Keywords

1 Introduction

With the accelerating process of China’s transportation construction, the choice of highway continues to extend to the plateau and high altitude areas. Due to the limitation of terrain conditions, it is inevitable to have long longitudinal slope section, and even the slope length and slope exceed the limit specified in the existing specifications [1]. Compared with the small ramp pavement, the diseases such as rutting and displacement in the long longitudinal slope section are very serious, this is mainly because when the vehicle is driving on the long longitudinal slope section, the vehicle speed is low and there will be frequent start-up and braking acceleration. The asphalt concrete in the long longitudinal slope section will not only produce serious rut, but also produce shear failure under the action of driving, this is because the slow start of the uphill section and the deceleration braking of the downhill section produce a larger horizontal shear stress on the top and inside of the asphalt pavement surface than on the flat section. The reasons for this destruction are manifold. It is not only related to traffic volume and vehicle overload, but also related to technical conditions such as route line type, pavement structure type and construction quality.

In recent years, many scholars have used the finite element method to study the mechanical properties of asphalt pavement with long longitudinal slope.

Shi Tingwei et al. [2] established a three dimensional finite layer analysis model of asphalt pavement with long longitudinal slope by using the finite layer software 3DMove Analysis. It is found that the acceleration or braking of the vehicle will lead to a large increase in the maximum shear stress peak in the asphalt pavement. The maximum shear stress peaks appear at 0–4 cm below the road surface, so it is particularly important to improve the anti-rutting performance of the upper part of the long longitudinal slope asphalt surface. Zhou Taohong et al. [3] used Aansys software to model typical structures based on the definition of heavy load conditions and the analysis of common diseases, calculated and analyzed the surface deflection, tensile stress, compressive stress and shear stress of the typical structure under different axle loads, and analyzed the damage of the pavement structure. Yang Zhenzi et al. [4] used ANSYS software to quantitatively analyze the influence of high temperature and heavy load traffic on surface deflection and structural stress of asphalt pavement. Li Yanchun et al. [5] established a three dimensional finite element model using Ansys finite element software. By applying pulse load, the strain variation rule of large longitudinal slope of asphalt pavement under different conditions is obtained. Jun Fu et al. [6] discussed the relationship between shear stress and slope angle, load, pavement depth, interlayer contact condition and modulus by three dimensional finite element model. Zhou Yaxin et al. [7] simplified the load distribution model by calculating the equilibrium speed of heavy-duty vehicles in the long longitudinal slope section under the equilibrium state, according to the commonly used pavement structure in china, a three dimensional finite element model of asphalt pavement was established to compare and analyze the mechanical response of asphalt pavement under different slope, temperature and asphalt layer thickness. Ruan Luming et al. [8], firstly, the traffic conditions in Chongqing are analyzed, and the typical heavy-duty vehicles and their climbing speed characteristics are obtained. The contact characteristics between the tire and the road surface of the heavy-duty vehicle are studied in depth, and a simplified model of tire grounding of heavy-duty vehicles is given. Then, the factors affecting the response indexes of asphalt pavement structure in long longitudinal slope section are studied. Finally, the fatigue damage variation rule of asphalt layer in high temperature month is analyzed based on Miner fatigue rule.

The research of the above scholars shows that the finite element method can be used to study the mechanical response of asphalt pavement with long longitudinal slope and its influencing factors. Therefore, this paper will use Abaqus calculation software to establish a finite element model of long longitudinal slope asphalt pavement, and discuss the influence of longitudinal slope, driving speed, temperature and braking coefficient on shear strain and tensile strain of asphalt pavement.

2 Analysis of Influencing Factors of Mechanical Model of Long Longitudinal Slope Section

The vehicle is subjected to various resistances when driving on the asphalt pavement. These resistances include rolling resistance F1, slope resistance F2, air resistance F3 and acceleration or deceleration resistance F4. In order to achieve a stable operating state, the traction of the car must be equal to the sum of the resistance encountered by the car during driving, that is:

$$ F = F_{1} + F_{2} + F_{3} + F_{4} $$
(1)

The driving state of the vehicle on the longitudinal slope can be divided into two types: gradually decelerating to a stable speed and maintaining a uniform speed after entering the slope; the vehicle gradually accelerates to a stable speed and maintains a uniform speed after entering the slope.

