Wave impacts on structures with rectangular geometries: Part 1. Seawalls

Abstract

a b s t r a c tThis paper considers steep wave impact on seawalls of various geometries. A simple analytical model for the pressure impulse due to a wave of idealized geometry and dynamics is developed and applied to the following geometries: (a) vertical seawall with a berm, (b) vertical seawall with a ditch at its base and (c) vertical seawall with a block missing (damaged condition).The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the rigid surface conditions and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, rigid wall conditions and by matching the values and the horizontal derivatives of the solutions in each rectangular region at their mutual boundary. The method yields the pressure impulse throughout the entire region. The overall impulse and moment impulse on the seawall and a simple model for the uprush of the spray jet after the impact are also presented. The effects of different impact regions and different geometries can therefore be quickly estimated and used to show trends in the results. It is shown that berms generally have a beneficial effect on reducing the impulse, moment impulse and uprush, but not the maximum pressure impulse on the seawall, whereas ditches are generally and sometimes strongly detrimental for all effects except uprush. A missing block in the seawall gives an almost constant or linearly decreasing value inside the gap (depending on the boundary condition applied at the rear of the gap being hard or soft respectively); the soft case can affect the pressure impulse on the front face of the seawall, thereby affecting the impulse and moment impulse.

Mathematical modelling of wave impact on floating breakwater

“…This presented paper continues the work of Noar and Greenhow [6,7] who extended Cooker's model with a ditch or berm into breakwater.…”

“…As to extending the work of Md Noar and Greenhow [6,7], we modeled the breakwater also with a berm but with both sides of the berm are filled with fluid as in Figure 1. This breakwater problem is split into three regions.…”

Use of impulses to determine the reaction force of a hydraulic structure with an overhang due to wave impact

“…Impulsive wave impacts can also be expected when the wave is confined at corners between walls and overhanging type structures (e.g., horizontal decks and beams), and by the influences of the air (e.g., Ramkema, 1978). For these cases, recently an analytical solution to determine the pressure impulse has been formulated (e.g., Wood and Peregrine, 1997;Md Noar, 2012;Md Noar and Greenhow, 2015). A brief introduction and the application of using the pressure-impulse are presented in Appendix A.…”

Three-dimensional steep wave impact on a vertical plate with an open rectangular section

“…For a vertical wall the wave front is considered everywhere vertical, thus ensuring maximum hydrodynamic load. In this context, Korobkin and Malenica [14] studied analytically steep wave impact on an elastic wall, and recently Noar and Greenhow [15] applied the steep wave impact concept to rectangular geometries using pressure-impulse theory. Again, both studies were conducted in 2D.…”