The influence of water vapor on the structural response of asphalt pavement

A series of water damage phenomena of asphalt pavement during service show that water is very important. To comprehensively analyze the influence of water vapor factors on the response of pavement structure, this article first tests the water vapor diffusion coefficient of asphalt pavement materials at different temperatures establishes the water vapor concentration field model of the pavement structure, and analyzes the actual water vapor distribution of the pavement structure; then, the relationship between viscoelastic parameters of the mixture and water vapor concentration is established. Based on this, the finite element model of the pavement structure considering the water vapor factor is established, and the influence of the water vapor factor on the pavement structure response and fatigue life is quantified. It is found that water vapor has an important influence on the mechanical response. On the hottest days in summer, the attenuation of surface modulus caused by water vapor has the greatest impact on the upper layer of the pavement structure. Under the influence of water vapor, the position just below the wheel of the upper layer at the bottom of the horizontal tension strain increases by 108.26%, and the horizontal tension strain of the other layers increases by about 5%, increasing the risk of upper layer cracking. At the same time, water vapor reduces the stress that can be borne by the surface layer, while the rest of the stress is borne by the base. Compared with the fatigue life calculation method in the specification, the actual non-uniform water vapor concentration field reduces the fatigue life of the surface layer by 12.246%. This shows that the current structural calculation does not consider the water vapor factor, which makes the pavement structure more dangerous, and the influence of the water vapor factor should be fully considered.


Introduction
In the field of road construction in China, asphalt pavement has become the main pavement form of expressways and other highways because of its advantages of smoothness, less dust, and smooth, and comfortable driving. Water damage is one of the common early damages of asphalt pavement; in severe cases, it affects traffic safety and shortens the service life of asphalt pavement. The traditional view holds that the water damage of asphalt pavement is mainly caused by liquid water, which affects the performance of the asphalt pavement structure through rainfall infiltration and rising capillary water. However, the phenomenon of water damage in many arid areas shows that liquid water is not the only source of water damage, and the influence of water vapor on the pavement structure and performance is also huge [1][2][3][4]. Compared with short-term rainfall and other liquid water effects, the pavement structure is at a certain water vapor concentration for a long time [4]. Under the long-term action of the water vapor, the performance of asphalt decreases and affects the adhesion of asphalt itself and between the asphalt and aggregate [5]. Therefore, it is necessary to study the influence of water vapor on the response of the pavement structure.
For analyzing the distribution of water vapor in the pavement structure, many scholars have carried out research on the movement law of the water vapor in a mixture [6,7]. On this basis, some scholars have established a simple water vapor concentration field model of the pavement structure, but this part of the model does not consider the influence of temperature on the diffusion coefficient and the dynamic change of the external water vapor concentration environment; the obtained water vapor concentration field is in an ideal state [8]. Knowing the actual water vapor distribution inside the asphalt pavement structure under the dynamic changes of external temperature and water vapor can provide real water vapor parameters for the analysis of the asphalt pavement structure and pave the way for analyzing the influence of water vapor on the response of the asphalt pavement structure.
To solve the shortcomings in the above research, this article first establishes a finite element model of temperature and the water vapor field of the pavement structure considering the actual service environment. Combined with the water vapor concentration field model, the water vapor concentration of each layer of the pavement structure is analyzed, the viscoelastic parameters of this water vapor are solved according to the joint shift factor formula, and the pavement structure response model considering the actual water vapor concentration field is established. Compared with the conventional model, the influence of water vapor factors is analyzed. The results provide a certain theoretical and practical basis for clarifying the water damage mechanism of asphalt pavement and guide the design of the asphalt pavement structure.
2 Establishment of a finite element model of the temperature and water vapor concentration field of the pavement structure considering the actual service environment In order to establish a finite element model of the mechanical response of the pavement structure considering fully of the water vapor, this section will establish a model of the uneven water vapor concentration field of the pavement structure in an all-weather temperature and water vapor concentration environment. First, the water vapor diffusion coefficient of pavement materials at different temperatures is quantified by the theory of penetrating water vapor diffusion and then the temperature field model of the pavement structure is established by taking the most unfavorable temperature as an example and combining it with the temperature situation in Yichun, Jiangxi Province, on July 31, 2021. Considering the temperature field as a predefined field, the unit grid reads the temperature data and then calculates the diffusion coefficient at the corresponding temperature according to the definition of the material diffusion coefficient for application. By inputting the boundary conditions of the water vapor concentration and simulating the water gas concentration field under the influence of a temperature field, the established temperature field model and the water gas concentration field model are analyzed. This research is based on Yisui (Yichun City to Sichuan County) high-speed project. The pavement structure of this project section is shown in Figure 1, and in this work, a pavement structure model based on this structure is established.

