Dynamic Viscoelastic Behavior of Epoxy Asphalt Mixture under Four-Point Bending

Abstract

Given the dominant failure mode of steel bridge deck pavement layers, which is flexural–tensile damage, the dynamic modulus parameters conventionally determined through uniaxial compression testing are found to be inadequate for the design or performance analysis of these layers. In order to simulate the actual stress of a pavement structure under wheel load, the four-point bending fatigue test method and uniaxial compression test method are used to measure the dynamic modulus of an epoxy asphalt mixture, and the differences between the two test methods are analyzed. Furthermore, the four-point bending fatigue test is employed to investigate the dynamic modulus and phase angle properties across varying temperatures and frequencies, facilitating the creation of master curves for these properties and utilizing Sigmoidal models to correlate dynamic modulus data at diverse temperature conditions. This study delves into the influence of epoxy resin content, mixture composition, and aging on the dynamic modulus. The experimental results show that the dynamic modulus measured by uniaxial compression exceeds that obtained from bending fatigue tests, with the difference initially increasing and then decreasing as temperature rises. This discrepancy significantly impacts the mechanical calculations of pavement layers, underscoring the importance of selecting the appropriate testing method. Temperature, frequency, and epoxy resin content have pronounced effects on the viscoelastic properties of the mixtures. Specifically, as temperature increases, the dynamic modulus undergoes a decrease, whereas the phase angle exhibits an increase. Additionally, the dynamic modulus augments with an increase in loading frequency, while the phase angle exhibits varied trends with frequency shifts across different temperatures. Both the WLF and Sigmoidal models are effective in constructing master curve representations for the dynamic flexural modulus and phase angle. The incorporation of epoxy resin transforms asphalt from a primarily viscous to a more elastic material, significantly enhancing the viscoelastic properties of the mixture. Notably, mixtures with 50% and 60% epoxy resin content exhibit comparable dynamic moduli and phase angles, while displaying notably superior performance compared to those with 40% epoxy resin content. For large-scale steel bridge deck pavement, 50% epoxy resin content is recommended. Moreover, epoxy asphalt mixtures demonstrate robust aging resistance, with minimal variations in the dynamic modulus and phase angle before and after aging. The research results can enable the acquisition of dynamic modulus and phase angle data in the whole temperature domain and the whole frequency domain, and provide reliable mixed performance parameters for the study of different application environmental performance of steel bridge deck pavement.

1. Introduction

The determination of material design parameters is one of the main pieces of structural design work, and the study of material design parameters is indispensable in the design of a steel bridge pavement layer. Among the material design parameters, the dynamic modulus parameter is one of the most important of all design parameters [1,2,3,4,5]. The dynamic modulus can more reasonably reflect the actual stress condition of the road surface under wheel load. The dynamic modulus of the mixture is studied to make the modulus value more reasonable. It is of great significance for pavement material design, and performance evaluation [6,7,8]. The indoor dynamic modulus evaluation primarily encompasses uniaxial compression testing, indirect tensile assessment, and four-point bending examination [9,10,11]. A uniaxial compression test serves as a means to evaluate the dynamic compressive modulus of various materials. Specifically, for asphalt mixtures, this technique is among the frequently employed methods for assessing their dynamic modulus [12,13].

A limitation lies in the fact that the cylinder specimen’s central point experiences biaxial stress during loading, which significantly deviates from the authentic stress conditions encountered in pavement structures. Furthermore, the specimen exhibits noticeable localized distortions at its extremities, thereby influencing its stress pattern directly. A uniaxial compression test and indirect tensile test adopt the form of compression load, and the obtained modulus parameters are the dynamic compression modulus and tensile modulus. A steel box girder is mainly composed of orthotropic plates. Under the action of temperature load, the whole bridge has huge deflection changes [14]. Relevant research shows that steel deck pavement mainly undergoes bending–tensile failure under the coupling action of traffic load, temperature stress, and steel plate deformation, while a uniaxial compression test and indirect tensile test cannot simulate bending–tensile load, and the obtained modulus parameters are not suitable for epoxy asphalt pavement [15,16,17,18,19].

