**2. Reinforcement Mechanism of Subgrades with a Capillary Barrier**

In the southeast coastal areas of China, the groundwater table isoline is generally below the original ground, and the subgrade is generally in an unsaturated state. Therefore, the soil strength is directly influenced by the distribution of matric suction in the subgrade soil. The matric suction is a manifestation of the energy produced by the water in the soil due to the capillary effect. Numerically, it is equal to the pore-air pressure minus the pore-water pressure (*u*<sup>a</sup> − *u*w). Based on the M-C model, Fredlund and Rahardjo [20] proposed a formula for the shear strength of unsaturated soil:

$$\pi\_{\mathfrak{u}} = \mathfrak{c}' + (\sigma - \mathfrak{u}\_{\mathfrak{a}}) \tan(\phi') + (\mathfrak{u}\_{\mathfrak{a}} - \mathfrak{u}\_{\mathfrak{w}}) \tan \left( \phi^{\mathfrak{b}} \right) \tag{1}$$

where *τ*<sup>u</sup> is the shear strength of unsaturated soil; *c* is effective cohesion; *u*<sup>a</sup> is the pore air pressure; *u*<sup>w</sup> is the pore-water pressure; *φ* is the effective internal friction angle; *φ*<sup>b</sup> is the shear strength increase rate with the change in matric suction. Figure 1 shows the traditional subgrade structure. After the expressway is completed, the pavement is an asphalt layer with good waterproofness. However, the fill slope is generally exposed in the atmosphere. When it rains, moisture flows into the subgrade from the slope shoulder. Because the subgrade is under unsaturated conditions, the soil suction in the subgrade is large, and the suction at the shoulder slope is small. Moisture gradually inflows into the subgrade soil along the suction gradient line. It is worth noting that the almost horizontal water flow is unsaturated flow. Therefore, the moisture content of the subgrade soil continues to increase, and the suction continues to decrease. According to formula (1), it can be seen that the reduction in shear strength is directly influenced by the reduction in suction, which may lead to the shear deformation and instability of the subgrade. Figure 2a shows the soil water characteristic curve of the subgrade soil. The water-entry value was approximately 6 kPa and the air-entry value was approximately 28 kPa. The difference between the water-entry value and the air-entry value of the subgrade soil was approximately 22 kPa. However, the standard design value of the vehicle load on the expressway was only 10.5 kPa [21]. Therefore, the strength change caused by the wetting subgrade should not be ignored.

**Figure 1.** Schematic diagram of a standard subgrade (unit: mm).

**Figure 2.** (**a**) Soil water characteristic curves and (**b**) permeability function of soils used in the subgrade.

In order to avoid the decrease in soil strength due to the presence of rainfall, this paper proposes to add a capillary barrier on the fill slope to protect the subgrade. The fine-grained soil in the capillary barrier was filled with the soil near the expressway. Gravel or sand was used as the coarse-grained soil. The fill slope soil from the surface to bottom was the fill near the expressway, gravel, and subgrade soil. Figure 2 shows the soil water characteristic curves and permeability coefficient curves of the two soils. The unsaturated permeability coefficients were estimated using the Mualem model [22].

$$k = k\_8 S\_\mathbf{e}^{0.5} \left( \int\_0^{S\_\mathbf{e}} \frac{\mathbf{dS\_\mathbf{e}}}{\Psi} \Big/ \int\_0^1 \frac{\mathbf{dS\_\mathbf{e}}}{\Psi} \right)^2 \tag{2}$$

where *k*<sup>s</sup> is equal to the saturated permeability coefficient; *S*<sup>e</sup> is equal to the effective saturation; *ψ* is equal to the soil suction. The slope in the soil water characteristic curve of the coarse-grained soil was steeper because of its large pores. Thereby, its water-holding capacity was worse, and the permeability coefficient curve was also steeper. The volumetric water content and permeability coefficient have a nonlinear distribution under different suction ranges. The suction where the permeability coefficients of two soils are equal is the critical failure suction, as shown in Figure 2b, which is the suction at point A.

With the water content continuously increasing when it rains, soil suction decreases. Rainwater enters the capillary barrier along the slope shoulder and inflows into the fill due to the fact of gravity. When soil suction is higher than the critical failure suction, the permeability coefficient of the fill is higher than that of the gravel. At this time, water accumulates only at the interface between the gravel and the fill. It does not breakthrough into the gravel layer. Because the capillary barrier is tilted, the moisture accumulated at the interface is drained laterally along the interface. When soil suction is less than the critical failure suction, the capillary barrier fails. At the interface, the diversion length is the distance from the point where the suction is equivalent to the critical failure suction to the surface of slope. It was evidently shown that the capillary barrier is effective within the diversion length. Walter [23], Tami [24], and Aubertin [25] pointed out that the diversion length of the capillary barrier was influenced by the slope angle, thickness of the finegrained soil, the properties of the fine-grained and coarse-grained soils, layer thickness, rainfall condition, etc. They all focused on the landfill cover system. Compared with the landfill, the slope length of the subgrade is relatively shorter, and the blocking effect of rainwater is better.
