This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and

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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 International Journal of Fatigue 59 (2014) Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: The combined effect of loading frequency, temperature, and stress level on the fatigue life of asphalt paving mixtures using the IDT test configuration Ghazi G. Al-Khateeb,1, Khalid A. Ghuzlan Department of Civil Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan article info abstract Article history: Received 8 April 2013 Received in revised form 7 August 2013 Accepted 9 August 2013 Available online 28 August 2013 Keywords: Asphalt mixture Fatigue Indirect tension Loading frequency Asphalt The main objective of this study was to investigate the combined effect of the loading frequency, temperature, and stress level on the fatigue life of asphalt paving mixtures. Asphalt mixtures were designed using the Superpave design procedure using a 60/70-penetration grade asphalt binder having a Superpave performance grade of PG and crushed limestone aggregate. The indirect tension (IDT) fatigue test was used to determine the fatigue behavior of asphalt mixtures. The IDT fatigue test was conducted in the stress-controlled mode of loading using five stress levels: 288, 360, 432, 504, and 576 kpa (approximately in the range of psi loading) representing truck or heavy traffic loadings in real-life conditions, two intermediate temperatures: 20 and 30 C, and four loading frequencies: 3, 5, 8, and 10 Hz representing truck speeds of about km/h. Three replicates were used for each IDT fatigue test. A total of 120 IDT fatigue tests were conducted in this study. Findings of the study showed that the increase in loading frequency resulted in an increase in the fatigue life at the two test temperatures 20 and 30 C. In addition, the rate of increase in the fatigue life with the loading frequency was exponential, and the difference in the fatigue life (N f ) between the different loading frequencies was found to be higher at lower stress levels than that at higher strain levels at the two temperatures. It was also found that the difference in the fatigue lives between the different stress levels was much higher at higher loading frequencies than that at lower loading frequencies for both temperatures. For the stress-controlled mode of loading, which was used in this study, an increase in temperature provided shorter fatigue lives for asphalt mixtures. Ó 2013 Elsevier Ltd. All rights reserved. 1. Background Fatigue is a phenomenon in which an asphalt pavement is subjected to repeated stress levels less than the ultimate failure stress. Fatigue behavior of asphalt mixtures is studied using two approaches, the traditional approach using the strain (or stress)- based models [19], and the dissipated energy approach were the dissipated energy is used and defined as a damage indictor of the material [14,5]. In addition, fatigue failure is defined using the stress strain hysteresis loop in each loading cycle of the fatigue test [6,7]. Fatigue behavior is also affected by asphalt mixture variables and testing variables (such as temperature and loading frequency). Corresponding author. Tel.: x22129, mobile: ; fax: addresses: ggalkhateeb@just.edu.jo (G.G. Al-Khateeb), kaghuzlan@just. edu.jo (K.A. Ghuzlan). URL: (G.G. Al-Khateeb). 1 Associate Professor of Civil Engineering, Vice Dean of Engineering. In asphalt pavements, higher speeds correspond to higher frequencies and higher dynamic stiffness and this will produce lower strains in the asphalt pavement [18]. Frequency of loading in asphalt concrete is defined as number of load cycles subjected to the material per unit of time. Studying the effect of loading frequency on fatigue life of asphalt concrete mixtures is difficult because it is interconnected with the load duration and rest period. Changing any of these variables will change the other variables [23]. Barksdale [9] correlated vehicle speed with vertical stress pulse time at different depths beneath pavement surface. He found that higher speeds are related to shorter loading times, which correspond to higher frequencies. Load duration time for a vehicle speed of 72 km/h at a depth a round 30.5 cm. is about ss (22.7 Hz). According to [15], for operating speed of 96 km/h on an interstate highway, the estimated loading frequency at the med asphalt layer depth (depth varies from 7.6 to 30.5 cm) is between 10 and 25 Hz. Furthermore, Mollenhauer et al. [18] developed a relation between vehicle speed and frequency of traffic loading. This relation was based on an in situ testing of real vehicle speed reached up to /$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved.

