1. Introduction
As a typical temperature-sensitive material, the modulus of an asphalt mixture changes with its temperature. As a result, the load-carrying capacities and pavement performances of asphalt pavements are significantly influenced by temperature. Various common types of damage to asphalt pavements, such as low-temperature cracking, high-temperature rutting, and fatigue damage, are also directly or indirectly related to the temperature distribution within the pavement [
1,
2,
3,
4].
Compared with green vegetation, asphalt pavement has different characteristics such as a darker surface color and greater thermal inertia. Asphalt pavement constantly absorbs solar heat radiation, causing the surface temperature to rise sharply, which not only accelerates its own high-temperature rutting damage, but also exacerbates the urban heat island (UHI) effect. The use of cool pavement to mitigate the UHI effect is a popular direction in recent research. The phrase "cool pavements" was recently defined by the United States Environmental Protection Agency (USEPA) as “cool pavements include a range of established and emerging technologies that communities are exploring as part of their heat island reduction efforts. The term currently refers to paving materials that reflect more solar energy, enhance water evaporation, or have been otherwise modified to remain cooler than conventional pavements.” [
5]. The cool pavement cooling principle mainly includes heat reflection, water evaporation, and road heat storage [
6].
The reflective coating is a pre-treatment solution that prevents the first surface layer from absorbing heat and reflects a significant amount of energy back into the environment, thus reducing the downward conduction of heat sources in the pavement structure [
7]. Zheng et al. [
8] developed different reflective coating materials and studied their effects on human comfort through field tests. The results show that the use of reflective coatings can effectively improve human comfort and alleviate the UHI effect. Evaporative pavements are often designed as water-locked structures, with water absorbing heat to transition from a liquid to a gas state. This process requires the absorption of heat from the surrounding environment, which cools the pavement. Parking lots, walkways, highway shoulders, and city streets are all examples of evaporative pavements [
9]. Another use of permeable pavement is for storing rainwater after high-intensity rainfall events [
10]. In absorbing the heat extracted by embedded asphalt solar collectors, collected heat pavement can be used as a sustainable energy source.
Research on the performance of asphalt pavement under a multi-physical field has been rapidly developing in recent years [
11]. Wang et al. [
12] studied the thermodynamics and mechanical properties of porous asphalt under high temperature and high-strength rainfall. The resistance of porous asphalt to rutting under this multi-physical field condition was evaluated. The results show that the rutting resistance of a porous asphalt mixture under rainfall conditions is lower than that under dry conditions. The rutting resistance of a porous asphalt mixture is more sensitive to temperature than to rainfall conditions. Ma et al. [
13] used measured weather data to simulate temperature transfer during asphalt pavement construction. The results show that the initial temperature and layer thickness affect the overall temperature field during compaction, and wind speed and temperature mainly affect the upper-temperature field of hot mix asphalt (HMA). Zhao et al. [
14] developed a three-dimensional (3D) finite element (FE) model based on transient heat transfer. The results show that the influence of temperature decreases with the increase in depth. Therefore, future subgrade temperature stress is less of a concern. Temperature differences should be considered in pavement design in regions with large temperature differences.
In summary, a comparison of the influence of temperature on the mechanical properties of conventional pavement and cool pavement with reflective coating is seldom seen in the literature. The main objective of this paper is to study the effects of temperature on the two types of asphalt pavements using the FE method, mainly in terms of the variation of their mechanical parameters. To this end, the heat transfer model for asphalt pavement is first introduced. The development of FE models for conventional and cool pavements is then described. The results derived from the FE simulations with respect to the heat transfer within and the mechanical responses of the two types of asphalt pavements are analyzed. Finally, the conclusions and outlook are provided.
2. Heat Transfer Model in Asphalt Pavement
For asphalt pavement structures, it is generally assumed that the horizontal temperature gradient is zero. Therefore, the side boundary conditions can be ignored, and the main boundaries considered are the surface boundary and the bottom boundary. The pavement surface is the main boundary of the pavement heat transfer, and the heat exchange between the pavement and the external environment is carried out mainly in three ways: solar radiation, thermal convection, and pavement surface radiation [
4], as shown in
Figure 1.
For solar radiation, the radiation flux incident on the surface or medium passes through three paths, namely, transmission, reflection, and absorption. According to the definition of energy conservation, the relationship between the transmissivity α, reflectivity ρ, and absorptivity τ of the radiation flux is as shown in Equation (1) [
15]:
Asphalt pavement is a black opaque solid. For the opaque surface, the transmittance α is 0, and then ρ + τ = 1. Therefore, the lower the absorption rate is, the higher the reflectivity of the opaque surface is. The higher the reflectivity, the lower the heat loss.
