In this paper, an integrated numerical model is developed to investigate wave-seabed interactions around multiple submerged permeable breakwaters in an elasto-plastic seabed foundation with Bragg effects. In this model, the wave motion is governed by VARANS equation and the Biot's u-p approximation is used to govern soil-pore fluid interactions in porous medium. The advanced elasto-plastic constitutive model (PZIII) is used to reproduce the plastic soil behaviour in seabed foundation under long-term cyclic wave loading. Numerical results show that the wave motion can be largely changed due to Bragg effects. Under the strongest Bragg effect, the soil permeability and degree of saturation can significantly affect the liquefaction potential in seabed foundation.


Breakwaters are the most commonly used offshore structures for protecting coast lines by reflecting incident waves back to offshore area. There are many forms of breakwaters, among them, the submerged permeable breakwaters have advantages like eco-friendly and wave energy dissipation efficiently because the breakwaters are under water surface that have less impact on ocean environment and porous medium allows it to reduce wave impact more efficiently. Bragg effect is defined as amplification of reflected waves by multiple breakwaters when the distance between two adjacent breakwaters are about half of incident waves length (Mei et al, 2005). Bragg effect is beneficial for breakwaters to protect the coast line as more waves will be reflected, on the other hand, it will imply more chance for seabed foundation to be liquefied as the wave height become larger in front of breakwaters. As reported, numerous damages of submerged breakwaters are caused by wave-induced seabed instability rather than from the construction deficiencies (Sumer, 2014). Therefore, it is essential to have a better understanding of wave induced seabed response around multiple breakwaters with Bragg effects.

In the past few decades, considerable studies have been conducted to investigate the wave induced soil response and wave-structures-seabed interactions (Jeng, 2003). In the early stage, analytical solutions are the most widely used method to study the wave induced soil response around submerged permeable breakwater (Jeng, 1996), in which the breakwaters are simplified as lines without width and weight. Later, numerous numerical models are developed to study the wave-breakwater-seabed interactions. These models normally consist of two sub-models: fluid model for fluid-structure interactions and soil model for dynamic soil response. The fluid-structure interactions have been intensively studied previously (Lin and Liu, 1998; Liu et al., 1999; Hsu et al., 2002). By integrating fluid and soil models, the integrated numerical models can simulate the more realistic engineering problems as the e_ect of structure shape, porous properties of structures and the gravity of structures can be included (Ye, 2012).

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