Insight into the critical evaluation indicators for fatigue performance recovery of rejuvenated bitumen under different rejuvenation conditions

Abstract


Introduction
The concept of sustainable development and circular economy is increasingly recognized by 28 infrastructural engineers and researchers [1,2]. Considering the limitation of bitumen resources, 29 it is worth advocating to reuse the waste reclaimed asphalt pavement (RAP) materials during  76 Based on the literature review, there are still research limitations on the fatigue performance 77 evaluation of rejuvenated bitumen, and some of them are described as follows: 78 (i) Although most previous studies mentioned that the rejuvenation efficiency of rejuvenator on 79 fatigue performance recovery of aged bitumen significantly depended on the material 80 properties of rejuvenator and aged bitumen, few researchers have comprehensively 81 investigated the effects of these factors on the fatigue performance of rejuvenated binders. 82 (ii) Different fatigue tests and evaluation parameters were utilized to characterize the fatigue 83 behavior of bituminous materials, but no uniform fatigue test and assessment indicators 84 have been identified, especially when exploring the aging, rejuvenation, and modification 85 influence. 86 (iii) The diversity of evaluation methods and material components remarkably hinders the 87 mechanism exploration and advanced material development for enhancing the fatigue 88 resistance and self-life of recycled asphalt pavements. 89 To this end, this study aims to systematically examine the impacts of rejuvenator 90 type/dosage and the aging degree of bitumen on the fatigue performance improvement of aged 91 bitumen. The critical fatigue tests and evaluation indicators on different rejuvenator-aged 92 bitumen blends will be proposed by comparison and screening for future standard formulation. 93 The detailed research methodology is illustrated in Fig.1. Large sample set will be achieved by 94 preparing different rejuvenated binders with three aging levels, four rejuvenator types, and six 95 rejuvenator dosages. Afterward, three popular fatigue tests (Linear viscoelastic, linear 96 amplitude, and time sweep) will be performed on all fresh/aged/rejuvenated binders to 97 synthetically assess the rejuvenation efficiency of various rejuvenators on the fatigue 98 performance recovery of aged bitumen. For each fatigue test, a series of evaluation parameters 99 will be considered and compared in terms of their sensitivities to variable factors to fully 100 understand the difference in fatigue behaviors of various rejuvenator-aged bitumen systems.   110 America are involved in this study, including the bio-oil (BO), engine-oil (EO), naphthenic-oil 111 (NO), and aromatic-oil (AO). Their material characteristics are listed in Table 3.

Research limitations and objectives
112  The fresh bitumen was used to artificially fabricate the aged bitumen using the Thin Film Oven 116 test (TFOT) and Pressure Aging Vessel (PAV) for short-term and long-term aging. For all aged 117 binders, the temperature and aging time of FTOT were 163 ℃ and 5 hours. The aging 118 temperature of PAV was 100℃, while the aging time varies from 20 to 40 and 80 hours for 119 preparing the aged bitumen with different long-term aging degrees. The fresh and various aging 120 bitumen were abbreviated as VB, LAB20, LAB40, and LAB80. 