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Recovery of asphalt mixture stiffness during fatigue loading rest periods
Construction and Building Materials 158 (2018) 591–600
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Recovery of asphalt mixture stiffness during fatigue loading rest periods Hassan Baaj a,⇑, Peter Mikhailenko a, Haya Almutairi a, Herve Di Benedetto b a b
Centre for Pavement and Transportation Technology, Department of Civil and Environmental Engineering, Faculty of Engineering, University of Waterloo, Waterloo N2L 3G1, Canada University of Lyon, École Nationale des TPE (LGCB), LTDS (CNRS UMR 5513), Rue Maurice Audin, 69518 Vaulx-en-Velin CEDEX, France
h i g h l i g h t s Introducing rest periods in fatigue loading of asphalt mixtures were examined. Neat and polymer modified asphalt was tested, with the polymer modified asphalt having a higher fatigue life. Rest periods extended fatigue life significantly at intermediate temperatures (10 °C and 20 °C). Rest periods at colder temperatures would have a detrimental effect on the fatigue life of the mixture.
a r t i c l e
i n f o
Article history: Received 5 June 2017 Received in revised form 25 September 2017 Accepted 2 October 2017
Keywords: Asphalt mixture Fatigue Self-healing Stiffness Modulus recovery Rest period
a b s t r a c t Asphalt is a self-healing material that has the ability to restore part of its stiffness and strength during rest periods and elevated temperatures, leading to a significant extension in service life. The selfhealing of asphalt mixtures has been investigated in this paper using a modified tension-compression fatigue test. Asphalt mixture specimens, prepared with different binders (neat and SBS polymer modified) and gradations, were sinusoidally loaded in strain control mode, with a rest period being introduced at the end of each loading period. Rest period temperatures varied at 0, 10 and 20 °C. This loading-rest sequence was repeated three or four times. For some tests, the samples were loaded to complete failure after the final rest period. The asphalt mixture with the polymer modified asphalt had much better resistance to fatigue loading compared to the samples with neat binder. The stiffness of the sample represented by the norm of complex modulus (|E⁄|) showed an increase during the rest periods. The fatigue life in terms of number of loading cycles was higher with an increase in rest time temperatures. Moreover, the fatigue life values of the samples with rest periods were significantly higher than for continuously loaded samples loaded under the same conditions. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The self-healing or stiffness recovery or intrinsic healing) of asphalt mixtures has been studied extensively during the last decade as a popular research topic. It is a process that counteracts the growth of fatigue cracks during rest periods [6] and elevated temperatures [26], leading to a significant extension in fatigue, and by extension, service life [32]. Therefore, it is important to investigate the fatigue behavior of asphalt mixtures in relation to their intrinsic healing properties. In 2004, the ‘‘RILEM TC 182-PEB” Technical Committee conducted a test campaign featuring 11 different test setups with more than 150 fatigue results [15]. In their investigation, the presence of three distinct phases during fatigue test has been
⇑ Corresponding author. E-mail address: [email protected] (H. Baaj). https://doi.org/10.1016/j.conbuildmat.2017.10.016 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
confirmed. The first phase is the initiation phase during which the rapid decrease of the modulus could not be solely explained by fatigue, but by the presence of other phenomena such as local heating and thixotropy [4]. During fatigue loading, micro-cracks will be initiated in the first phase and then start to propagate inside the material during the propagation phase. The first and second periods are related to crack-initiation, while the third period is related to ‘‘macro” crack evolution leading to sample failure [16]. The intrinsic healing has been found to have the greatest impact on fatigue life during the propagation phase [29]. During investigations of the complex modulus during the three phases of the fatigue test, [31] introduced the Poisson’s ratio as a parameter. Their tests were conducted in tension-compression at 10 °C, 10 Hz in strain control mode. The Poisson’s ratio was found to increase during the initiation phase, decreasing slowly during the propagation phase and rapidly decreasing during failure. Visible correlations were found between the volumetric strains and
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global damage in similar fatigue tests [32]. As the sample temperature increased during the test, the modulus decreased and the volume of the sample increased. The development of microcracks within the sample could explain the increase of volume obtained during fatigue test [32]. For the same tests, the temperature was found to rapidly decrease when rest periods were introduced [21]. Dynamic mechanical analysis DMA was performed by [19] on two SHRP-classified binders, AAD-1 which has a phase angle variation from 56° at 10 °C to 78° at 40 °C and AAM-1 which has a phase angle variation from 36° at 10 °C to 76° at 40 °C, to investigate fatigue damage and healing in asphalt mixtures during different rest periods. They found that the fatigue life was extended for both mixtures; however, AAM-1 healed considerably better than asphalt AAD-1. Another study by Shen et al. [28] used the dissipated energy approach and the dynamic shear rheometer test to investigate the healing of asphalt binder. The rate of dissipated energy recovery per unit of rest time was used as a tool to quantify the healing. Their study showed that the type of asphalt binder, the strain level applied, and the temperature all affect the perceived healing capability of asphalts. The effect of rest periods to extend fatigue life has been investigated by a number of researchers. It was concluded by Brown et al. [8] that stress amplitude, frequency, in situ healing rate and rest periods are the main variables that affect the degree of fatigue life extension. For instance, the fatigue life was more than doubled increased by 118%) when the rest period was optimized in rapidly growing cracks. Also, the results indicated that when the cracking growth rate is slower than the in situ healing rate, the fatigue life was extended noticeably. Castro and Sanchez [10] found that the mixture fatigue life of samples with rest periods noticeably increased by five to ten times compared to samples that were loaded continuously. The healing tests can be extended to different temperatures, load levels, and mix types [9]. Shan et al. [27] conducted fatigue tests with 10 Hz sinusoidal loading at temperatures of 20 °C and 25 °C to characterize a thixotropic model. The findings of their model showed that fatigue and healing were more likely associated with thixotropy, in which the microstructure of samples breakdown and build up causing the change of the sample behavior during fatigue and healing tests. Daniel and Kim [13] conducted a three-point bending test using the impact resonance method, carried out with cycles of loading and healing on asphalt mixture beams. A total of 3000 load cycles were first applied at 1.7 Hz. The beams were kept at two different temperatures of 20 °C and 60 °C, for a rest period of 4 h, and then these beams were conditioned for 6 h at 20 °C. The exact procedure was repeated at 10,000 and 20,000 cycles, and finally, the beams were fatigue loaded until they failed. The results showed that the rate of healing and stiffness increased with the increase in temperature and rest time. Breysse et al. [7] applied rest periods to the two-point bending fatigue test, and then modeled the sequences of fatigue and recovery. The findings indicated that the redamaging rate was a good indicator of non-recoverable damage. Grant [17] used the indirect tensile fatigue and resilient modulus to characterize the fatigue and healing properties of asphalt mixtures. Two different temperatures (10 °C and 15 °C) were used in the indirect tensile fatigue test. At the beginning, a 0.1 s load period was applied with a recovery period of 0.9 s for 1000 cycles. Furthermore, resilient modulus tests were conducted after the load was removed for 2, 4, 6, 10, 20, 40, and 60 min. The results found the healing to be a non-linear process which is rapidly occurred at the begging of the rest period and decreased over time. Results also indicated a dependent relationship between healing and temperature, since healing at relatively higher temperatures is much faster than for lower temperatures.
Abo-Qudais and Suleiman [1] monitored fatigue damage and crack healing using stress control indirect tensile fatigue test along with ultrasound pulse velocity (UPV) measurements. The fatigue test was performed in two stages, with a recovery period in between. Five different recovery periods (1, 3 h, and 3, 7, and 14 days) and five different temperatures (0, 15, 30, 45, and 60 °C) were applied in the study. The UPV measurements were conducted continuously before and after each stage of the fatigue tests and after the rest periods. The results showed that when the load increased, the UPV decreased, and when rest periods/temperatures increased, the UPV increased. However, the values of UPV were susceptible not only to rest period length and temperature, but also the aggregate gradation. Nguyen et al. [22,24] have shown experimental evidence of the validity of the time temperature superposition principle (TTSP) in the nonlinear domain, including crack propagation. This result may be of practical importance when modeling fatigue behavior. Babadopulos et al. [5], Di Benedetto et al. [14], Nguyen et al. [23] and Tapsoba et al. [28,29] have developed an original approach to identify and quantify the different physical phenomena existing during fatigue tests on bituminous mixtures. Beside transient effects existing only at the beginning of cyclic loading [13], these phenomena can be separated in two groups, i) reversible phenomena, including: non linearity, self-heating and thixotropy, that can be considered as biased effects when analyzing fatigue damage during fatigue test and, ii) irreversible phenomenon called fatigue damage. The category of healing generally groups reversible phenomena. The authors considered the recovery to be a better qualification than healing in qualifying the observed recovery of complex modulus during rest period. Healing appears as more adapted when a ‘‘macro-crack” exists. In general, characterizing fatigue-healing behavior would help pavement professionals to evaluate the fatigue life values of asphalt materials to effectively develop maintenance strategies and design long-lasting pavements [7]. In addition, long-lasting pavement will help to reduce CO2 emissions and the energy consumption required for pavement maintenance, rehabilitation and replacement [20]. This paper investigates the fatigue and healing behavior of asphalt mixtures using a modified tensioncompression fatigue test on three different mixes. 2. Materials and methods 2.1. Materials 2.1.1. Asphalt mixtures Three asphalt mixture formulations were selected for this study (Table 1), having been developed at ENTPE (known as ‘‘gradation 0/6), and used in several other projects. The mixtures E2 and E7 are dense-graded mixes, while E13 had very a similar gradation with a slightly larger proportion of course particles (passing 3.15–4 mm). Both the coarse and fine aggregates were diorite. The asphalt binder content for all three mixes was 6.8% of the mass of the mix, with the binder having a penetration value (EN 1426) of around 60. E2 and E13 were fabricated with neat binder where the binder for E7 had 4% of SBS polymer. 2.1.2. Sample preparation Asphalt concrete slabs were compacted using the French laboratory compactor [12]. The dimensions of the compacted slabs were 150 400 600 mm3. Two weeks after the compaction, cylindrical specimens with a diameter of 80 mm were cored vertically in the same direction as the compaction and then trimmed to a 120 mm height [3]. Table 1 Asphalt mixture binders. Mixture
Binder type
E2 E7 E13
60 Pen straight 60 Pen with 4% SBS 60 Pen straight
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The number of cycles for a loading period was set at 300,000 for the majority of tests at a frequency of 10 Hz. Only three E13 tests, which had an elevated strain amplitude of 100 mm/m, were limited to 150,000 cycles. The load time for these tests were reduced in order not to initiate failure too quickly and being able to observe several stress periods. Different thermal conditions were studied during the rest periods. For the loading periods, the temperature was kept constant at 10 °C in the chamber. For rest periods, 0 °C or 10 °C or 20 °C were applied. As shown in Table 2, one test was performed on E2 at a strain amplitude of 80 mm/m. Five tests were performed on E7, with two strain amplitudes of 80 and 160 mm/m. Seven tests were conducted on E13, with two strain amplitudes of 80 and 100 mm/m [3].
