<p>This study presents a reduced-order modelling framework for three-phase consolidation in partially saturated porous media using the Theory of Porous Media (TPM). A thermodynamically consistent three-phase high-fidelity model, accounting for a deformable solid skeleton, incompressible liquid water, and a compressible gas phase with van Genuchten-type capillary pressure and ideal-gas behaviour, is first formulated in two dimensions. Exploiting the slenderness of the domain, the governing equations are nondimensionalized and systematically reduced via asymptotic expansion with respect to the aspect ratio, leading to a ternary reduced system composed of a longitudinal limit problem and a transverse corrector problem. In contrast to existing thin-domain asymptotic reductions, which typically address single-pressure two-phase flow or saturated poroelasticity, the proposed limit-corrector structure preserves the coupled evolution of liquid and gas pressures, saturation, and solid deformation in a fully three-phase setting. Numerical simulations in FEniCSx compare the reduced model with the full 2D TPM formulation for representative partially saturated consolidation scenarios. The limit model reproduces settlement and pore-pressure responses with deviations below 3% in key regions while reducing CPU time by more than 25–40%, and the corrector problem recovers transverse mechanical effects that are absent in the pure limit formulation. The work complements recent developments in physics-informed and data-driven reduced-order modelling for poromechanics and porous media flow by providing an asymptotically justified three-phase TPM backbone that can be coupled with machine-learning-based correction strategies in future hybrid multiscale frameworks.</p>

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Asymptotic reduction modelling for partially saturated soil based on the Theory of Porous Media

  • Firat Araz,
  • Seyed Morteza Seyedpour,
  • Tim Ricken,
  • Alaa Armiti-Juber

摘要

This study presents a reduced-order modelling framework for three-phase consolidation in partially saturated porous media using the Theory of Porous Media (TPM). A thermodynamically consistent three-phase high-fidelity model, accounting for a deformable solid skeleton, incompressible liquid water, and a compressible gas phase with van Genuchten-type capillary pressure and ideal-gas behaviour, is first formulated in two dimensions. Exploiting the slenderness of the domain, the governing equations are nondimensionalized and systematically reduced via asymptotic expansion with respect to the aspect ratio, leading to a ternary reduced system composed of a longitudinal limit problem and a transverse corrector problem. In contrast to existing thin-domain asymptotic reductions, which typically address single-pressure two-phase flow or saturated poroelasticity, the proposed limit-corrector structure preserves the coupled evolution of liquid and gas pressures, saturation, and solid deformation in a fully three-phase setting. Numerical simulations in FEniCSx compare the reduced model with the full 2D TPM formulation for representative partially saturated consolidation scenarios. The limit model reproduces settlement and pore-pressure responses with deviations below 3% in key regions while reducing CPU time by more than 25–40%, and the corrector problem recovers transverse mechanical effects that are absent in the pure limit formulation. The work complements recent developments in physics-informed and data-driven reduced-order modelling for poromechanics and porous media flow by providing an asymptotically justified three-phase TPM backbone that can be coupled with machine-learning-based correction strategies in future hybrid multiscale frameworks.