Wave Attenuation on Seawall by Submerged Thick Porous Structure over a Step-Type Seabed

This study presents a novel model that features a thick submerged porous structure (SPS) designed to protect a seawall in the presence of M steps at bottom. Using the governing equation and boundary conditions through the eigenfunction expansion method, a system of equations is obtained. The system is solved through MATLAB to determine the unknown coefficients. The numerical values of force, reflection coefficient and dissipation coefficient are obtained and plotted through graphs. The model is validated by comparing with literature results and verifying energy identity. Compared to the scenario without steps, the present study results in a 57% reduction force on the wall. In comparison to the problem without SPS, the present study observed a 26% reduction in the force on the wall. Observations suggest that varying the submergence depth (ranging from 0.1 to 0.3) and length (ranging from 0.1 to 0.6) of SPS leads to wave reflection and force on the wall approximately less than 54% and 59%, respectively. In particular, with a larger width of SPS, the influence of the height of the steps becomes negligible. With increasing porosity and frictional coefficient, the force on the seawall decreases. The force on the wall exhibits harmonic peaks at angles θ = 38° and θ = 61°, while θ = 67° is identified as the critical angle for the reflection and dissipation coefficients. These results are crucial for developing SPS, where surface-piercing structures hinder navigation and bottom-standing structures may not be fitted over an unstable bottom.