## 4 Results and Discussion
### Inversion Results of Constitutive Model Parameters
#### 4.2.2 Parameter Inversion of Constitutive Model  
Existing studies have shown that the stiffness parameters of soil decrease with increasing strain and exhibit nonlinear changes, and a single and constant stiffness parameter value cannot describe the stress-strain response throughout the entire excavation phase [32]. In order to obtain a method to determine the constitutive parameters and initially assess and predict the deformation caused by foundation pit excavation during the design stage, this study conducts a inverse analysis of parameters using the measured deformation values of the foundation pit during the final stage of excavation, as the soil stiffness has basically evolved to its final state by this time. Using the optimal ratio obtained above and the \(E_{\text{s1-2}}\) value derived from laboratory soil tests, the numerical model predicted the horizontal displacement of the retaining wall, which are shown as the blue hollow triangles in Figure 8, where the black squares  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Soil** & \multicolumn{10}{c}{**Sully Clay**} \\
**Type** & \multicolumn{3}{c}{**Sandy Silt**} & \multicolumn{3}{c}{**Muddy Clay**} & \multicolumn{3}{c}{**Silty Clay**} \\ \hline Ratio & \(E_{50}^{ref}\):\(E_{\text{s1-2}}\) & \(E_{50}^{ref}\):\(E_{end}^{ref}\) & \(E_{\text{\emph{ref}}}^{ref}\) & \(E_{50}^{ref}\) & \(E_{50}^{ref}\):\(E  
represent the measured value. At excavation stages 4, 3, and 2, the differences between the calculated and measured maximum horizontal displacements of the retaining wall above the excavation face are 1.59 mm, 4.22 mm, and 8.33 mm, respectively, accounting for 34.1%, 22.9%, and 13.1% of the measured values. Compared to the numerical results calculated using the empirical parameters (as shown in Figure 5), the prediction results have been significantly improved. However, below the excavation face, the calculated values are generally too large, failing to meet the prediction accuracy requirements. This indicates that relying solely on the proportional relationship between soil constitutive parameters cannot fully satisfy the prediction requirements, and the soil constitutive parameters are still underestimated. Based on the obtained optimal proportional relationship, this study further inverted the values of key constitutive parameters. The calculated horizontal displacement of the retaining wall by the numerical model is shown as red hollow circles in Figure 8. In the fourth stage of excavation, the calculated results on the excavation face align well with the measured results. However, below the excavation face, especially at depths exceeding 25 m, there is a discrepancy of approximately 5 mm between the calculated and measured results. This is due to the underestimation of passive resistance, which leads to an overestimation of the lateral displacement of the piles below the excavation face. The relative error between the calculated and measured values on the excavation face in the third and second stages of excavation are 8.5% and 14.1%, respectively. Although the degrees of agreement between the calculated and measured results in the first two excavation stages are not as good as in the fourth stage, they still fall within the \(\pm\)15% range, meeting the prediction accuracy requirements. Therefore, in this case, the optimized constitutive parameters from the fourth stage of excavation can be adopted to predict the lateral displacement of the retaining wall in the third and second stages of excavation, indicating that the proposed step-by-step inverse method for the constitutive model parameters is feasible. In addition, to establish the relationship between soil constitutive parameters and the SPT blow counts, this study conducted layered modeling of the sandy silt mixed with silty sand, which located at the bottom of the foundation pit in the aforementioned numerical model. The layer thickness was set to 2 m to maintain consistency with the sampling interval of SPT.