#### Abstract

This study uses a test section of a highway, a study object, to explore the effect of thickness of the gravel base and asphalt layer on the vertical deformation of the road surface. The thickness of the asphalt layer and graded gravel base is changed. The nonlinear description equation of the relationship between the thickness () of the asphalt layer and the vertical deformation () is established: . The thickness of the asphalt pavement is then determined to reduce vertical deformation. Numerical calculation shows that the maximum vertical deformation of the foundation is within 8 mm, which is less than the 15 mm maximum vertical deformation of the embankment. This level meets the design requirements.

#### 1. Introduction

Semirigid base asphalt pavement is widely used as the main structure of highway pavements [1–3]. However, the widespread use of the semirigid base resulted in some problems, such as the short service life and reduced performance of the pavement, which will affect the safety of the highway [4–6]. The early destruction of the semirigid base asphalt pavement is affected by its structure [7–9]. Temperature and dry shrinkage tend to cause cracks on the semirigid base [10–12]. Zang et al. [13] developed a nondestructive FWD-based evaluation model to evaluate the semirigid base cracking condition. Wu et al. [14] simulated the interlayer bonding conditions between the semirigid base layer and the asphalt layer. Thus, rainwater easily enters from the pavement structure into the grassroots base and soil. This process is called subgrade softening, which causes early damage on the asphalt pavement. The particle material (graded gravel) between the asphalt surface layer and the semirigid base, which can be used as the stress dissipation layer, can effectively reduce the reflection crack of the semirigid material. Graded gravel is characterized by a certain degree of compaction of the medium material [15, 16]. Gravel particles can produce displacement and mutual dislocation and eventually achieve vibration compaction under the condition of traffic load vibration [17–19]. Volume compression in some gravel materials may cause the pore water pressure to rise due to dynamic loading, which decreases the material strength. Kuttah and Arvidsson [20] constructed a trial gravel road and exposed to various levels of the ground water table. Chang and Phantachang [21] investigated the effects of gravel content on the shearing characteristics of gravelly soils. The graded gravel base has good drainage performance. Thus, increased pore water pressure and decreased strength are not observed.

In this paper, the numerical simulation methods are used [22–26], which can simulate the construction of the road. A testing section of the Jiangxi Highway, China, is used as the engineering background to explore the effect of thickness of the bituminous pavement and the graded gravel base on the vertical deformation of the road surface. The thicknesses of the asphalt pavement and grading macadam base are changed. The vertical displacements are then studied.

#### 2. Modeling and Parameters

##### 2.1. Modeling

A section of a highway is selected for analysis (Figure 1). Given that most of road engineering embankments are symmetrical, the FLAC3D [27–31] is used for modeling analysis in half of the embankments, as shown in Figure 2. The total height of the embankment is 8 m, and the slope is 1 : 1.5. The width of the embankment is 25 m, and the width of the upper road is 13 m. The foundation is equal to the height of the slope, which is 10 m, and the slope to the right is about 1 time the width of the embankment, which is 25 m. Table 1 shows the parameters of the embankment modeling according to the actual data provided by the project. For the gravel base, the Mohr–Coulomb criterion [32–34] is used to describe the stress and strain relation, the cohesion is 0.8 MPa, and the friction angle is 24°.

##### 2.2. Calculation Scheme

The model range of the embankment is relatively large. The focus of the study is the vertical deformation of the embankment under road load. The action range is not large because the vehicle load force on the road of uniformly distributed load is 167 kPa. The vertical deformation of the pavement is largest in the pavement under load. Therefore, the main part of the study is the road surface. This study selects three kinds of pavement forms with different thicknesses of the asphalt layer and gravel layer. The main contents of analysis and parts of the embankment model are observed. The selection of the pavement and gravel thickness is based on three criteria (Figure 3): (1) the thickness of the asphalt pavement is 0.1 m and the gravel base thickness is 0.2 m, which is shortened to 10 to 20 types; (2) the thickness of the asphalt pavement is 0.18 m and the gravel base thickness is 0.2 m, which is shortened to 18 to 20 types; (3) the thickness of the asphalt pavement is 0.2 m and the gravel base thickness is 0.6 m, which is shortened to 20 to 60 types.