3. Results 3.1. Observations of loading and rest periods Some examples of the results used in the analysis of healing are presented in this section, focusing specifically on sample E13-10010 (Table 2). It allows to describe the general trends of the selfhealing fatigue test. The results are presented with respect to both loading cycles and time. 3.1.1. Change in modulus Fig. 3 shows the evolution of the modulus (norm of the complex modulus) with the number of cycles and with respect to time. As expected an increase in modulus is observed during the rest periods.
Fig. 1. Picture of the fatigue sample and testing system. 2.2. Test methods
i=2
3.1.3. Dissipated energy The dissipated energy per cycle of the samples, Wdis, was calculated during the loading phase and for cycles applied during rest periods (Fig. 5). Dissipated energy decreases during fatigue periods and seems rather constant during rest periods. 3.1.4. Evolution of the temperature The temperature measured at the surface of the sample is shown with respect to loading cycles and time in Fig. 6. During the loading, the samples experienced an increase in temperature, with the temperature rising rapidly during the first 50,000 cycles, after which, the temperature stabilized until the end of the loading
Rest Period 1
E(fin)1
24 Hours
Short Loading Periods for Modulus Measurement
Rest Period 2
Loading Period 2 150k or 300k cycles
E02
i=4
i=3 24 Hours
24 Hours
Loading Period 1 150k or 300k cycles
E01
3.1.2. Phase angle As for a typical fatigue test [25], the phase angle increased during cyclic loading (Fig. 4). During the rest time, the phase angle decreases as the sample becomes stiffer.
E(fin)2
Rest Period 3
Loading Period 3 150k or 300k cycles
E03
Short Loading Periods for Modulus Measurement
i=1
Short Loading Periods for Modulus Measurement
Deformation
A Tension-Compression fatigue test was performed at University of Lyon/ ENTPE, loading the cylindrical sample in strain control mode using a sinusoidal cyclic signal at 10 Hz. The advantage of this test is the homogeneous state of stress and strain inside the sample. With such homogeneous conditions, the behavior law could be obtained directly from measurements of force and displacements at the boundary of the sample, giving the stress and strain fields (r and e). The values of axial strain were obtained using three displacement transducers (Fig. 1). At each cycle, the strain in the sample is considered as the average of the measurements given by the three transducers. When one or more of the strain values reached a difference of ±25% from the average, the strain field within the sample was considered as highly non-homogeneous, and not considered in the results [4]. The experimental procedure consisted of first, a sinusoidal loading in strain control mode for a set number of loading cycles and then a rest period for each sample. The total duration of the loading and rest period together was 24 h, repeated three or four times. The time for loading periods 1, 2 and 3 was 4–8 h. The modulus (E0i) at the beginning of the loading period i and the modulus (E(fin)i) at the end of the loading period were measured as indicated in Fig. 2. After the last rest time, the sample was loaded to sample failure or voluntary stop in loading period 4. During the rest time, the modulus was measured. In order not to damage the sample, the loading is limited to fifteen cycles, with the same amplitudes as during the loading periods. These measurements were repeated three times during the first hour of rest time, then taken every hour until the loading was restarted.
E(fin)3
Time Loading Period 4 Until Sample Failure or Deliberate Stop
E04
Fig. 2. Schematic of fatigue healing test including loading and rest periods.
E(fin)4
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Table 2 Conditions for self-healing tests, all loading periods are at 10 Hz and 10 °C. # of cyclesa
# of rest periods
Temperature (°C). during rest periods
E2-80-10 E7-80-10 E7-80-20 E7-160-0 E7-160-10 E7-160-20 E13-80-0 E13-80-10 E13-80-20 E13-100-0 E13-100-10 E13-100-20 E13-80/100-10
80 80 80 160 160 160 80 80 80 100 100 100 80 and 100b
300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 150,000 150,000 150,000 300,000 and 150,000b
3 3 3 3 3 4 3 3 3 3 3 3 4
10 10 20 0 10 20c 0 10 20 0 10 20 10
For each of the loading periods except the last one. 300,000 cycles at 80 mm/m for rest periods 1 and 3 and 150,000 cycles at 100 mm/m for rest periods 2 and 4. The 4th rest time is completed without an increase in temperature.
11000
IE*I (MPa)
10000 9000 8000 7000 LR
6000
LR
LR
L
5000 0
300000
600000
900000
1200000
0
10 20 30 40 50 60 70 80 90 100
N (cycles)
Time (h)
Fig. 3. Evolution of modulus with respect to number of cycles (left) and time (right) during loading (L) and rest (R) periods for E13-100-10.
27 25
ϕ (°)
c
Strain Amplitude (mm/m)
23 21 19
LR 0
300000
600000
900000
1200000
0
LR
LR
L
10 20 30 40 50 60 70 80 90 100
N (cycles)
Time (h)
Fig. 4. Phase angle with respect to the number of cycles (left) and time (right) during loading (L) and rest (R) periods for E13-100-10.
120 110
Wdis (J/m3)
a b
Sample Name
100 90 80 LR
70 0
300000
600000
N (cycles)
900000
1200000
LR
LR
L
0 10 20 30 40 50 60 70 80 90 100
Time (h)
Fig. 5. Dissipated energy per cycle with respect to the number of cycles (left) and time (right) during loading (L) and rest (R) periods for E13-100-10.
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10.1 10.0
T (°C)
9.9 9.8 9.7 9.6 9.5 0
300000
600000
900000
1200000
N (cycles)
LR
LR
LR
L
0 10 20 30 40 50 60 70 80 90 100
Time (h)
Fig. 6. Temperature of sample with respect to the number of cycles (left) and time (right) during loading (L) and rest (R) periods for E13-100-10.
Fig. 7. Initial E0i and final EðfinÞi for each loading period (10 °C, 10Hz) from Asphalt E2 and E7.
period. For the fourth phase of loading, the temperature decreased somewhat after 750,000 cycles. The overall change in temperature at the surface during the loading was rather small (around 0.4 °C), while the temperature during the rest periods stayed mostly constant and equal to thermal chamber temperature. 3.2. Analysis of rest periods 3.2.1. Modulus recovery after the loading cycles When the loading was stopped after each loading cycle, the samples experienced a recuperation in the modulus until the next loading cycle. For each sample, the modulus value at the beginning and (E0i) and the end (E(fin)i) of each loading period (see Fig. 2 description of loading and rest periods) are shown in Figs. 7 and 8. Fig. 9 shows the ratio between the value of the modulus during the rest period (E) and the value of the modulus when starting rest period (E(fin)i), as a function of time for the 3 rest periods for sample E2-80-10. During the rest period, the modulus value increased rapidly after the end of loading. The modulus recuperation during the first hour represents the majority of the recuperation for the duration of the rest period and subsequently, this increase
becomes much more moderate. Toward the end of each rest period, the modulus increased at a much slower rate. It was also found that the modulus recoveries obtained for the different rest periods are very similar in rate and amplitude, as recuperation curves are nearly overlapping for the different rest periods. The modulus recuperations for each rest period were calculated and compared. The values of the recovered modulus (DE) during a rest period as a percentage of the modulus (E(fin)i) at the beginning of the rest period are presented in Table 3. The% recovery is higher for samples loaded with higher amplitudes.
