## 6 Slope Stability Analysis Considering the Evolution of Mechanical Parameters  
After the verification of the model considering the evolution of strength and dilation parameters, this model can be applied in the stability analysis of a submarine slope containing gas hydrate-bearing sediments. A submarine slope introduced in [45] is selected to build the geological model in this study. This slope is about 7\({}^{\circ}\), and it is located below seawater at a depth of 1200 m. The slope model is built in FLAC\({}^{\text{3D}}\) software with a size of 1500 m in length, 100 m in width, and 1200 m in height, and it is discretized into 25,200 cell grids. The stratum has several  
Figure 6: The calculated stress–strain curves compared with the laboratory testing results (scattered data points from [15] with permission) for the GHBS samples with different hydrate saturations ((**a**) \(\text{s}_{\text{h}}\) = 0%, (**b**) \(\text{s}_{\text{h}}\) = 27–34%, and (**c**) \(\text{s}_{\text{h}}\) = 41–45%) under various confining pressures. layers including clay, a hydrate reservoir, mudstone, and sandstone successively from top to bottom, as shown in Figure 7.  
The bottom boundary of the model is fixed. Every lateral boundary is fixed at the direction perpendicular to its surface. A seawater pressure of 1.2 MPa is applied on the top of this model. Because the failure usually occurs in the layer of the hydrate reservoir, a perfect elastoplastic model is adopted in the other layers such as clay, mudstone, and sandstone layers, and the mechanical parameters use constant values, as presented in Table 8 according to [45]. As we do not have detailed data on the hydrate reservoir considering the evolution of strength and dilation parameters, the parameters of the GHBS samples obtained in Sections 3 and 4 are used in this study. Therefore, this study actually just demonstrates the method for slope stability analyses with the proposed model considering the evolution of strength and dilation parameters. The strength reduction method is adopted in this stability analysis. It should be noted that the strength reduction method is usually used based on the perfect elastoplastic model, and the strength parameters \(c\) and \(\varphi\) are reduced to obtain the safety factor. However, the constitutive model used in this study has evolutionary strength parameters \(c\) and \(\varphi\). In this analysis, the initial strength parameters \(c_{\text{i}}\) and \(\varphi_{\text{i}}\) are reduced, as shown in Equation (13):  
\[ \begin{split} c_{\text{i}}^{\prime}=\frac{c_{\text{i}}}{F}\\ \tan\!\varphi_{\text{i}}^{\prime}=\frac{\tan\!\varphi_{\text{i}}}{F} \end{split}  \tag{13}\]  
where \(F\) is the reduction factor, and it is defined as the safety factor when the convergence cannot be reached in the calculation. With this method, the safety factors of the slope with different hydrate saturations are calculated, as shown in Table 9.  
With the decrease in gas hydrate saturation in the hydrate reservoir, the safety factor of the submarine slope gradually decreases. This model can well represent the changing trend in the safety factor with natural gas exploitation, i.e., slope stability gradually decreases with the exploitation of natural gas hydrate. It should be noted there are still some factors not  
Figure 7: FLAC\({}^{\text{3D}}\) model of a submarine slope containing a hydrate reservoir. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(S_{\text{h}}\)} & \(E\) & \(\
u\) & \(c\) & \(\varphi\) & \(\psi\) & **Density** \\  & **(Pa)** & **(KPa)** & **(\({}^{\circ}\))** & **(\({}^{\circ}\))** & **(\({}^{\circ}\))** & **(g/cm\({}^{3}\))** \\ \hline Clay layer & 3.73 \(\times\) 10\({}^{7}\) & 0.28 & 25 & 16 & 8 & 1850 \\ Mudstone layer & 2.72 \(\times\) 10\({}^{10}\) & 0.36 & 25 & 25 & 12.5 & 2350 \\ Sandstone layer & 5.85 \(\times\) 10\({}^{9}\) & 0.46 & 25 & 25 & 12.5 & 2600 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Basic parameter values of the FLAC\({}^{\text{3D}}\) model for the submarine slope model [45].