Vertical deformation is the vertical deformation of the pavement. The distance between the location and embankment center is given as follows:his id 1 gp zdis 0.0 0.0 0.0 his id 12 gp zdis 5.7 0.0 0.0his id 2 gp zdis 2.0 0.0 0.0 his id 13 gp zdis 6.4 0.0 0.0his id 3 gp zdis 2.6 0.0 0.0 his id 14 gp zdis 6.5 0.0 0.0his id 4 gp zdis 2.7 0.0 0.0 his id 15 gp zdis 6.6 0.0 0.0his id 5 gp zdis 2.8 0.0 0.0 his id 16 gp zdis 6.7 0.0 0.0his id 6 gp zdis 2.9 0.0 0.0 his id 17 gp zdis 7.6 0.0 0.0his id 7 gp zdis 3.6 0.0 0.0 his id 18 gp zdis 8.5 0.0 0.0his id 8 gp zdis 4.7 0.0 0.0 his id 19 gp zdis 8.6 0.0 0.0his id 9 gp zdis 4.8 0.0 0.0 his id 20 gp zdis 8.7 0.0 0.0his id 10 gp zdis 4.9 0.0 0.0 his id 21 gp zdis 8.8 0.0 0.0his id 11 gp zdis 5.0 0.0 0.0 his id 22 gp zdis 9.5 0.0 0.0

History is divided into two parts, namely, wheel load and unacted part.

His id 1, 2, 7, 12, 17, and 22 are the unapplied load parts located in the middle of the load interval between the two wheels. The other part of his id is the part of the wheel load. Each wheel load has two edges and a total of four points in the center. His id 3, 4, 5, and 6 are the first group. His id 8, 9, 10, and 11 are the second group. His id 13, 14, 15, and 16 are the third group. His id 18, 19, 20, and 21 are the fourth group.

The maximum vertical deformation under load is analyzed in this study. The vertical deformation of different positions is compared, as shown in Figures 4–6. The four curves in the upper part are the vertical deformation curves of the embankments in the corresponding four sets of wheel loads. The other part shows the vertical deformation curve of the embankment with the unapplied load. The vertical deformation of the position under the direct action of vehicle load is the same as that in engineering practice. Therefore, the vertical deformation value of the four groups of load is analyzed as follows. For the 10 to 20 type, the vertical deformations of his id 3, 4, 5, and 6 are compared with those of his id 13, 14, 15, and 16. The vertical deformation of the two places was between 6 mm and 7 mm, and the difference was not significant. Results are consistent with the 18 to 20 type.

#### 3. Results and Analysis

##### 3.1. Influence of Asphalt Pavement Thickness on Embankment

To study the effect of asphalt pavement thickness on the vertical deformation of the embankment, the following data are divided into three categories in accordance with the thickness of the gravel layer, which is 20, 40, and 60 cm, respectively.

As shown in the calculation in Figure 7, the vertical deformation of the pavement increases gradually with the increase of the thickness of the asphalt layer set at 10, 15, 18, and 20 cm when the gravel base thickness is set at 20 cm. However, the slope of the curve decreases. Therefore, the increase of asphalt thickness decreases the influence of vertical deformation. In addition, the relationship between the thickness () of the asphalt layer and the vertical deformation () presents nonlinear characteristics. The relationship between the two is quantitatively described by the following equation through the data fitting method:where and are the undetermined coefficients.

**(a)**

**(b)**

**(c)**

**(d)**

The fitting correlation coefficient of the four groups is higher than 0.99, which indicates high correlation. The vertical deformation of the pavement in the corresponding points is small when the thickness of the asphalt layer is 10 cm. The relative difference of vertical deformation is comparatively small when the thickness sizes of the asphalt layer are 15, 18, and 20 cm. The overall vertical deformation trend of the road is large in the middle and small on both sides. The vertical deformation of the near embankment center is larger than that of the close shoulder. The maximum vertical deformation of the road is at approximately 4.7 m from the embankment center.