3.2.2. Modulus evolution relative to the modulus at the beginning of the test To observe the modulus evolution for each sample, initial modulus for each loading cycle E0i, in relation to the initial modulus E01 was compared in Fig. 10. The modulus value E01 represents the stiffness of the sample at the beginning of testing before any loading. For a loading period i, E0i corresponds to the modulus at the beginning of the loading period. The modulus loss occurs mostly after the first loading period.
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Fig. 8. Initial E0i and final EðfinÞi for each loading period (10 °C, 10Hz) for Asphalt E13.
Table 3 Modulus recuperation during rest periods relative to the modulus at the end of the previous loading cycle.
1.18 1.16 1.14
E/E(fin)i
1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98
0
2
4
6
8
10
12
14
16
Time (h) Rest 1
Rest 2
Rest 3
Sample
%DE/E(fin)1 %D E/E(fin)2 %D E/E(fin)3 %D E/E(fin)4 % Average
E2-80-10 E7-80-10 E7-80-20 E7-160-0 E7-160-10 E7-160-20 E13-80-0 E13-80-10 E13-80-20 E13-100-0 E13-100-10 E13-100-20 E13-80/100-10
16.4 18.6 17.8 41.8 40.9 44.6 16.4 13.8 16.2 25.7 24.2 27.0 16.5
16.0 17.7 18.6 42.5 40.2 43.0 15.5 15.5 15.1 26.1 24.7 22.5 23.0
16.2 17.4 18.0 42.1 42.8 45.8 16.9 16.5 15.6 28.4 25.9 23.6 18.6
41.0
26.8
16.2 17.9 18.1 42.1 41.3 44.5 16.3 15.3 15.6 26.7 24.9 24.4 21.2
Fig. 9. Typical modulus recuperation during sample rest period (E2-80-10).
3.3. Analysis of loading cycles The evolution of the observed damage for each loading cycle period, taken as the modulus of the sample compared to the value of the initial modulus before any loading, is shown in Figs. 11–14. The results are compared to the results of samples tested continuous loading (no rest periods, NoRP), or in the case of Fig. 11, with much shorter rest periods (ShRP), in order to observe their effects [4]. In general, the modulus recovery is better for the samples with rest periods, which is sustained over all of the loading cycles. Figs. 12–14 show the relative modulus values for the samples with 0 °C rest period temperature were significantly lower than the 20 °C samples at the same loading amplitude. 3.4. Specimen fatigue life extension with rest periods In examining the specimen fatigue life values, we considered the life of the samples as the number of total number of accumulated cycles, Nf, before the rupture of the specimen, that is to say, its complete failure. The samples of asphalt E13 were all tested in fatigue until rupture. However, it was found that for asphalt
E7, the rupture conditions were very difficult to achieve and would take an impractical number of cycles under the testing conditions as the polymer modification made the fatigue life very long. Therefore, only the results for E13 were considered in this section. Table 4 shows the values of Nf for tests on asphalt E13 for both loading amplitudes 80 and 100 mm/m. In general, the introduction of rest periods during the fatigue test significantly improved the fatigue life of asphalt mixtures when the rest period was kept at 10 °C. Lowering the rest period temperature to 0 °C made the rest periods almost ineffective in improving the fatigue life or even having a negative effect. Increasing the temperature to 20 °C improves fatigue life somewhat compared to the test at 10 °C, but the difference in fatigue life values between the two cases is negligible. 4. Discussion The discussion of the results is divided into two parts: i) analysis of modulus evolution during loading periods ii) the effects of the rest periods on the fatigue life of the samples.
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104
E02/E01
102
E03/E01
0°C
0°C
E04/E01
20°C
E05/E01
E 0i /E 01 (%)
100
20°C
98 96
10°C
10°C
20°C
20°C
10°C
10°C
10°C
10°C
94
0°C 92 90 88 80 31 E
23
80 31 E
25
4 3 9 1 2 -3 -3 -2 -3 -3 80 00 00 00 00 3-1 -1 -1 -1 1 3 3 3 0 8 E E1 E1 E1 3E1
0-8 E7
8 E7
10 0-8
E7
-2 60 -1
E7
2 -1 60 -1 7 E
-3 60 -1
0-8 E2
21
Fig. 10. Initial modulus for each loading cycle (E0i) as a percentage of the Initial modulus (E01).
1.05 E2-Auto-80 (10°C)
Rest time 10mn
1
E2D80 (ShRP)
E*/E01
0.95 0.9
Rest time 60mn
0.85 0.8 0.75 0.7
0
500000
1000000
1500000
2000000
2500000
3000000
N (cycles) Fig. 11. Evolution of modulus relative to the original modulus for Asphalt E2 in self-healing and sample loaded with same conditions with short rest times of 10 and 60 min.
1.10
E7-Auto-160 (0°C) E7-Auto-160 (20°C)
1.00
(NoRP) E7-Auto-160 (10°C) E7D160
E*/E 01
0.90 0.80 0.70 0.60 0.50
0
1000000
2000000
3000000
4000000
5000000
N (cycles) Fig. 12. Evolution of modulus relative to the original modulus for Asphalt E7 at 160 mm/m in self-healing and continuous loading.
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1.1 E13-Auto-80-34 (0°C) E13-Auto-80-25 (20°C) E13-Auto-80-23 (10°C) E13D80-14 (NoRP) E13D80-11 E13D80-21
E*/E01
1
0.9
0.8
0.7
0.6
0
500000
1000000
1500000
2000000
2500000
3000000
N (Cycels) Fig. 13. Evolution of modulus relative to the original modulus for Asphalt E13 at 80 mm/m in self-healing and continuous loading.
1.1 E13-Auto-100-33 (0°C) E13-Auto-100-29 (20°C) E13-Auto-100-31 (10°C) E13D100-13 (NoRP) E13D100-1
1
E*/E01
0.9 0.8 0.7 0.6 0.5 0.4
0
200000
400000
600000
800000
1000000
1200000
1400000
N (Cycles) Fig. 14. Evolution of modulus relative to the original modulus for Asphalt E13 at 100 mm/m in self-healing and continuous loading.
4.1. Analysis of fatigue loading periods The rupture conditions for mixture E7 were very difficult to achieve compared to the other mixes. The higher fatigue resistance of mix E7 can be attributed to the effects of SBS polymer modified binder compared to the neat as found in previous studies [30,33], and confirming the viability of SBS in improving pavement performance by improving the durability of the asphalt binder matrix [18]. The highest loss of modulus occurred after the first loading cycle, the loss of modulus progressively decreasing with the next loading cycle as found in similar studies, as the energy of the sample tends to dissipate with the loading [17], through the formation of microcracks, heat energy and thixotropy. 4.2. Specimen fatigue life extension with rest periods Fig. 15 shows the fatigue life value of Nf (50%), obtained using the classical fatigue criterion corresponding to 50% of drop of the initial stiffness, for both the E13 samples with rest periods, as well as the E13 samples that were continuously loaded until failure, according to the loading amplitude. A comparison with the Nf (50%) for the
Table 4 Fatigue life in cycles for sample of asphalt mixture E13. Sample
Nf
E13-80-0 E13-80-10 E13-80-20 E13-100-0 E13-100-10 E13-100-20
1109860 2480000 2540000 762918 1273600 1300000
self-healing samples shows an improvement of the sample fatigue life with rest periods, which may indicate that the phenomenon contributes significantly to the long term performance of the pavement if the conditions are favourable. By comparing the self-healing fatigue life values with those from the continuous loading, the increase in fatigue life from self-healing at different conditions was determined by taking the fatigue life of the samples with a rest period as a percentage of those from continuous loading for the same loading amplitude (Table 5). The lifetimes obtained with the self-healing tests were
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Fig. 15. Fatigue life values in cycles for sample of asphalt mixture E13 in with fatigue-healing and continuous loading as a function of the loading amplitude e0.
Table 5 Increase in fatigue life cycles for sample of asphalt mixture E13 for samples tested with self-healing. Sample
E13-80-0
E13-80-10
E13-80-20
E13-100-0
E13-100-10
E13-100-20
Increase in Fatigue Life (%)
81%
181%
186%
121%
203%
207%
generally higher than those with continuous loading as found in previous fatigue-healing studies [8,10]. When the rest period temperature was kept the same as the loading temperature (10 °C), the fatigue performance significantly improved. The increase of the temperature to 20 °C made a very modest difference compared to 10 °C while when the temperature was brought down to 0 °C, the rest period made no contribution, or was even detrimental to fatigue performance. This indicates that the rest period can even have a negative effect on fatigue performance in cold climate conditions. This can be attributed to the binder being more malleable from 10 °C, allowing for it to heal the microcracks created in the asphalt matrix during fatigue loading. Secondly, the asphalt is generally more brittle at low temperatures [2], which would explain why the fatigue life decrease with rest periods of 0 °C. It has been shown elsewhere that higher temperatures increase the healing rate of asphalt [11]. This effect was more profound for the samples tested at a higher amplitude, as more microcracks would likely be formed that could be filled by the healing. This could also be attributed to an increase in sample temperature during loading and thixotropy [4]. For the rest time of 0 °C, that is, a decrease in the temperature during the rest time, the fatigue life both increased and decreased by 20% based on the loading amplitude. This difference, again, could be attributed to the increase in asphalt temperature at higher loading amplitudes, which contributes to the malleability and promotes self-healing.
