Influence of Filler/Binder Ratio on the Fatigue Behavior of Epoxy Asphalt Concrete

To further explore the influence of the filler/binder (F/B) ratio on the fatigue behavior of epoxy asphalt concrete (EAC), in this study, three typical F/B ratios are designed according to the EAC pavement of steel bridges in China, including 1.49, 1.95 and 2.48. The four-point fatigue behavior of the EAC with various F/B ratios was tested and analyzed. The results show that a higher F/B ratio leads a more rapid increase in the ratio of dissipated energy change (RDEC) during limited loading repetitions, as well as an increased likelihood of irreversible damage and a shorter fatigue life for the EAC. To ensure adequate fatigue performance of the EAC, it is recommended that the F/B ratio be controlled below 1.95.


Introduction
The application of epoxy asphalt concrete (EAC) in long-span steel bridge deck paving has been extensive owing to its exceptional mechanical properties and fatigue resistance [1,2].However, the practical implementation of steel bridge deck pavement in China also reveals that fatigue cracking at negative bending moments remains a prominent issue for EAC pavement [3,4].In recent years, researchers have increasingly focused on the fatigue behavior of the EAC and attempted to incorporate it into the mix design process [5].Previous studies have reported on the impact of binder type [3], loading mode [6], strain level [7,8], stress level [9,10], and test temperature [7] on the fatigue behavior of the EAC.
However, in the construction of EAC steel bridge decks in China, the pass ratio of the 0.075mm screen in the composite grading fluctuates between 7% and 14% [11], indicating variations in the filler/binder (F/B) ratio.The significance of the F/B ratio in asphalt concrete has been extensively demonstrated by numerous researchers [12,13], and it exerts a substantial influence on the internal bonding between aggregates within the asphalt mixtures [14,15].The presence of mastic, resulting from fillers with sizes smaller than 0.075mm and epoxy asphalt binder, is expected to significantly impact the fatigue performance of the EAC.Regrettably, limited research has been conducted on the correlation between the F/B ratio and fatigue properties of the EAC.
The objective of this article is to investigate the impact of the F/B ratio on the fatigue behavior of the EAC.In order to accomplish this goal, three representative F/B ratios have been devised based on those commonly employed in epoxy asphalt pavement for steel bridge decks in China.

Raw Materials
The epoxy asphalt binder is composed of epoxy resin and 70# matrix asphalt.The epoxy resin consists of component A and component B, with the physical properties of both components listed in Table 1.The mass ratio between component A and component B is 60:40, while the mass ratio between epoxy resin and 70# matrix is 100:100.The present study introduces three types of composite gradings, namely A, B, and C, which were developed based on the actual engineering practices of EAC pavement in China.The resulting composite gradings are presented in Table 2.According to JTG/T 3364-02-2019, utilizing the Marshall design method, the optimal binder to aggregate ratios for grading A, B and C are 7.0%, 6.5% and 6.0%, respectively, with corresponding F/B ratios of 1.49, 1.95 and 2.48.

Sample Preparation
The EAC was prepared in accordance with the following procedures: (1) preheating the mineral mixtures, epoxy resin, and matrix asphalt at temperatures of 180 °C, 60 °C, and 160 °C; (2) dry-mixing the mineral mixtures at a temperature of 180 °C for a duration of 30 seconds; (3) adding the epoxy resin and matrix asphalt, followed by wet-mixing for a period of 3 minutes; (4) rolling, compacting, and molding the EAC within 2 hours after mixing at temperatures ranging from 160 °C to 180 °C; (5) curing the EAC in an oven at a temperature of 60 °C for a duration of 4 days.

Characterization
The curves of stiffness modulus, phase angle, and accumulated energy consumption against the number of load cycles were obtained using the stand-alone servo-pneumatic four-points beam system (Pavetest, Italy) in accordance with AASHTO T321-2017.The four-point bending beam has dimensions of 380 mm × 40 mm × 40 mm and was subjected to a strain control mode test with a half sinusoidal load at a frequency of 10 Hz and temperature of 15 °C.Loading strain levels of 700, 800, and 900 were selected to assess the fatigue behavior of the EAC with different F/B ratios.The test was terminated after either one million load cycles or when the stiffness modulus decreased to half its initial value.

Stiffness and Phase Angle
The bending stiffness and phase angle of the EAC with different F/B ratios as a function of load repetitions are illustrated in Fig. 1.It is evident that the bending stiffness decreases with load repetition, while the phase angle increases with increasing load repetition.The rates of stiffness reduction and phase angle increase are determined by the level of strain.As depicted in Figure 1, a higher magnitude of strain leads to an accelerated rate of stiffness degradation and an expedited rate of phase angle elevation.The typical bending stiffness-load repetition curve can be categorized into three stages: an initial rapid decrease in bending stiffness within the first 0.1 million loads, followed by a gradual decline leading to a platform stage, and finally a sharp reduction in bending stiffness until it reaches 50% of its initial value when the load ceases.The trend of the phase angle-load repetition curve exhibits a resemblance to that observed in the bending stiffness.The fatigue behavior of the EAC with different F/B ratios is presented in Table 3.It was observed that the initial stiffness of the EAC increases from approximately 14000 MPa to around 18000 MPa as the F/B ratio increases from 1.49 to 2.48.Furthermore, no significant correlation between initial stiffness and strain level was found under the same F/B ratio.In contrast, there is no significant disparity observed in the initial phase angle across various F/B ratios, and a slight increase in the initial phase angle can be noted with an elevation in strain level under identical F/B ratio conditions.The repetition of the load decreases with increasing stress levels at the same F/B ratio.For example, when the F/B ratio is 1.49, the load repetitions at 700, 800, and 900 strain are recorded as 1 million, 1 million, and 0.41 million, respectively.The load repetition decreases with an increase in the F/B ratio at the same strain level.For example, when the strain level is 800, the load repetition for F/B ratio of 1.49, 1.95 and 2.48 are recorded as 1 million, 0.59 million, and 0.51 million, respectively.

