Ghuzlan, Carpenter

Traditional Fatigue Analysis of Asphalt Concrete Mixtures Submitted for Presentation and Publication by the Transportation Research Board At the 2003 Annual Meeting, January 2003 By Khalid A. Ghuzlan1 California Department of Transportation (Caltrans) Materials Engineering and Testing Services, Mail Station 5 5900 Folsom Blvd Sacramento, CA 95819 (916)-227-5848 [email protected] Samuel H. Carpenter Civil and Environmental Engineering Department University of Illinois at Urbana-Champaign 1206 Newmark CE Lab 205 N. Mathews Avenue Urbana, IL 61801 (217) 333-4188 [email protected]

Number of Words: 4600 + 8*250 = 6600 Number of Words in the Abstract: 245 Key Words: Traditional Fatigue Analysis, K1-K2 Relation, Asphalt Concrete Fatigue, S-N Approach, Fatigue Life, Flexural Fatigue Testing.

August, 2002

1

Corresponding author

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ABSTRACT Fatigue cracking is the accumulation of damage under repeated load applications in an asphalt pavement. Fatigue life is commonly defined as the number of load cycles to fail the asphalt concrete at strain (stress) occurring at the bottom of the asphalt layer. This approach of studying fatigue is known as the phenomenological or the S-N approach (Stress-Number of cycles to failure). This paper focuses on the traditional fatigue analysis using the S-N approach. Factors affecting fatigue response of asphalt concrete mixtures are investigated. The relation between the fatigue coefficients K1 and K2 in the traditional fatigue formula is discussed with emphasis on factors that may have effect on this relation. Furthermore, the K1K2 relation obtained from this study is compared with other studies. A large fatigue database of laboratory testing was developed to achieve these goals. Flexural fatigue testing was performed on about 480 asphalt concrete samples. Both modes of loading, controlled stress and controlled strain, and two testing temperatures are considered in this study. Findings of this study show that there is a high correlation between K1 and K2. The K1-K2 relation was found to be significantly affected by mode of loading, testing temperature and asphalt content in the mixture. Recommendations are made about the need for further study of the K1-K2 relation and factors affecting it. It was also recommended to investigate the possibility of using a simple test to predict the fatigue response of asphalt concrete mixtures.

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INTRODUCTION There are three major distresses in asphalt concrete pavements: fatigue cracking, permanent deformation, and thermal cracking. Fatigue cracking is the structural distress traditionally used for the actual structural design of a pavement. Fatigue is a phenomenon in which a pavement is subjected to repeated stress of levels less than the ultimate failure stress. Hveem (1) was one of the first researchers who reported fatigue failure caused by repeated loading on asphalt pavement over highly resilient soils. Hveem concluded there was a correlation between observations of cracking, fatigue type failures in bituminous pavements, and the measured repeated deflections that the pavement must undergo with each passing wheel. The capability of withstanding deflections is fatigue resistance. Fatigue properties are derived thorough testing in the laboratory. This laboratory data for fatigue behavior can be described by using phenomenological formulas or by fracture mechanics principles.

COMMON TYPICAL FATIGUE REPRESENTATION Fatigue life is commonly defined as the number of load cycles to fail the asphalt concrete specimen at a strain (stress) occurring at the bottom of the asphalt layer. Typically, fatigue life is shown by plotting the stress or strain at the initial load cycles at the bottom of the asphalt concrete layer versus number of load cycles to failure as shown in Figure 1. This approach of studying fatigue is known as the phenomenological or the S-N approach (stress-number of cycles to failure), (2, 3, 4, 5, 6, 7). The S-N approach was widely used in conjunction with Miner’s linear law of cumulative damage because of its simplicity (8). To overcome some limitations of these models, the modulus of the mix was introduced into the fatigue relation to account for the variation in load frequency and temperature (9,10). This representation of fatigue performance is dependent on the mode of loading. The failure criterion used to interpret fatigue test results is a very important factor in establishing fatigue life. In controlled stress testing conditions, failure is generally defined as the breaking of the sample. On the other hand, in controlled strain testing conditions, failure is defined at a specific percentage of reduction in modulus; a 50% reduction is typically used.