3 G.G. Al-Khateeb, K.A. Ghuzlan / International Journal of Fatigue 59 (2014) km/h, and then the curve was extrapolated up to 90 km/h. The relation between frequency (f) and vehicle speed (v) was represented by a power equation (f = v ). For instance, a speed of 31.4 km/h corresponds to 7.1 Hz while 60 km/h and 90 km/h corresponds to 13.2 and 19.4 Hz, respectively. According to Mollenhauer et al. [18], loading speeds in pavement structure depend on asphalt layer thickness. Loading speed at the bottom of thin asphalt layer is higher than the loading speed at thick asphalt layer. For 80 km/h traveling speed, the loading frequency varies between 8 Hz and 22 Hz based on the asphalt layer thickness. Deacon [11] studied the effect of load duration on fatigue life with keeping load frequency constant (the rest period changed simultaneously). It was found that longer load durations produced shorter fatigue lives. Epps and Monismith (1972) studied the effect of loading frequency on fatigue life. They used different loading frequencies, with keeping the load duration constant and changed the corresponding length of rest periods. The results showed that increasing the frequency (by decreasing the rest period) from 3 to 30 loads per minute had no effect on fatigue life. However, later research indicated that increasing loading frequency from 30 to 100 loads per minute decreased the fatigue life in the strain-controlled mode of loading. Jiang-Maio et al. [16]and Mollenhauer et al. [18] performed four-point bending beam fatigue tests using strain-controlled mode of loading and found that increasing loading frequency resulted in shorter fatigue lives. Pell [20] and Pell and Taylor [22] investigated the effect of increasing the load frequency on fatigue life by maintaining the ratio of rest period to load duration constant. Rotating bending cantilever was tested using sinusoidal load pulse under stress-controlled mode of loading. Load frequency varied from 80 to 2500 load cycles per minute. It was found that increasing load frequency increased fatigue life. The significant effect of load frequency was at low frequency levels (below 200 load cycles). Raithby and Sterling [24] performed two sets of tests using stress-controlled mode of loading; one with 40 ms loading period and rest periods of 0 and 80 ms and the other with 400 ms loading period with rest periods 0 and 800 ms. The specimens with 400 ms loading periods had much shorter fatigue lives. In other words increasing the frequency (by decreasing load duration) increased fatigue life. Based on stress-controlled mode of loading, Pell and Taylor [22] found that low temperatures produced longer fatigue lives for asphalt concrete mixtures. Epps and Monismith [13] found that under stress-controlled mode of loading, decreasing the test temperature increased the fatigue lives of asphalt concrete mixtures. Jiang-Maio et al. [16] conducted four-point bending beam fatigue tests using strain-controlled mode of loading and found that increasing the temperature resulted in an increase in the fatigue life. Minhoto et al. [17]also used the four-point bending test in the strain-controlled mode of loading. The tests were performed at four test temperatures of 5, 5, 15, and 25 C. The fatigue test results showed that the fatigue life decreased when the test temperature decreased up to a certain value. After that value, the fatigue life increased when the test temperature decreased. In this study, the combined effect of the loading frequency, test temperature, and stress level was investigated on the fatigue life of Superpave asphalt paving mixtures using the indirect tension (IDT) fatigue test in the stress-controlled mode of loading. The laboratory conditions including load, test temperature, and loading frequency were selected such that they represent to a certain extent the field conditions (truck loading, pavement intermediate temperature for fatigue, and truck speeds). The IDT fatigue test was used to study the effect of all these conditions on the fatigue life of Superpave asphalt mixtures tested in the stress-controlled mode of loading. 2. Materials and designing asphalt mixtures 2.1. Aggregate Aggregate gradation The aggregate used in this study was crushed limestone from Al-Huson quarry in the northern part of Jordan. Limestone is the most common aggregate type used for asphalt pavement construction in Jordan. For surface asphalt mixtures, Superpave typically recommends five types of asphalt mixtures with nominal maximum aggregate sizes (NMAS) of 37.5, 25.0, 19.0, 12.5, and 9.5 mm. In this study, the aggregate gradation was selected based on the Superpave specifications with a NMAS of 12.5 mm. The aggregate gradation is shown on the 0.45 power chart (Fig. 1) Aggregate properties The limestone aggregate was tested and evaluated for Superpave consensus properties and source properties as well. The tests for consensus properties included: Coarse Aggregate Angularity (CAA), Fine Aggregate Angularity (FAA), Flat and Elongated (F&E) Particles, Sand Equivalent (SE), whereas, the tests for source properties included: specific gravity and absorption of coarse aggregate, specific gravity and absorption of fine aggregate, Los Angeles (LA) Abrasion, and deleterious materials. Table 1 below shows the consensus properties and LA abrasion for the limestone aggregate Asphalt binder The asphalt binder used in this study was a 60/70-penetration grade asphalt binder obtained from Jordan Petroleum Refinery (JPR) having a Superpave performance grade of PG The conventional (traditional) asphalt binder tests and the needed Superpave asphalt binder tests were conducted on the asphalt binder. The conventional tests included: specific gravity, penetration, ductility, softening point, and flash and fire points. On the other hand, the Superpave tests included: Rotational Viscosity (RV) test, Dynamic Shear Rheometer (DSR) test, Rolling Thin-Film Oven (RTFO) test, Pressure Aging Vessel (PAV) test, and Bending Beam Rheometer (BBR) test required to grade the asphalt binder. The Superpave test results for the asphalt binder are summarized in Table Superpave asphalt mixtures Mixing and compaction temperatures Using the ASTM viscosity-temperature relationship, and based on the rotational viscosity test results of the asphalt binder at % Passing Sieve Size (mm) Fig Power chart for aggregate gradation used in this study.

