Calculating the rutting by the use of ABAQUS finite element software, it is assumed that the materials of each layer are uniform and isotropic, the asphalt surface layer conforms to the viscoelastic constitutive relation, and the other layers all satisfy Hooke’s law [5]. The three-dimensional model is simplified to two-dimensional, and the width and depth of the road model are defined by finite size, 3.75 m and 3 m respectively. The layered-form of the semi-rigid base pavement is shown in Figure 1. When the upper layer adopts AH-70 ordinary asphalt mixture, the pavement structure is ordinary asphalt pavement structure, and the mesh division adopts CPE8R (eight-node bidirectional secondary plane strain quadrilateral element, reduction integral), and the unit finite element model is shown in Figure 2.

The strain-hardening creep model in ABAQUS finite element is adopted to analyse rutting calculation. The constitutive equation [5] is Equation (1).

ε • c r = ( A q [ ( m + 1 ) ε ¯ c r ] m ) 1 m + 1 (1)

where ε • c r is uniaxial equivalent creep strain rate; ε ¯ cr is uniaxial equivalent creep strain; q is stress, MPa A, n, m are Model parameters, determined by indoor material creep test generally, A, n > 0, −1 < m ≤ 0.

It’s assumed that the material parameters of soil foundation, lime soil and cement stabilized macadam base remain constant under different temperature. Anti-pressure rebound test and creep test were performed to determine the elastic and creep parameters of asphalt mixture [6]. The specific values are shown in Table 1, and the thermal parameters of the materials are shown in Table 2.

The left and right sides of the model are set to zero displacement in the X direction, and the bottom boundary of model is fixed, as shown in Figure 3. Simplify vehicle load form from double-circle uniform load to double-round rectangular uniform load. The axle load takes the standard axle load BZZ-100 in the current road asphalt pavement design specification JTG D50-2017, Tire grounding pressure is 0.7 MPa. The rectangle has a length of 19.2 cm and a width of 18.6 cm. The distance between center of the two axes is 314 mm, as shown in Figure 4.

In this study, the effect of repeated loading of asphalt pavement rutting is simplified to a loading step to reduce the time of finite element analysis calculation, the calculation formula is as shown in Equation (2).

t = 0.36 NP n w p B v (2)

where t is Wheel load cumulative action time; N is times of wheel load; P is Vehicle axle weight; n_w is number of rounds of the axle; p is tire ground pressure; B is tire ground width; v is traffic speed. The load parameters can be obtained according to formula (2), as shown in Table 3.

Affected by the natural environment, the temperature of the road surface fluctuates greatly, while the deep sub-grade fluctuates slightly, it can be considered

that the temperature value remain constant [7]. According to the principle of heat transfer, the change of the road-surface heat is mainly affected by the short-wave radiation of the sun, the long-wave radiation of the road surface and

the atmosphere, and the heat convection [8]. The FILM and DFLUX subroutines in the ABAQUS software are applied to analyze solar radiation and road surface thermal convection exchange processes respectively, and atmospheric temperature is used to determine temperature field boundary conditions, establish transient and steady state analysis steps, and obtain asphalt surface temperature field files [9] [10]. In the rutting calculation model, owing to the elastic parameters and creep parameters are both take temperature variation into consideration, the asphalt temperature field file is imported into the corresponding analysis step to calculate the rutting [11].

The influence of temperature on asphalt mixture cannot be ignored. The increase of temperature will cause a rapid reduction of dynamic stiffness modulus of asphalt mixture in a short time. Accordingly, the ability of resistance to rutting deformation of pavement reduces, and the deformation expands gradually which will eventually lead to the damage of pavement. The permanent deformation under high temperature of asphalt mixture is main reason for rutting. The rutting usually occurs in summer when the temperature is higher than 25˚C - 30˚C. Road surface temperature fluctuates most with the increase of atmospheric temperature. Figure 5 shows the atmospheric temperature variation during a day in high temperature season of Guangdong city. Figure 6 shows the temperature variation of the asphalt road surface during a day.

It can be seen from Figure 6 that asphalt pavement surface reached 55˚C at 2:00 pm. Then take 25˚C, 35˚C, 45˚C, 55˚C as representative, study the effects of different temperatures on rutting, and the effect is shown in Figure 7(a), Figure 7(b).

As is shown in Figure 7(a), Figure 7(b), the maximum rut deformation of ordinary asphalt pavement at 55˚C is more than twice that of Thiopave modified asphalt pavement at the same load. When the temperature raised from 25˚C to 55˚C, the maximum deflection of the wheel center of the Thiopave asphalt pavement and the ordinary asphalt pavement increased by 2.65 mm and 5.97 mm, respectively. The rutting variation of Thiopave modified asphalt pavement is much smaller than that of ordinary asphalt pavement with the increase of temperature. Therefore, we can make a conclusion that Thiopave modifier may improve the rutting resistance of asphalt mixtures by reducing its temperature sensitivity.

Load is one of the crucial factors of the rutting deformation of asphalt pavement. The more overloaded vehicles, the more severe the deformation of the rutting is. Keep the thickness and the corresponding material of each layer constant, analyzing the rutting caused by different tire pressures under the condition at

500,000 times of the axle load and the atmospheric temperature was 30˚C. The results are shown in Figure 8.

From Figure 8, it can be seen that as the tire pressure increases from 0.7 MPa to 1.2 MPa, the rutting deformation of the Thiopave asphalt pavement increases from 3.7 mm to 5.2 mm, and the rutting deformation of the ordinary asphalt pavement increases from 9 mm to 12.8 mm, which means that deformation of the rut generated by Thiopave modification asphalt pavement is smaller than that of the ordinary asphalt pavement. The traffic volume has an important influence on the rutting deformation of asphalt pavement. The cumulative equivalent axis is positively correlated with the rutting deformation. Under the cyclic loads, the rutting deformation of the pavement will gradually increase. Also keep the thickness and corresponding material parameters of each layer constant, analyzing the rutting caused by different load under the condition that the axle load is 0.7 MPa and the atmospheric temperature is 30˚C. The results are shown in Figure 9, Figure 10.

It can be seen from Figure 9 that the depth of rutting changes with the times of loading irregularly under the cyclic loading, which appears nonlinear growth.

It can be seen from Figure 10 that rutting deformation of pavement is small when the times of axle load less than 10,000. And the rutting deformation of Thiopave modified asphalt pavement is close to that of ordinary asphalt pavement. However, the depth of rutting increases gradually when the times of loading exceeds 10,000, a clear gap begins to emerge between two pavement structures. And the rut depth of the ordinary asphalt pavement is significantly larger than that of the Thiopave modified asphalt pavement. When the times of loading reach 1,000,000 times, the difference of the rut depth between two pavement structures reaches 7.2 mm. It can be seen from Figure 10 that the upheaval on both sides of wheel track appears less obvious when the times of loading is less than 10,000, and the deformation of rutting mainly comes from vertical deflection.

With the increase of the times of loading, the upheaval on both sides of the wheel track gradually increases. When the cyclic load reaches 1,000,000 times, the deflection and elevation of the Thiopave modified asphalt pavement are both smaller than that of ordinary asphalt pavement. And the amplitude of variation is also smaller than that of ordinary asphalt pavement.