State-space solution of seabed–geotextile systems subjected to cyclic wave loadings

Analytical solutions for dynamic responses of seabed–geotextile systems subjected to cyclic wave loadings are presented in this paper, which contains the solutions of the transient and harmonic responses. The theory is based on the Biot consolidation equations in which the pore fluid as well as the soil skeleton is considered compressible and the flow in the porous seabed is assumed governed by Darcy's law. The present analysis is completely based on the state-space formulations, which is very effective for laminated systems analysis. Together with Laplace–Fourier transform techniques, state-space methods are used to solve the governing equations. Responses of seabed–geotextile systems can be calculated by using the matrix theory, boundary conditions and inverting integral transform. As illustrative examples, laboratory experiments, which conducted at the Oregon State University Wave Research Facility in USA by McDougal [1981. Ocean wave–soil–geotextile interaction. Ph.D. Dissertation, Oregon State University], are analysed. It is shown that the numerical results are in good agreement with those obtained from laboratory experiments, and the distinction between the transient and harmonic response should be taken into account for design of marine geosynthetic systems. Under the transient condition, the seabed is apt to liquefy. Seabed stability may be increased by placing geotextile beneath an armour layer. The numerical evaluations of the solution in the seabed–geotextile systems can be easily achieved with high efficiency and accuracy.