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FATIGUE MODELS There are several phenomenological fatigue models developed to predict fatigue cracking. Fatigue models are divided into two main types, the strain-based models and the strain modulus based models. These models use a relation between the radial strain at the bottom of the asphalt concrete layer and the number of load applications to crack appearance in the pavement. This relation can be expressed in the following form (11): Nf = K1 (1/ εo)K2 The fatigue coefficients K1 and K2 vary from one model to another. Usually, K2 value vary in a range between 3 and 6 while K1 may vary by several magnitudes. In some models the strain is replaced by the stress. Finn et al. (12) found that fatigue behavior is affected not only by strain but also by the modulus of the HMA. They proposed the following fatigue formula: Nf = K( ε)a (E*) b Where E* is the dynamic stiffness modulus of the HMA. Introducing the dynamic stiffness modulus into the fatigue relation quantifies some of the HMA temperature variations. These models are calibrated by applying shift factors based on observed field performance. Ideally laboratory fatigue tests should simulate field conditions. In reality this is almost impossible to do, because there are so many variables in the field that can not easily considered in laboratory testing, such as specimen fabrication, compound loading, random rest periods, and the multi stress state. Some laboratory tests simulate some of these variables but not all of them at the same time. Pell (11) reported the shift factor varied between 5 and 700. This paper focuses on the traditional fatigue analysis using the S-N approach. The K1-K2 relation in the traditional fatigue relation is discussed with emphasize on factors that may have effect on this relation. Furthermore, the K1-K2 relation obtained from this study is compared with other studies. A large fatigue database of laboratory testing was developed in this study to achieve these goals

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MATERIALS A wide variety of asphalt concrete mixtures were tested to examine the fatigue behavior of asphalt concrete at different conditions. These mixtures represent typical asphalt concrete mixtures used in different parts of the State of Illinois, United States and overseas along with especially formulated laboratory mixtures. More than 470 flexure beam fatigue tests were performed in this study. Both controlled stress and controlled strain testing were used to study the fatigue behavior of asphalt mixtures. The 84 asphalt mixtures in Table 1 represent 10 different sources. There are three main sets of data are included in this study, the Illinois DOT, Dubai and the Aggregate Interlock sets of data. The Illinois DOT set contains 25 mixtures obtained from trucks (at field). Two air void levels were targeted, 7 and 4 percent to represent the pavement after construction and after been trafficked several years. Dubai mixtures were designed and mixed at Dubai in the United Arab Emirates. Thirty mixtures are included in this group with 4 asphalt types, 2 aggregate types and 8 gradations. Finally, the Aggregate Interlock set of data, which including eight mixtures. Mixtures in this group were prepared with precise gradation control. One asphalt binder and aggregate source were used with constant asphalt content for all mixtures.

FATIGUE TESTING Sample Preparation Laboratory fatigue testing was performed on all asphalt mixes at the Advanced Transportation Research and Engineering Laboratory (ATREL) at the University of Illinois. Mixes were heated then compacted using a Rolling Wheel Compactor (RWC). The RWC was used to compact the specimens into asphalt concrete bricks measuring 375mm × 125mm × 75mm. RWC applies vertical pressure to the specimens by means of a rolling wheel with a moving table. After compaction, volumetric were checked for every compacted brick to determine air void content. The target density was checked 93 % or 96 % of theoretical maximum, corresponding to 7 % and 4% air voids to compare to field conditions immediately after construction and after years of being open to traffic respectively. The asphalt concrete bricks were cut to obtain two beams for each brick using diamond masonry saw.

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Beam Fatigue Equipment Digitally controlled, pneumatic beam fatigue equipment was used to test the asphalt concrete beams. The equipment consists of three main components: testing frame, environmental chamber, and control data and acquisition system (CDAS). The environmental chamber encloses the testing frame and specimens. All tests were conducted as specified in SHRP standards at 20° C (one group was tested at 20° C & 35° C), (13). Temperature transducers were used to measure the temperature at both skin and core of a representative specimen. The testing frame is completely self-contained. Digital closed loop servopneumatic controlled third point loading frame which satisfies the AASHTO TP8-94. The loading system operates under a position feedback control. This control system automatically adjusts the output waveform to match the input waveform allowing for a very precise control. The (CDAS) with a personal computer, controls the load deformation during testing as it collects the data.

Test Conditions Asphalt concrete specimens were stored in the chamber for at least two hours for temperature conditioning. Two modes of loading were considered in this study, controlled strain mode and controlled stress. The following parameters were used in the fatigue equipment: . Mode of loading: constant-strain, constant stress. . Wave shape: haversine in the controlled strain testing and sine in the controlled stress mode. . Load pulse width: 100 ms (10 Hz). . No rest period. . Temperature: 20° C (group “D” was tested at two temperatures 20° C and 35° C). All results based on controlled strain testing with exception to four mixtures where the controlled stress mode was used. These mixtures are the IDOT mixtures number 6, 10, 13 and I-88. At least four specimens were tested to establish a representative fatigue curve. Testing was conducted at varying strain (stress) levels to generate a fatigue curve for the material.