121 Twelve groups of rejuvenated bitumen were manufactured with three aging levels and four 122 rejuvenators. The aged bitumen was first preheated and then mixed with rejuvenators at 160 ℃ 123 for 10 mins to ensure homogeneous dispersion of the rejuvenator. Considering the slight aging 124 level, the rejuvenator dosages in LAB20 vary from 1.25% to 10%. To the severely-aged 125 bitumen (LAB40 and LAB80), the rejuvenator concentration changes from 2.5% to 15% with 126 an interval of 2.5%. In total, 72 kinds of rejuvenated binders were fabricated for relaxation 127 behavior characterization considering the coupling effects of rejuvenator type/dosage and aging 128 grade of bitumen. It should be mentioned that all samples were subjected to both TFOT and 129 PAV tests before performing the fatigue measurements. 130 3.3. Linear viscoelastic (LVE) measurements 131 The linear viscoelastic performance of aged and rejuvenated bitumen is assessed using a 132 frequency sweep test with a dynamic shear rheometer (DSR). The diameter and gap between 133 the upper and bottom plates are 8mm and 2mm. The frequency rises from 0.01 to 100 rad/s at 134 various testing temperatures of 0, 10, 20, and 40℃. The strain level keeps constant at 0.1% to 135 ensure the LVE response of bitumen. The fatigue parameter G*sinδ is outputted and the value 136 at 10rad/s is selected to determine the fatigue failure temperature (G*sinδ=5000kPa). In 137 addition, the G-R value is calculated following Eq.1. 138 G -R = |G * |(cosδ) 2 sinδ (1) 139 where G* and δ are the complex shear modulus and phase angle at 15 ℃ and 0.005 rad/s. 140 3.4. Linear amplitude (LAS) test 141 The LAS tests are performed on all fresh/aged and rejuvenated binders using a DSR device. 142 The graph illustration of applied strain variation and sample dimension of the LAS test is 143 displayed in Fig.2(a). The diameter and height of the bitumen specimen are 8mm and 2mm, 144 respectively. The applied strain increases linearly from 0.1% to 30%. The temperature and 145 frequency are selected as 20℃ and 10Hz. The total loading cycle number and test time are 3100 146 cycles and 310s. 147 148 Fig.2. Fatigue test methods on bituminous materials 149 The simplified viscoelastic continuum damage (S-VECD) modelling [31] is adopted to 150 analyze the LAS results. An internal parameter S is introduced to quantify the damaged state of 151 bituminous materials: where t refers to fatigue time, α shows a material constant related to the rate of damage 154 accumulation, and W R is the pseudo-strain energy density calculated as follows: (3) 156 The C function represents the pseudo stress quantitatively describing material integrity, defined 157 as the ratio of peak stress τ p and pseudo strain amplitude γ R . In addition, the γ R parameter is 158 defined as below: where γ p shows the strain amplitude in a fatigue cycle, G R and G * LVE are the arbitrary reference 161 modulus and linear viscoelastic shear modulus. Thus, the C function can be rewritten as Eq.5.
Meanwhile, the damage state parameter S can be derived as follows: 165 where N and i are the load cycles and the cycle number. A power law model is adopted to 166 describe the correlation between the material integrity C and damage parameter S shown in 167 Eq.7. The C 1 and C 2 are the constants.
Based on the above equations, the fatigue life N f of bituminous material can be predicted from 170 the strain amplitude γ p using Eq.8.
where f refers to the fatigue frequency, and S f is the damage at a failure point calculated as: The C f is the C parameter at the failure point reaching the peak stress. For simplification, the 175 Eq.8 can be rewritten as follows: where B=-2α, and A represents the term displayed in Eq.11, in which k=1-αC 2 +α.
