# Practical Approach for Assessing Wetting-Induced Slope Failure
## 1 Introduction
However, a rough estimate of SWCC is generally sufficient for unsaturated soil analysis [1] due to the significant order of difference between the SWCC of different soil types. Hence, a number of methods to estimate SWCC have been proposed, such as: (1) estimating SWCC based on basic soil properties [24; 25; 26]; (2) SWCC database, i.e SoilVision [27] and unsaturated soil hydraulic database (UNSODA) [28; 29]; or (3) SWCC sample data available in commercial software (i.e., Geostudio or MIDAS GTS NX). Estimating SWCC based on basic soil properties is perhaps the easiest to employ as it does not require any database and some of them have been incorporated in the commercial software. For instance, the Aubertin, Mbonimpa [25] method or modified Kovacs [24] can be used to determine SWCC based on basic geotechnical properties and have been employed in Geostudio. [PERSON], [PERSON] [25] assume that there is a distinction between the adhesion of water with a solid surface and surface tension at the interface with air causing capillary retention. These adhesion forces and capillary forces are acting simultaneously to create suction in the soil. The equation initially determined the degree of saturation-based SWCC (SWCC-S) and then converted to volumetric water-content-based SWCC (SWCC-\(\theta\)). The equation for the degree of saturation is provided in Equation (1):  
\[S_{r}=\frac{\theta}{n}=S_{c}+S_{a}^{*}(1-S_{c}) \tag{1}\]where \(S_{c}\) is the degree of saturation due to capillary forces, and \(S_{a}^{*}\) is the truncated values of the degree of saturation due to adhesive forces. The method to make sure that the adhesion component does not exceed unity at low suction \(S_{a}^{*}\) is defined in Equation (2):  
\[S_{a}^{*}=1-\left\langle 1-S_{a}\right\rangle \tag{2}\]  
The contribution of capillary component (which mainly contributed at low suction) to the total degree of saturation is defined in Equation (3):  
\[S_{c}=1-\left[\left(h_{co}/\Psi\right)^{2}+1\right]^{m}\!\!exp[-m(h_{co}/\Psi) ^{2}] \tag{3}\]  
where \(m\) is the pore-size distribution parameter, \(\Psi\) is the matric suction, and \(h_{co}\) is the equivalent capillary rise for granular soils which is provided in Equation (4):  
\[h_{co}=\frac{b}{eD_{10}} \tag{4}\]  
with:  
\[b=\frac{0.75}{1.17\log C_{u}+1} \tag{5}\]  
where \(C_{u}\) is the coefficient of uniformity. For plastic cohesive, \(h_{co}\) is defined as:  
\[h_{co}=\frac{\xi}{e}w_{L}^{1.45} \tag{6}\]  
where \(w_{L}\) is the liquid limit and \(\xi\) is a constant approximately equal to 402.2 cm\({}^{2}\). The contribution of the adhesion component (which mainly contributed at higher suction) to the total degree of saturation is defined as:  
\[S_{a}=a_{c}C\Psi\frac{\left(h_{co}/\Psi_{n}\right)^{2/3}}{e^{1/3}\left(\Psi/ \Psi_{n}\right)^{1/6}} \tag{7}\]  
where \(a_{c}\) is the fitting parameter, \(\Psi_{n}\) is the suction term to ensure dimensionless component, and \(C_{\Psi}\) is the correction function from [PERSON] and Xing [30] which is defined as:  
\[C_{\Psi}=1-\frac{\ln(1+\Psi/\Psi_{r})}{\ln(1+\Psi_{0}/\Psi_{r})} \tag{8}\]  
where \(\Psi_{r}\) is the suction corresponding to residual water content. Determination of the unsaturated permeability function is more difficult and tedious than obtaining SWCC. Hence, it is quite common to the estimate permeability function for unsaturated soil by using the [PERSON] [31] statistical method, which is defined as follows:  
\[k_{r}(\psi)=\frac{\int\limits_{\ln\psi}^{n_{s}}\frac{w(\varphi^{s})-w(s)}{e^{ \beta}}w^{\prime}(e^{y})dy}{\int\limits_{\ln s_{L}}^{n_{u}}\frac{w(\varphi^{s} )-w(s_{L})}{e^{\beta}}w^{\prime}(e^{y})dy} \tag{9}\]  
where \(k_{r}\) is the relative coefficient of permeability, and \(w\) is the water content that can be either gravimetric water content, volumetric water content, or degree of saturation.