FATIGUE COEFFICIENTS (K1-K2) The most important variables from the fatigue test are the intercept and the slope of the fatigue curve, K1 and K2 respectively, as it is shown in Figure 1. These variables represent the material properties

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of the mixture in constant strain fatigue and both K1 and K2 are representative of typical values for hot mix asphalt. The fatigue coefficients K1 and K2 are experimentally determined and are used in the fatigue based mechanistic design procedures. It was emphasized that field calibration models and performancederived models are structural model dependent. Therefore, different K1 and K2 values may be established for the same asphalt concrete mixture, depending on the type of the structural model been used. Large range of variability was noted in the values of K2. Typical range of K2 values are between 3 and 6 (14). Based on the database of fatigue testing carried out in this study it was noted most of the slopes of the fatigue curves (K2) are within this range. As shown in Table 2 .the minimum K2 value obtained in this database is 3.37 while the maximum K2 value is 6.13 and the average K2 value for all mixtures tested in this study is 4.36. In some fatigue models K2 was fixed to a specific number, as in the Asphalt Institute and Illinois fatigue equations where the K2 value is fixed to 3.29 and 3.0 respectively. In fact, the K2 value in Illinois’s fatigue equation is very conservative. Based on the fatigue data of the IDOT mixtures published in this paper the K2 value was raised to 3.25 for the rubberlized sections. It is should be noted small change in the slope of the fatigue relation K2 has great effect on the fatigue life. K1 values vary by several orders magnitude. The minimum and the maximum K1 values obtained in this study are 3.98E-15 and 1.247E-7 respectively. The huge difference between these two values shows the wide range of variability in K1 values.

CALCULATING THE K1 AND K2 FROM OTHER TESTS The Indirect Tensile Test (ITT) was used to evaluate the fatigue characteristics of asphalt concrete mixtures (15, 16). The unique thing about this test is that it can be used to characterize a variety of asphalt concrete mixture properties, especially properties related to resilient elastic, thermal cracking, fatigue cracking and permanent deformation (17). One of the latest studies of fatigue characterization using the ITT was carried out in Sweden by Said (18). Said in his work tested 300 cores from different pavement sections using repeated controlled stress loading at 2 temperatures, 4° C and 15° C. Said concluded the ITT is sufficiently accurate for routine investigation of asphalt concrete fatigue characterization with a shift factor of 10 to correlate to field. Maupin and Freeman (19) performed several simple flexure fatigue tests (third point loading) on asphalt concrete beams using controlled stress and controlled stain mode of loadings. In addition, they

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tested several samples using the ITT. The goal was to check the possibility of predicting fatigue behavior from a simple test. The simple test results such as stiffness, strength, and vertical deformation were correlated with the fatigue properties. The fatigue properties were Log K1 and K2 in the fatigue model. Regression analysis was performed between fatigue properties and the indirect tensile test results. Maupin and Freeman concluded for constant strain testing; acceptable correlation was found between the strain based fatigue equation [Nf = K1 (1/ ε)K2] and the simple tests as follows: K2 = 0.0374 σ IT - 0.744 LogK1 = 7.92 – 0.122 σ IT Where: σIT = indirect tensile strength at 72° F, (psi). It should be mentioned that, failure in controlled strain testing was defined as 30 percent reduction in the initial stiffness calculated at 200 cycles. However, there are still some concerns about using the results of the ITT in fatigue characterization especially, the biaxial stress state at the center of the sample is fixed to a specific ratio, which can not be varied to replicate the field conditions, and the underestimating the fatigue life compared to other fatigue tests (20). Statistical analysis was performed in attempt to predict K1and K2 based upon mixture properties (asphalt content, air voids, voids in mineral aggregate, voids filled with asphalt and gradation) and test parameters (initial values of stress, strain, stiffness, dissipated energy and phase angle). The three main sets of data IDOT, Dubai and the Aggregate Interlock were used in this analysis. Unfortunately, the resulted models had low coefficients of determination.

K1-K2 RELATION The K1 and K2 values from the flexural fatigue test are highly correlated. This is shown in Figure 2a, which plots K1 vs K2 in a semi log scale for Dubai mixtures. Dubai mixtures set of data includes 30 mixtures with 8 different aggregate gradations, 4 asphalt types (2 with polymers), 2 aggregate types and variable asphalt content. Fatigue samples were compacted at targeted air voids level of 4 percent with some variation around this level. As shown in Figure 2a K1 and K2 values located in one line in spite of the different mixtures properties.

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The IDOT set of data contains 25 mixtures represents Illinois filed mixtures obtained from construction sites. Mixtures in this set of data are with variable asphalt contents, different aggregate types and different aggregate gradations. These mixtures represents both surface and binder mixtures. The IDOT mixtures were compacted at two air voids levels 7% and 4% to represent both pavement immediately after construction and after been trafficked several years. Figure 2b shows the K1 vs K2 plots for the IDOT mixtures where all K1-K2 points are located on the same line regardless of different mixtures properties. The aggregate interlock set contains 8 mixtures with the same aggregate and asphalt type, one asphalt content (5.5 %). Mixtures in this group were prepared with precise gradation control where each mixture has different gradation. Plotting the K1-K2 relation for aggregate interlock mixtures produce straight line as shown in Figure 2c. The relation between K1-K2 for all mixtures from all sets of data included in this study is shown in Figure 2d, which gives good correlation as well. The relation between K1 and K2 for all mixtures from all sets of data included in this study is given as follows: K2 = -0.3269 Log (K1) + 1.1857