5. Conclusion and perspectives 5.1. Conclusions The current study of self-healing in asphalt highlighted the great importance of this phenomenon in pavement performance. The results of fatigue and self-healing tests lead to the following conclusions:
The asphalt mixture with the polymer modified binder had much improved performance to an equivalent mixture with neat binder in resistance to fatigue loading. The modulus loss from fatigue was the highest in the first loading periods of the test, as was the subsequent recovery during these periods. The fatigue life values of the samples with rest periods were higher than for continuously loaded samples when the rest temperature was kept at 10 °C or above. Having the temperature at 10 °C or higher during the rest periods led to a structural rearrangement in the material leading to extensive healing of microcracks, as well as increased recovery and fatigue life. Conversely, a decrease in temperature during the rest periods increases the rigidity of the sample, making it more difficult of the recovery to take place, and possibly allowing for more damage to take place in the asphalt. For future research, it would be useful to make a model the selfhealing phenomenon for a number of asphalt mixtures that factors temperature and rest time. This would allow us to more accurately consider this phenomenon in pavement design. References [1] S. Abo-Qudais, A. Suleiman, Monitoring fatigue damage and crack healing by ultrasound wave velocity, Nondestr. Test. Eval. 20 (2005) 125–145, https://doi. org/10.1080/10589750500206774. [2] D. Anderson, L. Lapalu, M. Marasteanu, Y. Hir, J.-P. Planche, D. Martin, Lowtemperature thermal cracking of asphalt binders as ranked by strength and fracture properties, Transp. Res. Rec. (2001) 1–6. [3] Baaj, H., 2002. Comportement à la fatigue des matériaux granulaires traités aux liants hydrocarbonés (PhD Thesis). INSA Lyon. [4] H. Baaj, H. Di Benedetto, P. Chaverot, Effect of binder characteristics on fatigue of asphalt pavement using an intrinsic damage approach, Road Mater. Pavement Des. 6 (2005) 147–174. [5] L.F. Babadopulos, A.L. de, C. Sauzéat, H. Di Benedetto, Softening and local selfheating of bituminous mixtures during cyclic loading, Road Mater. Pavement Des. (2017) 1–14, https://doi.org/10.1080/14680629.2017.1304260. [6] A. Bhasin, R. Bommavaram, M.L. Greenfield, D.N. Little, Use of molecular dynamics to investigate self-healing mechanisms in asphalt binders, J. Mater. Civ. Eng. 23 (2010) 485–492.
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[7] D. Breysse, V. Domec, S. Yotte, C. De La Roche, Better assessment of bituminous materials lifetime accounting for the influence of rest periods, Road Mater. Pavement Des. 6 (2005) 175–195. [8] E. Brown, S. White, N. Sottos, Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite—Part II: in situ self-healing, Compos. Sci. Technol. 65 (2005) 2474–2480, https://doi.org/10.1016/ j.compscitech.2005.04.053. [9] S. Carpenter, S. Shen, Dissipated energy approach to study hot-mix asphalt healing in fatigue, Transp. Res. Record (2006) 178–185. [10] M. Castro, J.A. Sanchez, Fatigue and healing of asphalt mixtures: discriminate analysis of fatigue curves, J. Transp. Eng. 132 (2006). [11] Y. Chen, R. Simms, C. Koh, G. Lopp, R. Roque, Development of a test method for evaluation and quantification of healing in asphalt mixture, Road Mater. Pavement Des. 14 (2013) 901–920, https://doi.org/10.1080/ 14680629.2013.844196. [12] P. Clec’h, C. Sauzéat, H. Di Benedetto, Linear Viscoelastic Behaviour and Anisotropy of Bituminous Mixture Compacted with a French Wheel Compactor, in: Paving Materials and Pavement Analysis, American Society of Civil Engineers, 2010, pp. 103–115. [13] J.S. Daniel, Y.R. Kim, Laboratory evaluation of fatigue damage and healing of asphalt mixtures, J. Mater. Civ. Eng. 13 (2001). [14] H. Di Benedetto, Q.T. Nguyen, C. Sauzéat, Nonlinearity, heating, fatigue and thixotropy during cyclic loading of asphalt mixtures, Road Mater. Pavement Des. 12 (2011) 129–158, https://doi.org/10.1080/14680629.2011.9690356. [15] H. Di Benedetto, C. De La Roche, H. Baaj, A. Pronk, R. Lundström, Fatigue of bituminous mixtures, Mater. Struct. 37 (2004) 202–216, https://doi.org/ 10.1007/BF02481620. [16] P. Gayte, H. Di Benedetto, C. Sauzéat, Q.T. Nguyen, Influence of transient effects for analysis of complex modulus tests on bituminous mixtures, Road Mater. Pavement Des. 17 (2016) 271–289, https://doi.org/10.1080/ 14680629.2015.1067246. [17] Grant, T.P., 2001. Determination of asphalt mixture healing rate using the Superpave indirect tensile test (Master’s Thesis). University of Florida. [18] B. Kim, R. Roque, S.-H. Lee, Cost analysis for use of SBS modifier in asphalt pavement using a performance-based fracture criterion, Road Mater. Pavement Des. 9 (2008) 571–588, https://doi.org/10.1080/ 14680629.2008.9690139. [19] Y.-R. Kim, D.N. Little, R.L. Lytton, Fatigue and healing characterization of asphalt mixtures, J. Mater. Civ. Eng. 15 (2003) 75–83. [20] Q. Liu, Á. García, E. Schlangen, M. van de Ven, Induction healing of asphalt mastic and porous asphalt concrete, Constr. Build. Mater. 25 (2011) 3746– 3752, https://doi.org/10.1016/j.conbuildmat.2011.04.016.
[21] S. Mangiafico, C. Sauzéat, H. Di Benedetto, S. Pouget, F. Olard, L. Planque, Quantification of biasing effects during fatigue tests on asphalt mixes: nonlinearity, self-heating and thixotropy, Road Mater. Pavement Des. 16 (2015) 73–99, https://doi.org/10.1080/14680629.2015.1077000. [22] M.L. Nguyen, C. Sauzéat, H. Di Benedetto, N. Tapsoba, Validation of the time– temperature superposition principle for crack propagation in bituminous mixtures, Mater. Struct. 46 (2013) 1075–1087, https://doi.org/10.1617/ s11527-012-9954-7. [23] Q.T. Nguyen, H. Di Benedetto, C. Sauzeat, Effect of fatigue cyclic loading on the linear viscoelastic properties of bituminous mixtures, J. Mater. Civ. Eng. 27 (2015) C4014003, https://doi.org/10.1061/(ASCE)MT.1943-5533.0000996. [24] Q.T. Nguyen, H. Di Benedetto, C. Sauzéat, N. Tapsoba, Time temperature superposition principle validation for bituminous mixes in the linear and nonlinear domains, J. Mater. Civ. Eng. 25 (2013) 1181–1188, https://doi.org/ 10.1061/(ASCE)MT.1943-5533.0000658. [25] D. Perraton, H. Baaj, A. Carter, Comparison of some pavement design methods from a fatigue point of view: effect of fatigue properties of asphalt materials, Road Mater. Pavement Des. 11 (2010) 833–861, https://doi.org/10.1080/ 14680629.2010.9690309. [26] J. Qiu, A. Molenaar, M. van de Ven, S. Wu, J. Yu, Investigation of self healing behaviour of asphalt mixes using beam on elastic foundation setup, Mater. Struct. 45 (2012) 777–791, https://doi.org/10.1617/s11527-011-9797-7. [27] L. Shan, Y. Tan, S. Underwood, Y. Kim, Application of thixotropy to analyze fatigue and healing characteristics of asphalt binder, Transp. Res. Rec. 2179 (2010) 85–92, https://doi.org/10.3141/2179-10. [28] S. Shen, H.-M. Chiu, H. Huang, Characterization of fatigue and healing in asphalt binders, J. Mater. Civ. Eng. 22 (2010) 846–852. [29] Z. Si, D.N. Little, R.L. Lytton, Characterization of microdamage and healing of asphalt concrete mixtures, J. Mater. Civ. Eng. 14 (2002), https://doi.org/ 10.1061/(ASCE)0899-1561(2002) 14:6(461). [30] H. Soenen, C. De La Roche, P. Redelius, Fatigue behaviour of bituminous materials: from binders to mixes, Road Mater. Pavement Des. 4 (2003) 7–27, https://doi.org/10.1080/14680629.2003.9689938. [31] N. Tapsoba, C. Sauzéat, H. Di Benedetto, Analysis of fatigue test for bituminous mixtures, J. Mater. Civ. Eng. 25 (2013) 701–710. [32] N. Tapsoba, C. Sauzéat, H. Di Benedetto, H. Baaj, M. Ech, Three-dimensional analysis of fatigue tests on bituminous mixtures: three-dimensional analysis of fatigue tests on bituminous mixtures, Fatigue Fract. Eng. Mater. Struct. 38 (2015) 730–741, https://doi.org/10.1111/ffe.12278. [33] C. Wang, C. Castorena, J. Zhang, Y.R. Kim, Unified failure criterion for asphalt binder under cyclic fatigue loading, Road Mater. Pavement Des. 16 (2015) 125–148, https://doi.org/10.1080/14680629.2015.1077010.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Recovery of asphalt mixture stiffness during fatigue loading rest periods Hassan Baaj a,⇑, Peter Mikhailenko a, Haya Almutairi a, Herve Di Benedetto b a b
Centre for Pavement and Transportation Technology, Department of Civil and Environmental Engineering, Faculty of Engineering, University of Waterloo, Waterloo N2L 3G1, Canada University of Lyon, École Nationale des TPE (LGCB), LTDS (CNRS UMR 5513), Rue Maurice Audin, 69518 Vaulx-en-Velin CEDEX, France
h i g h l i g h t s Introducing rest periods in fatigue loading of asphalt mixtures were examined. Neat and polymer modified asphalt was tested, with the polymer modified asphalt having a higher fatigue life. Rest periods extended fatigue life significantly at intermediate temperatures (10 °C and 20 °C). Rest periods at colder temperatures would have a detrimental effect on the fatigue life of the mixture.
