## 2 Numerical Modeling
### Validation of the Numerical Model  
A case history of an excavation in Tianjin, China (39.11\({}^{\circ}\) N, 117.20\({}^{\circ}\) W), utilizing an IVFRW is depicted in Figure 2. The retaining structure form of section E-E adopts a slope and the IVFRW. The excavation depth is 6 m, including a 1 m slope, and the width of the excavation is approximately 80 m. In section E-E, precast concrete piles with 500 mm sections, a 300 mm hollow diameter, and a center-to-center spacing of 1600 mm were used. Both the inclined and vertical piles had a length of 12 m, with the inclined piles inclined at an angle of 20\({}^{\circ}\), as shown in Figure 3. Clinometers (W18, 7 monitoring points) were used to monitor the lateral deformation of the vertical piles. Total stations (DLZ6-1,8 monitoring points) were utilized to monitor the soil settlement at different distances behind the retaining structure.  
Figure 4 shows a three-dimensional model of the excavation with inclined-vertical framed retaining walls. The lateral boundaries of the model are fixed horizontally, while the base is fixed both vertically and horizontally. The excavation width is 80 m, and only half of the entire model is considered due to the symmetry along the \(y\)-axis. The maximum excavation depth is 6 m. The retaining structure has a length of 12 m. According to the equivalence principle of stiffness, the walls are simulated using plate elements with a thickness of 0.272 m and a weight of 25 kN/m\({}^{2}\). The walls have a [PERSON]'s modulus of 38 GPa and a Poisson's ratio of 0.2.  
Figure 2: The project site and instrumentation layout.  
The numerical model, utilizing the HSS constitutive model, was created using PLAXIS 3D software (V20). All relevant parameters, except \(\gamma_{0.7}\), were determined from laboratory tests conducted on soil samples obtained using a thin-wall sampler. The strength parameters (\(c^{\prime}\) and \(\varphi^{\prime}\)) were obtained through triaxial tests [22]. Apart from the strength parameters, the HSS model requires additional parameters for analysis. These parameters include the secant stiffness, \(E_{50}^{\text{ref}}\) (obtained from the triaxial compression test); tangent stiffness, \(E_{\text{oed}}^{\text{ref}}\) (obtained from the oedometer loading test); unloading/reloading stiffness, \(E_{\text{oed}}^{\text{ref}}\) (obtained from the triaxial unloading/reloading test); initial shear stiffness, \(G_{0}^{\text{ref}}\) (obtained from the bender element test); threshold shear strain, \(\gamma_{0.7}\), which represents the shear strain at which  
Figure 4: Illustrations of section E-E of the excavation.  
Figure 3: Profile of section E-E. Note: Unless otherwise specified, all other units are in millimeters.  
the secant modulus (\(G_{\text{s}}\)) is reduced to 70% of \(G_{0}\); and effective stress to describe the stress-strain behavior of soil [23; 24]. For a detailed explanation, refer to [PERSON] et al. [25]. Considering the impact of groundwater-level changes on the deformation of the retaining structure during excavation, the undrained simulation type was chosen. Table 1 provides a summary of the physical and mechanical parameters of the soils.  
Figure 5 illustrates the comparison of the ground surface settlement and wall deflection between the field observations and predictions. The lateral deformation and settlement are reasonably predicted. Thus, the computed data are found to be in good agreement with the measured results, indicating that this FEM modeling approach is reliable for further analysis.