According to the research of Liao et al., solar radiation can be calculated as follows [
16]:
where q
s(t) is the function of heat flux of solar radiation with time (mJ/(h∙mm
2)), q
0 is the maximum value of q
s, Q
d is the total heat flux of solar radiation per day (mJ/(mm
2)), c is the effective duration of sunshine (h), β is a parameter (rad, 2π/24 = 0.2618), and t is the time (h).
The q
s values obtained by Equations (2)–(4) are not smooth and continuous, and there will be jumping points when calculating the temperature field. In accordance with the relevant principle of the Fourier series, the cosine function was expanded into the corresponding Fourier series form. When k reaches 30, it can meet the requirements of engineering accuracy [
16].
where Q
s is the effective solar radiation absorbed by the pavement mJ/(h∙m
2), and τ is the absorptivity of solar radiation [
16].
When affected by solar radiation, the air temperature will also show corresponding changes. The air temperature and wind speed are important factors affecting the heat exchange (thermal convection) between the road surface and the atmosphere. It is not accurate to use a single sine function to simulate the temperature change process during the day, and so a linear combination of two sine functions was used to simulate the temperature change process [
16], as shown in Equation (8):
where
is the average of the highest and lowest temperatures of the day, which can be expressed as [
16]:
where T
m is the magnitude of the temperature change during a day, i.e., half of the difference between the highest and lowest temperature values, which can be shown as [
16]:
The exchange coefficient of the heat exchange, h
c (mJ/(h∙mm
2 °C)), between the road surface and the atmosphere is mainly affected by the wind speed v
w, m/s, and the relationship between them is linear [
16], as shown in Equation (11):
The pavement surface radiation can be represented by Equation (12) [
16]:
where Q
ps is the effective road surface radiation (mJ/(h∙mm
2)), ε is the road surface radiation emissivity, σ = 2.04 × 10
−7 mJ/(h∙mm
2∙K
4) is a Stefan-Boltzmann constant, T
ps and T
a are the pavement surface temperature and air temperature, respectively, and T
z is the absolute zero temperature.
Due to the influence of the atmospheric environment, the temperature fluctuation of the pavement surface is large, while the temperature fluctuation of the deeper part of the subgrade is small compared to the atmospheric environment fluctuation, which can be considered as a constant. Some researchers have considered the bottom boundary as an adiabatic boundary. However, it has been found that whether the bottom boundary condition is set to a constant temperature or is adiabatic, its effect on the temperature field of the upper layer of the asphalt pavement is negligible.
3. Development of FE Model of Asphalt Pavement
Two asphalt pavement models were developed on the general-purpose FE software ABAQUS (2017, Dassault Systèmes SE, Vélizy-Villacoublay, France): one was thermal analysis, which was designed to simulate the heat transfer of asphalt pavement under the effects of solar radiation and atmospheric temperature, and the other was mechanical analysis, which had the same geometry as the first model, with the temperature field of the first model imported into this model. A time-dependent half-sine wave load was applied to observe and compare the stress and displacement distributions when considering the case of temperature variation effects and changes.
3.1. The FE Heat Transfer Model
In this study, two FE pavement heat transfer models without (conventional pavement) and with (cool pavement or reflective pavement) reflective coatings were developed. Both models had the same pavement structure, which was divided into six layers and designed mainly according to the German design standard RStO [
17]. In this standard, the width of a single-lane highway should be 3750 mm; however, a single-lane highway can be divided into two parts by the middle axis, and the left and right parts are essentially the same in structure and material properties. Therefore, the model could be simplified as an axisymmetric model, and the width of the model was set to 1875 mm. In addition, since the length of the asphalt pavement does not affect the whole temperature conduction process, the model length was selected as 2000 mm to improve the calculation efficiency of the model. To summarize, the size of the asphalt pavement model was 2000 mm × 1875 mm × 1750 mm, as shown in
Figure 2. The interaction relationship between the first three layers of asphalt surface was fully connected. The vertical displacement in the last four layers of the asphalt pavement structure was set to continuous, while sliding could occur in a horizontal direction in the three interfaces.
To simulate the cooling effect of the cool pavement, Perfect Cool, a dark pavement coating with a high reflectivity (recently developed by NIPPO Corporation Co. Ltd (Tokyo, Japan)) [
18] was selected. Perfect Cool aims to lower the temperature of pavement during the day by enhancing its reflectivity and minimizing the amount of heat absorbed. To decrease heat transmission, Perfect Cool combines dark, low-reflective colored pigments with high infrared-heat-reflecting pigments and small hollow ceramic particles [
18]. For the FE pavement heat transfer model with a reflective coating, one additional layer with a thickness of 0.6 mm was created on top of the asphalt surface layer. The thermal parameters used by Perfect Cool are shown in
Table 1.