a r t i c l e
i n f o
Article history: Received 5 June 2017 Received in revised form 25 September 2017 Accepted 2 October 2017
Keywords: Asphalt mixture Fatigue Self-healing Stiffness Modulus recovery Rest period
a b s t r a c t Asphalt is a self-healing material that has the ability to restore part of its stiffness and strength during rest periods and elevated temperatures, leading to a significant extension in service life. The selfhealing of asphalt mixtures has been investigated in this paper using a modified tension-compression fatigue test. Asphalt mixture specimens, prepared with different binders (neat and SBS polymer modified) and gradations, were sinusoidally loaded in strain control mode, with a rest period being introduced at the end of each loading period. Rest period temperatures varied at 0, 10 and 20 °C. This loading-rest sequence was repeated three or four times. For some tests, the samples were loaded to complete failure after the final rest period. The asphalt mixture with the polymer modified asphalt had much better resistance to fatigue loading compared to the samples with neat binder. The stiffness of the sample represented by the norm of complex modulus (|E⁄|) showed an increase during the rest periods. The fatigue life in terms of number of loading cycles was higher with an increase in rest time temperatures. Moreover, the fatigue life values of the samples with rest periods were significantly higher than for continuously loaded samples loaded under the same conditions. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The self-healing or stiffness recovery or intrinsic healing) of asphalt mixtures has been studied extensively during the last decade as a popular research topic. It is a process that counteracts the growth of fatigue cracks during rest periods [6] and elevated temperatures [26], leading to a significant extension in fatigue, and by extension, service life [32]. Therefore, it is important to investigate the fatigue behavior of asphalt mixtures in relation to their intrinsic healing properties. In 2004, the ‘‘RILEM TC 182-PEB” Technical Committee conducted a test campaign featuring 11 different test setups with more than 150 fatigue results [15]. In their investigation, the presence of three distinct phases during fatigue test has been
⇑ Corresponding author. E-mail address: [email protected] (H. Baaj). https://doi.org/10.1016/j.conbuildmat.2017.10.016 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
confirmed. The first phase is the initiation phase during which the rapid decrease of the modulus could not be solely explained by fatigue, but by the presence of other phenomena such as local heating and thixotropy [4]. During fatigue loading, micro-cracks will be initiated in the first phase and then start to propagate inside the material during the propagation phase. The first and second periods are related to crack-initiation, while the third period is related to ‘‘macro” crack evolution leading to sample failure [16]. The intrinsic healing has been found to have the greatest impact on fatigue life during the propagation phase [29]. During investigations of the complex modulus during the three phases of the fatigue test, [31] introduced the Poisson’s ratio as a parameter. Their tests were conducted in tension-compression at 10 °C, 10 Hz in strain control mode. The Poisson’s ratio was found to increase during the initiation phase, decreasing slowly during the propagation phase and rapidly decreasing during failure. Visible correlations were found between the volumetric strains and
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global damage in similar fatigue tests [32]. As the sample temperature increased during the test, the modulus decreased and the volume of the sample increased. The development of microcracks within the sample could explain the increase of volume obtained during fatigue test [32]. For the same tests, the temperature was found to rapidly decrease when rest periods were introduced [21]. Dynamic mechanical analysis DMA was performed by [19] on two SHRP-classified binders, AAD-1 which has a phase angle variation from 56° at 10 °C to 78° at 40 °C and AAM-1 which has a phase angle variation from 36° at 10 °C to 76° at 40 °C, to investigate fatigue damage and healing in asphalt mixtures during different rest periods. They found that the fatigue life was extended for both mixtures; however, AAM-1 healed considerably better than asphalt AAD-1. Another study by Shen et al. [28] used the dissipated energy approach and the dynamic shear rheometer test to investigate the healing of asphalt binder. The rate of dissipated energy recovery per unit of rest time was used as a tool to quantify the healing. Their study showed that the type of asphalt binder, the strain level applied, and the temperature all affect the perceived healing capability of asphalts. The effect of rest periods to extend fatigue life has been investigated by a number of researchers. It was concluded by Brown et al. [8] that stress amplitude, frequency, in situ healing rate and rest periods are the main variables that affect the degree of fatigue life extension. For instance, the fatigue life was more than doubled increased by 118%) when the rest period was optimized in rapidly growing cracks. Also, the results indicated that when the cracking growth rate is slower than the in situ healing rate, the fatigue life was extended noticeably. Castro and Sanchez [10] found that the mixture fatigue life of samples with rest periods noticeably increased by five to ten times compared to samples that were loaded continuously. The healing tests can be extended to different temperatures, load levels, and mix types [9]. Shan et al. [27] conducted fatigue tests with 10 Hz sinusoidal loading at temperatures of 20 °C and 25 °C to characterize a thixotropic model. The findings of their model showed that fatigue and healing were more likely associated with thixotropy, in which the microstructure of samples breakdown and build up causing the change of the sample behavior during fatigue and healing tests. Daniel and Kim [13] conducted a three-point bending test using the impact resonance method, carried out with cycles of loading and healing on asphalt mixture beams. A total of 3000 load cycles were first applied at 1.7 Hz. The beams were kept at two different temperatures of 20 °C and 60 °C, for a rest period of 4 h, and then these beams were conditioned for 6 h at 20 °C. The exact procedure was repeated at 10,000 and 20,000 cycles, and finally, the beams were fatigue loaded until they failed. The results showed that the rate of healing and stiffness increased with the increase in temperature and rest time. Breysse et al. [7] applied rest periods to the two-point bending fatigue test, and then modeled the sequences of fatigue and recovery. The findings indicated that the redamaging rate was a good indicator of non-recoverable damage. Grant [17] used the indirect tensile fatigue and resilient modulus to characterize the fatigue and healing properties of asphalt mixtures. Two different temperatures (10 °C and 15 °C) were used in the indirect tensile fatigue test. At the beginning, a 0.1 s load period was applied with a recovery period of 0.9 s for 1000 cycles. Furthermore, resilient modulus tests were conducted after the load was removed for 2, 4, 6, 10, 20, 40, and 60 min. The results found the healing to be a non-linear process which is rapidly occurred at the begging of the rest period and decreased over time. Results also indicated a dependent relationship between healing and temperature, since healing at relatively higher temperatures is much faster than for lower temperatures.
Abo-Qudais and Suleiman [1] monitored fatigue damage and crack healing using stress control indirect tensile fatigue test along with ultrasound pulse velocity (UPV) measurements. The fatigue test was performed in two stages, with a recovery period in between. Five different recovery periods (1, 3 h, and 3, 7, and 14 days) and five different temperatures (0, 15, 30, 45, and 60 °C) were applied in the study. The UPV measurements were conducted continuously before and after each stage of the fatigue tests and after the rest periods. The results showed that when the load increased, the UPV decreased, and when rest periods/temperatures increased, the UPV increased. However, the values of UPV were susceptible not only to rest period length and temperature, but also the aggregate gradation. Nguyen et al. [22,24] have shown experimental evidence of the validity of the time temperature superposition principle (TTSP) in the nonlinear domain, including crack propagation. This result may be of practical importance when modeling fatigue behavior. Babadopulos et al. [5], Di Benedetto et al. [14], Nguyen et al. [23] and Tapsoba et al. [28,29] have developed an original approach to identify and quantify the different physical phenomena existing during fatigue tests on bituminous mixtures. Beside transient effects existing only at the beginning of cyclic loading [13], these phenomena can be separated in two groups, i) reversible phenomena, including: non linearity, self-heating and thixotropy, that can be considered as biased effects when analyzing fatigue damage during fatigue test and, ii) irreversible phenomenon called fatigue damage. The category of healing generally groups reversible phenomena. The authors considered the recovery to be a better qualification than healing in qualifying the observed recovery of complex modulus during rest period. Healing appears as more adapted when a ‘‘macro-crack” exists. In general, characterizing fatigue-healing behavior would help pavement professionals to evaluate the fatigue life values of asphalt materials to effectively develop maintenance strategies and design long-lasting pavements [7]. In addition, long-lasting pavement will help to reduce CO2 emissions and the energy consumption required for pavement maintenance, rehabilitation and replacement [20]. This paper investigates the fatigue and healing behavior of asphalt mixtures using a modified tensioncompression fatigue test on three different mixes. 2. Materials and methods 2.1. Materials 2.1.1. Asphalt mixtures Three asphalt mixture formulations were selected for this study (Table 1), having been developed at ENTPE (known as ‘‘gradation 0/6), and used in several other projects. The mixtures E2 and E7 are dense-graded mixes, while E13 had very a similar gradation with a slightly larger proportion of course particles (passing 3.15–4 mm). Both the coarse and fine aggregates were diorite. The asphalt binder content for all three mixes was 6.8% of the mass of the mix, with the binder having a penetration value (EN 1426) of around 60. E2 and E13 were fabricated with neat binder where the binder for E7 had 4% of SBS polymer. 2.1.2. Sample preparation Asphalt concrete slabs were compacted using the French laboratory compactor [12]. The dimensions of the compacted slabs were 150 400 600 mm3. Two weeks after the compaction, cylindrical specimens with a diameter of 80 mm were cored vertically in the same direction as the compaction and then trimmed to a 120 mm height [3]. Table 1 Asphalt mixture binders. Mixture
Binder type
E2 E7 E13
60 Pen straight 60 Pen with 4% SBS 60 Pen straight
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The number of cycles for a loading period was set at 300,000 for the majority of tests at a frequency of 10 Hz. Only three E13 tests, which had an elevated strain amplitude of 100 mm/m, were limited to 150,000 cycles. The load time for these tests were reduced in order not to initiate failure too quickly and being able to observe several stress periods. Different thermal conditions were studied during the rest periods. For the loading periods, the temperature was kept constant at 10 °C in the chamber. For rest periods, 0 °C or 10 °C or 20 °C were applied. As shown in Table 2, one test was performed on E2 at a strain amplitude of 80 mm/m. Five tests were performed on E7, with two strain amplitudes of 80 and 160 mm/m. Seven tests were conducted on E13, with two strain amplitudes of 80 and 100 mm/m [3].