3.5. Time sweep (TS) test 180 As shown in Fig.2(b where PR is the rejuvenation percentage, and P represents the fatigue indices in Table 4. 207 Moreover, the P fresh , P aged , and P rejuvenated are the fatigue indices of fresh, aged, and rejuvenated 208 binders, respectively. 209 The G-R-based rejuvenation percentages GR-R of all rejuvenator-aged bitumen blends are 236 also presented in Fig.4. A higher rejuvenator dosage leads to a larger G-RR value of rejuvenated 237 bitumen. An exponential relationship between the G-RR and C parameters is observed for all 238 rejuvenation cases. It indicates that the positive effect of rejuvenator content on G-R recovery 239 of aged bitumen reduces gradually as more rejuvenator is added. The rejuvenator type and aging 240 degree significantly affect the G-RR values and its variation trend versus rejuvenator dosage. 241 The bio-oil and aromatic-oil show the strongest and smallest rejuvenation efficiency on the G-242 R value of aged bitumen. The engine-oil and naphthenic-oil rejuvenators have similar effects. 243 Meanwhile, a high aging degree of bitumen results in a low rejuvenation efficiency on G-R 244 value. Interestingly, the G-RR values of AORB and NORB binders are much close in LAB80, 245 indicating that aromatic-oil exhibits a significant rejuvenation efficiency in restoring the G-R 246 value of aged bitumen with severe aging degrees. In addition, it should be noted that the rejuvenation percentages of rejuvenators on the 289 G*sinδ value depend on the test temperatures. Table 5 lists the correlation equation parameters 290 of FPR-C curves at different temperatures of 0, 10, 20, 30, and 40℃. As the temperature rises, 291 the FPR values of rejuvenated bitumen gradually decrease, but the reduction trend is not 292 significant when the temperature is higher than 30℃. It means that the rejuvenation efficiency 293 of rejuvenators on G*sinδ restoration of aged bitumen tends to decrease at high temperatures. 294 Meanwhile, the variation rate of FPR value to rejuvenator dosage significantly reduces with the 295 increase of temperature and aging degree, which shows no effect on the ranking of FPR values 296 for four rejuvenators (BO > EO > NO > AO). 297 The LVE G* region of undamaged bitumen must be measured before performing the LAS tests. 322 The fresh/aged and rejuvenated bitumen results are plotted in Figs.8 and 9, respectively. As the 323 frequency increases, the complex modulus G* of all binders enlarges distinctly, and there is a 324 linear correlation between the Log(G*) values and frequency. The long-term aging promotes 325 the increment in G* value (especially at low-frequency regions) but reduces its sensitivity level 326 to the frequency. With the rejuvenator dosage rising, the G* value of rejuvenated bitumen 327 decreases, and its frequency sensitivity enlarges. The shear stress-strain curves of fresh and aged bitumen during the LAS tests are shown in 345 Fig.10(a). As the shear strain rises from 0.1% to 30%, the corresponding stress increases to a 346 maximum point and decreases gradually. Long-term aging significantly affects the stress-strain 347 response of bitumen. As the aging degree extends, the stress-strain curve of bitumen becomes 348 narrower and taller. The increased maximum stress of bitumen is associated with the high 349 stiffness of aged bitumen, and a high aging degree promotes the strain sensitivity of the shear 350 stress. Although the peak value of bitumen stress is enhanced, a high aging degree accelerates 351 the fatigue damage of bitumen. To quantitatively reflect the effects of aging and rejuvenation 352 on the stress-strain response of bitumen, the stress-strain curve is divided into three pieces: the 353 elastic stage, the stress accumulation stage, and the localized cracking [33], which are illustrated 354 in Fig.10(b). These evaluation indices derived from the strain-stress curve are the f se , f sr , ɛ se , ɛ sr , 355 E, G se, G ss , and G sl . The f se and ɛ se are the maximum elastic stress and strain in the elastic stage, 356 and the E parameter refers to the elastic modulus (E=f se /ɛ se ). Moreover, the f sr and ɛ sr represent 357 the peak stress and strain. The fracture energies at different stages are derived as follows: The effects of long-term aging time on the stress-strain curve parameters of bitumen are 364 shown in Fig.11. Linear relationships between the aging time with these parameters are 365 observed, which can be utilized to predict the stress-strain