Measurement of the water vapor diffusion coefficient
At present, when studying the water vapor movement of the pavement structure, the penetrating diffusion model is mostly used. This is because the pavement structure is under the water vapor difference between the soil base and the external environment, which is more in line with the penetrating water vapor diffusion model. Therefore, in this section, the penetrating water vapor diffusion model is adopted to measure the diffusion coefficient of the surface mixture, and, combined with the mass diffusion module in the finite element method, the uneven water vapor concentration field formed by the pavement structure under the dynamic action of the soil foundation and the external environment is simulated. Some research group has measured the diffusion coefficient of AC-13C and AC-20C asphalt mixtures [9]. This article supplements the measurement of the diffusion coefficient of the AC-25C asphalt mixture to obtain the diffusion coefficient of each surface layer at different temperatures, as shown in Table 1.

The temperature field model of the pavement structure
Because the water vapor diffusion coefficient of the asphalt mixture is greatly affected by temperature, it is necessary to establish the temperature field of the pavement structure before establishing the water vapor diffusion model of the pavement structure by using the finite element method. The establishment method of the temperature field is based on the results of Professor Yan Zuoren of Tongji University [10].
With the help of the FILM module (user subroutine to define the nonuniform film coefficient and the associated sink temperatures for heat transfer analysis) and DFLUX module (user subroutine to define the nonuniformly distributed flux in a heat transfer or mass diffusion analysis), the definitions of effective radiation, air temperature and convective heat exchange of the pavement structure are realized, and the temperature field model of the pavement structure is established.

Establishment of the temperature field model
In this study, referring to the meteorological statistics of the National Meteorological Science Data Center, the temperature field model of the pavement structure was established. The annual average wind speed in Jiangxi Province is about 2.7 m/s, and the temperature data of the hottest day in July (July 31) in Yichun, Jiangxi Province, were selected. In previous studies [10][11][12][13], research on the thermal parameters of the pavement structural materials has been carried out and the comparison shows that the thermal parameters of the same materials have little  difference. Therefore, the thermal parameters of the materials given in previous studies [11][12][13][14] are selected in this study and listed in Table 2.

Calculation results of the temperature field
To simulate the temperature field of the pavement structure, in this article, we have selected four typical points, the pavement surface, the bottom of the upper layer, the bottom of the middle layer, and the bottom of the lower layer, to analyze the temperature change trend, and the data are shown in Figure 2. From the simulation results, it can be seen that the surface layer is greatly affected by the external temperature, and the highest temperature of the pavement is 57°C. The calculation result file of the pavement structure temperature field is exported for the calculation of the water vapor concentration field.

The water vapor field model of the pavement structure
After the temperature field is established, it is regarded as a predefined field and the unit grid reads the temperature data. According to the definition of the material diffusion coefficient, the diffusion coefficient at the corresponding temperature is calculated. Then, combined with the input boundary conditions of the water vapor concentration, the water vapor concentration distribution under the influence of a temperature field is simulated, and the water vapor concentration field model of the pavement structure is established.

