## 4 Hydrodynamics around the Jack-Up Platform
### Wave Impact on Platform and Foundation  
Taking Case 1 (\(H\) = 7 m, \(d\) = 50 m, \(T\) = 15 s) as a typical case, the characteristics of the wave impact on the surface of the seabed foundation and the jack-up platform will be analyzed in this section. Figure 8 illustrates the time history of wave impact at different typical positions on the seabed surface. It is observed that the magnitudes of wave impact at S and A-F on the seabed surface are basically the same, about 20 kPa. Compared with the evolutionary time history of wave profiles at the corresponding positions demonstrated in Figure 7, the time history of wave impact in Figure 8 is smoother and closer to a simple harmonic wave. It is indicated that the nonlinearity in the time history of wave impact imposed on the surface of the seabed foundation is weak if there is no wave breaking.  
Figure 9 shows the time history of wave impact at the six typical points which are located at 2 m above the initial static water surface and on the pile legs in Case 1 (\(H\) = 7 m, \(d\) = 50 m, \(T\) = 15 s). It is found in Figure 9a that the wave impact on A is significantly greater than that on B and C, because A is located on the head-wave side. The maximum wave impact on A is about 24 kPa. For the point C which is at the back-wave side, there is only little difference in the magnitude of wave impact with that on B. It can also be found in Figure 9b that the wave impact on D, which is at the head-wave side of the No. 2 pile leg, is greater than that on E and F. Comparing Figure 9a,b, it is observed that the wave impact on A basically had no significant difference in magnitude with that on D, where the points A and D are at the head-wave side of the No. 1 and No. 2 pile leg, respectively.  
In addition to the wave impact on several individual points on the pile legs, the resultant force of the wave impact on these pile legs of the jack-up platform is also worth exploring. Figure 10 shows the time history of the resultant force of wave impact on the No. 1 and No. 2 pile legs of the jack-up platform under different wave conditions. It is observed that the wave-induced resultant force on the pile legs is positively related to the wave height. When the wave height \(H\) = 3 m, \(H\) = 5 m, and \(H\) = 7 m, the maximum wave  
Figure 7: Evolutionary time history of wave profiles at different typical positions around the pile legs of the jack-up platform (note: the typical positions A–F and S have been labeled in Figure 1b).  
induced resultant force on the No. 1 pile leg is about 400, 600, and 800 kN, respectively. When the wave height \(H\) = 7 m, the maximum resultant force on the No. 2 pile leg reaches about 700 kN. Therefore, the total resultant force on the whole offshore platform will reach about 3000 kN in Case 1 (\(H\) = 7 m, \(d\) = 50 m, \(T\) = 15 s). This magnitude of the resultant force imposed by ocean wave is considerable, and it may cause significant sloshing to the jack-up platform (the amplitude of sloshing will be quantitatively analyzed later), which would further affect the service performance of the offshore platform when carrying out engineering tasks.  
Figure 8: Time history of wave impact at different typical positions on the seabed surface in Case 1 (\(H\) = 7 m, \(d\) = 50 m, \(T\) = 15 s).  
Figure 9: \(Cont\).