## 3 Materials and Methods
### A Case Study of Excavation
#### 3.1.2 Adopted Parameters for FEM Analysis  
According to the borehole data obtained by the geotechnical engineering investigation [45], the soils predominantly distributed in the study area are grayish-yellow to greenish-gray clayey silt, which is slightly dense and has high water content. The oedometer test with several unloading excursions was performed to obtain the parameters (\(C_{c}\) and \(C_{s}\)) of the MCC model. The tests were launched in a triplex WG-type high-pressure consolidator, as shown in Figure 4. The scalped standard soil specimens of 61.8 mm in diameter and 20 mm in height were prepared from the in-situ samples obtained from thin-walled soil extractors during drilling. A total of three sets of specimens were prepared and placed in the retaining ring of the consolidation vessel. The test was performed in a step-by-step loading mode, and each load level was consolidated for 24 h until the total deformation of the specimen was less than 0.01 mm per hour, and the loading and unloading ratings are shown in Figure 4. All the sampling and launching procedures of the test were referred to the Standard geotechnical testing method (GB/T50123-2019) [50]. The \(e\)-lgp\(p\) curves obtained from three sets of parallel oedometer tests are shown in Figure 5. The compression index C\({}_{c}\) and the rebound index C\({}_{s}\) of the uniaxial oedometer test were then obtained according to the following equation:  
\[C_{c}\ \textbf{or}\ C_{s}=\frac{e_{i}-e_{i+1}}{\textbf{lg}\ p_{i+1}-\textbf{lg} \ p_{i}} \tag{7}\]\[e_{i}=e_{0}-(1+e_{0})\frac{\sum\Delta h_{i}}{h_{0}} \tag{8}\]  
where \(e_{i}\) is the void ratio at a certain level of pressure \(p_{i}\); \(e_{0}\) is the initial void ratio; \(\sum\Delta h_{i}\) is the total deformation height of the specimen at a certain pressure level, and \(h_{0}\) is the initial height of the specimen. As marked in Figure 5, the \(C_{c}\) of sample 3# is denoted as the slope of the straight line segment of the compression curve, which is the tangent of the reloading curve. The \(C_{s}\) is the slope of the line between the endpoint of the unloading curve and the intersection of the reloading and unloading curves. Then the average value of the three samples was employed for the final result. The results of \(C_{c}\) and \(C_{s}\) are also listed in Figure 5. Then according to Equations (3) and (4), \(\lambda\) and \(\kappa\) can be derived from \(C_{c}\) and \(C_{s}\). \(M\) can be obtained from the triaxial compression test performed by CRSSDGC [45] on the basis of Equation (5). Besides, the geotechnical investigation report also provided the physical and mechanical properties of the soil based on comprehensive laboratory and field tests. The parameters adopted in the deterministic simulation analysis are shown in Table 1. Specifically, the physical parameters (i.e., void ratio, dry density) were obtained from conventional laboratory tests. The lateral pressure coefficient (\(K_{0}\)) was obtained according to the \(K_{0}\) pedometer test, and the Poisson's ratio (\(\
u\)) can be derived from the correlation with \(K_{0}\) as \(\
u=K_{0}/(1+K_{0})\). The saturated hydraulic conductivity (\(K_{s}\)) was obtained from the field pumping test. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Void Ratio**} & \multirow{2}{*}{**Dry Density**} & \multicolumn{2}{c}{**Saturated**} & \multirow{2}{*}{**Poisson’s Ratio**} & \multirow{2}{*}{**Lateral Pressure Coefficient**} & \multirow{2}{*}{**MCC Model Parameters**} \\  & & & & & & & \\  & & & & & & \\ \hline \(e_{0}\) & \(p_{d}\) & \(K_{s}\) & \(\
u\) & \(K_{0}\) & \(\lambda\) & \(\kappa\) & \(M\) \\ - & kg/m\({}^{3}\) & m/s & - & - & - & - & - \\ \hline
0.78 & 1700 & \(1.82\times 10^{-6}\) & 0.28 & 0.39 & 0.106 & 0.00362 & 1.113 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical and mechanical parameters of silt for the excavation. Figure 4: The apparatus and loading ratings of the oedometer test. Figure 5: The \(e\)-l\(p\) curves obtained from the oedometer test.