Previous analysis shows that vertical deformation of the pavement is the smallest of the four asphalt pavement thickness schemes when the thickness of the gravel layer is certain and the thickness of the asphalt pavement is 10 cm. In addition, the increase of the thickness of the asphalt layer does not significantly decrease the vertical deformation of the road pavement. To better understand the influence of asphalt pavement thickness on the vertical deformation of the pavement, this study analyzes the vertical deformation of the overall difference of the road surface (Figure 8). When the thickness of the asphalt surface is 10 cm, the vertical deformation of the pavement varies significantly from place to place although the maximum vertical deformation produced by the pavement is the smallest. The asphalt pavement cannot easily facilitate stress coordination. The relative vertical deformation of the pavement is large, and ruts develop easily, thereby destroying the asphalt pavement. The vertical deformation of the pavement decreased at asphalt pavement thicknesses of 10, 20, and 40 cm, but the effect is not significant. When the thickness of the asphalt surface is 18 or 20 cm, the maximum vertical deformation of the pavement is slightly increased, but the differences of the vertical deformation of the road are relatively small. The asphalt pavement coordinates the stress, while the relative vertical deformation of the pavement decreases. Compared with the vertical deformation of the asphalt pavement with thicknesses of 10, 18, and 20 cm, increasing the thickness of the asphalt pavement can significantly decrease the uneven vertical deformation of the pavement.

##### 3.2. Influence of Gravel Base Thickness on Embankment

When the thickness of the asphalt pavement is 10 cm (Table 2), vertical deformation decreases on both sides of the road, and a trend of decrease after the first increase in the middle of the road is shown as the gravel base thicknesses of 20, 40, and 60 cm gradually increased. The vertical deformation of the pavement is smallest when the thickness of the gravel base is 60 cm, that is, when the gravel base is the thickest. The overall vertical deformation trend of the road is large and small on both sides. The vertical deformation of the near embankment center is larger than that of the close shoulder. The maximum vertical deformation of the road is at the direct part of the wheel load approximately 4.7 m from the embankment center.

When the thickness of the asphalt pavement is 15 cm (Table 3), the vertical deformation of the sides and the middle section decreases as the gravel base thicknesses of 20, 40, and 60 cm gradually increase, which is different from 10 cm thickness. The vertical deformation of the pavement in each group is smallest when the gravel base thickness is 60 cm, that is, when the gravel base is the thickest.

When the thickness of the asphalt pavement is 18 cm (Table 4), the vertical deformations on both sides of the road and of the middle two positions show a decreasing trend as the gravel base thicknesses of 20, 40, and 60 cm gradually increase.

When the thickness of the asphalt pavement is 20 cm (Table 5 and Figure 9), the vertical deformation caused by 20, 40, and 60 cm gravel base thicknesses is the same. Previous analysis shows that the increase of gravel base thickness can reduce the vertical deformation of the road when the thickness of the asphalt surface is certain. Therefore, the method of increasing the gravel base thickness can be used to reduce the vertical deformation of the road.

#### 4. Conclusions

(1)The vertical deformation of the pavement increases as the thickness of the asphalt layer increases gradually from 10 cm to 15, 18, and 20 cm, but the slope of the curve gradually decreases.(2)Asphalt pavement cannot easily facilitate stress coordination when the relative vertical deformation of the pavement is large. Ruts may develop easily, thereby destroying the asphalt pavement. Compared with the vertical deformation of the asphalt pavement with thicknesses of 10 cm, 18 cm, and 20 cm, increasing the thickness of the asphalt pavement can significantly reduce the uneven vertical deformation of the pavement.(3)When the thickness of the asphalt pavement is certain, the vertical deformation of the pavement decreases with the increase of the thickness of the gravel base from 20 cm, 40 cm, and 60 cm. The vertical deformation of the pavement in each group is smallest when the thickness of the gravel base is 60 cm.

#### Conflicts of Interest

The authors declare no conflicts of interest.