## 4 Numerical Simulation and Analysis
### Establishment of the Numerical Model
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Soil**} & \(\gamma\) & \(c_{\text{k}}\) & \(\varphi\) & \(\mathbf{E_{50}^{ref}}\) & \(E_{\text{ood}}^{ref}\) & \(E_{\text{ur}}^{ref}\) & \(\mathbf{G_{0}^{ref}}\) & \(\gamma_{0.7}\) & \(m\) & \(\mathbf{R_{\text{inter}}}\) & \(\mathbf{k_{H}}\) & \(\mathbf{k_{V}}\) \\  & **(kN\(\cdot\)m\({}^{-}\)3)** & **(kPa)** & (\({}^{\circ}\)) & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** & **(10\({}^{-}\)4)** & **(10\({}^{-}\)4)** & **(10\({}^{-}\)4)** & **(10\({}^{-}\)4)** & **(m\(\cdot\)d\({}^{-}\)1)** \\ \hline \multirow{2}{*}{1�⃝} & 17.50 & 10.00 & 18.00 & 4756 & 4756 & 19,024 & 9.51 \(\times\) 10\({}^{4}\) & 2 & 0.5 & 0.6 & 1.611 & 0.1611 \\  & 18.50 & 3.00 & 25.00 & 5000 & 5000 & 20,000 & 1.00 \(\times\) 10\({}^{5}\) & 2 & 0.5 & 0.6 & 1.728 & 0.1728 \\  & 19.00 & 3.00 & 28.00 & 6000 & 6000 & 24,000 & 1.20 \(\times\) 10\({}^{5}\) & 2 & 0.5 & 0.6 & 2.504 & 0.2504 \\  & 17.99 & 32.84 & 11.74 & 4968 & 4140 & 24,840 & 9.94 \(\times\) 10\({}^{4}\) & 2 & 0.8 & 0.7 & 0.004 & 0.0004 \\  & 19.00 & 5.00 & 25.00 & 8000 & 8000 & 32,000 & 1.60 \(\times\) 10\({}^{5}\) & 2 & 0.5 & 0.6 & 0.801 & 0.0801 \\  & 19.50 & 6.00 & 28.00 & 9000 & 9000 & 36,000 & 1.80 \(\times\) 10\({}^{5}\) & 2 & 0.5 & 0.6 & 1.614 & 0.1614 \\  & 1⃝2⃝ & 21.50 & 8.00 & 30.00 & 11,000 & 11,000 & 44,000 & 2.20 \(\times\) 10\({}^{5}\) & 2 & 0.5 & 0.6 & 2.398 & 0.2398 \\  & 18.88 & 38.31 & 14.03 & 7679 & 6399 & 38,394 & 1.54 \(\times\) 10\({}^{5}\) & 2 & 0.8 & 0.7 & 0.007 & 0.0007 \\  & 1⃝2⃝ & 21.00 & 10.00 & 30.00 & 15,000 & 15,000 & 60,000 & 3.00 \(\times\) 10\({}^{5}\) & 2 & 0.5 & 0.6 & 2.331 & 0.2331 \\  & 1⃝8.96 & 39.55 & 13.12 & 8154 & 6795 & 40,770 & 1.63 \(\times\) 10\({}^{5}\) & 2 & 0.8 & 0.7 & 0.006 & 0.0006 \\ \hline \hline \end{tabular} Note: \(\gamma\) is the weight of the soil; \(c_{\text{k}}\) is the soil cohesion; \(\varphi\) is the internal friction angle of the soil; \(E_{\text{ood}}^{\text{ref}}\) is the reference secant modulus of the triaxial consolidation drained shear test; \(E_{\text{ood}}^{\text{ref}}\) is the reference tangent modulus of the consolidation test; \(E_{\text{ood}}^{\text{ref}}\) is the reference unloading and reloading modulus of the triaxial consolidation drainage unloading–reloading test; \(G_{0}^{\text{ref}}\) is the reference initial shear modulus for the small strain stiffness test; \(\gamma_{0.7}\) is the shear strain corresponding to the initial shear modulus \(\zeta_{0}\) when the secant shear modulus \(G_{\text{sec}}\) decays to 70%; \(m\) is the power exponent related to the modulus stress level; \(R_{\text{inter}}\) is the strength reduction factor of the structural interface; \(k_{\text{H}}\) is the horizontal permeability coefficient of the soil; and \(k_{V}\) is the vertical permeability coefficient of the soil.  
\end{table} 
Table 1: Calculation parameters of the soil IRS model. Figure 10: Three-dimensional finite element calculation model of the foundation pit: (**a**) geological exploration borehole locations of the foundation pit; (**b**) schematic diagram of the overall model of the foundation pit; (**c**) supporting structure model diagram. In this study, the boundary of the model is set to the standard boundary; that is, the horizontal displacement of the model is constrained to the side surface, and the constant head seepage boundary is adopted. The horizontal and vertical displacements of the bottom are constrained simultaneously, an impervious boundary is adopted, the displacement of the upper part is not constrained, and a permeable boundary is adopted.