3 Mechanics Model and Calculation Parameters of Asphalt Pavement in Long Longitudinal Slope Section

3.1 Finite Element Model Establishment

Considering the computational efficiency and accuracy, this paper uses a three dimensional model for mechanical response analysis. The model size is 8-node hexahedral element. The boundary conditions are assumed as follows: the bottom surface of the model is completely constrained, there is no lateral displacement on the left and right sides, there is no longitudinal displacement on the front and rear sides, and the contact state between the layers is completely continuous. The calculated load is a double circular load: the standard load is the tire ground pressure of 0.7MPa, the load circle radius is 106.5 mm, and the center distance of the two wheels is 319.5 mm. Among them, X is the lateral direction of the road, Y is the driving direction, and Z is the vertical direction. The size of the model is 5 m × 10 m × 5 m, and its structure is shown in Fig. 1. Vertical moving load and horizontal moving load are applied by ABAQUS’s own subroutines DLOAD and UTRACLOAD.

Fig. 1.
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Finite element model of pavement structure.

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3.2 Determination of Asphalt Pavement Surface Material Parameters

The parameters of asphalt mixture under different temperature conditions are shown in Table 1 (Table 2).

Table 1. Asphalt mixture parameters under different temperature conditions.
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Table 2. Elastic parameters of base and soil materials.
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3.3 Pavement Computational Structural

The material and thickness of the pavement structure layer from top to bottom are shown in Table 3.

Table 3. Asphalt pavement structure.
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4 Analysis of Pavement Mechanical Response of Long Longitudinal Slope Section

In the mechanical calculation and analysis, the shear stress on the driving direction of the vertical road table position of the wheel load center is analyzed and calculated. In the analysis and calculation of uniform speed, only 0.7MPa vertical stress of road surface is considered, and the influence of friction force in parallel direction is ignored.

4.1 Analysis of Mechanical Response Changes with Depth

Under the conditions of running speed of 60 km/h and temperature of \(60\,^\circ {\text{C}}\), the variation of shear stress of pavement structure with depth is calculated, and the results are shown in Fig. 2 and Fig. 3.

Fig. 2.
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Variation of shear strain with pavement depth.

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Fig. 3.
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Variation of tensile strain with pavement depth.

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It can be seen from Fig. 2 and Fig. 3 that the shear strain and tensile strain of asphalt surface first increase and then decrease with the increase of depth, both the maximum tensile strain and the maximum shear strain are located in the middle surface layer, and the depth of the maximum tensile strain is greater than that of the maximum shear strain.

4.2 Influence of Longitudinal Slope Degree on Mechanical Response

When the driving speed is 60 km/h, the temperature is \(60\,^\circ {\text{C}}\), and the slope is 0%, 2%, 4%, 6% and 8% respectively, the maximum mechanical response and the change law of the position under different slope conditions are analyzed.

Fig. 4.
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Variation of shear strain under different slope conditions.

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Fig. 5.
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Variation of tension strain under different slope conditions.

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Fig. 6.
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Variation of maximum shear strain under different slope conditions.

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Fig. 7.
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Variation of maximum tensile strain under different slope conditions.

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It can be seen from Fig. 4 and Fig. 5 that under different slope conditions, the shear strain and tensile strain of asphalt surface layer increase first and then decrease with the increase of pavement depth. It can be seen from Fig. 6 and Fig. 7 that the maximum shear strain increases and the maximum tensile strain decreases with the increase of road slope.

4.3 Influence of Running Speed on Shear Stress

Under the conditions of temperature \(60\,^\circ {\text{C}}\) and longitudinal slope 4%, the maximum mechanical response and the change law of position were analyzed under different driving speeds of 40 km/h, 60 km/h, 80 km/h, 100 km/h and 120 km/h.

It can be seen from Fig. 8 and Fig. 9 that under different driving speeds, the shear strain and tensile strain of asphalt surface both increase first and then decrease with the increase of pavement depth. It can be seen from Fig. 10 and Fig. 11 that the maximum shear strain and maximum tensile strain both decrease with the increase of driving speed.

