Elastic wave propagation and attenuation through deformable porous media containing two immiscible fluids taking into account gravity effect

• Published in: Advances in water resources Vol. 205; p. 105069
• Main Author: Lo, WeiCheng
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2025
• Subjects: Elastic waves; Gravity; Poroelasticity; Unsaturated porous media; Unsaturated porous media; Elastic waves; Poroelasticity; Gravity
• DOI: 10.1016/j.advwatres.2025.105069
• ISSN: 0309-1708

•Elastic wave theory of poroelasticity in unsaturated soils incorporating gravity’s effect is developed.•A generalized dispersion equation accounting for gravity’s effect is derived.•Gravity’s effect is extended to dilatational waves and multiphase systems.•Gravity’s effect exhibits a positive correlation with excitation frequency.•Gravity’s effect is sensitive to the pore-fluid mixture properties and the soil texture. The present study develops a rigorous mathematical framework for describing elastic wave propagation and attenuation in a deformable porous medium containing two immiscible fluids, all under the influence of gravitational forces. Starting from the conservation laws of mass and momentum, we derive a comprehensive set of coupled partial differential equations, employing the displacement vectors of the solid matrix and the two fluids as the primary dependent variables. The classic dynamic equations for dilatational motions, as originally formulated by Biot to incorporate gravitational body forces, emerge as a limiting case of our model when reduced to a single-phase system. A sextic polynomial dispersion equation is subsequently derived, characterizing the relationship between the excitation frequency and the complex-valued dilatational wave number. This generalized dispersion equation includes 66 additional terms beyond existing formulations, thereby enabling a more detailed interpretation of variations in material density and volumetric fraction of both the solid phase and two immiscible interstitial fluids, all subject to gravitational acceleration. Numerical analyses reveal that gravitational effects can alter the attenuation coefficient by up to 23 % for the P1 wave across the examined frequency range. With respect to phase speed, gravitational forces induce a maximum variation of approximately 1.1 % in the P2 wave. The influence of gravity exhibits a positive correlation with excitation frequency, and demonstrates pronounced sensitivity to both the pore-fluid mixture properties and the soil texture. The critical mechanism deriving these physical behaviors is primarily attributed to the relative mobilities of the pore fluids. Our results, for the first time, extend the quantitative investigate of gravitational impacts from surface waves in saturated porous media to dilatational waves under unsaturated conditions, thereby underscoring their broader applicability. These findings highlight the significant and multifaceted role of gravity in interpreting compressional wave signatures within complex, fluid-bearing porous media.