## 5 Dynamics of Jack-Up Platform and Seabed Foundation
### Displacement, Effective Stresses, and Pore Pressure  
Taking the above-determined initial state as the initial condition, and when the wave impact is applied to the jack-up platform and its seabed foundation through the OlaFlow-ABAQUS coupling model, the wave-induced dynamic response of the jack-up platform and its seabed foundation is studied here. As is known, the wave-induced dynamic displacement of offshore structures is an important indicator to evaluate the service performance and the stability of offshore platforms. If the dynamic displacement is great, the jack-up platform may not be suitable for carrying out its engineering tasks because of the danger of capsizing. Therefore, the analysis of the displacement response of the jack-up platform is of significance for the evaluation of its service performance and stability. Figure 13 shows the time history of the horizontal displacement at the top of the jack-up platform under three conventional wave conditions. It is observed that the jack-up platform only has a small amplitude of periodic sloshing without significant residual displacement under the three wave conditions, in which the wave height \(H\) = 3 m, \(H\) = 5 m, and \(H\) = 7 m, respectively. The maximum amplitude of sloshing is about 5.0, 6.0, and 8.0 cm, respectively. This result indicates that there is no plastic deformation zone in the seabed foundation near the platform legs under the action of both the cyclic wave loading and the cyclic extrusion by the pile legs. Otherwise, there should be residual displacement for the jack-up platform. Therefore, the jack-up platform has good stability under the three conventional wave conditions. However, whether the periodic sloshing with an amplitude of 5.0-10.0 cm affects the normal service performance of the jack-up platform depends entirely on the requirements set by the engineering tasks; for example, a satellite launch mission maybe cannot be carried out when the wave height is \(H\) = 7 m, and the jack-up platform sloshes periodically with an amplitude of 10 cm. Figure 14a shows the wave surface when a wave trough reaches the jack-up platform in Case 2 (\(H\) = 5 m, \(d\) = 50 m, \(T\) = 15 s). Meanwhile, Figure 14b-g show the distribution of the wave-induced dynamic pore pressure, effective stress, and shear stress in the jack-up platform and its seabed foundation at this moment. It can be seen in Figure 14b that the dynamic pore pressure in the seabed below the platform is significant at \(t\) = 54.9 s, and the maximum dynamic pore pressure on the surface of the seabed is about 15 kPa, and the sign is negative. This means that an upward seepage is occurring in the seabed under the  
Figure 12: Displacement distribution in the \(x\) and \(z\) directions in the initial state. platform at this moment, the pore water in the seabed is flowing into the seawater, and the seabed in this zone is having an upward movement trend, as shown in Figure 15b. It can be seen in Figure 14c-e that the vertical dynamic effective stress, \(\sigma_{z}^{\prime}\), in the superficial layer of the seabed under the platform is positive (note: the positive value means tension in this study), indicating that this seabed zone is in a state of dynamic tension in vertical. The distribution form of the dynamic \(\sigma_{x}^{\prime}\) is basically the same as that of the dynamic \(\sigma_{z}^{\prime}\), but the dynamic \(\sigma_{x}^{\prime}\) is in a compressive state in horizontal. The dynamic effective stress, \(\sigma_{y}^{\prime}\), is mainly concentrated in the zone near the interface between the box-type platform and the four pile legs. It is also seen in Figure 14f,g that the dynamic shear stresses \(\tau_{xy}\) and \(\tau_{yz}\) are also mainly concentrated in the zone around the contact surface between the four pile legs and the seabed foundation, and the magnitude is about 10 kPa. Figure 14: _Cont._  
Figure 13: Time history of the horizontal displacement at the top of the jack-up platform under three conventional wave conditions.