3. Results 3.1. Observations of loading and rest periods Some examples of the results used in the analysis of healing are presented in this section, focusing specifically on sample E13-10010 (Table 2). It allows to describe the general trends of the selfhealing fatigue test. The results are presented with respect to both loading cycles and time. 3.1.1. Change in modulus Fig. 3 shows the evolution of the modulus (norm of the complex modulus) with the number of cycles and with respect to time. As expected an increase in modulus is observed during the rest periods.
Fig. 1. Picture of the fatigue sample and testing system. 2.2. Test methods
i=2
3.1.3. Dissipated energy The dissipated energy per cycle of the samples, Wdis, was calculated during the loading phase and for cycles applied during rest periods (Fig. 5). Dissipated energy decreases during fatigue periods and seems rather constant during rest periods. 3.1.4. Evolution of the temperature The temperature measured at the surface of the sample is shown with respect to loading cycles and time in Fig. 6. During the loading, the samples experienced an increase in temperature, with the temperature rising rapidly during the first 50,000 cycles, after which, the temperature stabilized until the end of the loading
Rest Period 1
E(fin)1
24 Hours
Short Loading Periods for Modulus Measurement
Rest Period 2
Loading Period 2 150k or 300k cycles
E02
i=4
i=3 24 Hours
24 Hours
Loading Period 1 150k or 300k cycles
E01
3.1.2. Phase angle As for a typical fatigue test [25], the phase angle increased during cyclic loading (Fig. 4). During the rest time, the phase angle decreases as the sample becomes stiffer.
E(fin)2
Rest Period 3
Loading Period 3 150k or 300k cycles
E03
Short Loading Periods for Modulus Measurement
i=1
Short Loading Periods for Modulus Measurement
Deformation
A Tension-Compression fatigue test was performed at University of Lyon/ ENTPE, loading the cylindrical sample in strain control mode using a sinusoidal cyclic signal at 10 Hz. The advantage of this test is the homogeneous state of stress and strain inside the sample. With such homogeneous conditions, the behavior law could be obtained directly from measurements of force and displacements at the boundary of the sample, giving the stress and strain fields (r and e). The values of axial strain were obtained using three displacement transducers (Fig. 1). At each cycle, the strain in the sample is considered as the average of the measurements given by the three transducers. When one or more of the strain values reached a difference of ±25% from the average, the strain field within the sample was considered as highly non-homogeneous, and not considered in the results [4]. The experimental procedure consisted of first, a sinusoidal loading in strain control mode for a set number of loading cycles and then a rest period for each sample. The total duration of the loading and rest period together was 24 h, repeated three or four times. The time for loading periods 1, 2 and 3 was 4–8 h. The modulus (E0i) at the beginning of the loading period i and the modulus (E(fin)i) at the end of the loading period were measured as indicated in Fig. 2. After the last rest time, the sample was loaded to sample failure or voluntary stop in loading period 4. During the rest time, the modulus was measured. In order not to damage the sample, the loading is limited to fifteen cycles, with the same amplitudes as during the loading periods. These measurements were repeated three times during the first hour of rest time, then taken every hour until the loading was restarted.
E(fin)3
Time Loading Period 4 Until Sample Failure or Deliberate Stop
E04
Fig. 2. Schematic of fatigue healing test including loading and rest periods.
E(fin)4
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Table 2 Conditions for self-healing tests, all loading periods are at 10 Hz and 10 °C. # of cyclesa
# of rest periods
Temperature (°C). during rest periods
E2-80-10 E7-80-10 E7-80-20 E7-160-0 E7-160-10 E7-160-20 E13-80-0 E13-80-10 E13-80-20 E13-100-0 E13-100-10 E13-100-20 E13-80/100-10
80 80 80 160 160 160 80 80 80 100 100 100 80 and 100b
300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 150,000 150,000 150,000 300,000 and 150,000b
3 3 3 3 3 4 3 3 3 3 3 3 4
10 10 20 0 10 20c 0 10 20 0 10 20 10
For each of the loading periods except the last one. 300,000 cycles at 80 mm/m for rest periods 1 and 3 and 150,000 cycles at 100 mm/m for rest periods 2 and 4. The 4th rest time is completed without an increase in temperature.
11000
IE*I (MPa)
10000 9000 8000 7000 LR
6000
LR
LR
L
5000 0
300000
600000
900000
1200000
0
10 20 30 40 50 60 70 80 90 100
N (cycles)
Time (h)
Fig. 3. Evolution of modulus with respect to number of cycles (left) and time (right) during loading (L) and rest (R) periods for E13-100-10.
27 25
ϕ (°)
c
Strain Amplitude (mm/m)
23 21 19
LR 0
300000
600000
900000
1200000
0
LR
LR
L
10 20 30 40 50 60 70 80 90 100
N (cycles)
Time (h)
Fig. 4. Phase angle with respect to the number of cycles (left) and time (right) during loading (L) and rest (R) periods for E13-100-10.
120 110
Wdis (J/m3)
a b
Sample Name
100 90 80 LR
70 0
300000
600000
N (cycles)
900000
1200000
LR
LR
L
0 10 20 30 40 50 60 70 80 90 100
Time (h)
Fig. 5. Dissipated energy per cycle with respect to the number of cycles (left) and time (right) during loading (L) and rest (R) periods for E13-100-10.
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10.1 10.0
T (°C)
9.9 9.8 9.7 9.6 9.5 0
300000
600000
900000
1200000
N (cycles)
LR
LR
LR
L
0 10 20 30 40 50 60 70 80 90 100
Time (h)
Fig. 6. Temperature of sample with respect to the number of cycles (left) and time (right) during loading (L) and rest (R) periods for E13-100-10.
Fig. 7. Initial E0i and final EðfinÞi for each loading period (10 °C, 10Hz) from Asphalt E2 and E7.
period. For the fourth phase of loading, the temperature decreased somewhat after 750,000 cycles. The overall change in temperature at the surface during the loading was rather small (around 0.4 °C), while the temperature during the rest periods stayed mostly constant and equal to thermal chamber temperature. 3.2. Analysis of rest periods 3.2.1. Modulus recovery after the loading cycles When the loading was stopped after each loading cycle, the samples experienced a recuperation in the modulus until the next loading cycle. For each sample, the modulus value at the beginning and (E0i) and the end (E(fin)i) of each loading period (see Fig. 2 description of loading and rest periods) are shown in Figs. 7 and 8. Fig. 9 shows the ratio between the value of the modulus during the rest period (E) and the value of the modulus when starting rest period (E(fin)i), as a function of time for the 3 rest periods for sample E2-80-10. During the rest period, the modulus value increased rapidly after the end of loading. The modulus recuperation during the first hour represents the majority of the recuperation for the duration of the rest period and subsequently, this increase
becomes much more moderate. Toward the end of each rest period, the modulus increased at a much slower rate. It was also found that the modulus recoveries obtained for the different rest periods are very similar in rate and amplitude, as recuperation curves are nearly overlapping for the different rest periods. The modulus recuperations for each rest period were calculated and compared. The values of the recovered modulus (DE) during a rest period as a percentage of the modulus (E(fin)i) at the beginning of the rest period are presented in Table 3. The% recovery is higher for samples loaded with higher amplitudes.
3.2.2. Modulus evolution relative to the modulus at the beginning of the test To observe the modulus evolution for each sample, initial modulus for each loading cycle E0i, in relation to the initial modulus E01 was compared in Fig. 10. The modulus value E01 represents the stiffness of the sample at the beginning of testing before any loading. For a loading period i, E0i corresponds to the modulus at the beginning of the loading period. The modulus loss occurs mostly after the first loading period.
