Study on temperature field and thermal stress of bridge deck pavement structure based on viscoelastic parameters

Abstract

Under heavy traffic loading combined with temperature effects, bridge deck pavement structures frequently exhibit a shortened service life, severely compromising both structural integrity and vehicular safety. This study developed a temperature field model for bridge deck pavement, with its reliability validated against published field measurements. Temperature distributions within the pavement layers across various temperature zones were obtained via Abaqus simulations. Prony series parameters for the asphalt mixture were fitted, enabling computation of temperature-induced stresses as a function of climatic variations and analysis of the influences of pavement material properties and structural layer thicknesses on these stresses. Results indicate that the pavement temperature field undergoes periodic fluctuations in response to ambient temperature, with temperatures decreasing progressively with depth. Employing high-thermal-conductivity materials in summer reduces peak pavement temperatures, whereas high-specific-heat-capacity materials in winter elevate minimum temperatures. The temporal variation of temperature-induced stresses mirrors that of the temperature field, with winter stresses significantly exceeding summer values. In summer, surface temperatures (e.g., 62.5 °C in extremely hot zones) are higher than those in lower layers, whereas in winter (e.g., −24.7 °C in severe winter zones), the pattern is reversed, providing a data foundation for thermodynamic analysis.

1 Introduction

As a critical protective layer in bridge engineering, bridge deck pavement not only bears the important mission of maintaining the integrity of the main structure but also provides service functions such as skid resistance and noise reduction (Lamichhane et al., 2022; Zhang et al., 2023). Its quality directly affects the service life of the bridge and the comfort of vehicular travel. Severely damaged bridge deck pavement can even endanger the main structure of the bridge and traffic safety (Zhang et al., 2021). However, according to relevant literature (Wang J. et al., 2023), issues such as early-stage rutting, cracking of the pavement layer, failure of interlayer bonding, difficul-ties in regular maintenance after pavement completion, frequent repairs, and high maintenance costs have led to varying degrees of damage in the pavement layers of many bridges before reaching their intended service life (He and Jiang, 2024). Severe damage to the bridge deck pavement can threaten the safety and durability of the main structure, necessitating large-scale repairs or even complete replacement (Liu et al., 2022; Zhang et al., 2023).

As the primary paving material, the mechanical properties of asphalt mixture are significantly sensitive to temperature variations. Research indicates that the non-uniform temperature field formed by external air temperature and solar radiation can cause significant changes in the modulus of asphalt mixture (Wang and Li, 2015). Cracks resulting from the contraction of asphalt layers, fatigue cracking of road asphalt layers, and rutting are closely related to the distribution of the pavement temperature field. Zuk analyzed thermal flow theory and established a temperature-field model considering ambient temperature, solar radiation, material thermal conductivity, and convective heat transfer (Zuk, 1965). Emerson et al. through measured temperature data from concrete, steel, and composite bridges, found that the temperature distribution within bridge structures is nonlinear (Emerson, 1973).

Thermal stress in bridge structures, induced by temperature effects, is a leading cause of cracking damage in pavement layers, and its generation mechanism and distribution patterns have attracted significant attention. Finite element analysis has shown that the relationship between stress and temperature gradient is highly evident in steel-concrete composite deck systems (Wang et al., 2015). Temperature-load coupling in steel-concrete composite girder bridge deck pavement has also been investigated, indicating the need to consider the combined effects of thermal action and traffic loading when evaluating pavement mechanical response (Li, 2022; Wang R. et al., 2023).