(R2 = 0.94)

It should be noted this line represents 84 mixtures from different sets of data with different mixtures properties. The K1 and K2 variables for each mixture are given in Table 2; more detailed mixture properties are given in Ghuzlan’s PhD thesis (23). The relationship shown here is consistent with the findings of a number of researchers (6, 21, 22). This emphasizes that even though different mixture properties alter K1 and K2 values, there is a uniform relationship between them that does not change and it may have a use in design. The relation between K1 vs K2 for all mixtures used in this study was compared to other data presented in other studies. Figure 3 shows the relation between K1 and K2 for data from this study and other studies (12, 19, 21, 22). As shown in Figure 3 the data from this study and Myre study (21, 22) produces one line. Keeping in mind that Myre used mainly center point and 4 point testing machine. The data from Maupin and Freeman study (19) and FHWA are located above and below the line obtained from this study respectively. While the Maupin data closely reproduces the trend observed in this study. To plot the same line based on Finn et al. fatigue relation (12), different values of the complex modulus (E*) are substituted in the fatigue relation. At different levels of modulus the exponent (K2) has a fixed value of

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3.29 while K1 changes over a narrow range. Therefore, plotting results from Finn et al. relation results in horizontal line as shown in Figure 3, indicating the error of assuming a constant K2 value. In Maupin’s data it should be noted that the K1-K2 line obtained from flexural fatigue testing and some points on the same line come from indirect tensile testing. The ITT points are predicted using the formulas mentioned earlier in term of the indirect tensile strength. This may indicate that, the relationship between fatigue coefficients and material properties (such as the tensile strength) could be expanded in the future to provide a rapid determination of fatigue coefficients for design purposes.

FACTORS AFFECTING K1-K2 RELATION Factors contributing to the wide range of K1 and K2 values include testing mode of loading (Controlled stress/Controlled strain), test conditions and loading variables, specimen type (beam trapezoidal, cylinder, etc.), and asphalt concrete mixture variables. In this study the following factors were investigated , asphalt type, air voids level, asphalt content, aggregate gradation, testing temperature, and mode of loading. To evaluate the effect of asphalt type on K1-K2 relation two sets of Dubai mixtures having the same properties with different asphalt types (i.e. EPPCO 60-70 + 4.5% SBS and EPPCO 60-70 + 5.5% EVA) were analyzed as shown in Figure 4a the K1-K2 relation for both sets of data. It is noted that both lines are close and it can be proven that there is no significance difference between the two lines (at 0.95 level of significance). Therefore, it is concluded that asphalt type has no significant effect on the K1-K2 relation of specific mixtures. In an attempt to account for the effect of the asphalt content two sets of data mainly from IDOT and Dubai mixtures were used. One set was with asphalt content less than or equal 4% and the other with asphalt content of 5.5% or higher. The K1-K2 lines were plotted for both sets of mixtures as shown in Figure 4b. Two different lines were obtained and it can be shown that they are statistically different. Figure 4c shows two K1-K2 lines for two sets of IDOT mixtures, which were compacted at two air voids levels; 4% and 7%. As shown in Figure 4c there is no statistical difference between the two lines and that it is possible to pool them in one line. To evaluate the effect of gradation on K1-K2 relation two sets of data from Dubai mixtures were considered. The first set with gradation line goes above the maximum density line and the other beneath it.

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Figure 4d shows that the two K1-K2 relation lines for both sets of mixtures were close, indicating that there is no significant difference between the curves. The temperature effect on K1-K2 relation was evaluated by testing six mixtures “D Mixtures” at two temperatures (20° C and 35° C). The K1-K2 relation was plotted in Figure 4e. Two distinct lines were obtained and it can be shown statistically that these two lines are significantly different. Table 3 shows the fatigue coefficients for the “D Mixtures”. The effect of mode of loading on K1-K2 relation was investigated by testing four IDOT mixtures using both modes of loading. Figure 4f shows the four IDOT mixtures tested using both controlled stress and controlled strain modes of loading. This shows that the two lines are statistically different. In summary it was found that K1-K2 relation was not significantly affected by asphalt type, air voids level, and aggregate gradation. On the other hand, the mode of loading and the testing temperature and asphalt content have a significant effect on the K1-K2 relation.. A full report of the detailed data and analysis for this study can be found in Ghulzan’s Ph.D thesis (23). Table 4 shows the statistical analysis results of the factors affecting the K1-K2 relation. The following analysis was used to determine if there is a significant difference between two regression lines. Given two lines: The expected value of an observation from production line 1 is: E(Yi1) = β01 + β11 The expected value of an observation from production line 2 is: E(Yi2) = β02 + β12 SSE(F) = SSE1 + SSE2 SSE1 = Sum of Square Errors for regression line 1 SSE2 = Sum of Square Errors for regression line 2 SSE(R)= Sum of Square Errors for Reduced regression line (Both together) The test statistic is given in this form:

F* =

SSE ( R) − SSE ( F ) SSE ( F ) ÷ 2 n1 + n2 − 4

n1 = Number of observations on regression line 1 n2 = Number of observations on regression line 2 The two alternatives conclusions are: C1: β01 = β02

and β11 = β12

(Both Lines are the same)

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and β11 ≠ β12

or both (The two lines are different)

The decision rule for the for controlling the error at α is: If F* ≤ F(1-α; 2, n1+ n2 – 4), conclude C1 If F* ≥ F(1-α; 2, n1+ n2 – 4), conclude C2

CONCLUSIONS A Large database of flexural fatigue testing results was developed in this study. The effect of mixture variables on fatigue performance was investigated as well as the effect of mode of loading and testing temperature. From the results of this study it can be concluded that different mixture parameters alter K1 and K2 values. There is a consistent uniform relationship between them that does not change and that may be useful in pavement design. Mode of loading, testing temperature and asphalt content have a significant effect on the K1-K2 relation. On the other hand, asphalt type, air voids levels and aggregate gradations have no significant effect on the K1-K2 relation. Finally, K1-K2 points predicted from the indirect tensile test come together at the same line with points obtained from flexural testing. This may indicate the possibility of determination of fatigue coefficients from simple tests such strength test.

RECOMMENDATIONS This study was conducted using flexural fatigue testing. The traditional fatigue analysis was performed by using the phenomenological fatigue model. More research is needed to further explore the importance of the K1-K2 relation in pavement design. It is recommended to investigate the possibility of predicting fatigue performance from simple tests such as indirect tensile test. This may provide a rapid determination of fatigue coefficients for design purposes. Furthermore, it is recommended to investigate more the effect of mixture properties and test parameters on K1 and K2, which in turn it may provide a relation between the fatigue coefficients and mixture properties.

ACKNOWLEDGEMENTS This paper was prepared from a study conducted in the Center of Excellence for Airport Pavement Research. Funding for the Center of Excellence is provided in part by the Federal Aviation Administration under Research Grant Number 95-C-001. The Center of Excellence is maintained at the University of Illinois at Urbana-Champaign who works in partnership with Northwestern University and the Federal

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Aviation Administration. Ms. Patricia Watts is the FAA Program Manager for the Air Transportation Centers of Excellence and Dr. Satish Agrawal is the FAA Technical Director for the Pavement Center. Also the Authors would like to thank Ms. Karen Krasnoperova for reviewing the paper and for the valuable comments she made.

REFERENCES 1.

Hveem, F.N., “Pavement Deflections and Fatigue Failures”, Highway Research Board, Bulletin 114, Washington D.C., 1955.

2.

Pell, P.S., ‘Fatigue Characteristics of Bitumen and Bituminous Mixes”, International Conference on The Structural Design of Asphalt Pavements, An Arbor, Michigan, August, 1962.

3.

Bazin, P., and Saunier, J.B., “Deformability, Fatigue and Healing Properties of Asphalt Mixes”, Second International Conference on The Structural Design of Asphalt Pavements Proc., Ann Arbor, Michigan, 1967.

4.

Epps, J.A., Monismith, C.L., “Influence of Mixture Variables on The Flexural Fatigue Properties of Asphalt Concrete”, Proc. of The Asphalt Paving Technologists, Los Angeles, Vol.38, 1969, pp. 423-464.

5.

Van Dijk, W., H. Moreaud, A. Quedeville, and P. Uge. The Fatigue of Bitumen and Bituminous Mixes. Proc., Third International Conference of the Structural Design of Asphalt Pavements. London, 1972, pp. 354-366.

6.

Pell, P.S., and Cooper, K.E., “The Fatigue of Testing and Mix Variables on The Fatigue Performance of Bituminous Materials”, Association of Asphalt Paving Technologists, Vol. 44 Proc., Baltimore, Phoenix, Arizona, 1975.

7.

SHRP, A-404, ”Fatigue Response of Asphalt-Aggregate Mixes”. Strategic Highway Research Program, National Research Council, 1994.

8.

Miner, M.A., “Cumulative Damage in Fatigue”, Transactions of the American Society of Mechanical Engineers, Vol. 67, 1945.

9.

The Asphalt Institute, “Research and Development of The Asphalt Institute’s Thickness Design Manual (MS-1) Ninth Edition”, Research Report No. 82-2, August 1982.