4 256 G.G. Al-Khateeb, K.A. Ghuzlan / International Journal of Fatigue 59 (2014) Table 1 Consensus properties and LA abrasion for limestone aggregate. Test Limestone Criteria Coarse aggregate Fine aggregate Flat and elongated (F&E) particles Coarse Aggregate Angularity 97/91 NA 95/90 (CAA) Fine Aggregate Angularity (FAA) 45 P45 Sand Equivalent (SE), % NA 58 P45 Los Angeles (LA) Abrasion Mass Loss, % 27 NA 645 Viscosity (Pa.s) 10 1 Compaction Range Mixing Range Temperature ( o C) Fig. 2. Mixing and compaction temperature ranges. Table 2 Superpave test results for asphalt binder. Test temperature ( C) RV a (MPa s = cp) Superpave criteria Fresh asphalt 135 C Pas 160 C 220 NA G a /sind (kpa) Before RTFO P1.0 kpa After RTFO (Mass Loss = 0.3%) P2.2 kpa G a sind (kpa) After PAV Creep stiffness (MPa) After PAV MPa m-value After PAV P0.300 a RV = Rotational Viscosity. AASHTO T 166 [2]. The theoretical maximum specific gravity (G mm ) test was also conducted on loose samples of the asphalt mixture (Fig. 4) in accordance with the procedure described in the AASHTO T 209 [1]. The CORELOK machine was also used in the G mm measurement. The design asphalt binder content for the asphalt mixture using the Superpave design procedure was determined as 5.1%. The Superpave volumetric properties at the design asphalt binder content are summarized in Table Fabrication of IDT fatigue specimens Using the design asphalt binder content (5.1%) obtained from the Superpave design procedure of the asphalt mixtures, sixty standard Superpave samples (diameter of 150 mm height of 115 mm) were compacted using the Superpave Gyratory Compactor (SGC). The target air voids level was 4.0 percent. All samples used in this study were with air voids of 4.0 ± 0.5%. Two IDT fatigue specimens were fabricated from each SGCcompacted sample having dimensions of 100 mm in diameter and 50 mm in height or thickness. A total of 120 IDT fatigue specimens were produced. A coring machine was used to core the SGC sample to obtain a core having a diameter of 100 mm (Fig. 5). Afterwards, the core was trimmed from the two ends using a sawing machine and then was cut into two 50-mm thick specimens. the two test temperatures of 135 and 160 C, the mixing temperature range was determined as C, while the compaction temperature range was found to be C as shown in Fig Design asphalt content The Superpave Gyratory Compactor (SGC) shown in Fig. 3 was used to prepare the hot-mix asphalt (HMA) specimens to design the asphalt mixtures prior to fabrication of the fatigue specimens used in the Indirect Tension (IDT) fatigue testing. The following design inputs that fitted Jordan s traffic and climatic conditions were used in the Superpave design procedure for asphalt mixtures: (1) design ESALs of million and (2) design air temperature of less than 39 C. Based on that, the three values for the number of gyrations were selected from the Superpave criteria shown in Table 3. The initial number of gyrations (N Initial ), the design number of gyrations (N Design ), and the maximum number of gyrations (N Max ) were 8, 109, and 174, respectively. The Superpave Gyratory Compactor (SGC) was used to compact the asphalt mixtures at four asphalt binder contents: 4.5%, 5.0%, 5.5%, and 6.0%. During the compaction process, the height and the number of gyrations of each specimen were recorded. The bulk specific gravity (G mb-measured ) test was conducted on gyratory-compacted specimens according to the procedure described in the Fig. 3. Superpave gyratory compactor.