Dissipated Energy
The fatigue failure process of asphalt mixture involves the dissipation of energy [16,17], and the damage to asphalt mixture is attributed to variations in the dissipated energy (DE) during consecutive loading cycles.The DE per cycle can be calculated by Eq. ( 1). sin Where DE i is dissipated energy per cycle, J/m 3 ; σ i , stress level in cycle i, N/m 2 ; ε i , strain level in the cycle i; Φ i , phase angle in cycle i.
Currently, existing literature primarily focuses on the fatigue life of EAC, with limited exploration from the perspective of DE.The DE-load repetitions curves of the EAC with different F/B ratios is shown in Fig. 2. With the progressive increase in loading repetitions, DE initially exhibited a steep upward trend, followed by a stabilization phase and eventually entering a gradual decline plateau.As the fatigue life approached its limit, DE demonstrated an initial rapid deterioration followed by a subsequent rapid improvement.When the damage incurred during each loading repetition is minimal, the DE in each loading repetition tends towards a constant value.Conversely, if there are microcracks or irreversible damages present during the loading process, the DE increases sharply due to their consumption of energy in the strain-controlled loading mode.As shown in Fig. 2(a)-(c), when both the F/B ratio and the loading strain level are low, the DE values are low and stationary, which indicates that the EAC shows no microcracks or irreversible damage and exhibits excellent fatigue properties during 1 million loading repetitions.When the F/B ratio or loading strain level is high, the DE values are high and unstable, which indicates that microcracks or irreversible damage is generated within the EAC near the fatigue life.
The value of the platform segment in the DE-load repetitions curve slightly increases with an increase in the F/B ratio under the same loading strain level.However, at the same F/B ratio, a significant increase is observed in the value of the platform segment in the DE-load repetitions curve with an increase in the loading strain level.Moreover, the cumulative average dissipated energy (CDE) and average dissipated energy per cycle (ADE) were utilized as indicators to demonstrate the impact of F/B ratio on the fatigue behavior of the EAC.As shown in Fig. 2(d), when the F/B ratio is 1.49, the ADE increased by 83.3% from 4.8 KJ/m 3 to 8.9 KJ/m 3 , with a corresponding increase in the loading strain level from 700 to 900.When the loading strain level is 700, the ADE increased by 28.2% from 4.8 KJ/m 3 to 6.2 KJ/m 3 , with a corresponding increase in the F/B ratio from 1.49 to 2.48.In summary, a higher F/B ratio or strain level increases the likelihood of the EAC inducing microcracks or irreversible damage, resulting in a shorter fatigue life.Moreover, the loading strain level has a greater impact on the fatigue life of EAC compared to the F/B ratio.The ratio of dissipated energy change (RDEC) approach has been reported as a superior method for analyzing the fatigue behavior of asphalt mixtures in academic research [18].The RDEC between two loading cycles could be calculated by Eq. (2).
Where RDEC a is the average RDEC at cycle a comparing to next cycle b; a, b, load cycle a and b, respectively.
The RDEC-load repetitions curves of the EAC with different F/B ratios is shown in Fig. 3.As shown in Fig. 3, the RDEC-load repetitions curve can be distinctly divided into three stages.In the first stage, RDEC decreases rapidly, potentially attributed to the alignment of epoxy asphalt molecular chain segments along the force direction during cyclic loading.In the second stage, RDEC tends towards a stable value, indicating linear accumulation of fatigue damage.In the third stage, there is a significant increase in RDEC which signifies near complete fatigue failure and nonlinear accumulation of fatigue damage.
The RDEC-load repetitions curve is mainly determined by loading starin level and F/B ratio.When the loading strain level is 700, the RDEC of the EAC with F/B ratios of 1.49 and 1.95 remains in a plateau stage even after 1 million loading repetitions, whereas the RDEC of the EAC with an F/B ratio of 2.48 exhibits a sudden and significant upward trend after approximately 0.67 million loading repetitions.Furthermore, When the F/B ratio is 1.49, the RDEC of the EAC with loading strain level of 700 and 800 remains in the plateau stage even after 1 million loading repetitions, whereas the RDEC of the EAC with loading strain level of 900 exhibits a sudden and significant upward trend after approximately 0.41 million loading repetitions.In summary, a higher loading strain level or F/B ratio

Figure 1 .
Figure 1.The fatigue behavior of the EAC with different F/B ratios

Figure 2
Figure 2 The DE-loading repetions currves of the EAC with different F/B ratios

Table 1 .
Physical properties of component A and B

Table 3 .
Fatigue behavior of the EAC with different F/B ratios