Abstract
Poroelasticity theory can be used to analyse the coupled interaction between fluid flow and porous media (matrix) deformation. The classical theory of linear poroelasticity captures this coupling by combining Terzaghi’s effective stress with a linear continuity equation. Linear poroelasticity is a good model for very small deformations; however, it becomes less accurate for moderate to large deformations. On the other hand, the theory of large-deformation poroelasticity combines Terzaghi’s effective stress with a nonlinear continuity equation. In this paper, we present a finite element solver for linear and nonlinear poroelasticity problems on triangular meshes based on the displacement-pressure two-field model. We then compare the predictions of linear poroelasticity with those of large-deformation poroelasticity in the context of a two-dimensional model problem where flow through elastic, saturated porous media, under applied mechanical oscillations, is considered. In addition, the impact of introducing a deformation-dependent permeability according to the Kozeny-Carman equation is explored. We computationally show that the errors in the displacement and pressure fields that are obtained using the linear poroelasticity are primarily due to the lack of the kinematic nonlinearity. Furthermore, the error in the pressure field is amplified by incorporating a constant permeability rather than a deformation-dependent permeability.
Highlights
A saturated porous medium is composed of a porous solid material, fully saturated by a viscous fluid, flowing through connected pores
In the last few decades, the mechanics of porous media has been of great interest due to its potential application in many geological and biological systems across a wide range of scales such as civil engineering [7, 13, 20, 21, 32, 40, 43, 45], energy and environmental technologies [14, 17, 26, 37, 39, 51], material science [29] and biophysics [18, 30], where poromechanics plays an important role in modelling bones and soft tissues [1, 15, 41]
We propose finite element methods for the resolution of the governing equations both in the theory of linear poroelasticity as in the largedeformation poroelasticity
Summary
A saturated porous medium is composed of a porous solid material, fully saturated by a viscous fluid, flowing through connected pores. In deformable porous materials such as soils, rocks and tissues, the flow of the pore fluid and the deformation of the solid matrix are tightly coupled to each other. In the last few decades, the mechanics of porous media has been of great interest due to its potential application in many geological and biological systems across a wide range of scales such as civil engineering [7, 13, 20, 21, 32, 40, 43, 45], energy and environmental technologies [14, 17, 26, 37, 39, 51], material science [29] and biophysics [18, 30], where poromechanics plays an important role in modelling bones and soft tissues [1, 15, 41]. Therein, we include dynamic effects, especially a time and space dependent porosity and permeability
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