## 3 Numerical Model  
### Establishment of a High-Piled Wharf Model  
Due to the brief duration of the ship impact load, the primary instantaneous force is absorbed by the front platform, exerting minimal influence on the rear platform and shore connection structure. Consequently, the model exclusively incorporates the beams and piles of the front platform, disregarding the impact of the rear platform on the front structure. The horizontal bent structure model constructed using FLAC 3D is illustrated in Figure 3. The straight piles are sequentially numbered from 1 to 5, spanning from the front to the rear, while the inclined piles are labeled as number 6.  
According to geological survey data, the foundational soil of this wharf is deemed non-liquefiable. The parameters for the Mohr-Coulomb model for each soil layer are presented in Table 1. Dynamic response analysis of pile-soil interaction necessitates the incorporation of mechanical damping. In this instance, Rayleigh and hysteresis damping models are employed. For the Rayleigh damping, the two parameters are taken as the minimum critical damping ratio of \(\xi_{\min}\) = 0.005 and a minimum center frequency of \(f_{\min}\) = 25. Meanwhile, the default model is utilized for hysteresis damping, where the respective parameters are set as \(L_{1}=-3.325\) and \(L_{2}\) = 0.823.  
The lateral bracing structure of the wharf, as expounded in this paper, employs beam elements integrated within FLAC 3D for the crossbeams, while the pile foundation utilizes internally embedded pile elements. The mechanical parameters of each structural element are delineated in the table below. Specifically, Table 2 delineates the model parameters of each segment constituting the transverse bracing structure of the elevated pile-supported  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Layer**} & **Composition of Each Layer** & **Thickness (m)** & **Density (kg/m3)** & **Bulk Modulus (MPa)** & **Shear Modulus (MPa)** & **Cohesion (kPa)** & **Internal Friction Angle (\({}^{\circ}\))** \\ \hline \multirow{3}{*}{3} & Miscellaneous & \multirow{3}{*}{\(-11.5\)\(\sim\)0.0} & \multirow{3}{*}{1730} & \multirow{3}{*}{16.06} & \multirow{3}{*}{2.71} & \multirow{3}{*}{8.0} & \multirow{3}{*}{14.0} \\  & fill & & & & & & \\ \cline{1-1}  & Mucky & \(-12.0\)\(\sim\)\(-11.5\) & 1560 & 11.44 & 1.93 & 8.0 & 14.0 \\ \cline{1-1}  & Muddy silly & \(-15.5\)—12.0 & 1670 & 14.69 & 2.48 & 9.0 & 9.5 \\ \cline{1-1}  & clay & \(-19.0\)—15.5 & 1730 & 16.06 & 2.71 & 15.0 & 13.5 \\ \cline{1-1}  & Silty clay & \(-22.5\)—19.0 & 1820 & 20.18 & 6.73 & 19.0 & 23.0 \\ \cline{1-1}  & Silty clay & \(-28.5\)—22.5 & 1960 & 15.40 & 9.24 & 41.0 & 19.5 \\ \cline{1-1}  & Sandy silt & \(-30.0\)—28.5 & 1910 & 12.88 & 7.73 & 8.0 & 31.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the Mohr–Coulomb model for soil.  
Figure 3: Structural model of the bracing structure at berth 8 in a high-piled wharf.  
sharf. This study adopts the Chinese \"Code for design of concrete structure-GB50010\" as the reference standard [29]. In Table 2, C40 and C50 represent the strength grades of concrete, with compressive strengths of 40 MPa and 50 MPa, respectively. Furthermore, Table 3 specifies the coupling spring parameters governing the interaction between the piles and the soil contact surface.