The four-point bending test primarily focuses on the fatigue characteristics of test materials [20,21]. The specimens were produced by compacting asphalt concrete into slabs through wheel rolling, subsequently cutting the slabs into standard-sized specimens for testing [22,23]. The loading modes include stress control and strain control, and the failure judgment varies according to different control methods [24]. When stress control is adopted, the failure condition is defined by either material fracturing or an increase in tensile strain to twice the initial value. The modulus is deemed to have failed when it drops to half of its initial stiffness value, under strain control conditions [25,26,27]. The repeated bending–tension mode of the four-point bending test can better simulate the bending–tension stress state of epoxy asphalt pavement under the coupling action of traffic load, temperature stress, and steel plate deformation, and the obtained modulus parameters belong to the dynamic bending–tension modulus, which can better reflect the performance level of steel deck pavement materials.

Researchers often use shear rheometers to analyze the dynamic modulus of epoxy asphalt blends, and sometimes opt for epoxy asphalt mortar as an alternative material for such investigations [28,29,30,31,32,33]. Xue et al. introduced the viscoelastic properties of asphalt using DSR tests [34]. Xue and colleagues characterized the viscoelastic attributes of epoxy asphalt through dynamic shear rheological examinations, encompassing frequency sweep and creep assessments [35]. Apostolidis examined the compositional and rheological alterations in epoxy asphalt, both with and without filler, utilizing infrared spectroscopy and a dynamic shear rheometer, along with conducting dynamic modulus assessments [36,37]. Guo used four epoxy resin asphalt materials with different crosslinking degrees to carry out dynamic rheological tests [38]. Zhang et al. carried out dynamic frequency scanning for an epoxy asphalt mortar by a dynamic shear rheometer, and obtained dynamic shear modulus parameters [39]. Extensive research has been conducted on the dynamic modulus parameters of epoxy asphalt and epoxy asphalt mastic and many studies have been carried out on the factors affecting the dynamic modulus parameters. However, these studies have been carried out on mastic or mortar specimens and have not considered the influence of the aggregate gradation of the mixes. The related dynamic modulus test has been well studied in common asphalt mixtures and formed a standard test. However, the experimental investigation into the dynamic modulus of epoxy asphalt mixtures is relatively scarce. Luo et al. elucidated the dynamic modulus measurement through uniaxial compression testing and formulated a master curve model for this property [40]. Chen et al. established a dynamic modulus prediction model for an epoxy asphalt mixture through compression tests [41,42]. Yao and their team conducted compression tests to assess the dynamic modulus of epoxy asphalt mixtures [43,44], but they only simply analyzed the changing trend of the dynamic modulus, and did not comprehensively analyze the factors affecting the dynamic modulus.

Reflecting upon the aforementioned analysis, it is evident that significant research on the dynamic modulus of epoxy asphalt mixtures has been conducted using uniaxial compression tests. However, these tests do not accurately replicate the bending and tensile loading conditions typical of steel bridge pavements. Furthermore, the literature lacks studies comparing the dynamic modulus results from four-point bending fatigue tests to those from uniaxial compression tests. There is a notable scarcity of research examining the factors that influence the dynamic modulus parameters of epoxy asphalt mixes, particularly those derived from flexural fatigue tests. In addition, there are few studies on the change in viscoelastic properties of epoxy asphalt mixtures with different grades and different aging degrees, and there are few studies on this part at present.

The four-point bending test is employed to measure the dynamic modulus and phase angle of epoxy asphalt mixtures, examining their trends across varying temperatures and frequencies. Leveraging the time–temperature equivalence principle, master curves for both the dynamic modulus and phase angle are constructed, facilitating data acquisition across the full temperature and frequency spectra. This provides crucial performance parameters for studying steel bridge deck pavement in diverse environments. Furthermore, the experiment serves to contrast the viscoelastic behaviors between epoxy asphalt blends with and without the inclusion of epoxy resin, as well as their changes due to aging, comprehensively elucidating the factors influencing these properties.

