## 3 Establishment of Numerical Model for the Foundation Pit
### Supporting Schemes and Parameters for the Simulation Model  
#### 3.3.1 Supporting Schemes  
In this investigation, both vertical and transverse supports were used to guarantee the stability of the foundation pit at different excavation stages. For vertical support, drilled grouting piles with a diameter of 1000 mm were utilized to control lateral displacements of the surrounding rocks. The pile intervals at standard and transfer sections were 1000 mm and 500 mm, respectively, and the pile lengths at standard and transfer sections were 24 m and 31 m, respectively. For transverse supports, commonly used support elements such as reinforced concrete bracings and steel bracings were adopted for further restraining the lateral displacement of the surrounding rocks and the settlement of the foundation pit at different excavation stages. Considering that the surrounding rocks at eight to fifteen meters underground were marl, prestressed anchorages were also adopted to further control displacements of the surrounding rocks at different excavation stages. The layout of the support elements is illustrated in Figure 4.  
According to the excavation depth of the foundation pit and the space required for the construction equipment, the minimum supporting depth for steel bracings was set to 4 m. Meanwhile, to further control the displacements of the surrounding rocks at different excavation stages, prestressed anchorages were set at 8 m and/or 22.5 m underground. In order to investigate the influences of steel bracings and prestressed anchorages on the stability of the foundation pit at different excavation stages, four different in-time transverse supporting schemes were considered in this simulation. The arrangements of the transverse supporting elements for the four in-time supporting schemes are illustrated in Table 1 and Figure 5.  
For the vertical supports, drilled grouting piles were set ahead of foundation pit excavation. For the transverse supports, reinforced concrete bracings were set at the top of the foundation pit, and steel bracings and prestressed anchorages were set when the excavation depth was 0.5 m deeper than the corresponding locations provided in Table 1.  
(1) Scheme A  
As shown in Figure 4(a), supporting scheme A included four-layer steel bracings at 4 m, 8 m, 12 m, and 16 m underground, respectively, and one-layer prestressed anchorages at 22.5 m underground. The raw distance of these transverse supporting elements was set to 4 m. This kind of supporting combination was advantageous for ensuring safety of the foundation pit at different excavation stages, but the corresponding costs were higher among the four supporting schemes, considering material cost, manpower costs, and construction equipment cost. Meanwhile, the construction sequence of scheme A is  
Figure 5: Support element arrangements and construction sequences of the four supporting schemes. rather complicated, and setting too many supporting elements along the excavation depth is disadvantageous for construction spaces. As shown in Figure 5b, supporting scheme B consisted of two-layer steel bracings located at 8 m and 16 m underground and one-layer prestressed anchorages 22.5 m beneath the ground. The raw distance of these transverse supporting elements was set to 8 m. This kind of supporting combination might be sufficient for controlling the lateral displacements of the surrounding rocks, thus ensuring the safety of the foundation pit at different excavation stages. The corresponding supporting techniques are relatively simple, and the construction costs are lower than those of Scheme A. As shown in Figure 5c, supporting scheme C included one-layer steel bracings 9 m beneath ground and prestressed anchorages located at 22.5 m underground.