5 G.G. Al-Khateeb, K.A. Ghuzlan / International Journal of Fatigue 59 (2014) Table 3 Superpave criteria for the number of gyrations. Design ESALs (millions) Average design high air temperature <39 C C C C N ini N des N max N ini N des N max N ini N des N max N ini N des N max < > Fig. 4. G mm loose mixture sample. Table 4 Asphalt mixture volumetric properties at the design asphalt content. Property Value Superpave criteria Design asphalt binder content (%) 5.1 Design air voids (%) VMA (%) 14.2 P14.0 VFA (%) DP %G N initial %G N Design %G N Max The final IDT fatigue specimen was obtained with a diameter of 100 mm and a thickness of 50 mm. 4. Fatigue performance testing The IDT fatigue test was conducted on all 120 fabricated specimens using the Universal Testing Machine (UTM) shown in Fig. 6 based on the test procedures described in the Standard AASHTO test method T 322 [3]. The UTM machine consists of three main components: the loading frame, the environmental chamber, and the control and data acquisition system. The IDT fatigue test was conducted in the stress-controlled mode at variable testing conditions: five stress levels of 288, 360, 432, 504, and 576 kpa, and 4.0 kn, two test temperatures of 20 and 30 C, and four loading frequencies of 3, 5, 8, and 10 Hz. Three replicates for each combination of the testing conditions were also used. The IDT fatigue testing matrix is shown in Table 5. Prior to the IDT fatigue test, specimens were conditioned at the desired test temperature for h. The temperature of the UTM environmental chamber was controlled at the target temperature using the UTM temperature controller. The IDT fatigue test setup was mounted inside the UTM as shown in Fig. 6. The deformation of the specimen was monitored through Linear Variable Differential Transducers (LVDTs). The LVDTs were clamped horizontally as shown in Fig. 7 to measure the horizontal deformation of the IDT specimen. The IDT fatigue test was conducted in the stress-controlled mode by applying a constant vertical compression load diametrically on the specimen. This diametric compression load produced an indirect tension. Five levels for the dynamic load (haversine) were used to create the different stress levels. The strain, stress, and cycle number were recorded during the fatigue test using the data acquisition system. The IDT fatigue test was stopped when actual failure on specimen was observed. A crack typically occurred in the vertical direction, which indicated that the specimen reached fatigue failure in the stress-controlled mode as shown in Fig. 8. Thus, the number of loading cycles to fatigue failure was recorded at this point. The relationship between the vertical applied compression load and the resulting tensile stress is shown in Eq. (1)below. Also, the horizontal and vertical deformations in the IDT test mode are related to each other through Eq. (2). r t ¼ 2P pdt l ¼ 3:59 H 0:27 V ð2þ Fig. 5. Cored sample from a Superpave SGC specimen. where r t is the tensile stress, P is applied vertical compression load, D is diameter of specimen, t is thickness of specimen, l is Poisson s ratio (0.35), H is horizontal deformation, and V is vertical deformation. 5. Fatigue results and discussion In this section, the fatigue results are presented based on the analysis conducted on the fatigue raw data for the testing matrix of the study. The combined effect of temperature, loading frequency, and strain level on the fatigue life of asphalt paving ð1þ

6 258 G.G. Al-Khateeb, K.A. Ghuzlan / International Journal of Fatigue 59 (2014) Fig. 6. Universal Testing Machine (UTM) with IDT setup. Table 5 IDT fatigue testing matrix. Variable (testing condition) No. Value Stress levels, r c (kpa) 5 288, 360, 432, 504, and 576 Loading frequency, f (Hz) 4 3, 5, 8, and 10 Test temperatures, T ( C) 2 20 and 30 C Replicates 3 Three IDT fatigue specimens Total number of IDT fatigue tests = 120 Tests Fig. 8. IDT fatigue specimens after fatigue failure. Fig. 7. LVDTs mounted on an IDT fatigue specimen. mixtures is investigated using the stress-controlled fatigue test mode in the IDT test configuration. The number of loading cycles to fatigue failure, N f (fatigue life) was plotted with the initial strain level at different loading frequencies at the test temperature of 20 C as shown in Fig. 9. In Fig. 9, the best model that fitted the scatter data at the four loading frequencies (3, 5, 8, and 10 Hz) was the power model with high coefficient of simple determination (r 2 ) of 0.910, 0.920, 0.900, and 0.919, respectively. The power model was used in the literature by many researchers to describe fatigue life of asphalt mixtures [8,25]. Fig. 9 shows