Analysis of Waves Interaction with Poro-elastic Structures

Abstract

In this paper, an analytical model is developed for the problem of periodic waves interaction with poro-elastic structures. Water waves are described using the linear wave theory. The poro-elastic structures are assumed to be homogeneous, isotropic, and can be elastic. The fluid motion and the structure response are also assumed to be periodic. Based on the momentum equation of Biot’s theory and the storage equation presented by Verruijt, the governing equations for the pore pressure and displacements of the poro-elastic medium are derived. Both kinematic and dynamic boundary conditions are used to solve the problem. The first study is the interactive problem of waves propagating over poro-elastic seabed. Continuity of dynamic pressure and flow flux at the interfacial seabed surface are considered. General solutions for the cases of infinite and finite thickness seabed are derived, respectively. The present analytic model is compared with experimental results and other analytic solutions to verify the correctness. Using present analytic solution, variations of the wavelength, wave damping and fluid pressure caused by coupling of waves and the poro-elastic seabed are discussed. It is shown that higher flexibility of the poro-elastic seabed induces larger interface pressure, but higher permeability causes smaller pressure on the seabed interface. Furthermore, the elasticity and porosity in affecting the interface pressure become apparent for larger seabed thickness. It is also shown that the wave length is affected by the poro-elastic seabed and becomes shorter for softer seabed and shallower water depth. For almost natural seabed, higher permeability induces larger wave damping. However, shear modulus of poro-elastic bed has little effect on wave damping. Next, the problem of waves interaction with a poro-elastic submerged structure is considered. The poro-elastic medium theory is redeveloped by means of that the momentum equation of Biot’s theory is modified for adopting the turbulent fricative effect presented by Sollitt and Cross (1972). Nonhomogeneous boundary conditions are included in the boundary value problem of waves interaction with a poro-elastic submerged structure. In the solution procedure, employing an analytic concept similar to Lee and Liu (1995), general solutions for the waves motion and the poro-elastic submerged structure are derived. Using the present analytic solution, effects of elasticity and permeability of poro-elastic submerged structures on wave reflection and transmission are studied. Results show that higher flexibility of the poro-elasitc submerged structure can induce resonant phenomena, but higher permeability causes larger damping and reduces the resonance. In last study, a series of experiments are conducted in a wave flume to survey the deformation of monochromatic waves as they propagate over poro-elastic submerged structures. Measurements of wave reflection and transmission induced by soft and permeable submerged structures are carried out. The material properties of experimental models are determined by means of physical model tests. Experimental results indicate some variations of wave reflection and transformation caused by poro-elastic submerged structures. It is shown that wave transmission for poro-elastic case is smaller than the one for rigid and impermeable case. The oscillatory motion of poro-elastic submerged structures can produce extra reflective waves and result larger reflection ratio. Furthermore, agreement between theory and experiment is achieved.