# Research on Construction Sequencing and Deformation Control for Foundation Pit Groups
## 2 Materials and Methods
### Numerical Simulation Framework
#### 2.3.2 Constitutive Model Selection  
Although PLAXIS 3D effectively simulates soil-structure interaction, simulation accuracy depends critically on the choice of soil constitutive model and parameter settings [33]. PLAXIS 3D offers 10 common soil constitutive models and a custom model interface. Conventional models like the Linear Elastic (LE) and Mohr-Coulomb (MC) models can generally predict retaining structure deformations with reasonable parameters but often fail to accurately estimate surface settlements and impacts on adjacent structures. Studies show that using conventional test parameters for small-strain deformation analysis can lead to significant overestimations. Thus, selecting parameters corresponding to the actual strain range is essential. Field data and simulations indicate that soil during excavation typically undergoes small strains (\(10^{-4}\) to \(10^{-3}\)) [34; 35; 36]. [PERSON] et al. [22] defined three strain ranges: very small (\(\leq\)\(10^{-6}\)), small (\(10^{-6}\) to \(10^{-3}\)), and large (\(>\)\(10^{-3}\)). Therefore, this study adopts the Hardening Soil Small-Strain (HSS) model to predict excavation-induced deformations. The HSS model parameters are divided into four categories: strength, stiffness, advanced, and small-strain parameters. Strength parameters include effective cohesion (\(c^{\prime}\)), effective internal friction angle (\(\phi^{\prime}\)), and dilatancy angle (\(\psi\)). Stiffness parameters include reference secant stiffness (\(E_{50}^{ref}\)) and tangent stiffness (\(E_{od}^{ref}\)) from drained triaxial tests, and reference secant stiffness (\(E_{ur}^{ref}\)) from unloading-reloading tests. Advanced parameters include reference stiffness pressure (\(p^{ref}\)), Poisson's ratio (\(v\)), lateral earth pressure coefficient (\(K_{0}\)), and failure ratio (\(R_{f}\)). Small-strain parameters include reference shear modulus (\(G_{0}^{ref}\)), shear strain at 70% \(G_{0}^{ref}\) decay (\(\gamma_{0.7}\)), and stiffness stress-level exponent (m). The HSS model requires multiple modulus-related parameters (e.g., \(E_{50}^{ref}\), \(E_{od}^{ref}\), \(E_{ur}^{ref}\)), which are challenging to obtain solely through laboratory tests. A practical approach is to establish relationships between these parameters and derive others empirically. The PLAXIS 3D manual suggests using the compression modulus (\(E_{s0.1-0.2}\)) from geotechnical reports to estimate \(E_{50}^{ref}\), \(E_{od}^{ref}\), \(E_{ur}^{ref}\)) and \(G_{0}\) for typical soils (soft to hard). For other soils, interpolation is applied, as shown in Table 2. However, this method depends heavily on the accuracy of \(E_{s1-2}\), and deviations can significantly impact results. Additionally, the empirical multipliers for modulus relationships vary widely, reducing precision. The reference initial small-strain shear stiffness (\(G_{0}^{ref}\)) can be determined through laboratory resonant column tests or in situ wave velocity tests. In the PLAXIS 3D finite element software, \(G_{0}\) is calculated based on different confining pressures \(\sigma_{3}^{{}^{\prime}}\)[22]:  
\[G_{0}=G_{0}^{ref}\Bigg{(}\frac{c^{\prime}\cos\varphi^{\prime}-\sigma_{3}^{{}^{ \prime}}\sin\varphi^{\prime}}{c^{\prime}\cos\varphi^{\prime}+p^{ref}\sin \varphi^{\prime}}\Bigg{)}^{m} \tag{1}\]  
However, extensive experimental studies have shown that \(G_{0}\) is not determined by \(\sigma_{3}^{{}^{\prime}}\) but by the mean effective stress. When \(K_{0}\) is small and \(m\) is large, using the above formula for calculation tends to underestimate the value.