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10. Monismith, C.L., Epps, J.A., and Finn, F.N., “Improved Asphalt Mix Design”, Proc. of Asphalt Paving Technologists, Vol., 54, San Antonio, Texas, 1985. 11. Pell, P.S., “Pavement Materials”, Sixth International Conference on The Structural Design of Asphalt Pavements, Vol. 2 Proc., Ann Arbor, Michigan, July 1987. 12. Finn, F., Saraf, C.L., Kulkarni, K., Nair, K., Smith, W., and Abdullah, A., “Development of Pavement Structural Subsystems”, Final Report, Project 1-10B, February 1977. 13. Standard Test AASHTO Provisional Standards, Standard Test Method for Determination the Fatigue Life of Compacted Hot Mix Asphalt (HMA) Subjected to Repeated Flexural Bending. TP8-94, September 1994. 14. Calibrated Mechanistic Structural Analysis procedures for Pavements, NCHRP 1-26, University of Illinois at Urbana-Champaign, Construction Technology Laboratories, The Asphalt Institute, December 1992. 15. Adedimila, A.S., and Kennedy, T.W., “Repeated-Load Indirect Tensile Fatigue Characteristics of Asphalt Mixtures”, Transportation Research Record, Number 595,Washington D.C., 1976. 16. Khosla, N.P., and Omer, M.S., “Characterization of Asphaltic Mixtures for Prediction of Pavement Performance”, Transportation Research Record, Number 1034, Washington D.C., 1985. 17. Kennedy, T.W., “Characterization of Asphalt Pavement Materials Using The Indirect Tensile Test”, Association of Asphalt Paving Technologists, proc. Vol. 46, February 1977. 18. Said, S.F., “Variable in Roadbase Layer Properties Conducting Indirect Tensile Test”, Eight International Conference on The Structural Design of Asphalt Pavements, Vol. 2 Proc., Seattle, Washington, August 1997. 19. Maupin, G.W. and Freeman, J.R., “Simple Procedure for Fatigue Characterization of Bituminous Concrete”, FHWA-RD-76-102, 1976. 20. Tangella, S.C., Craus, J., Deacon, J.A., and Monismith, C.L., “Summary Report on Fatigue Response of Asphalt Mixtures”, SHRP-A/IR-90-011, February 1990 21. Myre, Jostein, “Fatigue of Asphalt Pavements”, Third International Conference on Bearing Capacity of Roads and Airfields, The Norwegian of Technology Trondheim, Norway, July 1990, pp. 703-714.

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22. Myre, J., “Utmatting av Asfalttdekker” Doctoral Thesis, Institute for Veg-Og Jernbanebygging, Universitetet I Trondheim, Norges Tekniskole, Trondheim, Norway, 1988. 23. Khalid A. Ghuzlan, “Fatigue Damage Analysis in Asphalt Concrete Mixtures Based Upon Dissipated Energy Concepts”. Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2001.

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List of Figures Figure 1 Number of load cycles to failure versus initial strain at the bottom of the asphalt concrete layer based on controlled strain mode of loading. Figure 2 K1-K2 relation for different sets of data and for all data as one set. Figure 3: K1 vs K2 relation from different studies compared to U of Illinois database Figure 4 Factors affecting the K1-K2 relationship in AC fatigue mixtures.

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10,000,000 Mix-22-Dubai

Load Cycles to Failure

1,000,000

100,000

y = 4.105E-12x-4.678E+00 R2 = 9.954E-01

10,000

1,000

100 0.0001

0.001 Strain at the Bottom of AC Layer (mm/mm)

0.01

Figure 1 Number of load cycles to failure versus initial strain at the bottom of the asphalt concrete layer based on controlled strain mode of loading.

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a) Dubai Mixtures

b) IDOT-Mixtures

6

7 y = -0.315x + 1.2505

5

R2 = 0.9383

5

4

4 3

K2

K2

y = -0.3224x + 1.2471

6

R2 = 0.9492

3 2 2 1

1

0

0

-14.0

-12.0

-10.0

-8.0

-6.0

-4.0

-16

-11

-6

Log(K1)

c) Aggregate Interlock Mixtures

4

d) All Data from All Mixtures

7

4.8 4.6

y = -0.3217x + 1.262

4.4

R2 = 0.9961

y = -0.3269x + 1.1857

6

R2 = 0.9445

5

4.2

4

4

K2

K2

-1

Log(K1)

3.8

3

3.6 2

3.4

1

3.2 3 -11.0

0 -10.0

-9.0

-8.0

-7.0

-6.0

-16

-11

Log(K1)

-6

-1

4

Log(K1)

Figure 2 K1-K2 relation for different sets of data and for all data as one set.

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7

U of Illinois Maupin Results Myre FHWA Finn Linear (U of Illinois) Linear (Maupin Results) Linear (Myre) Linear (FHWA)

: Maupin Indirect Tensile Test : Maupin Flexural Test

6

5

K2

4

3

2

1

0 -16

-14

-12

-10

-8

-6

-4

-2

0

Log(K1)

Figure 3 K1-K2 relation from different studies compared to U of Illinois database.

