## 3 Results
### Soil Stress  
#### 3.2.1 Comparison Analysis of Soil Special Point Stress Paths for Four Simulation Methods  
Soil special points' stress paths may provide useful explanations for changes in soil stress caused by pit excavation [24; 31].  
In this paper, five representative special points near the wall are selected. The analysis of the stress paths under different pile simulation methods is carried out (the locations of points A, B, C, D, and E are shown in Figure 7a, where the light blue figure represents a schematic diagram of the pit at the end of the excavation stage). Points A and B are located near the bottom of the pile (approximately 17.6 m from the top). Point A is located at the front side of the pile, while point B is at the back side. Point C is located near the upper part of the back side of the pile (approximately 2.3 m from the top). Point D is located in the middle and upper part of the back side of the pile (approximately 5.8 m from the top). Point E is located at the back side of the pile, specifically at the end of excavation (around 13.9 m from the top). Respectively, the Arabic numbers 1, 2, 3... 6 represent the stages of the initial stress field, i.e., 1 st excavation, 2 nd excavation... 5 th excavation. Since all five special points are located within the second layer of soil, they share the same \(K_{f}\) and \(K_{0}\) lines, where the \(s\)-\(t\) rectangular coordinate system is adopted as the stress path coordinate system. \(s\), \(t\) are recommended as in Equation (3).  
\[s=\left(\frac{\sigma_{1}+\sigma_{3}}{2}\right),t=\left(\frac{\sigma_{1}-\sigma _{3}}{2}\right) \tag{3}\]  
where \(\sigma_{1}\) and \(\sigma_{3}\) are the first principal stress and the third principal stress, respectively. These values can be programmatically extracted using the FISH language in FLAC3D.  
Figure 7 shows a comparison of the stress paths at the special points for the four modes under various excavation stages. In the initial stress field stage, the \(s\)-\(t\) values for these five special points are all located at the \(K_{0}\) line for the four different simulations, which indirectly indicates the accuracy of the model simulation in the initial stress field. As for Mode 1, Mode 3, and Mode 4 in relation to points A and B, as the excavation depth increases, point A, being at the bottom of the excavation area, experiences a more intense stress unloading level compared to point B, resulting in a smaller mean stress at point A and a greater shift in its coordinates towards the left (Figure 7a,c,d). At the same time, because the horizontal stress unloading level at point A is lower than the vertical stress unloading level, its deviator stress becomes larger. As for points C, D, and E, which are located at the back side of the pile, their stress paths are all unloaded strongly horizontally, i.e., the minimum principal stress decreases continuously. From Figure 7a,c,d, it can be found that as the excavation depth increases, the coordinates of these three points shift to the left and steadily move from the initial \(K_{0}\) line to the \(K_{f}\) line.  
For Mode 2, it can be found from Figure 7b that the trend of the stress paths at these five special points during the first four excavation stages is similar to that in the other three modes. At the end of the excavation, the mean stress at point A decreases significantly compared to that of the other three modes, dropping from 250 kPa to nearly 160 kPa. The decrease in shear stress causes it to fall below the \(K_{0}\) line. On the other hand, the mean stress at point B slightly increases and also moves below the \(K_{0}\) line. Meanwhile, the mean stress at points C and D increases. The mean stress at point E increases significantly, from 175 kPa in the previous stage to 250 kPa; the reasons for these results will be discussed later in Section 4.2.