## 5 Analysis of the Resultant Force  
Although the experimental results show that there is a certain phase difference between the peak values of the transverse and inline forces under wave-current action (they generally do not occur simultaneously), the resultant force formed by the vector sum of the inline and transverse forces may still be much larger than the inline force. Under the combination of waves and a fast current in particular, the transverse force contributes significantly more to the hydrodynamic load on the pile, and the peak value of the resultant force is obviously greater than that of the inline force. This characteristic of the hydrodynamic load should be given full attention in theoretical analysis and practical engineering design. For better quantification of how the transverse force affects the resultant force on the pile, Figures 16 and 17 show the ratio of the peak resultant force to the  
For the super-large-diameter pile with \(D=10.5\) cm, \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) increase with increasing \(KC^{\star}\). The \(F_{H\_max}/F_{x\_max}\) values for \(KC^{\star}\approx 8\)-16 are larger than those for \(KC^{\star}<8\), exceeding 1.1 in most cases, and similarly \(\theta_{H}\) is larger, with all values exceeding \(20^{\circ}\). At \(KC^{\star}\approx 16\), \(F_{H\_max}/F_{x\_max}\) reaches its maximum value of 1.45, while \(\theta_{H}\) also achieves its maximum value of \(60^{\circ}\). For the pile with \(D=7.5\) cm, the distribution trend is similar to that for the pile with \(D=10.5\) cm, and both \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) increase with increasing \(KC^{\star}\). The larger values of \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) are distributed mainly in \(KC^{\star}\approx 12\)-23. At \(KC^{\star}\approx 23\), \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) reach their maximum values of about 1.35 and \(52^{\circ}\), respectively. For the pile with \(D=4.5\) cm and increasing \(KC^{\star}\), \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) increase for \(KC^{\star}\leq 28\) but decrease for \(KC^{\star}>28\), reaching their maximum values of ca. 1.24 and \(38^{\circ}\), respectively, at \(KC^{\star}\approx 28\). Overall, the significant range of \(KC^{\star}\) for \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) is \(KC^{\star}\approx 19\)-38. The analysis of the ratio of the peak resultant and inline forces (\(F_{H\_max}/F_{x\_max}\)) and the angle \(\theta_{H}\) between the resultant force and the incident flow direction in Table 2 shows further that the \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) values for the three piles are close in their insignificant \(KC^{\star}\) intervals. However, in their significant \(KC^{\star}\) intervals, the values of \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) for the super-large-diameter pile with \(D=10.5\) cm are significantly greater than those of the small-diameter pile with \(D=4.5\) cm. Figure 16: Ratio of peak resultant force to peak inline force. Figure 17: Angle between the direction of the peak resultant force and the incident direction of waves and current. Comparing Figures 15-17 shows that the significant range of \(K\)C* for \(F_{H\_max}/F_{x\_max}\) and \(\theta_{H}\) for each pile corresponds to that in which \(C_{L}\) is larger. Therefore, within a certain range of \(K\)C*, the influence of the transverse force on the peak value and direction of the resultant force cannot be ignored. This is particularly obvious under strong waves and currents. Furthermore, note that under the same wave-current action, the transverse force contributes more to the hydrodynamic load on a super-large-diameter pile than that on a small-diameter pile, making it easier to excite extreme structural loads. Therefore, in engineering design, the simplified method of taking the maximum inline force as the design hydrodynamic load is applicable only to a pile with a relatively small diameter and in its corresponding insignificant \(K\)C* interval.