curves of aged bitumen with various 366 aging degrees. As the aging level deepens, the Log(f se ) and Log(f sr ) values tend to increase 367 linearly, and the f se parameter shows greater sensitivity to the aging time. The ɛ se of all fresh 368 and aged bitumen are similar, but the ɛ sr value reduces linearly as the aging time extends. It 369 indicates that long-term aging does not influence the elastic region but weakens the bitumen's 370 stress accumulation capacity. Moreover, the elastic modulus E of bitumen significantly enlarges 371 due to the increased aging level. The stronger intermolecular interactions and lower free volume 372 between bitumen molecules reflect higher shear stress and modulus at a fixed strain level. 373 Further, the fracture energies G se and G sl of bitumen show a distinct increasing trend with the 374 aging time prolonging, but the G ss value decreases linearly. It suggests that long-term aging 375 improves the elastic performance and local fracture energy but shortens the cracking time. Due 376 to the low sensitivity of ɛ se and G ss to aging, these two parameters will not be considered while 377 evaluating the rejuvenation effects on the stress-strain curve of aged bitumen.    Fig.13. Rejuvenation effect on strain-stress parameters of aged bitumen 406 The stress-strain curve parameters and corresponding rejuvenation percentages of various 407 LAB40 rejuvenated bitumen are plotted in Fig.13. As the rejuvenator dosage rises, the 408 logarithmic values of f se , f sr , E, G se , and G sl of rejuvenated bitumen decrease linearly, whereas 409 the E parameter tends to increase linearly. These parameters of rejuvenated binders with 410 different rejuvenator types/dosages can be predicted with the correlation equations also 411 presented in Fig.13 The C-S curves can directly reflect the material characteristic variation during the fatigue 440 damage. Based on Eq.7, the material integrity C of bitumen shows an exponential relationship 441 with the damage intensity S. The changes of constants C 1 and C 2 can be detected to quantitively 442 evaluate the aging and rejuvenation effects on the C-S curves of bitumen. Fig.14(a) presents 443 the C-S curves and correlation formulas of fresh and aged bitumen. As the damage intensity S 444 rises, the C value decreases gradually. A high aging degree accelerates the reduction trend of 445 the C parameter. It shows that the deterioration level of bitumen intensifies as the long-term 446 aging time prolongs. The influence of aging on the constants C 1 and C 2 of C-S curves is depicted 447 in Fig.14(b). As the aging time extends, the C 1 value rises, but the C 2 parameter declines 448 linearly. It implies that a high aging degree intensifies the deterioration rate of material integrity 449 but relieves its sensitivity to the damage intensity S of bitumen. This phenomenon is also 450 observed in strain-stress curves, which reveal that the aging degree enlarges the destruction 451 threshold but promotes the damage rate.  488 test, the N f parameters at two strain levels of 2.5% and 5% are considered to assess the fatigue 489 life of bitumen with different aging and rejuvenation conditions. To the N f parameter at 2.5% 490 strain (N f2.5 ), the short-term aging shows a positive effect, slightly reducing after 20h long-term 491 aging. However, the N f2.5 values of LAB40 and LAB80 continue to rise, even larger than the 492 fresh bitumen. indicating that the N f is an effective indicator to evaluate and discriminate the fatigue life of 512 different rejuvenator-aged bitumen blends. 513 As the rejuvenator dosage increases, the N f R 5 increases linearly, but the N f R 2.5 shows a 514 linearly decreasing trend. The reason for the negative N f R 2.5 values is that the N f of aged 515 bitumen at 2.5% strain is higher than the fresh bitumen, and the inclusion of rejuvenators 516 continues to enlarge the N f2.5 value of aged bitumen. Therefore, the N f2.5 results violate the 517 rejuvenation definition and fail to assess the rejuvenation efficiency of rejuvenators on the 518 fatigue performance of aged bitumen. On the contrary, the N f R 5 values can effectively and 519 quantitatively estimate the rejuvenation efficiency of various rejuvenators on fatigue life, and 520 the scope of N f R 5 values (0-550%) is much wider than the stress-strain curve and C-S curve 521 parameters. It has been proved that the rejuvenation efficiency strongly relies on the evaluation parameters. 