## 3 Unsaturated Soil
### Mechanical Properties of Unsaturated Soil  
SWCC is closely related to the strength of unsaturated soil and is an important tool to study the mechanical properties of unsaturated soil. More specifically, SWCC describes the relationship between the thermodynamic potential energy of pore water in soil and the amount of water absorbed by soil system. The SWCC shape of various soils is mainly affected by the properties of soil materials. [PERSON] and [PERSON] [86] carried out a large number of tests on different types of unsaturated soils, and showed that the main factors affecting SWCC are mineral composition, pore structure, stress state of soil particles, property of liquid, pore gas, etc. Many researches have been performed to explore the relationship between water content and mechanical properties of unsaturated soil [87]. The shear strength formula of unsaturated soil can be proposed by [PERSON] effective stress. It is related to saturation \(S\), which is closely related to SWCC. \(\varphi^{b}\) is also closely connected with different sections of SWCC, thus it can \(\chi\) horn \(\varphi^{b}\) to simplify the test measurement and facilitate the engineering application. [PERSON] [88], based on the expanded micromechanical model, proposed the shear strength formula of unsaturated soil as follows:  
\[\tau_{f}=c^{\prime}+(\sigma-u_{a})\tan(\varphi^{\prime})+(u_{a}-u_{w})\theta_{ w}\tan(\varphi^{\prime}) \tag{14}\]  
\[c_{s}=(u_{a}-u_{w})\theta_{w}\tan(\varphi^{\prime}) \tag{15}\]  
where \(\tau_{f}\) is the shear strength of unsaturated soil; \(c^{\prime}\) and \(\varphi^{\prime}\) are effective cohesion and effective internal friction angle of saturated soil; \((u_{a}-u_{w})\) is the matrix suction; \((\sigma-u_{a})\) is the net normal stress; and \(\theta_{w}\) is the volume water content. [PERSON] et al. [89] developed a comment model for predicting the shear strength by SWCC, as shown in Equations (16) and (17). \[\tau_{f}=c^{\prime}+(\sigma-u_{a})\tan(\varphi^{\prime})+(u_{a}-u_{w})\Theta^ {\kappa}\tan(\varphi^{\prime}) \tag{16}\]  
\[c_{s}=(u_{a}-u_{w})\Theta^{\kappa}\tan(\varphi^{\prime}) \tag{17}\]  
where \(\Theta\) is the relative volume water content, \(\Theta=\theta_{w}/\theta_{s}\); \(\theta_{s}\) is the saturated volume water content; and \(\kappa\) is a fitting parameter. [PERSON] and [PERSON] [90] introduced the plasticity index \(I_{p}\) into the fitting model of the parameters \(\kappa\), as follows:  
\[\kappa=-0.0016I_{p}^{2}+0.0975I_{p}+1 \tag{18}\]  
Furthermore, the numerical simulation provides new insights into moisture and stress of unsaturated soil [91]. [PERSON] et al. [92] analyzed the changes of the yield stress with the capillary cohesion between particles by simulating isotropic compression and biaxial shear tests. [PERSON] et al. [93] proposed two shear strength functions to reflect both the nonlinear characteristics of unsaturated soil and the influence of grain size distribution. [PERSON] et al. [94] found that the density of the liquid bond is a decisive parameter for the overall cohesion of wet granular materials. Within the distance of the liquid bridge fracture, even at low water content, the uniform distribution of liquid will lead to the highest cohesion. [PERSON] et al. [95] introduced the micromechanics study of unsaturated granular media in the state of the pendulum liquid bridge. The resilient modulus (MR) of the subgrade is a key parameter to design pavement structures. The MR of unsaturated soil is dependent on the humidity state of subgrades [96]. In the range of low matric suction, the MR increases nonlinearly with the increase in matric suction; however, this trend cannot continue to a higher matric suction range [97]. [PERSON] et al. [98] found that the dynamic resilient modulus of red clay increases with the increase in matrix suction when the matrix suction is less than 1 MPa, and the increase in dynamic resilient modulus is not evident when it exceeds this value.