2. Methods

The four-point bending test and uniaxial compression test were used to test the difference in the dynamic modulus of the same grade epoxy asphalt mixture at the same frequency and temperature. At the same time, the four-point bending fatigue test method was used to test dynamic modulus and phase angle parameters at different temperatures and frequencies based on the viscosity–temperature equivalent principle, and the main curve of the dynamic modulus and phase angle was constructed to fit the Sigmoidal model of the dynamic modulus at different temperatures. Finally, the effects of epoxy resin parameters, mixture composition, and mixture aging on the dynamic modulus were analyzed. The flow chart is shown in Figure 1:

3. Experimental Plan

3.1. Materials

The composition of epoxy asphalt comprises TAF epoxy resin sourced from Japan and Shell matrix asphalt. Epoxy resin can enhance the crosslinked network structure of the mixture, thereby improving its strength, stiffness, durability, stability, and adhesion and other key performance indicators. Asphalt gradually changes from the original viscous material to elastic material, and the viscoelastic property of the mixture has been greatly improved, while the Japanese version of TAF epoxy resin has more excellent mechanical properties and thermal stability.

The epoxy resin and curing agent were preheated at 60 °C for about 1 h, and then manually stirred at the ratio of the main agent to curing agent of 56:44 for about 3 min. The mixed epoxy resin is mixed with 165 °C base asphalt in a certain proportion, and then sheared and dispersed by a high-speed shear instrument at 5000 r/min and 5 min rotational speed, mixing into epoxy asphalt with different epoxy ratios. The key technical specifications for the main and curing agents are detailed in

Table 1. Technical Index of TAF Epoxy Resin.

Physical Properties	Main Agent	Curing Agent
Specific gravity	1.15	0.862
Epoxy equivalent	204	-
Acid number (mg, KOH/g)	-	168
Flash point (°C)	239	169

. Diabase is used as an aggregate, and the specific mixture gradation is shown in

Table 2. Gradation of Epoxy Asphalt Mixture.

Gradation	Percentage of Mass through the Sieve (Square Hole Sieve, mm)
	13.2	9.5	4.75	2.36	1.18	0.6	0.3	0.15	0.075
Gradation 1	100	99.7	75	58	45.3	36	24.4	18.1	11.1
Gradation 2	100	97.4	44.2	31.1	24.2	19.7	16.3	13.2	9.8

. In Gradation 1, the mixture’s asphalt-to-aggregate ratio stands at 6.5% with an air void content of 1.4%, while for Gradation 2, they are 6.2% and 2.0%, respectively. The technical specifications of both mixtures are presented in

Table 3. Technical Index of Epoxy Asphalt Mixture [45].

Technical Index	Gradation 1	Gradation 2
Apparent density (g/cm3)	2.586	2.594
Air voids (%)	1.4	2.0
Marshall stability (kN)	68.3	46.3
Flow value (mm)	5.0	4.0
Residual stability (%)	92.5	93.6
Freeze–thaw splitting strength ratio TSR (%)	92.9	92.4

.

3.2. Experimental Method

The Cooper NU-14 (An independent four-point bending trabecular test system produced by Cooper Technologies, UK) four-point bending testing apparatus is utilized for conducting the four-point bending test, depicted in Figure 2. The size of the test specimen is 385 mm × 65 mm × 50 mm. Firstly, the epoxy asphalt mixture should be mixed, and the specimen with the size of 400 mm × 300 mm × 75 mm should be formed by vibrating wheel rolling equipment, and then the standard specimen with the size of 385 mm × 65 mm × 50 mm should be cut by double-sided dramatic cutting. Relevant research shows that epoxy asphalt pavement is in the linear elastic range during use, and the deformation of epoxy asphalt pavement can be quickly restored after stress is revoked [46]. Existing research indicates that the linear viscoelastic region of asphalt mixtures is typically confined to less than 100 macro-strains [47,48], so the test load strain is controlled to 100 micro-strains, and the load mode adopts a sine wave as the standard loading waveform. Relevant research shows that when the load frequency is 10 Hz, it corresponds to the vehicle load with a road speed of 60~65 km/h [49]. According to the requirements of the dynamic modulus test, the frequencies are set to 15 Hz, 10 Hz, 5 Hz, 1 Hz, 0.5 Hz, and 0.1 Hz, respectively. Considering the actual working temperature range of steel deck pavement, the test temperatures are set at −10 °C, 5 °C, 20 °C, 35 °C, and 50 °C, respectively. In order to compare the difference in the dynamic modulus between the flexural fatigue test and uniaxial compression test, MTS810 (The MTS 810 material test system is manufactured by MTS Systems) is used for the uniaxial compression test, the test frequency is 10 Hz, and the test temperature is consistent with the flexural fatigue test.