clearly that the increase in loading frequency resulted in an increase in the fatigue life (N f ) at a temperature of 20 C. In other words, higher traffic speeds in field could produce longer fatigue lives for asphalt pavements. The stiffness of asphalt mixtures normally increases with the increase in loading frequency; this increase could be considered in favor of fatigue resistance (fatigue life) at temperatures in the upper limit of the intermediate temperature range (approximately between C), which is typical for fatigue. On the other hand, at temperatures below 20 C, the case might be different since the increase in the loading frequency results in an increase in the stiffness and lowering the temperature also decreases the stiffness; the way that makes the asphalt mixture too stiff and therefore more susceptible to fatigue cracking (lower fatigue life). That is to say, the results highly depend on the temperature used and this is supported by Pell [20], Pell [21], and Pell and Taylor [22]. The difference in fatigue life (N f ) between the different loading frequencies was found to be higher at lower initial strain levels than that at higher initial strain levels. In a similar manner, the relationship between the number of loading cycles to fatigue failure was plotted with the strain level at a temperature of 30 C as shown in Fig. 10. The power model was the best function to fit the scatter data in this figure at the four loading frequencies: 3, 5, 8, and 10 Hz with coefficient of simple determination (r 2 ) of 0.781, 0.859, 0.908, and 0.946, respectively. An increase in the fatigue life (N f ) was obtained when the loading frequency increased from 3 to 10 Hz. Initial Strain (με) Hz_20C 8 Hz_20C 5 Hz_20C 3 Hz_20C ε = 73700N f R² = ε = N f R² = ε = N f R² = ε = N f R² = ,000 10, ,000 1,000,000 10,000,000 Number of Cycles to Failure (N f ) Fig. 9. N f versus initial strain level at T =20 C.

7 G.G. Al-Khateeb, K.A. Ghuzlan / International Journal of Fatigue 59 (2014) Initial Strain (με) Hz_30C 8 Hz_30C 5 Hz_30C 3 Hz_30C Table 6 Percentage decrease in fatigue life between 20 and 30 C at different loading frequencies and stress levels. f (Hz) Percentage decrease in fatigue life (N20/N30 a ) Stress level (kpa) Initial Strain (με) ε = N f R² = ε = 1E+06N f R² = ε = 2E+06N f R² = ε = 4E+06N f R² = ,000 10, ,000 1,000, Number of Cycles to Failure (N f ) Fig. 10. N f versus initial strain level at T =30 C ,000 10, ,000 1,000,000 10,000,000 Number of Cycles to Failure (N f ) 10 Hz_30C 8 Hz_30C 5 Hz_30C 3 Hz_30C 10 Hz_20C 8 Hz_20C 5 Hz_20C 3 Hz_20C Fig. 11. N f and initial strain level relationship: 20 C versus 30 C. At a temperature of 30 C, the difference in fatigue life (N f ) between the different loading frequencies was also found to be higher at lower initial strain levels than that at higher initial strain levels. The non-linear power models that best fitted the fatigue data along with the coefficient of simple determination (r 2 ) are presented in Figs. 9 and 10 at different loading frequencies for the two temperatures 20 and 30 C, respectively. The coefficient of simple determination (r 2 ) was significantly high for the two sets of models at the two temperatures, which ranged from 0.90 to 0.92 for T =20 C and from 0.78 to 0.95 for T =30 C as shown in these two tables. To compare the fatigue results at the two test temperatures (20 and 30 C), the number of cycles to fatigue failure was plotted versus the strain level for the two temperatures in the same figure (Fig. 11). This figure clearly showed that the fatigue life decreased with the increase in temperature from 20 C to 30 C. The relationship between temperature and fatigue life of asphalt mixtures is dependent on the mode of loading: stress-controlled mode or strain-controlled mode. The above finding, which is based on stress-controlled test mode, is supported by Pell and Taylor [22] who found that low temperatures produced longer fatigue lives, Epps and Monismith [13] who concluded that under controlled stress testing of asphalt concrete mixtures decreasing testing temperature increased fatigue lives, and De Freitas et al. [12] who showed that increasing temperature resulted in shorter fatigue life for top-down fatigue cracking. Under stress-controlled test mode of loading, fatigue life is highly dependent on temperature, it was found that decreasing the temperature will increase the fatigue life with other factors remaining constant [20 22]. On the other hand, fatigue life is a N20 and N30 = number of loading cycles to failure at 20 and 30 C, respectively. increased as temperature increases when strain-controlled mode of loading is used [21,19,16]. The