Recent research has shown that the service performance of bridge deck pavement is affected by material properties, structural response, traffic loading, and environmental actions. Long-life asphalt pavement and steel bridge deck pavement systems have been investigated to improve the durability of bridge deck surfacing (Liu et al., 2022). The dynamic and mesomechanical responses of asphalt bridge deck pavement under vehicle loading and complex structural conditions have also been analyzed in recent studies (Zhang et al., 2021; Cui et al., 2022). In addition, studies on curved bridge pavement and field distress characteristics have provided useful evidence for understanding the service behavior of asphalt bridge deck pavement (Wang J. et al., 2023; Zhang et al., 2023). Recent dissertation studies have further examined temperature-load coupling in steel-concrete composite girder bridge deck pavement and low-temperature damage of asphalt pavement on concrete bridge decks in cold regions (Li, 2022; Ren, 2023). Recent studies on temperature-field/modulus-field-based thermo-mechanical response and temperature fatigue damage have further shown that the interaction between temperature field, material modulus, and structural response should be considered in pavement thermal analysis (Fan, 2024). However, most existing studies still focus on material performance, load response, or field distress separately, while the coupled effects of climatic temperature zones, material thermophysical properties, asphalt mixture viscoelasticity, and structural layer thickness on temperature-induced stress remain insufficiently quantified. Therefore, this study establishes a field-validated thermo-mechanical analysis framework for asphalt bridge deck pavement by combining measured temperature validation, dynamic modulus testing, Prony series fitting, and finite element simulation. The proposed framework links the temperature-field evolution of bridge deck pavement with the viscoelastic response of asphalt mixtures and provides quantitative support for material selection and structural optimization under high- and low-temperature environments.

2 Objective

In this study, a field-validated thermo-mechanical analysis framework is developed to investigate the temperature field and temperature-induced stress of asphalt bridge deck pavement. A temperature-field model is established based on an actual bridge structure and validated using field-measured temperature data. Meteorological data from different temperature zones are introduced into Abaqus to simulate the temperature distribution of the pavement layers and to provide thermal boundary conditions for subsequent mechanical analysis. The viscoelastic behavior of typical asphalt mixtures is incorporated through dynamic modulus testing and Prony series fitting, and thermo-mechanical sequential coupling analysis is performed by defining the thermal expansion coefficients and viscoelastic parameters of the pavement materials. Based on this framework, the effects of climatic temperature zones, material properties, and structural layer thickness on temperature-induced stress are evaluated.

3 Methodology

This research is primarily divided into two parts. The first part involves converting the dynamic modulus data of different mixtures into Prony series. The second part utilizes the Prony series for temperature field modeling to study its impact on the temperature field under various environmental conditions.

3.1 Asphalt concrete mixture

3.1.1 Aggregate

The coarse aggregate used in this study is diabase, while the 3–5 mm aggregate is limestone. Their specific technical indicators are shown in Tables 1, 2 below.

In this study, 0–3 mm sand is used as the fine aggregate, with technical requirements specified in Table 3.

The technical requirements for the mineral filler used in this study are presented in Table 4 below.

3.1.2 Asphalt

FIGURE 1

In this study, a TLA-to-SBS ratio of 30:70 is adopted to ensure the performance of the gussasphalt mixture. Conventional tests (penetration, softening point, ductility) were conducted on the blended asphalt, and the results provided in Table 7.

3.1.3 Fiber

In this study, the fiber content in the SMA mixture is 0.3%, and the performance parameters of the fiber are presented in Table 8.

3.2 Pavement material design

3.2.1 Gradation

Gradation design was conducted for AC-20, AC-13, SMA-13, and GA-10. The gradation ranges for the four types of asphalt mixtures are shown in Table 9 below.

3.2.2 Optimum asphalt content

Unlike roller-compacted asphalt mixtures, the workability of gussasphalt mixtures during construction is determined by their flow characteristics. Therefore, this study adopts the standard Liu’er (or flow value) test apparatus specified in the relevant specifications to evaluate the fluidity of the gussasphalt mixture. The final optimum asphalt contents of GA-10. AC-20, AC-13, and SMA-13 is 8.5%,4.8%,4.5% and 6.0%.

3.3 Modulus testing and viscoelastic parameters

3.3.1 Dynamic modulus testing of asphalt mixtures and fitting of viscoelastic parameters

Asphalt mixture is a typical viscoelastic material that exhibits significant relaxation and creep characteristics. Its mechanical response is dependent on loading time, loading frequency, and environmental temperature, among other conditions. In Abaqus software applications, the Prony series of relaxation modules is typically employed to define relaxation properties, accounting for the relaxation effects of thermal stress in the asphalt layer (Pacheco et al., 2015). Different asphalt mixtures possess dis-tinct relaxation characteristics. This study utilizes data obtained from dynamic modulus tests as a foundation to accurately determine the relaxation modulus. Subsequently, through a numerical conversion process, the derived relaxation modulus is effectively expressed in the form of a Prony series.

