# Numerical Modeling of Single Pile Behaviors Due to Groundwater Level Rising
## 3 Numerical Modeling
### Constitutive Model and Model Parameters  
The piles were modeled as linear elastic (LE) materials and the soil model was defined Mohr-Coulomb (MC) and Hardening Small strain (HSsmall). Here, the constitutive model for all clay was based on the HSsmall model, an elastoplastic type of hyperbolic model. In addition, this model incorporated strain dependent stiffness moduli, simulating the different interactions of soils from small strains to large strains [28] (Figure 4). The HSsmall material data set, representing soft Kaolin clay for numerical modeling from Brinkgreve [29], is listed in Table 2 for verification of pile-soil movement. Using HSsmall model in the Bangkok subsoils condition, [PERSON] et al. demonstrated the result of pile load test from finite element method (FEM), that gives high accuracy for the entire range of the observed pile settlement curves [30]. For this study, the soil parameters of Bangkok subsoil  
Figure 3: Model and mesh used: (**a**) Pile dimensions and soil layers; (**b**) finite element mesh.  
were taken from [PERSON] et al. (2017), who calibrated the model for Bangkok soils. All parameters are summarized in Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Symbol** & **Unit** & **Speswhite Kaolin Clay** & **Pile** \\ \hline
**Material property** & & & & \\ Material model & - & - & HSsmall & LE \\ Drainage type & - & - & Drained & NP \\ Unit weight below phreatic level & \(\gamma_{Sat}\) & kN/m\({}^{3}\) & 17 & - \\ Unit weight above phreatic level & \(\gamma_{tunat}\) & kN/m\({}^{3}\) & 10.5 & 24 \\ Secant stiffness in standard drained triaxial test & \(E_{50}\)\({}^{\textit{ref}}\) & kN/m\({}^{2}\) & 1500 & E = \(2.7\times 10^{7}\) \\ Tangent stiffness for primary oedometer loading & \(E_{\textit{rad}}\)\({}^{\textit{ref}}\) & kN/m\({}^{2}\) & 750 & - \\ Unloading/reloading stiffness & \(E_{\textit{tr}}\)\({}^{\textit{ref}}\) & kN/m\({}^{2}\) & 8000 & - \\ Power for stress level dependency of stiffness & \(\textit{power}\) (\(m\)) & - & 1.00 & - \\ Cohesion & \(\textit{C}\)\({}^{\textit{ref}}\) & kN/m\({}^{2}\) & 0.00 & - \\ Friction angle & \(\varphi^{\textit{ref}}\) & degree & 21.00 & - \\ Dilatancy angle & \(\psi\) & degree & 0 & - \\ Shear strain at which Gs = 0.722G\({}_{0}\) & \(\gamma_{0.7}\) & - & 0.0002 & - \\ Shear modulus at very small strain & \(G_{0}\)\({}^{\textit{ref}}\) & kN/m\({}^{2}\) & 33300 & - \\ Poisson’s ratio & \(\
u^{\textit{ref}}\) & - & 0.20 & \(\
u(nu)=0.15\) \\ Reference pressure & \(P_{\textit{ref}}\) & kN/m\({}^{2}\) & 100 & - \\ Coefficient of lateral earth pressure for a normally & \(K_{0}\)\({}^{\textit{ref}}\) & - & 0.64 & - \\ Failure ratio & \(R_{f}\) & - & 0.9 & - \\ Interface reduction factor & \(R_{\textit{inter}}\) & - & 0.75 & 1 \\ Over consolidation ratio & OCR & - & 1.00 & - \\ References & - & - & after Benz (2018) & \\ \hline
**Groundwater property** & & & & \\ Data set & & - & User-defined & Non porous \\ Model & & - & Van Genuchten & - \\ Residual saturation & \(S_{\textit{res}}\) & - & 0.0500 & - \\ Saturated saturation & \(S_{\textit{sat}}\) & - & 1.000 & - \\ Fitting parameters (Van Genuchten) & \(g_{n}\) & - & 1.600 & - \\ Fitting parameters (Van Genuchten) & \(g_{a}\) & 1/m & 0.0400 & - \\ Fitting parameters (Van Genuchten) & \(g_{l}\) & - & 0.5000 & - \\ Horizontal Permeability & \(k_{x}\) & m/day & \(8.64\times 10^{-3}\) & - \\ Vertical Permeability & \(k_{y}\) & m/day & \(8.640\times 10^{-3}\) & - \\ References & & & Gallipoli et al. (2017) & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Speswhite kaolin clay parameters for numerical method verification.  
Figure 4: Characteristic stiffness–strain behavior of soil with typical strain ranges for laboratory tests and structures.