## 3 Materials and Methods  
### A Case Study of Excavation  
#### 3.1.1 Numerical Model, Boundary Conditions and Calculation Conditions  
A metro excavation project in Hangzhou, Zhejiang Province of China, was chosen as the research object of this study. According to the borehole data of geotechnical engineering investigation implemented by China Railway Siyuan Survey and Design Group Co., Ltd. (CRSSDGC) [45], a typical drill core representing the stratigraphic profile of the soil layer of the excavation is shown in Figure 2. The lithology of the soil is mainly silt, combined with thin layers (thickness less than 5 m) of clayey silt, miscellaneous fill, and pebble soil. In this study, the spatial variability of soil deformation parameters requires massive computations. Thus it would increase the computational effort if all these thin soil layers are manifested. Moreover, if the spatial variability of parameters of all the soil layers is considered, a curse of dimensionality may arise. Therefore, we generalized the soil layers into a homogeneous and isotropic silt layer to simplify the computation. Moreover, the buried depth of phreatic water level by drilling during the investigation was typically 0\(\sim\)2.6 m [45]. Hence, the seepage path of groundwater was increased by setting up a suspended seepage barrier curtain during excavation, combined with draining in the pit, enabling the groundwater level to be dropped in the pit while the head loss outside the pit was reduced. Given the regularity of the planar shape of the pit, this study established a 2D planar finite element model for analysis, as shown in Figure 3. The size of the pit calculation model is 422 m \(\times\) 50 m, with an excavation width of 22 m and a depth of 12 m. The excavation was braced by a suspended seepage barrier curtain (also known as an underground diaphragm wall), reinforced concrete support of 1000 mm \(\times\) 1000 mm, and two inner steel braces with a diameter of 800 m and a spacing of 4 m between the braces. In the FEM analysis, a numerical model was developed. It employed the CPE4P (4-node plane strain quadrilateral) elements for soil, the B21 (2-node linear beam in a plane) elements for the reinforced concrete support and steel support, and the CPE4 (4-node bilinear plane strain quadrilateral) elements for the suspended seepage curtain. The grid size near the pit was set as 1 m \(\times\) 1 m, and the grid size near the horizontal boundary of the model was 5 m \(\times\) 1 m. Thereby, the model was divided into a total of 4682 elements and 14,724 nodes. The top of the model was a free boundary. Both horizontal and vertical displacement at the bottom boundary were restricted. The shearing behavior of the soil on the lateral boundaries [46; 47; 48] was not considered due to the sufficient distance from the excavation. Figure 3: The excavation model adopted in the finite element analysis. Figure 2: A typical drill core in the study area. However, the horizontal displacement of the lateral boundaries was restricted, but the vertical movement was allowed for safety considerations. The horizontal displacement of the sidewalls of the drainage well was also restricted. A phreatic water boundary condition on the ground surface was set on both sides of the model to simulate the distal seepage recharge. Considering the significance of the water level to the settlement [49], the phreatic water level was set to the highest level of 0 m based on the survey observation to consider the most unfavorable scenario with the maximum drawdown and water level difference inside and outside the pit. Both sides of the drainage wells were fixed-head boundaries to simulate the draining process. The bracing exertion and soil excavation were simulated using the raw and dead unit method. Foundation pit draining and excavation is a process of joint action of stress field and seepage field, involving soil stress equilibrium, pore water seepage, and the coupling action between them.