To characterize the structural layer response of different asphalt mixture types under the influence of factors such as vehicular loads and environmental conditions, the Asphalt Mixture Performance Tester (AMPT) system was employed to determine the dynamic modulus of fabricated AC-13, SMA-13, AC-20, and GA-10 cylindrical specimens. The specimens were first compacted into cylinders with a diameter of 150 mm and a height of 170 mm, and then cored and saw-cut into standard cylindrical specimens with a diameter of 100 mm and a height of 150 mm for dynamic modulus testing, as shown in Figure 2.

FIGURE 2

In accordance with the test specifications, the equipment includes three high-precision linear variable differential transformers (LVDTs) and an environmental temperature chamber. The test was conducted in a stress-controlled mode using a haversine (half-sine) load. The loading frequencies were set at 25 Hz, 10 Hz, 5 Hz, 1 Hz, 0.5 Hz, and 0.1 Hz. The test temperatures were set at 50 °C, 40 °C, 30 °C, 20 °C, and 10 °C. For each target temperature, the asphalt mixture specimen was conditioned in the environmental chamber for at least 4 h to ensure thermal equilibrium was reached before testing. This procedure allowed for the measurement of the dynamic modulus and phase angle corresponding to each specific temperature condition and the various loading frequencies.

3.3.2 Linear viscoelastic parameter conversion

Viscoelastic models include fundamental forms such as the Maxwell model, Kel-vin model, and Burger model, as well as extended versions like the generalized Max-well model, generalized Kelvin model, and modified Burgers model. The generalized Maxwell model adopted in this study serves as theoretical foundation for defining viscoelastic material behavior in Abaqus. The generalized Maxwell model—constructed by connecting N Maxwell elements (a spring and dashpot in series) in parallel with an isolated spring—can effectively serve as the viscoelastic constitutive model for asphalt mixtures (Fu et al., 2023).

The dynamic modulus of an asphalt mixture is equal to the magnitude of its com-plex modulus. The complex modulus consists of real and imaginary parts, as shown in Equation 1. The storage modulus is calculated using Equation 2, and the relaxation modulus is calculated using Equation 3.

Where, —Dynamic Modulus of Asphalt Mixtures,MPa;

—Storage Modulus of Asphalt Mixture,MPa;

—Phase Angle;

—Relaxation Modulus,MPa;

—Adjustment Function

After obtaining the dynamic modulus from the test, the fitting temperature was set at 20 °C. Using the WLF equation based on the time-temperature equivalence principle, the shift factors for each curve were calculated. Then, the sigmoidal function of the asphalt mixture’s master curve was fitted using the least squares method. The sigmoidal function used to fit the dynamic modulus master curve is expressed in Equation 4.

Where, —Dynamic Modulus of Asphalt Mixture,MPa;

—The dynamic modulus of asphalt mixture when the frequency approaches zero is also known as the static modulus.,MPa;

—The dynamic modulus of asphalt mixture when the frequency approaches infinity is also known as the glassy modulus,MPa;

, and are the parameters to be fitted for the morphological characteristics of the Sigmoidal model curve.

The WLF Equation 5 is used to determine the parameters C₁ and C₂.

Where, —Shift Factor;

, —Constant;

—Reference Temperature, °C.

The shear modulus can be calculated using Equation 6.

Where, —Shear Modulus,MPa;

—Relaxation Modulus,MPa;

—Poisson’s Ratio.

The Prony series is calculated as shown in Equation 7 below:

Where, —Number of series;

—Material Constant;

—Relaxation Time.