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Fig. 8. Initial E0i and final EðfinÞi for each loading period (10 °C, 10Hz) for Asphalt E13.
Table 3 Modulus recuperation during rest periods relative to the modulus at the end of the previous loading cycle.
1.18 1.16 1.14
E/E(fin)i
1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98
0
2
4
6
8
10
12
14
16
Time (h) Rest 1
Rest 2
Rest 3
Sample
%DE/E(fin)1 %D E/E(fin)2 %D E/E(fin)3 %D E/E(fin)4 % Average
E2-80-10 E7-80-10 E7-80-20 E7-160-0 E7-160-10 E7-160-20 E13-80-0 E13-80-10 E13-80-20 E13-100-0 E13-100-10 E13-100-20 E13-80/100-10
16.4 18.6 17.8 41.8 40.9 44.6 16.4 13.8 16.2 25.7 24.2 27.0 16.5
16.0 17.7 18.6 42.5 40.2 43.0 15.5 15.5 15.1 26.1 24.7 22.5 23.0
16.2 17.4 18.0 42.1 42.8 45.8 16.9 16.5 15.6 28.4 25.9 23.6 18.6
41.0
26.8
16.2 17.9 18.1 42.1 41.3 44.5 16.3 15.3 15.6 26.7 24.9 24.4 21.2
Fig. 9. Typical modulus recuperation during sample rest period (E2-80-10).
3.3. Analysis of loading cycles The evolution of the observed damage for each loading cycle period, taken as the modulus of the sample compared to the value of the initial modulus before any loading, is shown in Figs. 11–14. The results are compared to the results of samples tested continuous loading (no rest periods, NoRP), or in the case of Fig. 11, with much shorter rest periods (ShRP), in order to observe their effects [4]. In general, the modulus recovery is better for the samples with rest periods, which is sustained over all of the loading cycles. Figs. 12–14 show the relative modulus values for the samples with 0 °C rest period temperature were significantly lower than the 20 °C samples at the same loading amplitude. 3.4. Specimen fatigue life extension with rest periods In examining the specimen fatigue life values, we considered the life of the samples as the number of total number of accumulated cycles, Nf, before the rupture of the specimen, that is to say, its complete failure. The samples of asphalt E13 were all tested in fatigue until rupture. However, it was found that for asphalt
E7, the rupture conditions were very difficult to achieve and would take an impractical number of cycles under the testing conditions as the polymer modification made the fatigue life very long. Therefore, only the results for E13 were considered in this section. Table 4 shows the values of Nf for tests on asphalt E13 for both loading amplitudes 80 and 100 mm/m. In general, the introduction of rest periods during the fatigue test significantly improved the fatigue life of asphalt mixtures when the rest period was kept at 10 °C. Lowering the rest period temperature to 0 °C made the rest periods almost ineffective in improving the fatigue life or even having a negative effect. Increasing the temperature to 20 °C improves fatigue life somewhat compared to the test at 10 °C, but the difference in fatigue life values between the two cases is negligible. 4. Discussion The discussion of the results is divided into two parts: i) analysis of modulus evolution during loading periods ii) the effects of the rest periods on the fatigue life of the samples.
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104
E02/E01
102
E03/E01
0°C
0°C
E04/E01
20°C
E05/E01
E 0i /E 01 (%)
100
20°C
98 96
10°C
10°C
20°C
20°C
10°C
10°C
10°C
10°C
94
0°C 92 90 88 80 31 E
23
80 31 E
25
4 3 9 1 2 -3 -3 -2 -3 -3 80 00 00 00 00 3-1 -1 -1 -1 1 3 3 3 0 8 E E1 E1 E1 3E1
0-8 E7
8 E7
10 0-8
E7
-2 60 -1
E7
2 -1 60 -1 7 E
-3 60 -1
0-8 E2
21
Fig. 10. Initial modulus for each loading cycle (E0i) as a percentage of the Initial modulus (E01).
1.05 E2-Auto-80 (10°C)
Rest time 10mn
1
E2D80 (ShRP)
E*/E01
0.95 0.9
Rest time 60mn
0.85 0.8 0.75 0.7
0
500000
1000000
1500000
2000000
2500000
3000000
N (cycles) Fig. 11. Evolution of modulus relative to the original modulus for Asphalt E2 in self-healing and sample loaded with same conditions with short rest times of 10 and 60 min.
1.10
E7-Auto-160 (0°C) E7-Auto-160 (20°C)
1.00
(NoRP) E7-Auto-160 (10°C) E7D160
E*/E 01
0.90 0.80 0.70 0.60 0.50
0
1000000
2000000
3000000
4000000
5000000
N (cycles) Fig. 12. Evolution of modulus relative to the original modulus for Asphalt E7 at 160 mm/m in self-healing and continuous loading.
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1.1 E13-Auto-80-34 (0°C) E13-Auto-80-25 (20°C) E13-Auto-80-23 (10°C) E13D80-14 (NoRP) E13D80-11 E13D80-21
E*/E01
1
0.9
0.8
0.7
0.6
0
500000
1000000
1500000
2000000
2500000
3000000
N (Cycels) Fig. 13. Evolution of modulus relative to the original modulus for Asphalt E13 at 80 mm/m in self-healing and continuous loading.
1.1 E13-Auto-100-33 (0°C) E13-Auto-100-29 (20°C) E13-Auto-100-31 (10°C) E13D100-13 (NoRP) E13D100-1
1
E*/E01
0.9 0.8 0.7 0.6 0.5 0.4
0
200000
400000
600000
800000
1000000
1200000
1400000
N (Cycles) Fig. 14. Evolution of modulus relative to the original modulus for Asphalt E13 at 100 mm/m in self-healing and continuous loading.
4.1. Analysis of fatigue loading periods The rupture conditions for mixture E7 were very difficult to achieve compared to the other mixes. The higher fatigue resistance of mix E7 can be attributed to the effects of SBS polymer modified binder compared to the neat as found in previous studies [30,33], and confirming the viability of SBS in improving pavement performance by improving the durability of the asphalt binder matrix [18]. The highest loss of modulus occurred after the first loading cycle, the loss of modulus progressively decreasing with the next loading cycle as found in similar studies, as the energy of the sample tends to dissipate with the loading [17], through the formation of microcracks, heat energy and thixotropy. 4.2. Specimen fatigue life extension with rest periods Fig. 15 shows the fatigue life value of Nf (50%), obtained using the classical fatigue criterion corresponding to 50% of drop of the initial stiffness, for both the E13 samples with rest periods, as well as the E13 samples that were continuously loaded until failure, according to the loading amplitude. A comparison with the Nf (50%) for the
Table 4 Fatigue life in cycles for sample of asphalt mixture E13. Sample
Nf
E13-80-0 E13-80-10 E13-80-20 E13-100-0 E13-100-10 E13-100-20
1109860 2480000 2540000 762918 1273600 1300000
self-healing samples shows an improvement of the sample fatigue life with rest periods, which may indicate that the phenomenon contributes significantly to the long term performance of the pavement if the conditions are favourable. By comparing the self-healing fatigue life values with those from the continuous loading, the increase in fatigue life from self-healing at different conditions was determined by taking the fatigue life of the samples with a rest period as a percentage of those from continuous loading for the same loading amplitude (Table 5). The lifetimes obtained with the self-healing tests were
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Fig. 15. Fatigue life values in cycles for sample of asphalt mixture E13 in with fatigue-healing and continuous loading as a function of the loading amplitude e0.
Table 5 Increase in fatigue life cycles for sample of asphalt mixture E13 for samples tested with self-healing. Sample
E13-80-0
E13-80-10
E13-80-20
E13-100-0
E13-100-10
E13-100-20
Increase in Fatigue Life (%)
81%
181%
186%
121%
203%
207%
generally higher than those with continuous loading as found in previous fatigue-healing studies [8,10]. When the rest period temperature was kept the same as the loading temperature (10 °C), the fatigue performance significantly improved. The increase of the temperature to 20 °C made a very modest difference compared to 10 °C while when the temperature was brought down to 0 °C, the rest period made no contribution, or was even detrimental to fatigue performance. This indicates that the rest period can even have a negative effect on fatigue performance in cold climate conditions. This can be attributed to the binder being more malleable from 10 °C, allowing for it to heal the microcracks created in the asphalt matrix during fatigue loading. Secondly, the asphalt is generally more brittle at low temperatures [2], which would explain why the fatigue life decrease with rest periods of 0 °C. It has been shown elsewhere that higher temperatures increase the healing rate of asphalt [11]. This effect was more profound for the samples tested at a higher amplitude, as more microcracks would likely be formed that could be filled by the healing. This could also be attributed to an increase in sample temperature during loading and thixotropy [4]. For the rest time of 0 °C, that is, a decrease in the temperature during the rest time, the fatigue life both increased and decreased by 20% based on the loading amplitude. This difference, again, could be attributed to the increase in asphalt temperature at higher loading amplitudes, which contributes to the malleability and promotes self-healing.
