This talk presents a numerical framework for elastic wave propagation in fluid-saturated multi-porous media, with particular emphasis on multi-phase flow interactions and constitutive characterization. The governing equations are derived using Lagrangian mechanics, where the coupling between the solid matrix and multiple pore fluids is modelled through generalised dissipation terms based on a multi-phase extension of Darcy’s law. This formulation enables a systematic representation of inter-phase momentum transfer and permeability effects across distinct pore networks. The effective elastic properties are identified via compliance-based Gedanken experiments, providing a physically consistent approach to determining macroscopic constitutive parameters from idealized mechanical responses. This allows the model to capture the influence of multiple interacting pore systems without relying on purely empirical assumptions. The resulting system supports multiple compressional wave modes associated with solid and fluid phases, along with a rotational mode in the solid skeleton. A finite element discretization is employed to simulate wave propagation, and the formulation is validated through dispersion analysis, stability considerations, and convergence studies. The proposed framework highlights the critical role of multi-phase Darcy coupling and experimentally motivated parameter identification in accurately modelling wave phenomena in complex multi-porous media.

For full-length work: https://doi.org/10.1098/rspa.2023.0863, Proc. A (2024) 480 (2290): 20230863.

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