## 2 Materials and Methods
### Three-Dimensional Numerical Simulation
#### 2.3.2 Constitutive Model and Material Properties  
Two constitutive models were employed for the comparative analysis of the soft soil: (1) the MC model, which follows the Mohr-Coulomb failure criterion and is usually used to simulate an isotropic elasto-plastic material, and (2) the CVISC model, which considers the rheological characteristics of soft soils. The viscoelastic-plastic model in FLAC(3D) is the CVISC model [36], which describes the relationship between strain and time at each stage and is rather sketchy [37]. Compared with the MC model, the CVISC model was expected to simulate the delayed deformation of the foundation pits in soft soils due to surcharge loading or excavation unloading. This was reasonable because the rheological effect was time-dependent. The results of case studies have shown good agreement between prediction and measurements [38,39]. As layer 2\({}_{y}\) of Huaxi Park Station exhibited low strength, a high water content, and significant rheological behavior, it was essential to accurately present its time-dependent deformation characteristics during excavation. The CVISC rheological model was adopted to simulate the behavior of layer 2\({}_{y}\). The CVISC model was a self-contained viscoelastic-plastic model, as shown in Figure 4. The CVISC model consisted of a Kelvin element, a Maxwell element, and a Mohr-Coulomb friction element arranged in series. The Kelvin element represented the instantaneous elastic response and primary creep stage, while the Maxwell element governed long-term viscous deformation, capturing the stable creep phase. The Mohr-Coulomb yield criterion defined the plastic behavior during the accelerated creep stage, where the material experienced plastic deformation due to stress redistribution following excavation unloading or surcharge loading. The plastic flow law used in the model was an uncorrelated Mohr-Coulomb flow law, where the strain rate depends on stress rather than on time. Figure 3: A 3D numerical model of the Huaxi Park Station foundation pit. The CVISC model parameters included traditional mechanical properties such as cohesion, internal friction angle, and tensile strength (as in the MC model) but also incorporated rheological parameters, namely, Maxwell shear modulus (\(E_{M}\)), Maxwell viscosity (\(\eta_{M}\)), Kelvin shear modulus (\(E_{K}\)), and Kelvin viscosity (\(\eta_{K}\)). The rheological characteristics were correlated negatively with the values of \(E_{M}\), \(E_{K}\), \(\eta_{M}\), and \(\eta_{K}\). The parameters of the model were determined by laboratory tests and are shown in Table 1.  
The corresponding rheological equation for the CVISC model is as follows:  
\[\varepsilon(t)=\sigma_{0}\bigg{[}\frac{1}{E_{M}}+\frac{t}{\eta_{M}}+\frac{1}{ E_{K}}\Big{(}1-e^{-tE_{K}/\eta_{K}}\Big{)}\bigg{]}+\varepsilon_{P}, \tag{1}\]  
where, \(E_{K}\) and \(E_{M}\), and \(\eta_{K}\) and \(\eta_{M}\), are the modulus of elasticity and coefficient of viscosity of the Kelvin and Maxwell bodies, respectively. Since the creep effect of strata other than the 2\({}_{\rm y}\) layer of silty powdery clay was not obvious in the process of excavation, the Mohr-Coulomb model was used for the layers. According to \"Huaxi Park Station of Suzhou Metro Line S1 Detailed Geotechnical Engineering Investigation Report\" and the creep test results of the Suzhou 2\({}_{\rm y}\) layer silty powdery clay, the mechanical parameters of each soil layer were obtained and are shown in Tables 1 and 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Parameter** & \(E_{M}\) **(kPa)** & \(E_{K}\) **(kPa)** & \(\eta_{M}\) **(kPa-h)** & \(\eta_{K}\) **(kPa-h)** \\ \hline Value & 200 & 100 & 80,000 & 2000 \\ \hline \end{tabular}
\end{table} 
Table 1: Burgers rheological parameters for mucky soils of Huaxi Park Station. Figure 4: Structure of CVISC model. In order to simulate the interactions between theretaining structure and soil, the diaphragm wall of the pit was simulated by a solid unit, and the steel support and concrete internal support were simulated by a structural unit.