100 ms with samples being tested to between 38 and 46 million cycles. They con- cluded that low strain testing in the range of 70 ms resulted in “extraordinarily long fatigue life.” Researchers at the Univer- sity of Illinois, under the direction of Carpenter, have con- ducted a number of low strain beam fatigue tests that indicated a break in fatigue life behavior for samples with fatigue lives in excess of 11 million cycles (37). Tests were also conducted that indicated that periodic overloads (loads cre- ating strain levels in excess of the endurance limit) would not substantially reduce the fatigue life where the majority of the load cycles were less than the endurance limit (37). The Asphalt Institute conducted a study to identify the endurance limit for the Asphalt Pavement Alliance (38, 39). Beam samples were tested to a maximum of 4 million cycles. Extrapolations support the presence of an endurance limit between 70 and 100 ms. Shen and Carpenter (40) developed a new method for determining/predicting the endurance limit. Their research indicated a linear relationship between the log of the plateau value of the ratio of dissipated energy curve (previously called DER) and the log of cycles to 50% initial stiffness for both normal and low (below the endurance limit) strain levels. Further, they believe this methodology can be used to ex- trapolate the failure point for tests conducted in as little as 500,000 cycles. A tentative plateau value of 8.57E-9 was iden- tified as indicating the endurance limit. This appears to be a promising technique for analyzing the endurance limit. Modeling Fatigue and Relationship to Field Performance The NCHRP 1-37A Design Guide has instituted an 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 of loading. With this model, pavement thickness will contin- ually increase with increasing design traffic loads. The litera- ture indicates a number of factors that must be accounted for if an alternate approach for fatigue life determination, which incorporates the endurance limit, is developed. Previous studies indicate a coefficient of variation of approximately 40% for beam fatigue tests (3, 30). This vari- ability must be accounted for when making fatigue life pre- dictions and extrapolations. Several methods for accounting for this variability have been proposed (30, 42–44). For fatigue-life predictions below the endurance limit, varia- bility of design traffic estimates should also be considered (30, 43). However, if a truly infinite fatigue life is estimated by the endurance limit, design traffic reliability may be of lesser importance. Harvey et al. (43) developed a method that incorporates the variability from laboratory fatigue tests, materials production, and construction. Material pro- duction variability includes asphalt content and in-place air voids. Construction variation is represented by variation in pavement thickness and subgrade support. Monte Carlo sim- ulation is used to estimate the combined affect of material and construction variation. Savard et al. (44) report on a French methodology to determine an acceptable strain limit 13

based on variability in the fatigue tests and subgrade sup- port. This methodology could be used to shift the measured endurance limit for a mixture from a 50% reliability of the laboratory test data to an acceptable level of reliability for the constructed pavement. Fatigue tests are typically conducted at 20°C. However, pavement damage varies with temperature and the result- ing changes in stiffness of the HMA layers. Methodologies have been developed to shift fatigue life results at 20°C to an equivalent annual or monthly temperature (30, 43–45). Overloads, or strain levels exceeding the endurance limit, are most likely to occur either in the warmest summer months (37) or when the spring thaw occurs, depending on environ- mental conditions. Finally, in-service pavements tend to have longer fatigue lives than those indicated by laboratory tests. Thus, a shift factor is applied to laboratory fatigue life to predict field fatigue life (41, 43–44, 46–47). The shift factor is believed to account for such things as the affect of rest periods and healing. Shift factors may range from 10 to 100 (43). Leahy et al. (46) recommended a shift factor of 10 for up to 10% fatigue cracking in the wheel path. Harvey et al. (43) cali- brated shift factors for California conditions. The shift fac- tor calculated with their equation increases with decreasing strain levels. A shift factor of 16.6 would be calculated for 70 ms. Pierce and Mahoney (47) note that Washington State uses shift factors between 4 and 10. Smaller shift fac- tors are used for thicker pavements. 14