A unified computational framework for fluid-solid coupling in marine earthquake engineering

The simulation of seismic wavefield at seafloor and seismic response of marine structures involves the coupling between seawater, saturated seabed, elastic bedrock and structure. That means, we target simulation where several types of equations are involved such as fluid, solid and saturated porous media equation. The conventional method for this fluid-solid-saturated porous media interaction problem is to use exsisting solvers of different equations and coupling method, which needs data mapping, communication and coupling algorithm between different solvers. Here, we present an alternative method, in which the coulping between different solvers is avoided. In fact, when porosity equals to one and zero, the saturated porous media is reduced to fluid and solid respectively, so we can use the porous media equation to describe the ideal fluid and solid, and the coupling between porous media, solid and fluid turns to the coupling between porous media with different porosity. Based on this idea, firstly the Biot's equations are approximated by Galerkin scheme and the explicit lumped-mass FEM is chosen, that are well suited to parallel computation. Then considering the traction and velocity continuity on the interface between porous media with different porosity, the coupled algorithm is derived, which is proved to be suitable for the coupling between fluid, solid and saturated porous media. Thus, the coupling problem between fluid, solid and saturated porous media can be brought into a unified framework, in which only the solver of saturated porous media is used. The three-dimensional parallel code for this proposed method is programed, examples for analysis of layered water-saturated seabed, water-bedrock, and water-saturated seabed-bedrock semi-infinite systems subjected to plane P-SV wave are given, and the proposed unified framework is verified through comparison between the results obtained through the proposed unified framework combined with tansmitting boundary condition and those obtained through tansfer matrix method. © 2019, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.