4. Test Results

Four-point bending specimens and uniaxial compression specimens are made by Gradation 1, and corresponding tests are carried out. Figure 3 and Figure 4, along with

Table 4. Dynamic Modulus Test Results of Different Tests (10 Hz).

Method	Dynamic Modulus (MPa)
	−10 °C	5 °C	20 °C	35 °C	50 °C
Bending test	26,848	20,810	8470	5505	2266
Compression test	28,177	23,969	13,414	7581	2982
Difference	1329	3159	4944	2076	716
Proportion	5%	15%	58%	38%	32%

, present the results. Notably, Figure 3 reveals that at a test frequency of 10 Hz, the dynamic modulus obtained from the four-point bending test is lower compared to that from the uniaxial compression test. As can be seen from Figure 4, with the change in temperature, the dynamic modulus difference between the bending test and uniaxial compression test is constantly changing. The difference between them first increases with temperature. The difference between the dynamic modulus of asphalt mixtures measured by the uniaxial compression test and four-point bending test is the largest at 20 °C, mainly because the viscosity of asphalt at this time is at a medium level and the internal microstructure of the mixture is highly sensitive to the loading method. With the increase in temperature, the viscosity of asphalt decreases gradually and the fluidity of mixtures increases. This makes the stress distribution and transfer mechanism inside the mixture gradually converge in the uniaxial compression test and four-point bending test. At the same time, the elastic recovery ability of asphalt at a high temperature is weakened, and the viscosity is prominent, resulting in a decrease in the dynamic modulus measured by the two test methods. Since this downward trend has a similar rule in both test methods, the difference between them gradually decreases. The research shows that the test result of the bending test and uniaxial compression test is similar at low-temperature and high-temperature stages, but there is a big difference between the two tests’ results at the medium-temperature stage. It can be seen from Table 4 that at 20 °C, the dynamic modulus of the bending test is 4944 MPa lower than that of the uniaxial compression test, and the deviation ratio is as high as 58%. The design parameters usually take the dynamic modulus at 20 °C as the calculation standard. It can be seen that the uniaxial compression test will have a great impact on the parameters of steel deck pavement.

The mixture specimen was made with Gradation 1, and the four-point bending test results are shown in Figure 5 and Figure 6. As depicted in Figure 4, the dynamic modulus of the epoxy asphalt blend diminishes with rising temperatures at a constant load frequency, highlighting a significant influence of temperature on the blend’s dynamic modulus. As temperature rises, the epoxy asphalt binder softens, weakening the adhesion between it and the aggregate, resulting in a gradual shift from elasticity to plasticity in the mixture and a consequent decrease in the dynamic modulus. Conversely, at a constant temperature, an increase in load frequency leads to an enhancement in the dynamic modulus of the epoxy asphalt mixture. The epoxy asphalt mixture is a kind of viscoelastic material, which does not deform under the action of external force. After the external force is revoked, the deformation does not recover instantaneously and completely, which shows the hysteresis of load response. With the increase in load frequency, the load time is shortened, and the deformation of the mixture is also small. Therefore, an increase in load frequency leads to a corresponding increase in the dynamic modulus value.

As depicted in Figure 6, the epoxy asphalt mixture exhibits a small and stable phase angle at −10 °C, indicative of robust elastic characteristics with minimal dependence on frequency. As temperature rises, the impact of frequency on the mixture’s phase angle intensifies. Specifically, at 5 °C, the phase angle diminishes with increasing load frequency, whereas, at 20 °C, it initially rises and subsequently declines. At higher temperatures of 35 °C and 50 °C, the phase angle consistently increases with frequency. In low-temperature settings, the asphalt binder significantly influences the mixture’s modulus. When the loading frequency is low (i.e., longer loading durations), the mixture displays pronounced viscosity, leading to an increase in the phase angle as frequency decreases. As temperature increases, the epoxy asphalt binder softens, diminishing its bonding strength with aggregates, thereby transitioning the mixture from elastic to plastic behavior. Under low load frequencies (longer action times), the rigidity of the mixture is largely governed by the embedded mineral aggregate skeleton, contributing to a smaller phase angle. Conversely, with higher load frequencies (shorter action times), the mixture exhibits enhanced hysteretic load response, equivalent to an enlarged phase angle, highlighting its more evident external delay in responding to load changes.