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a) Effect of Asphalt Types on K1-K2 Relation

b) Effect of AC% on K1-K2 Relation

7

6 y = -0.2652x + 1.7752

Dubai-A1-M1

R = 0.9094

5

y = -0.3754x + 0.7601 R2 = 0.9953

6

2

Dubai-A1-M2

AC% < or = 4% AC%> or = 5.5%

5 4

K2

K2

y = -0.2876x + 1.4854 2

R = 0.9465

3

4 y = -0.3096x + 1.1761

3

2

2

1

1

R2 = 0.9803

0 0 -12

-11

-10

-9 Log (K1)

-8

-7

-16

-6

-14

-12

-10

c) Effect of Air Voids on K1-K2 Relation

-6

d) Effect of Gradation on K1-K2 Relation 7

7.000 6.000

y = -0.3317x + 1.1564

IDOT-AV-4

R2 = 0.9527

IDOT-AV-7

Open Graded (SMA) 6

Dense Graded

5.000

5

4.000

4

R2 = 0.9404

K2

K2

y = -0.3075x + 1.4368

y = -0.3154x + 1.3174

3.000

y = -0.3707x + 0.8035 3

R2 = 0.9256

2.000

2

1.000

1

0.000

R2 = 0.9745

0

-16

-12

-8

-4

0

-11

-10

-9

Log (K1)

-8

-7

-6

Log (K1)

f) Effect of Moide of Loading on K1-K2 Relation

e) Effect of Temp on k1-K2 Relation

6.0

6 IDOT-Control-Strain

Temperature = 20 C

5.0

Temperature = 35 C

5

4.0

y = -0.3272x + 1.477

4

IDOT-Control-Strees

y = -0.2801x + 1.3139 R2 = 0.9796

2

y = -0.2753x + 1.4553

3.0

R = 0.9924

K2

K2

-8

Log (K1)

R2 = 0.9628

y = -0.3683x + 0.6859

3

2.0

2

1.0

1

R2 = 0.9901

0

0.0 -16

-12

-8 Log (K1)

-4

0

-16

-14

-12

-10

-8

-6

Log K1

Figure 4 Factors affecting the K1-K2 relation in AC fatigue mixtures.

21 TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Ghuzlan, Carpenter

List of Tables Table 1 Mixtures Included In This Study Table 2 Fatigue Database of All Mixtures (Testing Temperature = 20° C) Table 3: Fatigue Coefficients for “D” Mixtures Tested at Two Temperatures (20 ° C & 35° C). Table 4: The Significance of the Effect of Different Variables levels on K1-K2 Relation

22 TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Ghuzlan, Carpenter

Table 1 Mixtures Included In This Study Source IDOT FAA Dubai “D” Group MnRoad WES Agg. Inter. Michigan NAPTF I-88 Wisconsin Total

Number of mixtures 25 1 30 6 4 6 8 1 1 1 1 84

No. of Samples on Each Mix 8 26 4 4 4 4 4 8 16 4 8 478

AV level 2 Different Different 1 1 1 1 1 1 1 2

Mode of Loading C-Strain C-Stress/Strain C-Strain C-Strain C-Strain C-Strain C-Strain C-Strain C-Strain C-Stress/Strain C-Strain

Notes One mix with Pol. W/O rest period Target AV =4 % Temp. = 20 and 35 °C One strain setting 5 mixes with poly. W/O Fiber 4-Conditions

23 TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Ghuzlan, Carpenter

Table 2 Fatigue Database of All Mixtures (Testing Temperature = 20° C) IDOT-Mixtures- AV=4% Mix # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

IDOT-Mixtures- AV=7%

K1 2.43E-07 1.46E-13 4.01E-10 7.24E-12 8.93E-11 2.11E-12 4.61E-10 3.20E-12 2.13E-11 1.84E-11 1.01E-10 3.98E-15 2.29E-14 9.60E-10 9.20E-11 5.05E-11 2.14E-11 2.24E-09 1.86E-09 3.65E-11 1.34E-10 6.47E-12 3.37E-10 2.02E-09

K2 -3.58 -5.64 -4.28 -5 -4.41 -4.99 -4.22 -5.07 -4.64 -4.57 -4.41 -6.13 -5.38 -4.39 -4.55 -4.62 -4.79 -4.11 -4.07 -4.56 -4.28 -4.68 -4.14 -4.01

25 4.75E-13 25 1.76E-11 I-88 1.54E-11 Other Mixtures:

