## 3 Prediction of Excavation-Induced Ground Movement
### Determination and Validation of the Settlement Profile  
Figure 11 shows the dimensionless curve obtained by taking the average of the settlement with different parameters. Figure 12 shows a dimensionless curve of soil settlement behind the IVFRW. The settlement curve of the IVFRW for different inclination angles is concave, similar to the ground settlement curve of the braced excavations proposed by [PERSON] and [PERSON] [2]. Figure 9: Comparison of the computed maximum surface settlement of hypothetical cases obtained from the FEM analysis and those from the prediction model. Figure 11: Dimensionless curve of soil settlement behind the IVFRW (\(\theta=20^{\circ},z/H_{\rm e}=0.25\)). Figure 10: Base function distribution diagram. The \(X\) and \(Z\) coordinates in Figure 12 change with the inclination angle and the depth of the soil. With an increase in the inclination angle and the depth of the soil layer, the concave shape of the settlement curve becomes more pronounced. Coordinates \(X\) and \(Z\) are only related to the inclined pile angles \(\theta\) and \(z/H_{\rm e}\) and can be expressed as follows:  
\[X=k_{28}(e^{k_{28}x_{5}}-1)(k_{30}e^{k_{31}x_{6}}-1) \tag{5}\]  
\[Z=k_{32}(e^{k_{33}x_{5}}-1)(k_{34}e^{k_{35}x_{6}}-1)+1 \tag{6}\]  
where \(k_{28}\) = 1.0, \(k_{29}\) = \(-\)8.6, \(k_{30}\) = 0.7, \(k_{31}\) = \(-\)0.3, \(k_{32}\) = 2.0, \(k_{33}\) = 0.1, \(k_{34}\) = \(-\)2.6, and \(k_{35}\) = 1.0; and the determination coefficients, \(R^{2}\), of coordinates \(X\) and \(Z\) are calculated to be 0.98 and 0.99, respectively. The deformation mode of the retaining wall and the rotation phenomenon of the principal stress are the reasons why the settlement curve of the soil behind the IVFRW is concave. The deformation mode of the IVFRW is similar to that of braced excavations [17]. The excavation of the IVFRW leads to a principal stress rotation in the soil near the wall. This causes vertical unloading of the soil and results in a concave settlement curve. With increasing depth, the vertical unloading of the soil becomes more pronounced, resulting in a more pronounced concave shape of the settlement curve. The proposed simplified evaluation method was validated using three IVFRW-retained excavations that provided detailed construction information and measurement data. Figure 13 shows the site plans of the projects and profiles of the sections. Note that, unless otherwise specified, the data in the figure are presented in millimeters. All cases correspond to residential buildings in China, and the areas of the three cases are between 40,000 m\({}^{2}\) and 50,000 m\({}^{2}\). The excavation depths of the three cases are 4.5 m, 4.9 m, and 5.6 m, and the lengths of the piles are 11 m, 15 m, and 17 m, respectively. The vertical and inclined piles have identical lengths, and the angle of the inclined piles is 20\({}^{\circ}\) for all three cases. Each pile has a rectangular section measuring 0.375 m \(\times\) 0.5 m, with a hollow diameter of 0.21 m.  
Figure 12: Dimensionless curve of soil settlement behind the IVFRW. The center-to-center spacing between adjacent piles of Case 1 is 0.85 m, while the spacing of the other cases is 0.6 m.  
Table 3 provides details of the excavation geometry and soil properties used in the simplified evaluation. The predicted maximum ground surface settlement can be calculated by the proposed equations (Equations (1)-(3)), and the predicted surface settlement profile can be calculated by Equations (5) and (6). The predicted surface settlement profiles for these cases are shown in Figure 14, along with the corresponding field observations. All observed surface settlement profiles are concave in shape in the three cases and are consistent with the prediction method for the ground movements proposed in this study.