3.4 Finite element modeling, model validation, and thermo-mechanical coupling analysis

The finite element software ABAQUS was employed to establish a three-dimensional finite element model of the bridge deck system for a box-girder bridge using solid elements. The initial model was constructed with the following layer dimensions: concrete box girder, a 10 cm concrete leveling course, a 6 cm asphalt lower surface layer, and a 4 cm asphalt upper surface layer. Parameter variations were implemented in subsequent calculations. For the temperature field model, all mesh elements were defined as 8-node linear heat transfer hexahedral elements (DC3D8R). A fine mesh was applied to the asphalt concrete pavement layers to ensure the accuracy of the simulated temperature field within these layers. The finite element model of the pavement system on the concrete box-girder bridge, along with details of the mesh discretization, is shown in Figure 3.

FIGURE 3

Before the parametric simulations, the temperature-field model was validated using measured temperature data reported for a cement concrete box-girder bridge deck pavement under summer conditions (Ren, 2023). The meteorological parameters corresponding to the measured condition were introduced into the temperature-field model, and the simulated temperatures were compared with the measured data at different pavement depths. As shown in Figure 4, the simulated and measured temperature curves showed consistent diurnal variation. The maximum deviation occurred at 17:00 at the top of the upper asphalt layer, where the measured and simulated temperatures were 42.3 °C and 38.4 °C, respectively, corresponding to a relative error of 9.3%. This result indicates that the temperature-field model can reasonably reproduce the thermal response of the bridge deck pavement and provides reliable thermal boundary conditions for the subsequent thermo-mechanical analysis.

FIGURE 4

For the mechanical analysis of the asphalt concrete pavement layer using the finite element method, the following assumptions were made for the model (Wang et al., 2022): The boundary conditions were set as simply supported constraints according to the original bridge design; the asphalt bridge deck pavement layer and the cement concrete bridge deck layer are perfectly continuous and deform compatibly; since the thickness of the bonding layer is very small compared to the pavement layer thickness, typically only 1–3 mm, and the actual bonding layer integrates with the bridge deck pavement layer, it is not modeled in the finite element calculations; the self-weight of both the cement concrete slab and the asphalt pavement layer is neglected; and the cement concrete bridge deck and bridge girder remain in the elastic stage.

The thermal conductivity and specific heat capacity of the four mix designs (SMA-13, AC-13, AC-20, and GA-10) developed 3.3 were measured using a thermal conductivity tester. This provides the necessary thermal parameters for the subsequent Abaqus simulation of the temperature field in the bridge deck pavement. Furthermore, by referencing the thermal expansion coefficients of these pavement materials from literature and incorporating the dynamically measured modulus and fitted Prony series, a material parameter basis is established for the subsequent mechanical simulation of the bridge deck pavement in Abaqus. This study, based on temperature fields and thermal stress, investigates the temperature field and thermal stress analysis under different temperature conditions and with different material combinations. It also analyzes the impact of variations in the thickness of the asphalt layer and the concrete layer on thermal stress. The technical roadmap is shown in Figure 5 below.

FIGURE 5

4 Results and discussion

4.1 Dynamic modulus and prony series

4.1.1 Linear viscoelastic parameter conversion

Plot the curves showing the variation of dynamic modulus with temperature and loading frequency for four asphalt mixtures, as Figure 6 shows. As the ambient temperature increases, the dynamic modulus of the mixture shows a significant decreasing trend. This is due to the softening of the asphalt under heat and the weakening of the bond strength between the asphalt and aggregates, directly leading to a reduction in the overall modulus of the material. When the temperature decreases, the asphalt mixture hardens, resulting in a significant increase in the dynamic modulus. Addition-ally, the slope of the dynamic modulus curve is steeper under low-temperature conditions, indicating that the asphalt mixture is more sensitive to changes in loading frequency at lower temperatures. In terms of the frequency of dynamic loading, as the loading frequency increases, the strain lag phenomenon in the asphalt mixture be-comes more pronounced, leading to an increase in the dynamic modulus with faster loading frequencies.

FIGURE 6

The fitting results of the dynamic modulus master curves for four asphalt mixtures at 20 °C are shown in Figure 7. In the master curve plot, the low-frequency and high-frequency ends approach the maximum and minimum modulus values, respectively. The slope of the master curve represents the sensitivity of the mixture’s modulus to the loading frequency—a steeper slope indicates higher sensitivity, while a gentler slope indicates lower sensitivity. As the loading frequency increases from low to high, the slope of the master curve first increases and then decreases, indicating that the mixture’s modulus changes only slightly in the low- and high-frequency ranges but is more significantly influenced by the loading frequency in the mid-frequency range. Furthermore, the master curves show that the low-frequency and high-temperature performance of SMA and AC structures is significantly better than that of the GA structure.

