# Seismic Performance Assessment of Wide Pile-Supported
## 2 Methods
### Finite Element Modeling  
PLAXIS 2D [25] was used to create a 2D FEA model. PSW models were constructed using 15 nodal-point triangular elements and analyzed as plane strain models. This analysis utilized two sequential loading phases to represent the actual state of the structure: static (i.e., only accounting for PSW and soil self-weight) and earthquake phase. In the static phase, the boundary conditions for side boundaries were set as normally fixed, while that for the bottom boundary was endowed with fully fixed. Regarding the earthquake phase, free-field and compliant base boundaries were applied to the side boundaries and bottom boundary, respectively [26]. The fine mesh option was selected when choosing the mesh coarseness to transmit ground motions in a high-frequency range. The hardening soil small-strain (HSS) model was applied to account for nonlinear soil behavior. The HSS model is a modification of the hardening soil model that accounts for the increased stiffness of soils at small strains [26], which is described by two additional material parameters of \(G_{0}\)\({}^{\prime\prime}\)(the small-strain shear modulus) and \(\gamma^{0.7}\) (the shear strain level at which the small-strain shear modulus has decreased to approximately 70% of its initial  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Layer** \\ **Code** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **N-** \\ **SPT** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Layer** \\ **Thickness** \\ **(m)** \\ \end{tabular}  } & \multirow{2}{*}{**Soil Type**} & \multirow{2}{*}{ \begin{tabular}{c} **Specific** \\ **Gravity** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Water** \\ **Content** \\ **(G5)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Unit Weight** \\ **(Wm (s))** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Void Ratio** \\ **(s)** \\ \end{tabular}  } & \multirow{2}{*}{
\begin{tabular  
value) [27]. In this study, the drainage condition was modeled as undrained- A, which provides better numerical simulation performance in the seismic case than other options in PLAXIS [26]. Plate elements were used to model the deck. An embedded beam row element was applied to model the piles. This feature allows for the 2D modeling of piles with a particular spacing in out-of-plane direction and has been validated by comparisons with three-dimensional FEA models and measurements from actual tests [28; 29; 30]. The 2D FEA was divided into two scenarios to allow for a more accurate comparison of PSW seismic performance between the two modeling approaches. In Scenario 1, the PSW was modeled without regard to the seabed's slope and displacement (Figure 2a). Scenario 2 took the seabed slope and its displacement into account (Figure 2b). Each scenario was subjected to two distinct waveforms of varying durations as the input motion. Thus, four analysis cases were conducted in this study. Table 2 describes the soil parameters used in the HSS model. The compression (\(C_{c}\)) and swelling (\(C_{s}\)) indices were calculated based on Bowles [31] (Equations (1) and (2)). The initial void ratio (\(e_{init}\)) was evaluated as a function of \(Wn\)[32] (Equation (3)). The \(\gamma^{0.7}\) was calculated using Equation (4) based on its correlation with \(PL\)[33]. The \(G_{0}^{n\prime\prime}\) was estimated in correlation with the N-SPT value based on [PERSON] and Tonouchi [23] (Equation (5)). \[C_{c}=0.007\ (LL-7) \tag{1}\]  
\[C_{s}=1/5\ C_{c} \tag{2}\]  
\[e_{init}=0.0197\ Wn+0.2143 \tag{3}\]  
\[\gamma^{0.7}=1.10^{-4}+5.10^{-4}\ PL \tag{4}\]  
\[G_{0}^{n\prime\prime}=14.12\ N^{0.68}\ (\text{MPa}) \tag{5}\]  
Figure 2: Finite element model. (**a**) Scenario 1; (**b**) Scenario 2. Table 3 describes the pile parameters used in the embedded beam row element. The pile was modeled as an elastoplastic circular tube beam and divided into three pile types, namely, pile 1 for trestle foundation and piles 2 and 3 for wharf foundation.