The two modes of heat transfer—steady and transient—were set in the simulation step. The steady-state heat transfer state was set to a very small time, and the transient state simulated the temperature change process of a 24 h period.
The solar radiation acts as a surface heat flux load on the pavement models in the heat transfer model. The action surface was chosen as the upper surface of the asphalt pavement. The solar radiation fluxes defined by Equations (5)–(7) were written by the subroutine DFLUX in ABAQUS [
19]. As established by the analytical Equations (8) and (11), the air temperature and wind speed will influence the simulated thermal convection. In this study, hot summer weather was considered. The specific data are shown in
Table 2.
The heat exchange coefficient and air temperature were defined using the subroutine FILM in ABAQUS, according to Equations (8) and (11). In this study, the bottom boundary of the pavement structure was set to be insulated.
The reliability of this FE heat transfer model has been validated by comparing the results from this model to the results from [
16], using the same parameters.
3.2. The FE Mechanical Pavement Model
Because the reflective coating is very thin compared to the structural layers of the pavement, its influence on the mechanical response of the pavement can be ignored. Therefore, in the FE mechanical pavement modeling, only the pavement structure with six structural layers was used. The relevant mechanical parameters of the model mainly refer to RStO [
17] and RDO Asphalt 09 [
21], and the damping coefficient refers to the data used in the existing reference [
16].
Table 3 shows the parameters of each layer of the pavement model in ABAQUS.
The temperature-dependent material properties were applied for the three asphalt layers. Due to the limited testing results, the viscoelastic parameters of the asphalt surface course and asphalt base course were derived from laboratory tests. The asphalt surface course and the asphalt base course are related to the rutting and fatigue cracking, respectively. The respective Prony series data used in ABAQUS are shown in
Table 4 and
Table 5. For the asphalt binder course, the temperature-dependent Young’s modulus referred to RDO Asphalt 09 [
21].
The completed heat transfer model results (temperature distribution) at specific times were imported to the mechanical model for the mechanical response of the pavement. All nodes at the bottom of the model were restricted from moving in all degrees of freedom. The four sides of the FE model were restrained from making any perpendicular movements to the side of the model. The interaction between the asphalt layers was fully coupled. The interfaces between the asphalt base course, hydraulically bound base course, frost protection course, and subgrade were assumed to be partially bound, which means that the vertical displacements of the adjacent layers were consistent, while the horizontal displacements could be different. When studying the mechanical response of the asphalt pavement model, to simplify the computational time and effect, the conventional standard load of 0.7 MPa was used. The load was applied to a circular area with a diameter of 300 mm [
17]. In order to simulate the process of a tire passing over the road (45 km/h), a time-dependent half-sine wave load was created, i.e., the load was applied gradually and reached the maximum value at 0.012 s, and then the load was gradually removed until it reached zero at 0.024 s. The completed pavement model with structural boundary conditions is shown in
Figure 3. The reliability of this mechanical FE model has been validated in previous investigations [
22,
23,
24,
25].
5. Conclusions and Outlook
In this study, the 3D models of asphalt pavements were established through the FE method. The stable temperature field of the pavement structure was calculated by applying different temperature boundary conditions to the pavement surface and applying the mechanical model to analyze the mechanical response of conventional pavement and cool pavement in a real environment. The simulation of the pavement structure temperature distribution under summer weather conditions shows that the pavement surface temperature can exceed 50 °C, which can easily lead to permanent deformation of the pavement surface and affect the service life of asphalt pavement. The cool pavement has a significant cooling effect, which makes the surface temperature of asphalt pavement and the atmospheric temperature nearly flat, and the temperature of each depth has a certain degree of reduction. The cool pavement mainly reduces the temperature of the top of the asphalt pavement. Particularly, cool pavement reduces the surface temperature of pavement by more than 15 °C, and it reduces the vertical displacement of pavement by approximately 11.3%, which proves that cool pavement can effectively improve anti-rutting performance. However, the use of cool pavement does not change the horizontal strain at the bottom of the asphalt base course, and so it does not increase the fatigue resistance of asphalt pavement.
In summary, the mechanical response of asphalt pavement was studied considering the characteristics of asphalt material changing with temperature. In future research, more environmental conditions should be considered, such as variable wind speed and humidity. The different interlayer bonding conditions between the asphalt layers should be investigated by experimental tests and numerical simulations. Additionally, wheel load should be calculated by establishing a vehicle dynamics model.