-5.08 -4.47 -4.62

0.976 0.966 0.885

Dubai Mixtures

R^2 Mix # K1 K2 0.959 1 2.37E-11 -4.73 0.975 2 1.09E-14 -5.99 0.996 3 2.02E-11 -4.67 0.991 4 8.67E-08 -3.7 0.979 5 9.39E-10 -4.08 0.985 6 1.26E-11 -4.75 0.891 7 5.68E-09 -3.95 0.983 8 1.63E-10 -4.53 0.992 9 3.65E-11 -4.6 0.98 10 2.55E-09 -3.87 0.977 11 3.30E-12 -4.89 0.954 12 5.16E-10 -4.48 0.996 13 1.81E-09 -3.89 0.996 14 1.47E-09 -4.03 0.994 15 1.32E-09 -4.18 0.994 16 2.56E-13 -5.31 0.997 17 4.29E-10 -4.38 0.997 18 5.36E-13 -5.21 0.997 19 1.64E-10 -4.38 0.998 20 1.39E-09 -4.02 0.982 21 1.02E-10 -4.3 0.984 22 4.39E-11 -4.47 0.961 23 4.17E-12 -4.85 0.993 Agg. Interlock Mixtures: 6-40 1-5 1+ 5 1-10

2.91E-11 3.65E-10 7.92E-10 1.62E-09

-4.64 -4.33 -4.18 -4.08

R^2 0.987 0.997 0.999 0.859 0.949 0.996 0.965 0.979 0.997 0.872 0.997 0.95 0.892 0.955 0.999 1 0.968 0.996 0.99 0.978 0.978 0.99 0.971 0.992 0.99 1 0.999

Mix # 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 22 23 24

K1 1.75E-08 1.22E-08 2.46E-09 1.41E-09 1.70E-08 1.22E-10 4.20E-12 6.55E-13 1.47E-10 1.16E-08 1.36E-09 2.29E-09 5.23E-09 5.30E-08 1.25E-07 5.55E-09 1.18E-09 1.45E-08 1.46E-09 6.04E-11 6.04E-11 4.11E-12 6.07E-12 7.54E-11

25 26 27 28

1.12E-09 8.92E-08 3.81E-10 9.53E-09

K2 R^2 -3.68 0.92 -3.76 1 -4.03 0.99 -3.96 0.95 -3.55 0.94 -4.35 0.99 -4.85 0.97 -5.23 1 -4.46 0.99 -3.98 1 -4.2 0.98 -3.94 0.85 -3.77 0.97 -3.53 1 -3.37 1 -3.91 0.99 -3.96 0.99 -3.75 1 -3.99 1 -4.6 1 -4.6 1 -4.68 1 -4.64 1 -4.42 0.89 -4.08 -3.54 -4.27 -3.56

1 0.99 0.98 1

WIS M-F M-C FAA M-1

1.58E-11 1.40E-08 3.18E-08 1.97E-10 9.48E-13

-4.6 -4.03 -3.86 -4.16 -5.26

0.987 1+10 2.08E-09 -4.04 0.999 29 1.17E-11 -4.61 0.98 0.97 2 LW 4.42E-09 -3.95 1 30 4.03E-11 -4.56 0.99 0.915 1 LW 5.48E-09 -3.94 0.996 Where: K1, K3 = Fatigue Intercepts 0.771 4 LW 8.90E-09 -3.84 0.981 K2, K4 = Fatigue Slope 0.986 IDOT Mixes 6, 10, 13 & I-88 C-Stress Note:

M-2

4.11E-11

-4.69

0.979

Mix #

M-3

1.77E-11

-4.95

0.987

6

5.65E-12

-4.52

0.981

M-4

2.25E-11

-4.87

0.95

10

2.19E-14

-5.13

0.998

NAC

3.73E-09

-4.02

0.996

13

2.37E-10

-3.94

0.911

NAD

1.46E-08

-3.83

0.996

I-88

NAL

1.60E-08

-3.65

0.966

NDL

7.95E-09

-3.9

0.981

NRE

1.40E-09

-4.1

0.995

TRB 2003 Annual Meeting CD-ROM

K3

4.41E-11

K4

-4.25

R^2

C-Stress = Controlled Stress Mode

of loading was used

0.969

Paper revised from original submittal.

Ghuzlan, Carpenter Table 3: Fatigue Coefficients for “D” Mixtures Tested at Two Temperatures (20 ° C & 35° C) 20 ° C 35 ° C Testing Temp Mix ID K1 K2 R^2 K1 K2 R^2 D1 8.772E-09 -3.758 0.999 1.453E-07 -3.745 0.976 D2 3.046E-09 -3.820 0.981 4.612E-03 -2.353 0.953 D3 1.435E-09 -3.911 0.989 9.062E-06 -3.076 0.864 D4 2.180E-10 -4.016 0.982 1.699E-04 -2.577 0.974 D5 3.517E-09 -3.816 0.991 5.911E-08 -3.888 0.941 D6 1.033E-06 -3.045 0.979 1.857E-11 -4.984 0.987

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Ghuzlan, Carpenter

Table 4: The Significance of the Effect of Different Variables levels on K1-K2 Relation Variable F* F Significant Mode of Loading 15.3 6.94 Yes Temperature 30.8 4.46 Yes Asphalt Content 22.7 4.1 Yes Asphalt Type 0.71 4.46 No Aggregate Gradation 0.56 9.55 No % Air Voids 0.23 3.2 No

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.