*3.2. Material Properties*

The physical properties of soils for the subgrade with a capillary barrier are shown in Tables 1 and 2. Based on the data in Figure 4, the coefficient of uniformity of the gravel was 14 and that of the fill soil was 6.4. The coefficient of the curvature of the gravel was 2.8 and that of the fill soil was 1.2. According to the Standard for Classification of Engineering Soils [26], the fill soil was classified as the silty clay of well gradation, and the gravel was well graded. The soil involved in this paper included foundation soil, subgrade soil, and gravel. In view of the similar moisture migration properties of the foundation and the subgrade, the identical hydraulic characteristic parameters were used for the subgrade and the foundation to facilitate the study. In the numerical simulation, the soil water characteristic curve of the subgrade soil was based on the test data from Jun Luo [3]. The soil water characteristic curve of the gravel was based on the test data used by Morris et al. [27]. The saturated permeability coefficient of the soil was measured by the constant head method. However, the unsaturated permeability coefficient equation was predicted on the basis of the soil water characteristics using the van Genuchten functions as shown in Figure 2. The ideal elastoplastic M-C model was adopted as the mechanical model for the deformation, and the strength parameters of the foundation soil and subgrade soil were determined by consolidated drained triaxial tests. The results of the triaxial shear test are shown in Table 1. The gravel was only 0.2 m thick due to the fact of its small thickness. In order to ensure the calculations were convenient, the strength characteristics were set to elastic materials and the data, listed in Table 1, were selected based on the elastic modulus test by Yuedong Wu et al. [28].


**Table 1.** The physical properties of various soils for the subgrade with a capillary barrier.

**Table 2.** Strength properties of the various soils for the subgrade with a capillary barrier.


**Figure 4.** Grain size distribution of the soils.

## *3.3. Simulation Steps and Boundary Conditions*

In order to simulate the impact of rainfall on the expressway, it was necessary to eliminate other factors that cause settlement. This paper simulated the following four steps.

The first step was to perform an analysis on the stress and deformation (SIGMA/W) of the subgrade. The design load on the pavement (AB) was set to complete the load and geo-stress balance. According to the expressway design code, the standard design load of the pavement was 10.5 kPa. The left and right boundaries (i.e., AF and DE) were set to the displacement boundary condition, restraining in the horizontal direction. The bottom boundary (EF) was set to the displacement boundary conditions, restraining in the horizontal and vertical directions.

The second step was to conduct a water seepage analysis (SEEP/W) on the subgrade and design the flow boundary conditions on the shoulder slope (BC) and the ground (CD). The annual precipitation in Guangdong, eastern Guangxi, Fujian, Jiangxi, and most of Zhejiang along the southeast coast of China is 1500–2000 mm. The middle and lower reaches of the Yangtze River are 1000–1600 mm. The Huaihe River, Qinling Mountains, and the Liaodong Peninsula have an annual precipitation of 800–1000 mm. Moreover, the

seasonal distribution is uneven, with summer accounting for approximately 50% of the annual rainfall. Particularly, in this study, we focused on the long-term performance of the subgrade. The subgrade soil can store water. Unsaturated drainage still occurs from the topsoil when it does not rain. Therefore, the most extreme rainfall intensity was selected, which was 1000 mm in the summer and the rainfall on the rainfall surface was set to 1.27 × <sup>10</sup>−<sup>7</sup> m/s. In order to fully study the law of subgrade infiltration, the duration was chosen as 365 days, which considered the humid climate in the eastern coastal area. Due to the large stiffness and small deformation, we assumed that the impermeable bedrock was the bottom of the groundwater. Considering the surface runoff, the set flow boundary was a flow boundary condition that allowed for correction. The bottom boundary condition (EF) was the pressure head boundary condition. Assuming that the initial water level was 3 m below the ground, the pressure head of EF was set to 17 m.

The third step was to perform stress and deformation analysis (SIGMA/W) on the subgrade at the corresponding time. Using the stress conditions in step 1 and the porewater pressure results at different moments in step 2 as suction conditions, the deformation response in the wetting conditions was calculated. The boundary conditions were the same as in Step 1 and Step 2. The results obtained were calculated with the load and geo-stress balance as the starting point.

In the fourth step, the slope stability analysis (SLOPE/W) of the subgrade was performed. The initial stress condition was the result of step 3. The initial pore-water pressure distribution condition was the result of step 2. The boundary conditions were the same as in step 1.
