Dual-phase coupled u–U analysis of wave propagation in saturated porous media using a commercial code

This paper presents a method for incorporating dual-phase u–U wave propagation analysis for saturated porous media in commercial codes. Biot’s formulation is first re-formulated in terms of effective stress and pore pressure, followed by its finite element discretization. The method of incorporating the dual-phase computation involves representing the solid and pore fluid phases by two overlapping meshes with collocated elements and nodal points. Viscous coupling between the solid and fluid phases are realized by connecting each pair of collocated nodal points using viscous Cartesian connectors. Volumetric compatibility between the solid and fluid phases is enforced by coding the behaviour of the two phases and their volumetric interaction within a user-defined material subroutine. Non-linear behaviour of the soil skeleton can also be prescribed within the same subroutine. Comparison with existing analytical or numerical solutions for three one-dimensional elastic problems shows remarkably good agreement. Finally, a three-dimensional elasto-plastic example involving impulsive surface loading on dry sand overlying saturated sand, which is akin to a dynamic compaction problem, is analyzed to demonstrate the potential application of the u–U analysis on a more realistic transient loading problem. The results of the analysis highlight the importance of the slow wave in dynamic compaction process. Although this approach was developed on the ABAQUS Explicit platform, it is, in principle, applicable to other existing codes with the right features. Its main advantage is that users can still access the computational functionalities and stability, as well as pre- and post-processing features that often come with commercial codes.