Parameter setting and the model establishment
The relationship between the water vapor diffusion coefficient and temperature can be fitted by the Arrhenius equation [9], as shown in Formula (1). With the help of this, the diffusion coefficients of each material layer were fitted and obtained at 10-60°C. The data are shown in Table 3. For the base-cement-stabilized macadam material, the properties of 5 and 3% cement-stabilized macadam are similar. Therefore, according to Rong and Tingting [8], the diffusion coefficient of the base material is obtained as follows: The diffusion coefficients given in Table 3 correspond to different mixture types. In terms of setting the boundary conditions of the water vapor concentration, it is generally believed that the relative water vapor of the soil foundation is 100% according to the water vapor concentration conditions at the lower boundary of the pavement structure [15]. In the pavement structure selected in this article, the upper layer of the soil foundation is a graded crushed stone with a large void ratio; therefore, it can be considered that the relative water vapor of the graded crushed stone is the same as that of soil foundation, which is 100%. According to the calculation results of the temperature field, the temperature of the graded crushed stone is stable at 28.73°C, and the water gas concentration is 28.33 g/mm 3 according to the conversion of the relative water vapor. In this article, it is assumed that the upper boundary condition of the water vapor concentration of the pavement structure is equal to the water vapor concentration of an external environment. In this article, referring to the data   of the National Meteorological Science Data Center, the relative water vapor data of the Yichun area on July 31 was obtained, and the change of the water gas concentration in this area was obtained by conversion. The water vapor concentration conditions at the upper and lower boundaries are introduced into the model and then the uneven water vapor concentration field of the pavement structure on July 31 in this area can be obtained.

Analysis of the water vapor concentration field on the road surface
In order to analyze the change law of the water vapor concentration field of the pavement structure, three typical positions of the bottom of the upper layer, the bottom of the middle layer, and the bottom of the lower layer are taken for analysis. In this article, the water vapor concentration changes in this environment for 7 days; the simulation results are shown in Figure 3.
From the results of the analysis of Figure 3, it can be inferred that the upper and middle surface layers of the pavement structure are greatly affected by the change in the external water vapor concentration but the bottom of the middle surface layer to the bottom of the lower layer is affected by the external water vapor concentration and the mixture at this place is in a relatively constant water vapor concentration. In this article, the temperature and water vapor concentration environment of the hottest day are loaded for 7 days, and the water vapor concentration value of the pavement structure at the bottom of the upper layer is shown as a periodic change after reaching equilibrium. At the same time, ten time points within 24 h are selected to study the distribution of the water vapor concentration in the depth direction of the pavement, and the change curve is plotted in Figure 4.
From the analysis of the results of Figure 4, it can be seen that the water vapor concentration is not uniformly distributed along the depth of the pavement structure and the water vapor concentration is high. After the water vapor concentration field reaches a dynamic equilibrium state, the area affected by the change in the external water vapor concentration is concentrated in the upper layer and the middle surface layer, and the lower layer is less affected. The concentration of the water vapor at the base level is maintained at a stable value. From the numerical analysis of the water vapor concentration, the overall road structure is in the range of 17-28 g/m 3 water vapor concentration, which is determined by the subgrade water vapor concentration and the external water vapor concentration. From this study, it is found that the pavement structure is in a high-water vapor concentration environment, which shows that it is necessary to consider the non-uniform water vapor concentration field factor when calculating the response of the pavement structure. Next, the effect of water vapor on the viscoelastic properties of the mixture was studied, and the response model of the pavement structure was established.
3 The response model of the pavement structure considering water vapor factors In this section, the water vapor concentration is linked with the mechanical properties of the mixture, and the dynamic modulus is determined by using the dynamic  test system (DTS) to measure the specimen health of the sample at different water vapor concentrations. Then, according to the combined temperature-water-gas concentrationfrequency shift method, the dynamic modulus under different temperatures, water vapor concentrations, and frequencies of the same mixture is unified into a main curve. At the same time, according to the actual water vapor concentration of each layer, the corresponding main curve is selected and the dynamic modulus is converted to the Prony series form of relaxation modulus, which is input into the finite element, and then the mechanical response of the pavement structure is calculated.

Dynamic modulus test of mixtures maintained at different water vapor concentrations
Long et al. have tested the dynamic moduli of AC-13C and AC-20C asphalt mixtures at different water vapor concentrations [16]. The same approach is used in this section, referring to previous studies [16,[17][18][19][20]. Dynamic modulus tests were performed on AC-25C asphalt mixtures at different water vapor concentrations.

Regimens
The molded asphalt mixture dynamic modulus standard specimen is maintained with the help of a constant temperature and water vapor environment box. The health time of the specimen is determined according to Long et al. [16], and the specific health regimen is shown in Table 4. The reasons for choosing these four moisture concentrations are as follows: on the one hand, the moisture concentration should be selected to cover a large span as far as possible to comprehensively analyze the mechanical performance of the mixture in the whole service life; on the other hand, according to the above non-uniform moisture concentration field model, the pavement structure is in a high moisture concentration for a long time in summer so the moisture concentration is set in a high humidity environment.