5. Viscoelastic Analysis

5.1. Master Curve of Dynamic Modulus

The research indicates that the mechanical state of asphalt mixtures remains consistent under varying load frequencies and temperatures. It implies that the mechanical behavior of viscoelastic materials during their action process is influenced by time and temperature in a manner that exhibits certain comparable processes [50]. This equivalence can be achieved by a shift factor. This suggests that the mechanical data measured at one temperature can be converted into mechanical data at another temperature by the shift factor, which is called the time–temperature equivalence principle. Based on this principle, the main curve at a certain temperature is formed. This displacement, $\lg {\alpha }_T$, is called the shift factor, and the shift factor $\lg {\alpha }_T$ is only related to temperature. The WLF equation is used to calculate the shift factor [51], and the calculation equation is shown in Equation (1).

$$\lg {\alpha }_T={\displaystyle \frac{-8.86(T-T_s)}{101.6+(T-T_s)}}$$

(1)

where T is any other temperature, and T_s is the fiducial temperature.

In practice, the fiducial temperature T_s is unknown and is not included in the measured temperature conditions achieved. Therefore, it is necessary to calculate the fiducial temperature T_s by derivation. A certain temperature T₀ is selected as the reference temperature in the measured temperature conditions, and the shift factor $\lg {\alpha }_T$ of other temperatures T_i to the reference temperature T₀ is as follows: assuming T is any temperature, Equation (1) is applied for T₀ and T.

$$\lg {\alpha }_{T_0}={\displaystyle \frac{-8.86(T_0-T_s)}{101.6+(T_0-T_s)}}$$

(2)

$$\lg {\alpha }_T={\displaystyle \frac{-8.86(T-T_s)}{101.6+(T-T_s)}}$$

(3)

The viscoelastic characteristic function curve is moved at temperature T to T₀, and the shift factor is recorded at this time as $\lg {\alpha }_{T_0}^{\prime }$. Therefore, from Equations (2) and (3), we can obtain

$$\lg {\alpha }_{T_0}^{\prime }=-8.86\times 101.6{\displaystyle \frac{(T-T_0)}{(101.6+T-T_s)(101.6+T_0-T_s)}}$$

(4)

In the above Equation (4), there is only one unknown number T_s. By solving the quadratic equation about T_s, the fiducial temperature T_s corresponding to T ~ T₀ is obtained. After the fiducial temperature T_s is obtained, Equation (4) is substituted to obtain the shift factor when the required temperature translates to the selected reference temperature T₀. Meanwhile, the master curve can be obtained under the reference temperature condition. According to Equations (1) and (4), the reference temperature is selected as 35 °C, and the value of the fiducial temperature T_s is calculated inversely.

Table 5. The reference temperature is the base temperature T_s at 35 °C.

Temperature/°C	Displacement Factor $\mathbf{lg}{\mathit{\alpha }}_{{\mathit{T}}_0}^{\prime }$	${\mathit{T}}_{\mathit{s}1}$/°C	${\mathit{T}}_{\mathit{s}2}$/°C
20	2.50	55.23	202.97
35	0	-	-
50	−1.8	57.16	231.04
Average	0.233	56.2	217

presents the detailed computation outcomes:

It can be seen from Table 5 that two different analytical solutions can be obtained by solving the quadratic equation about $T_s$, which are denoted as $T_{s1}$ and $T_{s2}$, respectively. Zhang verified that the fiducial temperature range of asphalt materials is generally between 30 °C and 60 °C [44]. Therefore, $T_{s1}$ is the fiducial temperature value when the reference temperature is 35 °C, and its average value is 56.2 °C. By substituting the fiducial temperature into Equation (4), the translation factors of dynamic modulus viscoelastic curves of the epoxy asphalt mixture at −10 °C, 5 °C, 35 °C, and 50 °C relative to those at 20 °C are calculated, respectively. The outcomes are presented in

Table 6. Displacement factors of different temperature conditions relative to 20 °C temperatures.

Temperature/°C	−10	5	35	50
$\lg {\alpha }_T$	11.66	4.10	−2.57	−4.33

for specific details.

