## 4 Dynamic Time-History Analysis of Wharf Structures Subjected to Impact Loads  
### Analysis of Structural Response to Normal Operating Loads  
For high-piled wharf structures, following the configuration of pile and beam units, it becomes essential to ascertain the comprehensive stability of both the structure and its foundation. This ensures that, during regular operations, the structure can maintain equilibrium. On this basis, further analysis will be conducted on the impact of ship collisions on the high-piled wharf structure.  
Following the establishment of soil layer boundary conditions and default gravity parameters, service loads are applied to the wharf surface. These loads include uniformly distributed loads (3 t/m\({}^{2}\)), gantry crane loads (10 t gantry crane), and train loads (medium to level-18 trains). The program was executed to compute the internal force distribution in each pile under these service loads. Figure 5 illustrates that under normal service loads, regions exhibiting significant bending moments in the pile foundation appear at soil layer transitions and at the pile tops. Specifically, the maximum bending moment for straight piles occurs at the pile top, while inclined piles experience their maximum bending moment near the soil's surface, approximately reaching 352.6 kN\(\cdot\)m. Overall, the bending moments remain within an acceptable range. Figure 6 shows that the axial force in the wharf pile body is observed to range between 556.0 kN and 1391.0 kN. The distribution and values of axial force across each pile exhibit minimal variation. Notably, inclined piles sustain relatively lower axial forces, with each pile experiencing its maximum axial force at the base.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Ship Form (t)** & **Berthing Speed** & **Effective** & **Maximum** & **The Impact Force** & \\  & **(m/s)** & **Impact Energy** & **Impact Force** & **Impact Force** & **Borne by a Single** & **Load Time (s)** \\  & & **(kJ)** & **(kN)** & **(kN)** & **Bent Frame (kN)** & **Load Time (s)** \\ \hline Scenario 1 & 20,000 & 0.2 & 320 & 1320 & 409.2 & 1.0 \\ Scenario 2 & 40,000 & 0.2 & 640 & 1780 & 551.8 & 1.0 \\ Scenario 3 & 20,000 & 1.0 & 8000 & 7300 & 2263.0 & 1.0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The ship impact load scenarios.  
Figure 4: Time–history curve of ship impact load.  
From the shear force in Figure 7 of the pile structure, it is evident that the shear force within the piles varies in response to changes in soil parameters. The maximum shear force within the wharf pile body ranges from 9.46 kN to 117.60 kN. Specifically, the maximum shear force in straight piles occurs above the soil level, whereas the maximum shear force in inclined piles occurs near the soil. Overall, the shear force in inclined piles surpasses that of straight piles.  
Figure 5: The bending moment of pile foundation under a normal operational load.  
Figure 6: The axial force of pile foundation under a normal operational load.  
The stress distribution within the foundation soil of the high-piled wharf structure is illustrated in the stress nephogram in Figure 8. The stress tends to vary along the vertical axis, with the surface stress of the soil being primarily negligible (close to 0). As depth increases, the absolute value of stress gradually amplifies, showing a negative polarity (pressure is negative). Notably, the stress within the soil at the pile foundation significantly differs from the surrounding soil. The upper structural load is transmitted through the pile foundation to the bottom of the soil layer, inducing the maximum stress at the base of the soil layer beneath the piles. Overall, the pile structure and the underlying foundation soil achieves a stable equilibrium state. This calculated outcome aligns with the fundamental principles governing the actual stress distribution.