Modulus test and results
The dynamic modulus of the post-cured specimen is measured using a DTS instrument, and the test schematic diagram is shown in Figure 5. The method in the test reference [16] controls the ambient water vapor concentration during the dynamic modulus test. This study was conducted following the Dynamic Modulus Test Protocol in the US State Highway and Transportation Association Code [18], and the test was strain control. The test results of the dynamic modulus corresponding to each water vapor concentration of the AC-25C mixture specimen are shown in Table 5.

Main curve drawing
In this article, the generalized Sigmod mathematical model is selected as the main curve model, and the   dynamic modulus and phase angle of the linear viscoelastic stage can be converted by the approximate Kramers-Kronig relationship (the relationship model between viscoelastic parameters of the asphalt mixture is described) [20]. At present, the widely used shift factor in asphalt mixtures is the WLF equation (an equation describing the dependence of relaxation time on the temperature), which considers the effects of temperature and frequency but does not consider the effects of water vapor. Luo and Liu have used the Doolittle equation to derive the combined temperature-water vapor-frequency shift factor of the mixture under the tensile state [21], as shown in equation (2); the value of water vapor in this displacement factor is the concentration of water vapor. Considering that the formula was quoted from other scholars' literature, no specific derivation process was written. With this shift factor, the dynamic modulus values at different water vapor concentrations are unified into a single main curve: (2)

T T α H H f α T T α H H C C T T C H H C C C T T C H H
In order to compare and analyze the influence of different graded asphalt mixtures on the concentration of water vapor, the dynamic modulus data of AC-13C and AC-20C asphalt mixtures were selected from the study of Qiuhua [15]. The dynamic modulus of AC-13C, AC-20C, and AC-25C mixtures is fitted with the help of a combined shift factor, and the fitting results are listed in Tables 6 and 7; the main curve diagram is shown in Figure 6.
From the data in Table 7, it can be seen that the main curve model using the joint shift factor fits well, and the good fit of both the dynamic modulus and the phase angle main curve reaches 0.950 or more, thus indicating that the use of this method to unify the dynamic modulus of each water vapor concentration is accurate and effective.

Viscoelastic parameter conversion
After fitting the parameters of the dynamic modulus main curve of the mixture under different water vapor concentrations, the material parameters were converted to obtain the viscoelastic parameters and WLF shift factor that needed to be defined in the finite element model to realize the finite element analysis of the viscoelastic parameters. The most unfavorable time was selected from 2 p.m., and the water vapor concentration value at the midpoint of each layer of the surface layer at that time was taken as the representative value. The dynamic modulus value and the WLF shift factor at the water vapor concentration of each layer were converted. The material parameters were converted into the prony series form of the relaxation modulus according to Qiang [22]. In order to quantify the influence of the water vapor concentration field on the response of the pavement structure, it is also necessary to compare the results of the mechanical response of the pavement structure with the conventional method. Xi Lei et al. [17] measured that the internal water vapor concentration of asphalt mixture specimens without water vapor maintenance treatment was usually 7 g/m 3 at room temperature (20°C). At present, the calculation method of pavement structure response in China's current specifications [23] is to directly use the dynamic modulus measured by the indoor specimen (i.e., the dynamic modulus at a concentration of 7 g/m 3 water vapor) for the simulation of pavement structure, and the actual response of the pavement structure under a single water vapor concentration of 7 g/m 3 is obtained. The viscoelastic parameters of each layer are shown in Tables 8 and 9.   The response analysis of the asphalt pavement structure is carried out considering the actual water vapor concentration field and only considering the single water vapor concentration. Also, the influence of the water vapor concentration field on the structural response is quantified by vertical displacement, strain, stress, and other indicators, so as to infer the cause of water damage of the pavement structure and provide a theoretical reference for the optimization of pavement materials and structural design in the rainy areas of the south.

