Coupled problems of wave propagation in materially incompressible saturated soil based on the theory of porous media

Abstract eng:
Saturated geomaterials like soil basically represent a two-phase material consisting of interacting solid skeleton and pore fluid. This interaction is particularly strong in dynamic problems and leads from a modeling perspective to a strongly coupled system of differentialalgebraic equations (DAE), which requires a special numerical treatment particularly for the case of materially incompressible constituents. Here, the chosen governing balance equations are obtained based on the macroscopic Theory of Porous Media (TPM), where the presentation is restricted to the isothermal and geometrically linear case. The simulation of infinite domains is introduced using mapped infinite elements with a viscous damping boundary at the interface between the finite and the infinite subdomain. The resulting set of DAE, basically the solid and fluid momentum balances and the algebraic mixture volume balance, is solved using two different approaches: (1) a monolithic implicit time integration scheme, where the equations are first discretized in space using the mixed Finite Element Method (FEM) and then in time using a composite TR-BDF2 integration scheme, combining the advantages of the Trapezoidal Rule (TR) and the 2nd-order Backward Difference Formula (BDF2); (2) a splitting time integration strategy based on a semi-explicit-implicit scheme, where the DAE are first discretized in time, splitted using intermediate variables, and then discretized in space using the standard FEM. The time stepping algorithms are implemented into the FE program PANDAS and a Scilab FE routine and compared on numerical wave propagation examples. The advantages and the drawbacks of the different approaches are worked out and presented against the background of multi-phase soil dynamics.

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