Theory of flow and deformation of swelling porous materials at the macroscale

Schreyer-Bennethum, Lynn

doi:10.1016/j.compgeo.2007.02.003

Cited by 24 publications

(7 citation statements)

References 48 publications

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“…J. Larsson and R. Larsson, [14] researched the problem of coupled deformation and fluid diffusion in porous media based on the elastic-plastic solid theory. SchreyerBennethum [15] developed a theoretical foundation for flow and deformation in a highly interacting porous media, assuming that the porous material consists of a solid phase and liquid phase. Khoshghalb and Khalili [16] proposed a fully coupled meshfree algorithm to simulate the flow-deformation analysis of saturated porous media.…”

Section: Introductionmentioning

confidence: 99%

Study of the effects of stress sensitivity on the permeability and porosity of fractal porous media

Tan

Liu

et al. 2015

Physics Letters A

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Section: Introductionmentioning

confidence: 99%

Study of the effects of stress sensitivity on the permeability and porosity of fractal porous media

Tan

Liu

et al. 2015

Physics Letters A

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“…This paper considers a general quasi-static model of linear poroelasticity which is broad enough to contain the well-known Biot's consolidation model from soil mechanics (cf. [19,21]) and the Doi's model for polymer gels (cf. [11,26]).…”

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confidence: 99%

Analysis of a multiphysics finite element method for a poroelasticity model

Feng

2017

IMA Journal of Numerical Analysis

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This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To better describe the multiphysics process of deformation and diffusion for poro-elastic materials, we first present a reformulation of the original model by introducing two pseudo-pressures, one of them is shown to satisfy a diffusion equation, we then propose a time-stepping algorithm which decouples (or couples) the reformulated PDE problem at each time step into two sub-problems, one of which is a generalized Stokes problem for the displacement vector field (of the solid network of the poro-elastic material) along with one pseudo-pressure field and the other is a diffusion problem for the other pseudo-pressure field (of the solvent of the material). To make this multiphysics approach feasible numerically, two critical issue must be resolved: the first one is the uniqueness of the generalized Stokes problem and the other is to find a good boundary condition for the diffusion equation so that it also becomes uniquely solvable. To address the first issue, we discover certain conserved quantities for the PDE solution which provide ideal candidates for a needed boundary condition for the pseudo-pressure field. The solution to the second issue is to use the generalized Stokes problem to generate a boundary condition for the diffusion problem. A practical advantage of the time-stepping algorithm allows one to use any convergent Stokes solver (and its code) together with any convergent diffusion equation solver (and its code) to solve the poroelasticity model. In the paper, the Taylor-Hood mixed finite element method combined with the P 1 -conforming finite element method is used as an example to demonstrate the viability of the proposed multiphysics approach. It is proved that the solutions of the fully discrete finite element methods fulfill a discrete energy law which mimics the differential energy law satisfied by the PDE solution and converges optimally in the energy norm. Moreover, it is showed that the proposed formulation also has a built-in mechanism to overcome so-called "locking phenomenon" associated with the numerical approximations of the poroelasticity model. Numerical experiments are presented to show the performance of the proposed approach and methods and to demonstrate the absence of "locking phenomenon" in our numerical experiments. The paper also presents a detailed PDE analysis for the poroelasticity model, especially, it is proved that this model converges to the well-known Biot's consolidation model from soil mechanics as the constrained specific storage coefficient tends to zero. As a result, the proposed approach and methods are robust under such a limit process.

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“…Over the past two decades, numerous eforts have been devoted to developing general theoretical frameworks for modeling multiphase and multispecies porous media. Among these, we mention the biological tissues-oriented theory of porous media developed by Huyghe and his coworkers (Huyghe and Janssen, 1997;Huyghe et al, 2004Huyghe et al, , 2007 and the hybrid theory of swelling porous media (Bennethum and Cushman, 1996a,b;2002a,b;Bennethum et al, 1996Bennethum et al, , 2000Bennethum, 2007Bennethum, , 2012. hrough these eforts, general macroscopic governing equations have been developed that can be used to address the physicochemical and electrochemical coupling in multiphasic and multispecies systems.…”

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confidence: 99%

A Theoretical Framework for Modeling the Chemomechanical Behavior of Unsaturated Soils

Wei

2014

Vadose Zone Journal

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A theoretical framework is presented for modeling the chemomechanical behavior of multiphase porous media, in general, and unsaturated soils, in particular, which can address skeletal deformation, fluid flow, heat conduction, solute diffusion, chemical reaction, and phase transition in a consistent and systematic way. A general expression is derived for the electrochemical potential of a fluid species with explicitly accounting for the effects of osmosis, capillarity, and adsorption. The equilibrium behavior of porous media is investigated, and the composition of pore water pressure is identified. Explicit formulations are developed for the effective stress and intergranular stress, with consideration of physicochemical effects. It is shown that the negative water pressure measured by a conventional transducer can be significantly different than the true pore water pressure. It is also theoretically revealed that, other than the soil water characteristic function, a new pressure (or potential) function accounting for the physicochemical effects is generally required in analyzing the coupled chemomechanical processes in unsaturated soils. The new theory is capable of effectively explaining many salient phenomena occurring in water-saturated porous media with a degree of saturation varying from an extremely low value to 100%, including Donnan osmosis, capillary fringe, air entry value, initial hydraulic head during seepage, and pressure solution. The new theory can be used to analyze the multiple coupled physical and chemical processes in the vadose zone.Abbreviations: AEV, air entry value; PWP, pore water pressure; REV, representative volume.Chemomechanical behavior of porous media with multiphases and multispecies is of great interest in many diverse fields of science and engineering. To mention a few, this includes the industries of nuclear, hazardous, and municipal waste isolation; petroleum and gas extraction; technologies of methane gas hydrates exploitation; CO 2 sequestration; and weak soil reinforcement, landform stability assessment, structural material durability, and weathering of rock masses. Understanding, controlling, and predicting the long-term effect of physicochemical processes on the mechanical performance of geomaterials is becoming an indispensable part of environmental impact assessment and performance assessment analysis. Thus, there is a clear need to develop comprehensive chemohydromechanical mathematical modeling capacities that are able to address realistically the reactive multispecies transport, multiphase flow, chemical reaction, phase transition, chemically induced deformation, and other related physicochemical processes in deformable soils.The coupling of multiple processes in porous media, including skeletal deformation, seepage, diffusion, and heat conduction, has been extensively investigated, and the poromechanic theory that is capable of describing these coupled physical processes has been very well developed (e.g., Coussy, 2004). Thus far, however, the behavior of porous medi...

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Theory of flow and deformation of swelling porous materials at the macroscale

Cited by 24 publications

References 48 publications

Study of the effects of stress sensitivity on the permeability and porosity of fractal porous media

Study of the effects of stress sensitivity on the permeability and porosity of fractal porous media

Analysis of a multiphysics finite element method for a poroelasticity model

A Theoretical Framework for Modeling the Chemomechanical Behavior of Unsaturated Soils

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