Model building
Among the layers of materials in the pavement structure, the surface layer is defined by viscoelastic materials, and the data are derived from the actual measurement and calculation of Section 2.3. Elastic materials are defined as base layers and soil foundations, and the data are summarized in Table 10 [12,24]. Double-wheel uniaxial load specified in the Design Code for Asphalt Pavement was adopted as the standard load [25]; the tire grounding pressure is 0.7 MPa, the equivalent circle diameter is 0.213 m, and the center distance between the two wheels is 1.5 times the diameter.
First, according to the actual pavement structure combination form, the finite element model of the pavement structure is drawn with ABAQUS software. Its size is 3 m high and 3.75 m wide. It is divided into the surface course and base course of the corresponding thickness concerning datum points, and the load loading position is reserved at the same time. Then, the section is created,  and material properties are assigned to the section. In terms of grid setting, the global seed is set to 0.02, that is, the cell length is 0.02, so the upper layer with a thickness of 0.04 has two layers of the grid. At the same time, seed distribution is set by edges and fewer grids are arranged in the lower half of the model, for example, set 35 grids by edges in the soil foundation.
The two action points are selected directly below the wheel and in the middle of the two wheels, the analysis points are set, as shown in Figure 7. The vertical displacement, strain, and stress values in the depth direction of the pavement structure at the analysis point are retrieved, and the influence of water vapor on the response of the pavement structure is analyzed; the finite element model is shown in Figure 8.  The vertical displacement values of each structural layer are compared under action point A (directly below the wheel) and action point B (in the middle of the two wheels), and the vertical displacement values are plotted considering the actual water vapor concentration field and conventional methods, respectively, in Figure 9. It can be seen from the data in the figure that the maximum displacement value of each structural layer is not much different, and the displacement under the load is mainly in the soil base. Compared with the maximum displacement value of each structural layer at point A, the displacement value of each structural layer is 2.285 mm  considering the actual non-uniform water vapor concentration distribution, and the displacement value is 2.257 mm by the conventional calculation method, and the displacement of the pavement structure is increased by about 1.24%. The change in the displacement at point B is consistent with that at point A, but the maximum displacement occurs in the lower layer because the upper and middle surface layers have a certain degree of a bulge under the squeeze between the wheel loads. Considering that the actual non-uniform water vapor concentration affects the vertical displacement value of the bottom of the lower layer (2.279 mm), the displacement value under the conventional calculation method is 2.235 mm; the water vapor concentration makes the displacement of the pavement structure also increase by about 1.97%, and the influence of the water vapor concentration on the vertical displacement of the structure is small. This is because the displacement occurs mainly in the soil foundation part, and the surface layer part itself contributes less to the displacement values.

The bottom strain of pavement structural layers
The horizontal strain changes of each layer are analyzed, and the depth direction of the pavement structure at A and B points is also analyzed. The horizontal strain values considering the actual water vapor concentration field and conventional methods are plotted in Figure 10.
From the data in Figure 10, it can be seen that the horizontal strain at the bottom of the graded gravel layer at the two points A and B is the largest. For the surface layer, the maximum horizontal strain occurs at the bottom of the upper layer. The middle surface layer has the lowest modulus, so it is in a state of pressure, and the upper and lower layers are stretched. Comparing the horizontal strain value diagrams of each layer in different water environments, it can be found that after the modulus of the surface layer is attenuated by water vapor, the horizontal strain of each structural layer increases. Among the layers affected by the horizontal strain at the bottom of each layer, the upper layer is particularly serious. The data are presented in Table 11 for analysis (as shown in the table, the tensile strain is positive and the compressive strain is negative).
From Table 12, it can be seen that the actual least unfavorable non-uniform water vapor concentration field has a huge impact on the upper layer. The horizontal strain of the upper layer at point A is increased by 108.26%, and the strain is a tensile strain that is prone to fatigue cracking, which is more harmful. The horizontal strain of the remaining layers increases by about 5%. This means that the presence of a water vapor  concentration field in the pavement structure will cause the horizontal strain of the upper layer to increase with the service life, inducing fatigue cracking. At the same time, the horizontal strain at the grass-root level increases, further increasing the risk of cracking at the grass-root level. The horizontal strain change at point B is the same as that of point A, and after considering the concentration of water vapor, the horizontal pressure strain of the upper layer increases the most, reaching 42%. The horizontal tension strain of the grass-root part increases by about 5% and the risk of cracking at the grass-root level increases.