FIGURE 7

Based on the process of converting the dynamic modulus to the relaxation modulus, the calculated relaxation modulus was fitted to a master curve, as shown in Figure 8. Using the relaxation modulus master curve and the inherent Poisson’s ratio characteristics of the asphalt mixture, the transient shear modulus of the asphalt mixture was calculated. Furthermore, the viscoelastic Prony series of relaxation modules for the asphalt mixture was obtained according to Equation 7, as presented in Table 10.

FIGURE 8

4.2 Temperature field

4.2.1 Different temperature

Under the combined influence of ambient temperature, solar radiation, and other environmental factors, the surface temperature of the pavement layer materials exhibits a distinct diurnal cyclical fluctuation pattern. After importing the six selected temperature and weather datasets and performing multiple iterative analyses of the bridge deck pavement temperature field model until a steady state was achieved, the diurnal temperature variation curves for the top of the upper layer, the top of the low-er layer of the asphalt concrete pavement, and the top of the cement concrete base layer were obtained. The finite element contour plot of the temperature field is shown in Figure 9, and the simulation results are presented in Figure 10.

FIGURE 9

FIGURE 10

As shown in Figure 10, the temperature field variation trends of each pavement structural layer on the bridge deck are synchronized with the air temperature but exhibit significant hysteresis and temperature attenuation behavior. During the daytime, under the combined influence of solar radiation and high ambient temperatures, the pavement surface acts as the primary heat-absorbing interface, reaching its peak temperature around 14:00 and forming a temperature gradient that decreases from the surface to the interior of the pavement. At night, after the solar radiation heat source disappears, the surface continuously releases energy through thermal convection, reaching its lowest temperature around 07:00. At this time, the deeper layers of the pavement structure, due to the hysteresis in temperature changes, maintain relatively higher temperatures, resulting in a reverse temperature gradient.

In summer, the maximum surface temperatures of the asphalt pavement layer in severely hot, hot, and cool summer climate zones can reach 62.5 °C, 51.5 °C, and 35.5 °C, respectively. Since the lower pavement layer and the concrete layer are not directly exposed to solar radiation, and heat attenuates as it passes through the upper layer, the temperatures of the lower pavement layer are 51.9 °C, 41.9 °C, and 27.8 °C, respectively, while the temperatures of the concrete layer are 45.7 °C, 37.1 °C, and 22.3 °C, respectively. In winter, the minimum surface temperatures of the pavement layer are as follows: 3.7 °C in the mild winter zone, −12.6 °C in the cold winter zone, and −24.7 °C in the severe winter zone. Due to lower heat loss, the temperatures of the lower pavement layer and the concrete layer are slightly higher than the surface temperatures, measuring 4.0 °C, −12.3 °C, and −23.9 °C for the lower pavement layer and 4.4 °C, −11.4 °C, and −22.4 °C for the concrete layer, respectively. The numerical simulation results provide thermodynamic boundary conditions for subsequent material performance testing and thermomechanical coupled finite element analysis.

4.2.2 Different material

To investigate the impact of material property variations on the temperature field distribution of the pavement layer, this section utilizes ABAQUS to import climate parameters from severe winter and severely hot summer regions. The temperature field variations over time for six pavement composite structures (with surface layers of SMA-13 or AC-13, and lower layers of AC-13, AC-20, or GA-10) under low and high temperature conditions were calculated. A systematic analysis was conducted to ex-amine the differences in temperature distribution caused by variations in thermal conductivity and heat capacity of the materials. The results are shown in Figure 11.

FIGURE 11

According to the simulation results of the high-temperature field in summer shown in Figures 11A,B, the maximum temperature of AC-13 as the surface layer is higher than that of SMA-13. This is primarily due to differences in the thermal conductivity of the materials. Compared to AC-13, SMA-13 has a denser structure and lower porosity. The aggregates in SMA-13 form effective heat conduction paths, and the reduced presence of low-thermal-conductivity air in the voids allows heat to transfer more rapidly through the solid skeleton from the surface to the underlying layers, thereby lowering the maximum temperature of the pavement layer.

