MPM simulation of solitary wave run-up on permeable boundaries

Waves attenuate rapidly as they propagate through porous media due to significant energy dissipation. The ability of permeable armour layers to absorb wave energy is therefore of great interest to the researchers and engineers tasked with the construction of structures that defend vulnerable coastlines from the wave attack. The goal of this research is to determine the effectiveness of vertical and sloped permeable barriers in minimising the wave run-up. Traditional methods for ascertaining the efficacy of protective barriers have used small-scale physical models. However, these are expensive and have been shown to suffer from the scaling problems, therefore numerical methods are gaining popularity. This paper investigates the effect of modifying the mean grain size of a permeable barrier on the run-up response to a solitary wave, using the Material Point Method (MPM), which is capable of handling large deformation problems within a Lagrangian framework, with a background mesh facilitating the solution of the governing equations and allowing for simple imposition of the boundary conditions. A double-point MPM is adopted, with two sets of material points representing the solid and liquid phases respectively, to accurately model situations where the fluid moves through the solid skeleton, such as in the case of wave run-up on porous structures. The multi-phase version of the MPM package Anura3D (www. anura3d.com) is used in the study, with a focus on the influence of changing the mean grain size of composition particles of a porous structure on solitary wave run-ups, on both vertical and sloped permeable boundaries. It has been shown that with an increase in the mean grain size, and therefore the permeability, the overall wave run-up height can be significantly reduced. The proposed study could contribute to a better understanding on the wave run-up reduction on porous structures, and provide useful design guidelines to the coastal defences.