533 The LAS results analysis introduces various parameters in Eqs.8-11, including the α, k, 534 G*sinδ initial , S f , A, and B. The influence of aging and rejuvenation on fatigue performance from 535 LAS tests is a joint result of their effects on these parameters. This section aims to investigate 536 these parameters' variation of bitumen due to different aging and rejuvenation conditions and 537 propose several critical evaluation indicators reflecting the rejuvenation efficiency of various 538 rejuvenator-aged bitumen blends. The results of fresh and aged bitumen are shown in Fig.19. 539 The parameters α, k, and G*sinδ initial increase linearly as the aging time prolongs. By definition, 540 parameter α refers to the rate of damage accumulation, and a high aging level promotes the 541 deterioration rate of bitumen. The k is derived from the parameters α and C 2 , which increases 542 and reduces as the aging degree deepens. It results in a positive correlation between the k and 543 aging time t. The aging time dependence of the k parameter is determined by the variation rate 544 of α and C 2 , and the former is much larger than the latter. Thus, the k parameter shows less 545 sensitivity to the aging time than the α. Similar to the fatigue parameter discussed in section  EORB ranking. To these three parameters, the AORB binder shows a lower rejuvenation 570 percentage at low rejuvenator dosages (<7.5%) but a higher value than the BORB when the 571 rejuvenator content is higher than 7.5%. Based on these three parameters, it is difficult to 572 completely distinguish the rejuvenation efficiency of bio-oil and aromatic-oil rejuvenators on 573 the fatigue performance of aged bitumen. As expected, the bio-oil exhibits the largest rejuvenation efficiency on the G*sinδ initial , 580 followed by engine-oil and naphthenic-oil, while the aromatic-oil shows the lowest effect. 581 However, the G*sinδ initial parameter is the fatigue parameter of bitumen without damage, which 582 has been considered and discussed in the LVE fatigue section. Furthermore, the difference in  The G*-N curve is the main output from the time sweep test, which of fresh and aged bitumen 595 at two stress of 2.5% and 5% are shown in Fig.21(a). Different important evaluation parameters 596 can be derived from the G*-N curves, such as the fatigue life with 50% residue G* (N 50% ) and 597 phase angle at the peak point (δ peak ). Meanwhile, the dissipated energy ratio (DER) variation 598 versus load cycles (illustrated in Fig.21(b)) can be used to determine two parameters (fatigue 599 life N p20 and initial dissipated energy W 0 ). The aging effects on these TS fatigue parameters are 600 also plotted in Fig.21. As the load cycle prolongs, the G* value of bitumen decreases gradually, 601 which is more significant at high strain. Moreover, the descent rate of the G* value becomes 602 faster after long-term aging. High strain level results in a large δ peak value of bitumen, decreasing 603 significantly due to aging. Regarding the DER-N curves, the high strain and aging intensify the increasing rate of 608 DER curves dramatically, reducing the derived N p20 value of bitumen. Regardless of the strain 609 levels, the linear relationships between the aging time with parameters N 50% , δ peak , N p20 , and W 0 .
Long-term aging reduces the N 50% , δ peak , and N p20 values but increases the W 0 parameter of 611 bitumen. It suggests that a high aging level significantly shortens the fatigue life, enlarges the 612 elastic ratio, and increases the energy dissipation of bitumen. Further, the high strain decreases 613 the N 50% and N p20 and expands the δ peak and W 0 values of bitumen, which weakens the 614 sensitivities of N 50% , N p20 , and W 0 parameters to the aging time. strain, the magnitude of N 50% R for rejuvenated binders is EORB > NORB > BORB > AORB. 625 Additionally, the δ peak and δ peak R values of AORB are the highest, while the NORB shows the 626 lowest values. Nevertheless, the sequence in δ peak and δ peak R of BORB and EORB inverts as the 627 strain level changes from 2.5% to 5%.    Fig.24(c) 770 Exploring the potential connections between these critical evaluation indicators from 771 different fatigue tests is interesting. Fig.28 depicts the correlation curves between the C 500 with 772 FFT, N f5 , ɛ sr , and E parameters. The crack width connects well with these parameters, and thus 773 the crack width can be predicted with these correlation equations without conducting the time-