126 An integrated model of wave-seabed-structure interactions Ji-sheng Zhang 1 , Bo Wang 1 , Dong-sheng Jeng 1* , Philip L. –F. Liu 2 , Ping Dong 1 1 Division of Civil Engineering, University of Dundee, Dundee DD1 4HN, UK 2 School of Civil and Environmental Engineering, Cornell University, New York , USA * E-mail: d.jeng@dundee.ac.uk ABSTRACT: The phenomenon of wave-seabed-structure interactions have occurred in the marine environment with a coastal permeable (or partially permeable) structure, which has attracted great attention from coastal engineers involved in the design of marine structures. In this study, a porous seabed model based on Biot’s consolidation equation and pore-elastic theory is integrated into the COBRAS wave-structure model. This integrated model is verified by the laboratory experiments. Some dominant factors affecting the wave motion and its induced seabed response are examined by using this model, including wave parameters and structure properties. KEY WORDS: Wave motion; Porous seabed; Submerged permeable breakwater; Mathematical model 1 INTRODUCTION The submerged breakwaters, permeable or partially permeable, have been commonly constructed on porous seabed to reduce the wave impact on the coastal region. One of the main advantages of applying these submerged permeable structures is that wave energy can be additionally dissipated due to the flow friction within the porous media. However, the existence of breakwaters may significantly affect the wave motion and its induced seabed response in the vicinity of structures. Many coastal structures have been damaged by the wave-induced seabed response, rather than from the construction deficiencies [1-2] . To understand the functionality and stability of a submerged permeable breakwater on porous seabed, the wave motion and its induced seabed response around such a structure must be determined. Some laboratory experiments [3-4] and mathematical models [5-6] on wave-permeable structure-porous seabed interaction have been conducted in the recent years. All previous research results indicated that the degree of wave-permeable structure-porous seabed highly depends on the incident wave conditions and structure parameters. The aim of this study is to develop a two-dimensional (2D) integrated model that is efficient in investigating wave-permeable structure-porous seabed interaction with acceptable computational cost. An assumption is made that the poro-elastic deformations in seabed are small and do not affect the wave transformations or its induced pressure on the surface of the poro-elastic seabed [3] . This assumption simplifies the boundary condition at seabed interface where the water pressure and shear stress calculated from wave model are passed into the seabed. This model is verified with the well-documented laboratory experiments of [3], and it is applied to study the effects of wave parameters (wave period and wave height) and structure properties (structure porosity and structure height) on the wave motion and seabed response around a submerged permeable breakwater. 2 THEORETICAL FORMULATIONS While the extended Volume-Averaged/Reynolds- Averaged Navier-Stokes (VARANS) equations are solved for the outer and inner flows of porous breakwater (above the seabed surface), the Biot’s consolidation equations with poro-elastic theory are solved for the seabed response under the floor. 2.1 Governing equations The VARANS equations for the wave motion can be expressed as [7] :