When navigating in coastal areas, a ship may collide with a coastal bank, resulting in grounding. This issue involves interactions among the wave, the ship, and the coastal bank, with the key aspect being the contact between the ship and the bank. To solve this problem, a smoothed particle hydrodynamics (SPH) method is employed to simulate wave motion, wave-ship interaction, and wave-bank interaction. A discrete element method (DEM) is used to handle the interaction between the ship and the bank. Accordingly, a coupled SPH-DEM approach is established to study ship grounding. Numerical analysis is conducted for a bank with a 1:10 gentle slope under three wave periods, focusing on ship motion responses of pitch, surge, heave, and contact forces between the ship and the bank. The results show that under short-wave-period conditions, the ship remains grounded on the bank with small motion responses. Under the long-wave-period condition, the ship lifts off the bank and floats freely, with significantly increased motion responses. Regarding the contact forces between the ship and the bank, the vertical components are significantly larger than the horizontal components. In the early stage of grounding, the vertical components of the contact forces reach their peak values, accounting for up to 65.52% of the ship's gravity for all test cases. In the stable stage, the vertical components account for 32.84% and 41.89% of the ship's gravity for the two short-wave-period cases, and decrease to 0% for the long-wave-period case as the vessel is no longer grounded.

The shuttle boat that navigates in the polar seas will encounter ice floes, causing the hull of the shuttle boat to collide and ride these ice floes. In this case, the motion of the hull and the interaction between the hull and the ice floes are issues that demand attention. The SPH-DEM method is adopted to solve this problem, which involves the interaction between the wave and the floating bodies, and the interaction between these floating bodies. The smooth particle hydrodynamics (SPH) is used to solve the wave motion, the interaction between the wave and the hull and the interaction between the wave and the ice floe. And the discrete element method (DEM) is used to solve the interaction between the hull and the ice floe. The pitch, surge and heave response of the hull and the ice floe, and the interaction between the ship and the ice floe are then calculated for four conditions of 0 degree and 180 degree wave directions and two longitudinal centers of gravity in front of and behind the mid-ship section, respectively. The results show that the hull and the ice floe connect closely with relatively consistent motion response amplitude and frequency when the center of the gravity is in front of the mid-ship section. The interaction force between the hull and the ice floe is dominated by the vertical component, and the stable time-averaged values of the vertical components corresponding to 0 degree and 180 degree wave directions can reach to 44.6% and 88.9% of the hull weight, respectively. However, the hull and the ice floe are free-floating when the center of the gravity is behind the mid-ship section, with stable time-averaged values of the vertical components approximately close to zero.