Figure 7 portrays the primary curve showcasing the dynamic modulus of the epoxy–asphalt blend at 20 °C, utilizing the shift factors derived from Table 6 for various temperatures in relation to 20 °C. The Sigmoidal modulus approach is adopted to align with the experimental outcomes of the dynamic modulus tests conducted on the blend. As a result, a Sigmoidal representation of the mixture’s dynamic modulus primary curve is obtained at the reference temperature of 20 °C. This fitted curve is illustrated in Figure 7, while the corresponding fitting model is presented in Equation (5).

$$E^{*}=3600-{\displaystyle \frac{\mathrm{35,560}}{1+e^{0.3806\ln f-2.02}}}$$

(5)

where $f$ is the load frequency, Hz. E* is the dynamic modulus of the asphalt mixture.

The correlation coefficient R² is 0.99773, which indicates that the model fits the experimental results well. What is more, this paper evaluates the translocation factors under various alternative reference temperatures and obtains the master curve family of the dynamic modulus of the epoxy asphalt mixture through the time–temperature equivalence principle, as shown in Figure 8.

As evident from Figure 8, the primary curves for the dynamic modulus at varying temperatures exhibit comparable shapes, indicating a dependency of the mixture’s dynamic modulus on load frequency across temperature ranges. The consistent pattern of morphological shifts with frequency changes further underscores this relationship. Distinct intervals exist between various master curves, reflecting varying temperature sensitivities of the mixtures under different thermal conditions. Notably, the extreme points of the viscoelastic curves for the same asphalt mixture remain consistent across different temperatures, suggesting that these extreme values are not constrained by temperature variations. The Sigmoidal function is applied to fit the modulus test outcomes of the epoxy asphalt mixture, yielding the Sigmoidal form of the dynamic modulus master curve for the mixture under various reference temperature conditions. Refer to

Table 7. Sigmund model expressions at different reference temperatures.

Reference Temperature/°C	Model Expression	Correlation Coefficient R2
−10	$E^{*}=\mathrm{44,000}-{\displaystyle \frac{\mathrm{43,800}}{1+e^{0.2942\ln f-0.53}}}$	0.986
5	$E^{*}=\mathrm{42,000}-{\displaystyle \frac{\mathrm{41,750}}{1+e^{0.3086\ln f-1.24}}}$	0.996
20	$E^{*}=\mathrm{36,000}-{\displaystyle \frac{\mathrm{355,600}}{1+e^{0.3806\ln f-2.02}}}$	0.994
35	$E^{*}=\mathrm{33,000}-{\displaystyle \frac{\mathrm{32,730}}{1+e^{0.3463\ln f-3.12}}}$	0.986
50	$E^{*}=\mathrm{30,000}-{\displaystyle \frac{\mathrm{29,710}}{1+e^{0.3404\ln f-4.38}}}$	0.976

Note: $f$ in the table is the load frequency, Hz. $E^{*}$ is the dynamic modulus.

for specific modeling details. It can be seen from Table 7 that the correlation coefficient R2 is above 0.975, which indicates that the regression model has a good fitting effect on the test results. Using the model equation in Table 7, the dynamic modulus parameters under different temperatures and frequencies can be obtained, which is of great significance to the structural design of epoxy asphalt mixture pavement.

As can be seen from

Table 8. Comparison of dynamic modulus between bending test and Sigmund model at 5 Hz.

Method	Dynamic Modulus (MPa)
	−10 °C	5 °C	20 °C	35 °C	50 °C
Bending test	22,126	14,113	8241	3054	1105
Sigmund model	21,481	13,705	7400	2616	920
Difference	645	408	841	438	185
Proportion	3%	3%	11%	17%	20%

, the difference between the dynamic modulus of the mixture obtained from the Sigmoidal model and the four-point bending test is small, which proves that the Sigmoidal model has strong reliability.

5.2. Phase Angle Principal Curve

The drawing method is the same as the main curve of the dynamic modulus of the epoxy asphalt mixture. According to Equations (1) and (4), the fiducial temperature $T_s$ can be calculated inversely by selecting the reference temperature. According to the WLF equation, the shift factor of the phase angle curve under other temperature conditions relative to 20 °C temperature conditions is obtained, so as to make the phase angle master curve of the epoxy asphalt mixture under the 20 °C temperature conditions, as shown in Figure 9.

Figure 9 reveals that the phase angle of the epoxy asphalt mixture is significantly influenced by load frequency, initially rising and subsequently declining as frequency increases. At low frequencies and longer durations, the stiffness of the mixture is primarily governed by the embedded mineral skeleton, resulting in a smaller phase angle. Conversely, at high frequencies with brief action times, the mixture’s deformation is minimal, and external viscosity becomes less pronounced. In summary, the effect of load frequency on the phase angle of the epoxy asphalt mixture is different only in different frequency stages, which is obviously different from the dynamic modulus.

