A Two-dimensional Study Of Wave Loadings On A Submerged Horizontal Plate Over Variable Topography

A horizontal plate is a kind of simplified structures in the field of coastal and ocean engineering,from horizontal-plate breakwater,plate-type power generation device,very large floating structure to offshore oil platform,sea bridge.It is an important subject in engineering practice to quickly and accurately estimate the dynamic response of the structure in the real sea environment.Considering the actual situation of marine environment in coastal area or near island reefs,when the structural scale is relative large or the local water depth is relative shallow,the variation of the seabed topography needs to be taken into account when estimating the wave loads of marine structures.Therefore,a two-dimensional study of wave loadings on a submerged horizontal plate with finite thickness over variable seabed topography is carried out by theoretical analysis,laboratory experiments and numerical simulations to understand the effects of wave parameters and seabed variation on the hydrodynamic forces acting on the structure.Based on the linear potential theory and matching eigenfunction expansion method,a new analytical solution is developed for wave scattering of a submerged horizontal plate over variable bottom.Three typical seabed topography,a simple slope,a hump and a combined bottom are considered based on the analytical solutions.Wave reflection and wave loads on a submerged plate are calculated with different relative wave length for regular incoming waves.The results show that the maximum reflection coefficient of the horizontal plate is significantly affected by the topography,and the influence of the topography on wave load is not obvious.Specifically,for a simple slope or a hump,maximum reflection coefficient increases with the relative slope or hump height.The horizontal force and vertical force of the horizontal plate are not significantly changed,while the maximum overturning moment will decrease with the increasing of relative slope height or relative hump height.Pressure amplitude on the surface of the plate are also influenced by the bottom.Pressure on upper surface of the plate fluctuates with different wavelength,and pressure amplitude on the bottom surface of the plate is significantly affected by the uneven bottom.In general,pressures amplitude on the bottom surface shows that magnitude in the weather side is larger than that in the lee side.Considering a solitary wave to be as a typical waveform for tsunami waves,a linear theoretical solution for the solitary wave-plate scattering problem based on the long wave assumption is proposed in this paper.Similarly,solitary wave loads over the three typical variable bottom topography are discussed.Results show that variable bottom has a significant effect on wave loads of a horizontal plate.When the relative slope height or the hump height increases,the maximum and minimum values of the horizontal force increase and the peak value of the overturning moment becomes larger.For the vertical force,the first peak will become larger and the negative peak will be smaller as well as the second peak in the cases on a simple slope.There is no obvious difference of the vertical force for a hump bottom or a combined bottom.A series of laboratory experiments are carried out in a wave flume.A system is designed to measure wave loads acting on a large-scale model.Nonlinear wave forces of the structure are obtained and the effects of variable bottom are discussed.For the cases of regular wave,variation of the nonlinear wave loads to the relative wavelength is given.It is shown that the present 1:10 slope has little effect on the nonlinear wave loads in intermediate water depth.For the cases of solitary waves,1:10 slope has a significant effect on the wave load of a horizontal plate.The first peak of the vertical force becomes larger and the peak value of the negative vertical force decreases.The negative overturning moment is slightly smaller and the second peak of the overturning moment decreases significantly as the relative wave height becomes larger.An empirical formula for wave force on a horizontal plate over a 1: 10 slope is given for a solitary wave.Based on SPHysics open source software,a two-dimensional numerical wave tank is established.A piston-type paddle is placed at one end of the numerical wave flume to generate regular waves and solitary waves and wave absorption zone is arranged at another end.Different numerical parameters in the numerical model are tested by validation cases.The interactions between the regular wave or solitary wave and a submerged horizontal plate are simulated.Comparing numerical results and measured data,it can be concluded that for the regular wave-plate problem,SPH results on a 1: 10 slope are not significantly different from the results on a flat bottom,which is consistent with the conclusion from the experimental results.For the solitary wave-plate problem,numerical results are also consistent with the experiments on different bottoms.Results of pressure field show that the narrow channel between the plate and the 1:10 slope leads to the increase of the pressure in the lower surface of the plate.The numerical simulation also shows that a high-velocity flow and complex vortex structure near the trailing edge are observed on a 1:10 slope,which is also responsible for the change of wave loads.