Fig. 8.
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Shear strain variation diagram at different running speeds.

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Fig. 9.
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Variation diagram of tension strain at different running speeds.

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Fig. 10.
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Maximum shear strain variation at different running speeds.

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Fig. 11.
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Maximum tensile strain variation diagram at different running speeds.

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4.4 Influence of Temperature on Shear Stress

Under the conditions of driving speed of 80 km/h and longitudinal slope of 4%, the maximum mechanical response and the change law of position at different temperatures of \(20\,^\circ {\text{C}}\), \(30\,^\circ {\text{C}}\), \(40\,^\circ {\text{C}}\), \(50\,^\circ {\text{C}}\) and \(60\,^\circ {\text{C}}\) were analyzed.

Fig. 12.
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Variation of shear strain at different temperatures.

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Fig. 13.
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Variation of tensile strain at different temperatures.

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Fig. 14.
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Maximum shear strain variation at different temperatures.

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Fig. 15.
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Maximum tensile strain variation at different temperatures.

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It can be seen from Fig. 12 and Fig. 13 that under different temperature conditions, the shear strain of asphalt surface increases first and then decreases with the increase of pavement depth. When the temperature is less than or equal to \(40\,^\circ {\text{C}}\), the tensile strain of asphalt surface increases first and then decreases with the increase of pavement depth. When the temperature is greater than \(40\,^\circ {\text{C}}\), the tensile strain of asphalt surface increases with the increase of pavement depth. It can be seen from Fig. 14 and Fig. 15 that the maximum shear strain and maximum tensile strain both increase with the increase of temperature.

4.5 Influence of Braking Coefficient on Shear Stress

Under the conditions of running speed of 80 km/h, temperature of \(60\,^\circ {\text{C}}\) and longitudinal slope of 4%, the maximum mechanical response and the change law of position under different braking coefficients f of 0.1, 0.3, 0.5, 0.7 and 0.9 were analyzed (Fig. 19).

Fig. 16.
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Variation of shear strain under different braking coefficients.

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Fig. 17.
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Variation of tensile strain under different braking coefficients.

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Fig. 18.
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Maximum shear strain variation under different braking coefficients.

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Fig. 19.
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Maximum tensile strain variation under different braking coefficients.

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It can be seen from Fig. 16 and Fig. 17 that under the conditions of different braking coefficients, when the braking coefficient is less than 0.1, the shear strain of asphalt surface increases first and then decreases with the increase of pavement depth. When the braking coefficient is 0.3, the shear strain of asphalt surface decreases first, then increases and then decreases with the increase of pavement depth. When the braking coefficient is greater than 0.3, the shear strain of asphalt surface decreases with the increase of pavement depth. The tensile strain of asphalt surface increases first and then decreases with the increase of pavement depth. It can be seen from Fig. 17 and Fig. 18 that the maximum shear strain increases and the maximum tensile strain decreases with the increase of the braking coefficient.

5 Conclusions

The asphalt pavement calculation model was established by finite element calculation software Abaqus, and the shear strain and tensile strain of the asphalt layer of the asphalt pavement with long longitudinal slopes were analyzed under the conditions of different slopes, travel speeds, temperatures and braking coefficients. The above analysis leads to the following conclusions:

  1. (1)

    Maximum shear strain increases with increasing pavement gradient, temperature and braking factor and decreases with increasing travel speed. The maximum tensile strain increases with increasing pavement gradient, travel speed and braking factor and decreases with increasing temperature.

  2. (2)

    Vehicles in the smooth running, the maximum shear strain and the maximum tensile strain appear in the middle surface layer. In the design stage, need to target to improve the middle surface layer of asphalt concrete shear resistance and tensile properties, in order to enhance the long longitudinal slope section of the asphalt surface layer of road performance.

  3. (3)

    Vehicle braking coefficients have a small effect on tensile strains and a large effect on shear strains. When the braking coefficient is large, the road surface will produce a large shear strain. In the design phase, the top layer of asphalt concrete needs to be targeted to improve the shear resistance of asphalt concrete.