Bottom stress of each layer of the pavement structure
Similarly, the depth direction of the pavement structure at points A and B is selected as the value points to analyze the variation of the horizontal stress at the bottom of each structure layer, as plotted in Figure 11; data are listed in Table 12.
As can be seen from Figure 11, compared with other surface layers, the bottom of the layer below the pavement structure is subjected to greater tensile stress. This is because the temperature gradually decreases along the direction of the pavement structure, resulting in a higher modulus of the lower layer, which then bears a larger stress. After considering the actual most unfavorable water vapor concentration field, the horizontal stress on the pavement structure surface at point A decreases by about 10%. In terms of the maximum horizontal stress, the variation of the horizontal strain at the bottom of the layer at point B is the same as that at point A, and the bottom of the lower layer is subject to greater horizontal stress. Considering the most unfavorable non-uniform water vapor concentration field, the horizontal stress of the surface layer decreases by about 10% and the base layer increases by about 5%.

Fatigue life analysis of the pavement structure under the influence of the water vapor and conventional model
It can be seen from the previous two sections that the horizontal strain of the pavement structure changes under the action of water vapor, leading to the attenuation of fatigue life. In order to further visually express the influence of the non-uniform water vapor concentration field on the pavement structure during the whole service cycle, in this section, we will analyze the influence of the nonuniform water vapor concentration field on the fatigue life of the pavement structure. By referring to the calculation method of the fatigue life in the study of Xi et al. [23], we considered the actual non-uniform water vapor concentration field and the pavement structure model of the conventional method and then introduced the horizontal strain of the surface layer into the empirical formula to calculate the fatigue life. In order to analyze and consider the influence of the actual non-uniform water vapor concentration field on the fatigue life of the pavement structure, four value points [23] of ABCD (as shown in Figure 12) are selected in this section according to the specification, and the horizontal strain of the pavement structure under this condition is simulated as shown in Table 13.
By comparing the four calculation points of ABCD, the fatigue life of the pavement structure can be obtained by substituting the maximum underlayer tensile strain and its correlation value. The horizontal direction of the upper and middle surface layer is the compressive strain, so its fatigue life is not considered. The fatigue life calculation results of the lower layer are listed in Table 14.
It can be seen from the above fatigue life calculation results that the fatigue life of the lower layer is reduced from 1.967 × 10 7 to 1.726 × 10 7 by 12.246% after considering the actual non-uniform water vapor concentration field. This indicates that the current conventional method represented by the specification is larger than the actual fatigue life of the pavement when calculating the fatigue life [23], and overestimates the anti-fatigue performance of the pavement structure, resulting in the design of the pavement structure being biased toward danger.
Here, we can reasonably infer the cause of the result. Moisture causes the modulus of the asphalt mixture to decay, while the uneven moisture concentration in the depth direction of the pavement structure will lead to the uneven distribution of the modulus of the pavement structural materials, and the modulus of the upper layer will decay most seriously. The horizontal strain of the upper layer increases by 108.26% under the effect of the vehicle load without considering water and gas. The increase of the horizontal strain further leads to the decrease of fatigue life.

Conclusion
By comparing the conventional method with the pavement structure calculation method considering the actual water vapor concentration field, the following conclusions are drawn: (1) Considering the actual non-uniform water vapor concentration field in high-temperature environment in summer, the vertical displacement of the pavement structure increases by about 1%. Under the influence of water vapor, the position just below the wheel of the upper layer at the bottom of the horizontal tension strain increases by 108.26% and the horizontal tension strain of the other layers increases by about 5%.This indicates that the presence of actual water-gas concentration field makes the upper layer more likely to crack.
(2) Compared with the fatigue life calculation method in the specification, the actual non-uniform water vapor concentration field reduces the fatigue life of the surface layer by 12.246%, indicating that the fatigue life calculated by the conventional method is larger than the actual fatigue life of the road surface and overestimates the fatigue resistance performance of the road surface structure, resulting in the design of the road surface structure being more dangerous. (3) The attenuation of the surface material modulus caused by water vapor is the root of the problem. The nonuniform water vapor concentration field in the depth direction of the pavement structure leads to the nonuniform distribution of the material modulus of the pavement structure, which leads to the inability of conventional methods to accurately calculate and measure the pavement structure response.