Effective transfer properties of partially saturated geomaterials with interfaces using the immersed interface method

Do, Duc-Phi; Hoxha, Dashnor

doi:10.1002/nag.2187

Cited by 8 publications

(12 citation statements)

References 32 publications

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“…Several expressions for the effective stress σ have been proposed in the literature. Many of them have brought substantial progress in micromechanical modeling beyond mixture theories [24,29,30,40,41,65,95]. Each expression has its own origin and merits, and, accordingly, some differences in the form of the effective stress exist.…”

Section: Theorymentioning

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: Theorymentioning

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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“…xy τ � c (c) xy τ . (25) Note that ε (a) xx , ε (a) yy , and ε (b) xx , ε (b) yy designate the averaged normal and lateral strain under uniaxial stress in x and y directions correspondingly, while ε (c) xy indicates the average shear strain under pure stress loading.…”

Section: Methodology For the Determination Of The Effective Elasticmentioning

confidence: 99%

“…In the numerical simulations, all terms on the right-hand side of Equation (25), except for K x and K y , are specified, while the steady flow rate Q x and Q y are calculated numerically. us, K x and K y can be back calculated.…”

Section: Methodology For the Determination Of The Effectivementioning

confidence: 99%

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Effective Elastic and Hydraulic Properties of Fractured Rock Masses with High Contrast of Permeability: Numerical Calculation by an Embedded Fracture Continuum Approach

Dang

Hoxha

2019

Advances in Civil Engineering

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In this work, the hydromechanical modeling of the fractured rock masses was conducted based on a new numerical simulation method named as embedded fracture continuum (EFC) approach. As the principal advantage, this approach allows to simplify the meshing procedure by using the simple Cartesian meshes to model the fractures that can be explicitly introduced in the porous medium based on the notion of fracture cells. These last elements represent the grid cells intersected by at least one fracture in the medium. Each fracture cell in the EFC approach present a continuum porous medium whose hydromechanical properties are calculated from ones of the matrix and ones of the intersected fractures, thanks for using the well-known solution of the joint model. The determination of the hydromechanical properties of the fracture cells as presented in this work allows to provide the theoretical base and to complete some simple approximations introduced in the literature. Through different verification tests, the capability of the developed EFC approach to model the hydromechanical behavior of fractured rock was highlighted. An analysis of different parameters notably the influence of the fracture cell size on the precision of the proposed approach was also conducted. This novel approach was then applied to investigate the effective permeability and elastic compliance tensor of a fractured rock masses taken from a real field, the Sellafield site. The comparison of the results calculated from this approach with ones conducted in the literature based on the distinct element code (UDEC) presents a good agreement. However, unlike the previous studies using UDEC, which limits only in the case of fractured rock masses without dead-end fractures, our approach allows accounting for this kind of fractures in the medium. The numerical simulations show that the dead-end fractures could have a considerable contribution on the effective compliance moduli, while their effect can be neglected to calculate the overall permeability of the of fractured rock masses.

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“…In a previous work of the present authors [18], the IIM was used to take into account the interfacial resistance between linear constituent phases. In this context, the IIM allows calculating the effective transfer properties and enables demonstrating the role of various factors such as shape, size, spatial distribution, and volume fraction of constituents as well as their properties of constituents and those of interface on overall effective properties.…”

Section: Introductionmentioning

confidence: 99%

Temperature and Pressure Dependence of the Effective Thermal Conductivity of Geomaterials: Numerical Investigation by the Immersed Interface Method

Hoxha

2013

Journal of Applied Mathematics

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The present work aims to study the nonlinear effective thermal conductivity of heterogeneous composite-like geomaterials by using a numerical approach based on the immersed interface method (IIM). This method is particularly efficient at solving the diffusion problem in domains containing inner boundaries in the form of perfect or imperfect interfaces between constituents. In this paper, this numerical procedure is extended in the framework of non linear behavior of constituents and interfaces. The performance of the developed tool is then demonstrated through the studies of temperature- and pressure-dependent effective thermal conductivity of geomaterials with imperfect interfaces.

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Effective transfer properties of partially saturated geomaterials with interfaces using the immersed interface method

Cited by 8 publications

References 32 publications

Stabilized mixed finite elements for deformable porous media with double porosity

Stabilized mixed finite elements for deformable porous media with double porosity

Effective Elastic and Hydraulic Properties of Fractured Rock Masses with High Contrast of Permeability: Numerical Calculation by an Embedded Fracture Continuum Approach

Temperature and Pressure Dependence of the Effective Thermal Conductivity of Geomaterials: Numerical Investigation by the Immersed Interface Method

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