decrease in the fatigue life when the temperature increased from 20 to 30 C was quantified. The percentage decrease instead of the absolute reduction in the fatigue life was computed for each stress level and loading frequency. The results are summarized in Table 6. In general, the percentage decrease ranged from 95% to 99%. This decrease could be due to the fact that increasing the temperature from 20 to 30 C (which is considered at the upper limit for the typical temperature range for fatigue cracking) leads to a decrease in the stiffness of asphalt mixtures beyond a minimum acceptable range that weakens the resistance of the asphalt mixture to fatigue cracking and hence decreases the fatigue life. Likewise, by decreasing the temperature to values at the lower limit for the typical temperature range for fatigue cracking (like 5 C) would result in an increase in the stiffness probably higher than a maximum acceptable limit that again would subside the resistance of the asphalt mixture to fatigue cracking and therefore decreases the fatigue life as well. In conclusion, the effect of temperature on the fatigue life of asphalt mixtures is considered sometimes vague. Generally, fatigue damage occurs at low to medium temperatures where the material has higher stiffness values. On the other hand, rutting is occurred at high temperatures where the material has lowers stiffness values and it becomes more susceptible for rutting. Therefore, the Strategic Highway Research Program (SHRP) asphalt binder specification recommend asphalt binder to be tested for fatigue resistance at temperature range between 16 and 31 C for PG 64 asphalt binders (for example), while the rutting resistance of the asphalt binder is measured through testing at high temperature of 64 C for the same grade of binder [26]. Deacon et al. [10] defined the critical temperatures, as the temperature in situ where most of the damage occurs. They found more than 40% of fatigue damage occurs 5 C around the critical temperature. They recommended proper temperature ranges of Number of Cycles to Failure 3,500,000 3,000,000 2,500,000 2,000,000 1,500,000 1,000, , kpa 360 kpa 432 kpa 504 kpa 576 kpa Loading Frequency (Hz) Fig. 12. Loading frequency (f) versus number of loading cycles to failure (N f )at T =20 C.

8 260 G.G. Al-Khateeb, K.A. Ghuzlan / International Journal of Fatigue 59 (2014) Number of Cycles to Failure 20,000 15,000 10,000 5, kpa 360 kpa 432 kpa 504 kpa 576 kpa Loading Frequency (Hz) Fig. 13. Loading frequency (f) versus number of loading cycles to failure (N f )at T =30 C. Table 7 Non-linear regression models. Stress level (kpa) Exponential model r 2 T =20 C 288 N f = 42,756 e 0.430f N f = 36,943 e 0.361f N f = 16,785 e 0.383f N f = 7750 e 0.406f N f = 3494 e 0.400f T =30 C 288 N f = 1499 e 0.240f N f = 1034 e 0.235f N f = 490e 0.261f N f = 207e 0.303f N f = 281e 0.193f N f = number of loading cycles to fatigue failure and f = loading frequency. Number of Cycles to Failure 10,000,000 1,000, ,000 10,000 1, Loading Frequency (Hz) 288 kpa-20c 360 kpa-20c 432 kpa-20c 504 kpa-20c 576 kpa-20c 288 kpa-30c 360 kpa-30c 432 kpa-30c 504 kpa-30c 576 kpa-30c Fig. 14. Loading frequency (f) versus number of loading cycles to failure: 20 C versus 30 C C for laboratory fatigue testing while the permanent-deformation laboratory testing temperature was recommended between 30 and 45 C. AASHTO provisional TP 8 [4] adopted the simple flexural setup to evaluate fatigue performance of asphalt concrete mixtures with testing temperature of 20 C. In this study, two testing temperatures were used namely 20 and 30 C since this range is considered the most critical range for fatigue damage to occur at moderate climate regions, while at lower temperatures low temperature cracking is more critical. The direct effect of the loading frequency on the number of cycles to failure (fatigue life) was also investigated in this study. The scatter plots between the loading frequency and the number of cycles to fatigue failure (N f ) were illustrated in Figs. 12 and 13 at the test temperatures 20 and 30 C, respectively. In these two figures, the best model that fitted the fatigue data obtained using the IDT test was the exponential model with high coefficient of simple determination (r 2 ), which ranged from and for T =20 C, and from and for T =30 C as shown in Table 7. In Fig. 12, the fatigue life at a temperature of 20 C increased with the increase in loading frequency. In addition, the rate of increase in the fatigue life with the loading frequency was exponential. The exponential increase in the fatigue life with the loading frequency implied that at higher loading