For the lower pavement layer materials, the high compactness of GA-10 results in higher thermal conductivity. This advantage in heat conduction enables it to absorb heat from the upper layer and transfer it quickly to the concrete layer. AC-20, with a higher proportion of coarse aggregates, facilitates the formation of heat conduction paths more easily than AC-13, exhibiting greater thermal conductivity and allowing heat to transfer to the concrete layer more rapidly. As a result, when AC-13 is used as the lower layer, the pavement surface reaches the highest temperature, followed by AC-20, while GA-10 yields the lowest surface temperature.

Under low-temperature conditions in winter, the maximum temperature of SMA-13 as the surface layer is higher than that of AC-13. This is because SMA-13 has a higher asphalt content compared to AC-13, and asphalt possesses a higher heat capacity. This gives SMA-13 a greater ability to store heat, requiring more energy to heat or cool the material. When solar radiation is absent at night, the stored heat in SMA-13 is released slowly, resulting in a slower decrease in pavement surface temperature. For the lower pavement layer materials, GA-10, with its high asphalt and fine aggregate content, exhibits a higher heat capacity than AC-13 and AC-20. Consequently, in win-ter, the pavement structure with GA-10 as the lower layer maintains slightly higher temperatures compared to structures using AC-13 or AC-20.

4.3 Thermal stress analysis

4.3.1 Different temperature

Temperature variation is the root cause of thermal stress within the asphalt pavement structure. To investigate the influence of temperature changes on thermal stress, this section focuses on a composite pavement structure of 4 cm SMA-13 + 6 cm AC-20. Meteorological data from the severely hot and hot summer regions (for high-temperature conditions) mentioned above, combined with data from the cold winter and severe winter regions (for low-temperature conditions), are imported to conduct thermal stress research. This study aims to reveal the distribution patterns of thermal stress in the pavement layer under high and low-temperature conditions across different temperature fields. Figure 12 presents the transverse and longitudinal thermal stress-time distribution diagrams for the bridge deck asphalt pavement layer in different temperature zones.

FIGURE 12

As shown in Figure 12A, during the low-temperature season, the thermal stress in the bridge deck pavement layer exhibits significant diurnal cyclical fluctuations, with transverse tensile stress consistently higher than longitudinal tensile stress. The difference between the two gradually decreases as the temperature increases. During the non-solar cooling phase (00:00–08:00), the drop in ambient temperature causes the asphalt layer to contract, while the cement concrete layer, with its lower coefficient of thermal expansion, constrains this contraction. This leads to a continuous increase in transverse tensile stress on the pavement surface. In severe winter regions, the thermal stress during this period can rise from 3.4 MPa to a peak of 4 MPa. Comparing other low-temperature zones, it can be observed that as the minimum temperature of the pavement layer decreases, the peak stress of the pavement layer continues to rise. During the solar heating phase (08:00–15:00), solar radiation causes a sharp rise in pavement temperature. The thermal expansion of the asphalt reduces tensile stress or even converts it into compressive stress (with stress values turning from positive to negative). During the subsequent cooling phase (15:00–24:00), the asphalt pavement contracts again, leading to an increase in stress. It is worth noting that the pavement layer remains under prolonged tensile stress or cyclic tension-compression during diurnal cycles. This stress state is a primary cause of pavement cracking in winter.

As shown in Figure 12B, under high-temperature conditions in summer, the trend of thermal stress in the pavement structure is similar to that under low-temperature conditions. During the non-solar cooling phase (00:00–08:00), the asphalt pavement exhibits elasticity, with thermal stress gradually increasing as the temperature drops. The transverse and longitudinal tensile stresses are very close during this phase. During the solar heating phase (08:00–15:00), high summer temperatures cause a significant rise in the surface temperature of the pavement, which can reach 50 °C–60 °C. At this point, the viscous characteristics of the asphalt material become ap-parent, and the pavement layer develops a slight compressive stress of about 0.4 MPa. However, this compressive stress diminishes as the temperature continues to rise. During the subsequent cooling phase (15:00–24:00), the stress state transitions from compressive to tensile and stabilizes at a relatively low tensile level. Overall, the ten-sile stress during the high-temperature season is lower than during the low-temperature season. This is because asphalt mixture is a temperature-sensitive material: it exhibits elasticity and a higher modulus at low temperatures, while it shows viscosity and a lower modulus at high temperatures.