6. Analysis of Influencing Factors of Dynamic Viscoelastic Properties

6.1. Content of Epoxy Resin

Specimens of the epoxy asphalt mixture with epoxy resin contents of 30%, 40%, 50%, and 60% were prepared using Gradation 1. A dynamic frequency scanning test was conducted at various temperatures using a COOPER testing machine. The test results of the dynamic modulus and phase angle are shown in Figure 10 and Figure 11.

According to Figure 10 and Figure 11, under the conditions of 20 °C and 35 °C, the dynamic modulus of the epoxy asphalt mixture increases with the increase in epoxy resin content, and the phase angle decreases with the increase in epoxy resin content. This indicates that with the addition of epoxy resin, the crosslinked network structure of the mixture is enhanced, thus improving its strength, stiffness, durability, stability, adhesion, and other key performance indicators. The asphalt gradually changes from the original viscous material to the elastic material, and the viscoelastic property of the mixture is greatly improved. At the same time, when the epoxy resin content is 50% and 60%, the dynamic modulus and phase angle of the mixture have a small difference, but compared with the 40% content, the dynamic modulus of the mixture with 50% epoxy resin content is increased by 25.88% at 10 Hz and 20 °C, and by 34.48% at 10 Hz and 35 °C. The phase angle decreases by 58.04% at 10 Hz and 20 °C, and 36.23% at 10 Hz and 35 °C, showing better performance. Compared with the mixture with 60% epoxy resin content, the dynamic modulus only decreased by 1.45% at 10 Hz and 20 °C, and the phase angle only increased by 7.6%. Therefore, considering the influence of epoxy resin content on the performance of the mixture, combined with the actual situation such as the engineering cost, the epoxy resin content is recommended to be 50%.

At the same time, in order to analyze the changes in microscopic morphology of mixtures with different epoxy resin contents, SEM was used to conduct a microscopic analysis of mixtures with different epoxy resin contents, as shown in Figure 12.

The fluorescence microscope observation images are summarized in Figure 12. Yellow is for epoxy resin and black is for basic asphalt. From Figure 12, with the gradual increase in the epoxy resin content, the yellow particles in the picture gradually increased, and the size of the particles also enlarged. When the proportion of epoxy reaches 10%, the epoxy is just doped into the asphalt base in a tiny medium, which is only equivalent to the role of a modifier. When the proportion of epoxy resin reaches 20%, the number of yellow particles increases significantly. When the proportion of epoxy resin is increased to 30%, the epoxy resin particles aggregate with each other and form larger epoxy resin particles. The whole mixture is still mainly coated with asphalt epoxy resin. When the proportion of epoxy resin reaches 40%, epoxy asphalt has changed from bitumen-based to epoxy resin-based. The epoxy resin has formed a skeleton, and asphalt is distributed in the epoxy skeleton, but the particle size of the asphalt is not uniform. When the proportion of epoxy resin reaches 50%, asphalt particles are evenly distributed in epoxy. The performance of the epoxy asphalt mixture has been improved. The asphalt mixture with the epoxy resin content can be used for the pavement of a long-span steel bridge deck.

6.2. Composition of Mixture

The test specimens were made with Gradation 1 and Gradation 2, respectively, and the test frequency was 10 Hz. Figure 13 presents the outcomes of the dynamic modulus testing. Gradation 1 is typically used as the lower layer of steel deck pavement due to its fine gradation, high asphalt content, and good fatigue performance. On the other hand, Gradation 2 is usually used as the upper layer of steel deck pavement because of its coarse gradation, large surface structure, and good anti-skid performance. As can be seen from Figure 11, coarse gradation has a higher dynamic modulus. Due to the fact that a coarse aggregate accounts for a larger proportion and a fine aggregate is less evenly distributed in coarse gradation, it is possible to form a better skeleton structure, which increases the friction force within the material. Hence, the coarse gradation asphalt mixture exhibits a higher dynamic modulus than the fine gradation counterpart.

