## 5 Parametric Analysis
### Effect of Scour Depth  
Illustrated in Figure 3a, in the context of three-dimensional asymmetric local scour where the scouring depth, \(S_{\text{d1}}\), exceeds \(S_{\text{d2}}\), fixed constraints are applied to the partially embedded pile section from \(-(S_{\text{d1}}-S_{\text{d2}})\) m to 0 m in the \(z\) direction. The vertical effective stress at any depth, \(z\), within this partially embedded portion is linearly interpolated utilizing the vertical effective stress values at \(-(S_{\text{d1}}-S_{\text{d2}})\) m and 0 m.  
To determine the effect of the scour depth, parameter analysis was performed by changing the scour depth (using 2.0 D, 4.0 D, 6.0 D, and 8.0 D depths) while keeping other parameters constant; Figures 8 and 9 show the lateral displacement and internal force diagrams calculated under different upstream scour depth \(S_{\text{d1}}\) values and the downstream scour depth \(S_{\text{d2}}\), respectively. With the increase in \(S_{\text{d1}}\) from 2.0 D to 8.0 D, the maximum bending moment of the pile gradually moves down from 9 D to 12 D from the top of the pile. The reason for these results Is that, with the increase in the scour depth, the loss of sand around the pile increases, so the constraint of the soil on the pile is weakened. With the increase in the scour depth \(S_{\text{d1}}\) from 2.0 D to 8.0 D, the maximum bending moment increases from 643.9 kN\(\cdot\)m to 851.4 kN\(\cdot\)m (an increase of 32.2%). Moreover, it can be noted that the zero points of bending moment are located at 22 D, 23 D, 24 D, and 25 D respectively. As \(S_{\text{d2}}\) increases, the point of contraflexture of the pile moves downward. As \(S_{\text{d2}}\) increases by 1, 2, and 3 times, while keeping the other parameters constant, the grounding displacement of the pile increases by 29.43%, 52.22%, and 76.95%, respectively. Through a comparison between the curves depicted in Figure 8a,b and Figure 9a,b the consistent trend shows that the influence of the scour depth on the lateral deformation and internal force of a single pile is particularly obvious. The reason for these results is that, with the increase in the scour depth, the soil around the pile is scoured and lost, and  
Figure 7: Lateral bearing performance of pile at varying \(S_{\text{w1}}\) values: (**a**) lateral displacement curves and (**b**) bending moment curves.  
the lateral resistance provided via the soil on the pile side disappears. It can be seen that the existence of an asymmetric scour hole leads to a difference in pile displacement. This phenomenon leads to a large horizontal stress difference in the pile body, so the pile will undergo significant bending displacement. Therefore, in the design of an offshore pile foundation, it is particularly important to strengthen the maximum bending moment of the pile. Anti-scouring materials are used to cover the surface around the pile foundation, such as rock filling and a protective concrete wall, so as to reduce erosion via water flow to the soil around the pile foundation, avoid the deepening of the scour depth around the pile and improving the lateral bearing performance of the pile foundation.