## 3 Slope Stability Calculation and Analysis Method
### Slope Stability Analysis Method Considering Pore Gas Pressure  
Rainfall infiltration of an unsaturated soil is a dynamic process where water and gas displace and'squeeze' each other. When rainwater percolates downward through the soil, pore gas starts to move slowly. This can also lead to a gas pressure gradient acting on the sliding mass. Therefore, the pore gas pressure will result in the failure of the slope. In this research, the key problem was to consider the pore gas pressure gradient when evaluating slope stability.  
The slope angle at the bottom of each slice is different, and the pore gas pressure cannot be considered as an internal force to be put into the residual thrust method. In  
Figure 2: The calculation diagram of residual thrust method.  
addition, pore gas pressure can be regarded as airflow that is similar to water flow when the pressure in all directions is the same value. In this study, the shape of the soil slice was assumed to be vertical, the pore gas pressure acted vertically on the boundary of each slice, and the gas pressure between two slices had the same value in opposite directions. The diagram of the residual thrust method that considers pore gas pressure is shown in Figure 3. The modified residual thrust method can be written as follows:  
\[\begin{split} P_{i}=W_{i}sin\alpha_{i}&=\frac{[c_{i} ^{\prime}l_{i}^{\prime}+\left(W_{i}cos\alpha_{i-}p_{e}^{i}l_{i}\right)tang_{i} ^{\prime}+l_{i}\left(p_{e}^{i}-p_{w}^{i}\right)tang^{\textrm{p}}]}{F_{s}}+(P_ {i-1}+\Delta p_{i})\psi_{i}\\ &\psi_{i}=[\cos(\alpha_{i-1}-\alpha_{i})-\frac{tang_{i}^{\prime} }{F_{s}}\sin(\alpha_{i-1}-\alpha_{i})\end{split} \tag{9}\]  
where \(\Delta p_{i}\) is the horizontal gas pressure gradient, \(\Delta p_{i}=p_{g}^{i-1}-p_{g}^{i}\), and \(p_{g}^{i}\) is the pore gas pressure for slice \(i\).  
The load variables in Equation (9) are detailed further below:  
1. The weight of soil slice, \(W_{i}\): the increase in the soil weight caused by infiltrated water is considered in the variable. In this calculation, the soil density is equal to the sum of the dry density of soil and the weight of water content per unit volume. 2. The shear strength parameters \(c_{i}\) and \(\varphi_{i}\) vary with water content, which can be tested by the shear strength test, after which the relationship between \(c_{i}\), \(\varphi_{i}\), and water moisture can also be obtained. 3. Pore gas pressure \(p_{a}^{i}\), the gas pressure between soil slices \(p_{g}^{i}\), and pore water pressure \(p_{w}^{i}\) can be obtained by the pore gas pressure and pore water pressure for each soil slice that is calculated by the simulation for the slope rainfall infiltration.  
The variation in the weight of soil slice \(W_{i}\) and the shear strength parameters were closely related to the water content in the slope. The distribution of pore gas pressure, pore water pressure, and water saturation was obtained in advance to get the dynamic variation of the load on the slope. Then the load can be put into the slope analysis using the residual thrust method. In order to calculate the safety factor of slope stability accurately,  
Figure 3: Diagram illustrating the calculation of the residual thrust method considering pore gas pressure.  
the soil should be further stratified so that the material properties of each layer are basically the same.