6.3. Aging of Mixture

With the increase in service life of steel bridge deck pavement, pavement materials will continue to age, and its performance will also change accordingly. It can be seen that the anti-aging ability of pavement materials is an important factor affecting the service quality and life of pavement structures. The samples underwent a simulated long-term aging process in an oven at 85 °C for 5 days, mirroring the aging of real bridge deck pavement. Following this, a dynamic modulus scanning test was performed utilizing a COOPER material tester. Figure 14 and Figure 15 present the outcomes, revealing minimal changes in the dynamic modulus and phase angle of the epoxy asphalt mixture before and after aging. This stability demonstrates the excellent aging resistance of the epoxy asphalt mixture.

7. Conclusions

The viscoelastic parameters of the epoxy asphalt mixture are ascertained through four-point bending tests, upon which a master curve model of viscoelastic parameters is formulated; based on a laboratory test and microscopic analysis, the effects of epoxy resin content, mixture gradation, and mixture aging on the modulus of an epoxy asphalt mixture were investigated, leading to the derivation of research conclusions.

(1)

The dynamic modulus ascertained via uniaxial compression tests exceeds that derived from bending tests; this disparity initially increases and then diminishes as temperature rises. At 20 °C, this discrepancy peaks, with a deviation of 58%.

(2)

As temperature rises, the dynamic modulus diminishes while the phase angle augments. Conversely, the dynamic modulus intensifies with an increase in load frequency, but the phase angle’s response to frequency alterations varies across temperatures.

(3)

Utilizing the WLF and Sigmoidal models enables the construction of a master curve model for the dynamic bending–tensile modulus and phase angle, thereby facilitating the extraction of these parameters across the entire temperature and frequency spectra.

(4)

When the epoxy resin content is 50% and 60%, the dynamic modulus and phase angle of the mixture have a small difference, but compared with the 40% content, the dynamic modulus of the mixture with 50% epoxy resin content is increased by 25.88% at 10 Hz and 20 °C, and by 34.48% at 10 Hz and 35 °C. The phase angle decreases by 58.04% at 10 Hz and 20 °C, and 36.23% at 10 Hz and 35 °C, showing better performance. Compared with the mixture with 60% epoxy resin content, the dynamic modulus only decreased by 1.45% at 10 Hz and 20 °C, and the phase angle only increased by 7.6%. Therefore, considering the influence of epoxy resin content on the performance of the mixture, combined with the actual situation such as the engineering cost, the epoxy resin content is recommended to be 50%.

(5)

The epoxy asphalt blend demonstrates robust resistance to aging, exhibiting minimal variation in its dynamic modulus and phase angle before and after the aging process.

By comparing the dynamic modulus parameters obtained by the four-point bending test and uniaxial compression test, it is found that the results of the conventional uniaxial compression test are on the high side, which is not conducive to the mechanical calculation results of steel deck pavement. In the stage of pavement structure design, the dynamic modulus is one of the important parameters to calculate the stress and strain of the pavement structure. Through the dynamic modulus master curve proposed in this paper, the mechanical response of a pavement structure under vehicle load can be calculated more accurately, so as to optimize the thickness and combination of the pavement structure layer, and improve the overall bearing capacity and service life of pavement.

In order to ensure the repeatability of the test data, the standardized process, environmental conditions, and equipment calibration of the test should be strictly controlled. Since the asphalt mixture is a temperature-sensitive material, when measuring the dynamic modulus at different temperatures, the temperature of the test piece should be accurately controlled by using an incubator or heating/cooling device. The loading method should also be carried out in strict accordance with the test standards to ensure that the loading rate, loading direction, loading point position, and other parameters of each test are the same. In the four-point bending test, it is necessary to pay special attention to the position of the loading point and the distribution of the loading force to ensure the uniform force of the specimen in the bending process.

In this paper, the main curve equation of the dynamic modulus and phase angle is established by using the four-point bending fatigue test, and the factors affecting the dynamic modulus are studied. However, the influence of temperature and loading frequency on the dynamic modulus of an epoxy asphalt mixture is only carried out, and the influence of the oilstone ratio, voidage, and other factors on the dynamic modulus of an epoxy asphalt mixture needs to be further studied. In the next step, the microstructure of epoxy asphalt mixtures can also be studied in detail. Due to the limitation of space, this paper only studies the main curve of phase angle parameters at 20 °C, hoping to preliminarily analyze the trend of the phase angle through the main curve of a temperature, and then carry out systematic research on the phase angle.