Finite Deformation and Fluid Flow in Unsaturated Soils with Random Heterogeneity

Song, Xiaoyu; Borja, Ronaldo I.

doi:10.2136/vzj2013.07.0131

Cited by 62 publications

(31 citation statements)

References 72 publications

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“…To focus on the topic at hand, namely, stabilization, we shall limit the solid behavior to linear elasticity in the infinitesimal setting. A modeling framework for elastoplastic double porosity materials in the finite deformation range, such as those developed for single porosity problems in [2,14,16,76,77], will be presented in future publications.…”

Section: Introductionmentioning

confidence: 99%

Stabilized mixed finite elements for deformable porous media with double porosity

Choo

Borja

2015

Computer Methods in Applied Mechanics and Engineering

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Natural geomaterials such as fissured rocks and aggregated soils often exhibit a pore size distribution with two dominant pore scales, usually termed macropores and micropores. High-fidelity descriptions of these materials require an explicit treatment of the two pore regions as double porosity. In this paper, we present stabilized mixed finite elements for coupled flow and deformation in porous media with double porosity based on a thermodynamically consistent modeling framework. Mixed finite elements that interpolate the solid displacement and pore pressures in the macropores and micropores are used for this purpose. In the limit of undrained deformation, the two pore pressures become incompressibility constraints that cause an inf-sup instability in the form of spurious oscillation at the two pore scales. To circumvent this instability we develop a variant of the polynomial pressure projection technique for a twofold saddle point problem. The proposed stabilization allows the use of equal-order (linear) interpolations of the displacement and two pore pressure variables throughout the entire range of drainage condition.

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Section: Introductionmentioning

confidence: 99%

Stabilized mixed finite elements for deformable porous media with double porosity

Choo

Borja

2015

Computer Methods in Applied Mechanics and Engineering

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“…This endeavor has been hindered by the fact that unsaturated soil is a complex, multi-phase mixture whose physical attributes vary drastically with varying mositure and soil particle size [16][17][18]. It has been well recognized that geomaterials are prone to discontinuous material response such as shear bands or cracks that can be triggered by spatial heterogeneities in density [19,20] and matric suction [21] as well as changes in temperature [22]. As water escapes the pore space through evaporation, very high negative pore water pressure (suction) can develop through the formation of water menisci between soil grains [23,24].…”

Section: Introductionmentioning

confidence: 99%

Coupled Analysis of Desiccation Cracking in Unsaturated Soils through a Non-Local Mathematical Formulation

Menon

Song

2019

Geosciences

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The formation of desiccation cracks in unsaturated soils as a discontinuity phenomenon can compromise the integrity of civil infrastructure on unsaturated soils. Because of the singularity at such discontinuities, the mathematical modeling of desiccation cracking is challenging. In this study, we apply a coupled nonlocal peridynamic poroelastic framework to model desiccation cracking in unsaturated soils. The soil skeleton is modeled by a nonlocal peridynamic elastic solid. A peridynamic equivalence of the generalized Darcy’s law is utilized to model unsaturated fluid flow. Cracking is determined by a critical stretch criterion between material points as well as an energy criterion. We present numerical simulations of desiccation cracking in soil bars and thin soil discs for one-dimensional cracking and two-dimensional cracking networks, respectively. The numerical results have demonstrated that the proposed nonlocal mathematical framework is a promising and robust method for modeling desiccation cracking in unsaturated soils.

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“…The continuous Galerkin (CG) finite element method, along with a total Lagrangian or an updated Lagrangian approach, is the most widely used method for the simulation of large deformations in solids. As such, the majority of the existing work on large deformation poromechanics has developed and used CG finite element methods for discretization of the fluid flow (mass balance) equation as well as the solid deformation (linear momentum balance) equation . The resulting mixed CG finite elements can provide faithful numerical solutions for many problems.…”

Section: Introductionmentioning

confidence: 99%

Large deformation poromechanics with local mass conservation: An enriched Galerkin finite element framework

Choo

2018

Numerical Meth Engineering

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Numerical modeling of large deformations in fluid-infiltrated porous media must accurately describe not only geometrically nonlinear kinematics but also fluid flow in heterogeneously deforming pore structure. Accurate simulation of fluid flow in heterogeneous porous media often requires a numerical method that features the local (elementwise) conservation property. Here, we introduce a new finite element framework for locally mass conservative solution of coupled poromechanical problems at large strains. At the core of our approach is the enriched Galerkin discretization of the fluid mass balance equation, whereby elementwise constant functions are augmented to the standard continuous Galerkin discretization. The resulting numerical method provides local mass conservation by construction with a usually affordable cost added to the continuous Galerkin counterpart. Two equivalent formulations are developed using total Lagrangian and updated Lagrangian approaches. The local mass conservation property of the proposed method is verified through numerical examples involving saturated and unsaturated flow in porous media at finite strains. The numerical examples also demonstrate that local mass conservation can be a critical element of accurate simulation of both fluid flow and large deformation in porous media. KEYWORDS finite element method, enriched Galerkin method, poromechanics, large deformation, local mass conservation 66

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Finite Deformation and Fluid Flow in Unsaturated Soils with Random Heterogeneity

Cited by 62 publications

References 72 publications

Stabilized mixed finite elements for deformable porous media with double porosity

Stabilized mixed finite elements for deformable porous media with double porosity

Coupled Analysis of Desiccation Cracking in Unsaturated Soils through a Non-Local Mathematical Formulation

Large deformation poromechanics with local mass conservation: An enriched Galerkin finite element framework

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