5. Conclusion and perspectives 5.1. Conclusions The current study of self-healing in asphalt highlighted the great importance of this phenomenon in pavement performance. The results of fatigue and self-healing tests lead to the following conclusions:
The asphalt mixture with the polymer modified binder had much improved performance to an equivalent mixture with neat binder in resistance to fatigue loading. The modulus loss from fatigue was the highest in the first loading periods of the test, as was the subsequent recovery during these periods. The fatigue life values of the samples with rest periods were higher than for continuously loaded samples when the rest temperature was kept at 10 °C or above. Having the temperature at 10 °C or higher during the rest periods led to a structural rearrangement in the material leading to extensive healing of microcracks, as well as increased recovery and fatigue life. Conversely, a decrease in temperature during the rest periods increases the rigidity of the sample, making it more difficult of the recovery to take place, and possibly allowing for more damage to take place in the asphalt. For future research, it would be useful to make a model the selfhealing phenomenon for a number of asphalt mixtures that factors temperature and rest time. This would allow us to more accurately consider this phenomenon in pavement design. References [1] S. Abo-Qudais, A. Suleiman, Monitoring fatigue damage and crack healing by ultrasound wave velocity, Nondestr. Test. Eval. 20 (2005) 125–145, https://doi. org/10.1080/10589750500206774. [2] D. Anderson, L. Lapalu, M. Marasteanu, Y. Hir, J.-P. Planche, D. Martin, Lowtemperature thermal cracking of asphalt binders as ranked by strength and fracture properties, Transp. Res. Rec. (2001) 1–6. [3] Baaj, H., 2002. Comportement à la fatigue des matériaux granulaires traités aux liants hydrocarbonés (PhD Thesis). INSA Lyon. [4] H. Baaj, H. Di Benedetto, P. Chaverot, Effect of binder characteristics on fatigue of asphalt pavement using an intrinsic damage approach, Road Mater. Pavement Des. 6 (2005) 147–174. [5] L.F. Babadopulos, A.L. de, C. Sauzéat, H. Di Benedetto, Softening and local selfheating of bituminous mixtures during cyclic loading, Road Mater. Pavement Des. (2017) 1–14, https://doi.org/10.1080/14680629.2017.1304260. [6] A. Bhasin, R. Bommavaram, M.L. Greenfield, D.N. Little, Use of molecular dynamics to investigate self-healing mechanisms in asphalt binders, J. Mater. Civ. Eng. 23 (2010) 485–492.
600
H. Baaj et al. / Construction and Building Materials 158 (2018) 591–600
[7] D. Breysse, V. Domec, S. Yotte, C. De La Roche, Better assessment of bituminous materials lifetime accounting for the influence of rest periods, Road Mater. Pavement Des. 6 (2005) 175–195. [8] E. Brown, S. White, N. Sottos, Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite—Part II: in situ self-healing, Compos. Sci. Technol. 65 (2005) 2474–2480, https://doi.org/10.1016/ j.compscitech.2005.04.053. [9] S. Carpenter, S. Shen, Dissipated energy approach to study hot-mix asphalt healing in fatigue, Transp. Res. Record (2006) 178–185. [10] M. Castro, J.A. Sanchez, Fatigue and healing of asphalt mixtures: discriminate analysis of fatigue curves, J. Transp. Eng. 132 (2006). [11] Y. Chen, R. Simms, C. Koh, G. Lopp, R. Roque, Development of a test method for evaluation and quantification of healing in asphalt mixture, Road Mater. Pavement Des. 14 (2013) 901–920, https://doi.org/10.1080/ 14680629.2013.844196. [12] P. Clec’h, C. Sauzéat, H. Di Benedetto, Linear Viscoelastic Behaviour and Anisotropy of Bituminous Mixture Compacted with a French Wheel Compactor, in: Paving Materials and Pavement Analysis, American Society of Civil Engineers, 2010, pp. 103–115. [13] J.S. Daniel, Y.R. Kim, Laboratory evaluation of fatigue damage and healing of asphalt mixtures, J. Mater. Civ. Eng. 13 (2001). [14] H. Di Benedetto, Q.T. Nguyen, C. Sauzéat, Nonlinearity, heating, fatigue and thixotropy during cyclic loading of asphalt mixtures, Road Mater. Pavement Des. 12 (2011) 129–158, https://doi.org/10.1080/14680629.2011.9690356. [15] H. Di Benedetto, C. De La Roche, H. Baaj, A. Pronk, R. Lundström, Fatigue of bituminous mixtures, Mater. Struct. 37 (2004) 202–216, https://doi.org/ 10.1007/BF02481620. [16] P. Gayte, H. Di Benedetto, C. Sauzéat, Q.T. Nguyen, Influence of transient effects for analysis of complex modulus tests on bituminous mixtures, Road Mater. Pavement Des. 17 (2016) 271–289, https://doi.org/10.1080/ 14680629.2015.1067246. [17] Grant, T.P., 2001. Determination of asphalt mixture healing rate using the Superpave indirect tensile test (Master’s Thesis). University of Florida. [18] B. Kim, R. Roque, S.-H. Lee, Cost analysis for use of SBS modifier in asphalt pavement using a performance-based fracture criterion, Road Mater. Pavement Des. 9 (2008) 571–588, https://doi.org/10.1080/ 14680629.2008.9690139. [19] Y.-R. Kim, D.N. Little, R.L. Lytton, Fatigue and healing characterization of asphalt mixtures, J. Mater. Civ. Eng. 15 (2003) 75–83. [20] Q. Liu, Á. García, E. Schlangen, M. van de Ven, Induction healing of asphalt mastic and porous asphalt concrete, Constr. Build. Mater. 25 (2011) 3746– 3752, https://doi.org/10.1016/j.conbuildmat.2011.04.016.
[21] S. Mangiafico, C. Sauzéat, H. Di Benedetto, S. Pouget, F. Olard, L. Planque, Quantification of biasing effects during fatigue tests on asphalt mixes: nonlinearity, self-heating and thixotropy, Road Mater. Pavement Des. 16 (2015) 73–99, https://doi.org/10.1080/14680629.2015.1077000. [22] M.L. Nguyen, C. Sauzéat, H. Di Benedetto, N. Tapsoba, Validation of the time– temperature superposition principle for crack propagation in bituminous mixtures, Mater. Struct. 46 (2013) 1075–1087, https://doi.org/10.1617/ s11527-012-9954-7. [23] Q.T. Nguyen, H. Di Benedetto, C. Sauzeat, Effect of fatigue cyclic loading on the linear viscoelastic properties of bituminous mixtures, J. Mater. Civ. Eng. 27 (2015) C4014003, https://doi.org/10.1061/(ASCE)MT.1943-5533.0000996. [24] Q.T. Nguyen, H. Di Benedetto, C. Sauzéat, N. Tapsoba, Time temperature superposition principle validation for bituminous mixes in the linear and nonlinear domains, J. Mater. Civ. Eng. 25 (2013) 1181–1188, https://doi.org/ 10.1061/(ASCE)MT.1943-5533.0000658. [25] D. Perraton, H. Baaj, A. Carter, Comparison of some pavement design methods from a fatigue point of view: effect of fatigue properties of asphalt materials, Road Mater. Pavement Des. 11 (2010) 833–861, https://doi.org/10.1080/ 14680629.2010.9690309. [26] J. Qiu, A. Molenaar, M. van de Ven, S. Wu, J. Yu, Investigation of self healing behaviour of asphalt mixes using beam on elastic foundation setup, Mater. Struct. 45 (2012) 777–791, https://doi.org/10.1617/s11527-011-9797-7. [27] L. Shan, Y. Tan, S. Underwood, Y. Kim, Application of thixotropy to analyze fatigue and healing characteristics of asphalt binder, Transp. Res. Rec. 2179 (2010) 85–92, https://doi.org/10.3141/2179-10. [28] S. Shen, H.-M. Chiu, H. Huang, Characterization of fatigue and healing in asphalt binders, J. Mater. Civ. Eng. 22 (2010) 846–852. [29] Z. Si, D.N. Little, R.L. Lytton, Characterization of microdamage and healing of asphalt concrete mixtures, J. Mater. Civ. Eng. 14 (2002), https://doi.org/ 10.1061/(ASCE)0899-1561(2002) 14:6(461). [30] H. Soenen, C. De La Roche, P. Redelius, Fatigue behaviour of bituminous materials: from binders to mixes, Road Mater. Pavement Des. 4 (2003) 7–27, https://doi.org/10.1080/14680629.2003.9689938. [31] N. Tapsoba, C. Sauzéat, H. Di Benedetto, Analysis of fatigue test for bituminous mixtures, J. Mater. Civ. Eng. 25 (2013) 701–710. [32] N. Tapsoba, C. Sauzéat, H. Di Benedetto, H. Baaj, M. Ech, Three-dimensional analysis of fatigue tests on bituminous mixtures: three-dimensional analysis of fatigue tests on bituminous mixtures, Fatigue Fract. Eng. Mater. Struct. 38 (2015) 730–741, https://doi.org/10.1111/ffe.12278. [33] C. Wang, C. Castorena, J. Zhang, Y.R. Kim, Unified failure criterion for asphalt binder under cyclic fatigue loading, Road Mater. Pavement Des. 16 (2015) 125–148, https://doi.org/10.1080/14680629.2015.1077010.