## 4 Wave-Current Force on Pile
### Wave-Current Force Analysis
#### 4.3.2 Effects of Wave Height  
To investigate how the wave height affects the pile wave-current forces, Figures 11 and 12 compare the peak values of the inline and transverse wave-current forces on the three piles (i.e., \(D\) = 4.5 cm, 7.5 cm, and 10.5 cm) at water depth \(d\) = 1.0 m and the wave-current parameters of \(U\) = 0 m/s, 0.1 m/s, and 0.4 m/s and \(H_{0}\) = 5.6-13.0 cm (\(H_{0}/L\) = 0.020-0.047).  
Figure 11 shows that with increasing wave height, the peak inline forces on all three piles increase. For \(U\) = 0 m/s and 0.1 m/s, the peak values of the inline force \(F_{x}\) on the three piles increase approximately linearly with increasing wave height. For \(U\) = 0.4 m/s, the peak value of the inline force on the pile with \(D\) = 4.5 cm still increases approximately linearly with increasing wave height, but for the larger-diameter piles with \(D\) = 7.5 cm and 10.5 cm, the growth rate of the peak inline forces increases obviously when the wave height exceeds \(H_{0}\) = 10.6 cm. Meanwhile, for \(U\) = 0.4 m/s and \(H_{0}\) = 5.6-13.0 cm, the peak values of the inline wave forces on the piles with \(D\) = 4.5 cm, 7.5 cm, and 10.5 cm increased by ca. 36%, 58%, and 80%, respectively. This indicates that with a nonlinear wave flow field comprising strong waves and current, it is easier to excite an extreme inline wave-current force on a pile with a super-large-diameter than on one with a smaller diameter.  
Figure 12 shows that with increasing wave height, the peak transverse forces on all three piles increase. In particular, for \(U\) = 0.4 m/s, the peak values of the inline force on the piles with \(D\) = 4.5 cm, 7.5 cm, and 10.5 cm for \(H_{0}\) = 13.0 cm are about 2.2, 6.8, and 3.7 times those for \(H_{0}\) = 5.6 cm, respectively (Figure 12c). Under the combination of waves and a fast current, the increasing trend of the transverse force on the larger-diameter piles (\(D\) = 7.5 cm and 10.5 cm) is more significant than that on the smaller-diameter pile (\(D\) = 4.5 cm).  
Figure 11: Inline wave-current forces on pile models versus wave steepness: (**a**) \(U\) = 0 m/s, \(H_{0}/L\) = 0.020–0.047; (**b**) \(U\) = 0.1 m/s, \(H_{0}/L\) = 0.020–0.047; (**c**) \(U\) = 0.4 m/s, \(H_{0}/L\) = 0.020–0.047.  
Figure 12: Transverse wave–current forces on pile models versus wave steepness: (**a**) \(U\) = 0 m/s, \(H_{0}/L\) = 0.020–0.047; (**b**) \(U\) = 0.1 m/s, \(H_{0}/L\) = 0.020–0.047; (**c**) \(U\) = 0.4 m/s, \(H_{0}/L\) = 0.020–0.047.  
In general, both current velocity and wave height are important factors affecting the inline and transverse forces on a pile. For a super-large-diameter pile in particular, the peak wave-current force growth trend is more significant as the current velocity and wave height increase. Meanwhile, the combination of strong waves and current is more likely to excite inline and transverse ultimate wave-current loads on such a structure. In addition, the large peak value of the transverse force will inevitably have a significant influence on the hydrodynamic load characteristics of the pile. Therefore, in the engineering design, sufficient attention should be paid to the transverse wave-current load on such a super-large-diameter pile in deep water under the combination of strong waves and current.