frequencies, the rate of increase in the fatigue life at a certain stress level magnified. As shown in Fig. 12, the difference in the fatigue life (the number of cycles to fatigue failure (N f )) between the different stress levels was much higher at higher loading frequencies than that at lower loading frequencies. Similarly, at a temperature of 30 C, the fatigue life of asphalt mixtures increased with the increase in the loading frequency exponentially. Specifically, the rate of increase in the fatigue life at a certain stress level was higher at higher loading frequencies as shown in Fig. 13. However, the exponential rate of increase in the fatigue life with the loading frequency at a temperature of 30 C was lower than that at a temperature of 20 C. That was also clear from the slope coefficients in the models summarized in Table 7. In this table, at T =20 C, the slope coefficient ranged from to at different stress levels; whereas, in the same table at T =30 C, the slope coefficient ranged from to at different stress levels. This is to conclude that in the stress-controlled test mode using the IDT test, the effect of loading frequency on the fatigue life of asphalt mixtures at lower temperatures is more significant than that at higher temperatures. As shown in Fig. 13 at T = 30 C, the difference in the fatigue life or the number of cycles to failure (N f ) between the different stress levels was again higher at higher loading frequencies than that at lower loading frequencies. Fig. 14 shows a comparison between the fatigue life curves at 20 and 30 C. This figure again shows that at the same loading frequency, the fatigue life at T =20 C was higher than the fatigue life at T =30 C. 6. Conclusions Based on the results of this study conducted in the laboratory where the IDT fatigue test configuration was utilized and the stress-controlled mode was used, the following conclusions were drawn: 1. The fatigue life (the number of cycles to fatigue failure (N f )) of asphalt paving mixtures increased with the increase in loading frequency at both temperatures 20 and 30 C. 2. The best model that fitted the fatigue data (the number of loading cycles to fatigue failure, N f versus the loading frequency, f) was the exponential model with high coefficient of simple determination (r 2 ), which ranged from and for T =20 C, and from and for T =30 C. 3. The rate of increase in the fatigue life with the loading frequency was exponential at the two temperatures 20 and 30 C. However, the exponential rate of increase in the fatigue life with the loading frequency at a temperature of 30 C was lower than that at a temperature of 20 C. In other words, at lower temperatures in the stress-controlled mode, the effect of loading frequency on the fatigue life of asphalt paving mixtures was more significant than that at higher temperatures.

9 G.G. Al-Khateeb, K.A. Ghuzlan / International Journal of Fatigue 59 (2014) The difference in fatigue life (N f ) between the different loading frequencies was found to be higher at lower stress levels than that at higher stress levels. This was valid at the two test temperatures: 20 and 30 C. 5. The non-linear power model best fitted the fatigue data at different loading frequencies for the two temperatures 20 and 30 C. The coefficient of simple determination (r 2 ) was significantly high for the two sets of models at the two temperatures, which ranged from to for T =20 C and from to for T =30 C. 6. The fatigue life of asphalt paving mixtures decreased with the increase in temperature from 20 C to 30 C. However, it increased with the increase in loading frequency at the same temperature. 7. The percentage decrease in the fatigue life from 20 to 30 C was quantified for all stress levels and loading frequencies and found to be in the range of 95 99%. The difference in the fatigue life between the different stress levels was much higher at higher loading frequencies than that at lower loading frequencies for the two temperatures 20 and 30 C. Acknowledgment The results of this paper are part of a research project funded from the Deanship of Scientific Research at Jordan University of Science and Technology. The authors of this paper are grateful for their financial support. References [1] American Association of State Highway and Transportation Officials (AASHTO), AASHTO T Theoretical maximum specific gravity of bituminous mixtures. Standard specifications for transportation materials and methods of sampling and testing, Part II-Tests, 20th ed.; [2] AASHTO T Bulk specific gravity of compacted bituminous mixtures using saturated surface-dry specimens. 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