We study unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in variably saturated porous media, here modeled by a non-linear extension of Biot’s well-known quasi-static consolidation model. The coupled elliptic-parabolic system of partial differential equations is a simplified version of the general model for multi-phase flow in deformable porous media, obtained under similar assumptions as usually considered for Richards’ equation. In this work, existence of weak solutions is established in several steps involving a numerical approximation of the problem using a physically-motivated regularization and a finite element/finite volume discretization. Eventually, solvability of the original problem is proved by a combination of the Rothe and Galerkin methods, and further compactness arguments. This approach in particular provides the convergence of the numerical discretization to a regularized model for unsaturated poroelasticity. The final existence result holds under non-degeneracy conditions and natural continuity properties for the constitutive relations. The assumptions are demonstrated to be reasonable in view of geotechnical applications.
Keywords: Poroelasticity, Biot model, variably saturated porous media, Richards’ equation
@article{M2AN_2021__55_6_2849_0,
author = {Both, Jakub Wiktor and Pop, Iuliu Sorin and Yotov, Ivan},
title = {Global existence of weak solutions to unsaturated poroelasticity},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2849--2897},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/m2an/2021063},
mrnumber = {4344860},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021063/}
}
TY - JOUR AU - Both, Jakub Wiktor AU - Pop, Iuliu Sorin AU - Yotov, Ivan TI - Global existence of weak solutions to unsaturated poroelasticity JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2849 EP - 2897 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021063/ DO - 10.1051/m2an/2021063 LA - en ID - M2AN_2021__55_6_2849_0 ER -
%0 Journal Article %A Both, Jakub Wiktor %A Pop, Iuliu Sorin %A Yotov, Ivan %T Global existence of weak solutions to unsaturated poroelasticity %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2849-2897 %V 55 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021063/ %R 10.1051/m2an/2021063 %G en %F M2AN_2021__55_6_2849_0
Both, Jakub Wiktor; Pop, Iuliu Sorin; Yotov, Ivan. Global existence of weak solutions to unsaturated poroelasticity. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2849-2897. doi: 10.1051/m2an/2021063
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