4.3.2 Different material

Rational selection of asphalt mixtures plays a critical role in mitigating pavement damage induced by thermal effects and enhancing the overall performance of bridge deck pavements. Based on the analysis in the previous section, extreme low temperatures in winter represent the most critical condition for thermal stress in bridge deck pavements. Therefore, this section utilizes meteorological data from severely cold regions and focuses on typical bridge deck pavement structural systems to conduct a comparative analysis of the maximum tensile stress (transverse tensile stress) for six pavement combination schemes (SMA-13/AC-13 + AC-20, SMA-13/AC-13 + AC-13, SMA-13/AC-13 + GA-10). The study aims to investigate the influence of pavement material properties on thermal stress, with the results presented in Figure 13.

FIGURE 13

According to Figure 13A, when AC-13 is used as the surface layer, its maximum tensile stress is generally higher than that of the SMA-13 pavement system. This is primarily due to the higher modulus and greater coefficient of thermal expansion of AC-13. Additionally, the thermal expansion characteristics of the underlying layer in-fluence the stress state of the surface layer through deformation transmission. When GA-10 is used as the underlying layer, the tensile stress in the surface layer is greater than when AC-13 or AC-20 is used. This is because the higher coefficient of thermal expansion of GA-10 leads to superimposed deformation in the surface layer under temperature changes, thereby generating greater thermal stress.

As shown in Figure 13B, when the same surface layer material is used, the differences in thermal stress among the underlying layers are relatively small. This indicates that the surface layer material has a limited influence on the thermal stress of the underlying layer. The ranking of thermal stress for different underlying layer materials is AC-20 > AC-13 > GA-10, which is directly related to their respective thermomechanical parameters. AC-20, with its higher modulus and larger coefficient of thermal expansion, produces the greatest thermal stress. Although GA-10 has a relatively high coefficient of thermal expansion, its lower modulus results in lower thermal stress. Therefore, material selection should consider both modulus and thermal expansion behavior, and a quantitative criterion is further introduced below.

The similar time-dependent trends of base-layer thermal stress among the six pavement combinations do not contradict the differences in heat transfer and dissipation behavior discussed in Section 4.2.2. The temperature-field differences mainly reflect the effects of mixture thermophysical properties on heat conduction, heat storage, and temperature attenuation. In contrast, the temporal trend of base-layer thermal stress is mainly controlled by the same daily temperature cycle and structural boundary constraints applied to all pavement combinations. Therefore, the stress curves show similar increasing and decreasing trends over time, while the material properties mainly affect the stress magnitude. This is consistent with the stress ranking of AC-20 > AC-13 > GA-10, where AC-20 produces higher thermal stress due to its higher modulus, whereas GA-10 exhibits lower stress because its lower modulus reduces stress accumulation.

For engineering material selection, the elastic modulus and thermal expansion coefficient should be considered jointly rather than independently. In this study, the product of the elastic modulus and thermal expansion coefficient, Eα, was used as a first-order thermal-stress sensitivity index. Based on the material parameters used in the finite element model, the Eα values of GA-10, AC-13, SMA-13, and AC-20 were approximately 0.221, 0.256, 0.265, and 0.276 MPa/°C, respectively. Therefore, within the range of materials investigated in this study, lower-layer materials with Eα not exceeding approximately 0.26 MPa/°C are preferred when thermal-stress control is the dominant objective, whereas materials with Eα close to or higher than 0.27 MPa/°C should be used with caution in severe cold regions. However, this index should not be used alone. Material selection should also consider thermal expansion compatibility between layers, viscoelastic relaxation capacity, and the calculated maximum tensile stress.

5 Conclusion

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