# Numerical Simulation of Piles in a Liquefied Slope Using a Modified Soil-Pile Interface Model
## 2 Numerical Simulation
### Soil-Pile Interface Model Development  
The group pile was modeled using beam elements with interface springs to simulate its flexural behavior and interaction with the soil. The interface springs represented the relationship between a pile node and a soil grid containing the node. The interface at each pile node was simulated by two different springs: the shear spring in the pile axial direction and the normal spring in the direction perpendicular to the pile axis. Note that the normal spring differs from the commonly used _p-y_ curve in two fundamental aspects. First, the purpose of the interface normal spring is to simulate the force exerted on the pile as a result of the displacement of liquefied soil, directly representing the effective force without incorporating an elastic behavior due to its high stiffness. Second, the interface normal spring accounts for the behavior between a single soil element and a corresponding pile node, necessitating separate modeling of the free field. The relationship between the force and displacement of the interface springs followed an elastic-perfectly plastic manner. The parameters used to characterize the behavior of the interface spring were stiffness and strength. The interface stiffness should not be too large or small because it can cause ineffective force transference or penetration at the interface, respectively [39; 40]. In this study, several preliminary analyses were conducted and it was found that the spring stiffness of 1.0 GN/m was reasonable to support the effective force transference at the interface. Since sandy soil was considered in this study, the strength parameter of the interface spring was defined as the interface friction angle in relation to the confining soil stress at the pile node. A value of two-thirds of the soil friction angle was applied to the friction angle of the shear spring [41]. To model the interaction between the liquefied soil and the pile, it was necessary to simulate the push and pull between the two, which depended on the interfacial normal spring. The friction angle of the normal spring for piles embedded in a drained condition was proposed to be no less than 80 degrees, or not allowing separation, regardless of the soil type [42; 43]. [PERSON] [32] suggested a static simulation of pushing a section of a pile under single-stress conditions to determine the friction angle of the normal spring. However, the compatibility of the pile-pushing analysis with the advanced soil model for liquefaction remains unverified. Consequently, this study evaluated the compatibility of the PM4S and model for the static pile-pushing analysis. By conducting the pile-pushing analysis, the friction angle of the normal spring was determined to be 60 degrees and 7.8 degrees for the soil modeled using the Mohr-Coulomb model and PM4 Sand model, respectively. To the authors' awareness, no proposal has been made yet for the strength parameter of the normal spring used to simulate the interaction between the liquefied soil flow and \begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Values** \\ \hline Density (kg/m\({}^{3}\)) & 9684 \\ Bulk modulus (Pa) & 6.21 \(\times\) 10\({}^{10}\) \\ Shear modulus (Pa) & 2.38\(\times\)10\({}^{10}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Input properties of elastic deck element. \begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Values** \\ \hline Density (kg/m\({}^{3}\)) & 2690 \\ Young’s modulus (Pa) & 6.33 \(\times\) 10\({}^{10}\) \\ Area (m\({}^{2}\)) & 1.24 \(\times\) 10\({}^{-1}\) \\ Moment of inertia (m\({}^{4}\)) & 1.19 \(\times\) 10\({}^{-2}\) \\ Perimeter (m) & 2.89 \\ Spacing (m) & 3.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Input properties of the pile beam element. pile. Therefore, the suggestion of [PERSON] et al. [44] considering the effect of confining stress through the friction angle of the normal spring was applied in this study. [PERSON] et al.