Homogenization Approach of Advection and Diffusion in Cracked Porous Material

Dormieux, Luc; Lemarchand, Éric

doi:10.1061/(asce)0733-9399(2001)127:12(1267)

Cited by 52 publications

(33 citation statements)

References 8 publications

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“…Inside the RVE, microscopic ionic fluxes j fulfill the mass conservation law (Dormieux and Lemarchand 2001) …”

Section: Representative Volume Element For Diffusive Transport In Cemmentioning

confidence: 99%

“…It is suitable to assign, to the test function, the nature of a "virtual concentration"; namely when defining boundary conditions for the RVE. Following (Dormieux and Lemarchand 2001), we prescribe "microscopic" concentrations at the boundary of the RVE of cement paste, which are compatible with a homogeneous "macroscopic" concentration gradient GRAD C; this reads mathematically as…”

Section: Representative Volume Element For Diffusive Transport In Cemmentioning

confidence: 99%

“…Notably, Eq. (7) considers that no fluxes occur in the solid phase, see also (Dormieux and Lemarchand 2001). Transport in the pores is governed by Fick's first law of diffusion, reading in a phase-specific format as…”

Section: Representative Volume Element For Diffusive Transport In Cemmentioning

confidence: 99%

“…(16); and b the porosity-dependent ratio of D hom paste to d pore , comparing the self-consistent homogenization scheme resulting in Eq. (16), on the differential homogenization scheme by Dormieux and Lemarchand (2001), and on the self-consistent bispherical model of Hashin (1968) gives, by comparing Eqs. (13) and (14), finally access to the macroscopic diffusivity tensor D hom paste :…”

Section: Figmentioning

confidence: 99%

“…In this context, repeated inclusion of infinitely small solid spheres into a repeatedly homogenized diffusive medium, as is customarily done in the so-called differential schemes (Dormieux and Lemarchand 2001), proposes that the isotropic diffusivity of cement paste depends on the (capillary) fluid volume fraction to the power of 1.5, times the chloride diffusivity of the pore solution. This allows for translating experimental data obtained from cement paste specimens with different mixtures into one "universal" chloride diffusivity of the cement paste pore solution, d pore = 1.07 × 10 −10 m 2 /s (Pivonka et al 2004).…”

Section: Introductionmentioning

confidence: 99%

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Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

et al. 2017

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Chloride ingress into concrete is a major cause for material degradation, such as cracking due to corrosion-induced steel reinforcement expansion. Corresponding transport processes encompass diffusion, convection, and migration, and their mathematical quantification as a function of the concrete composition remains an unrevealed enigma. Approaching the problem step by step, we here concentrate on the diffusivity of cement paste, and how it follows from the microstructural features of the material and from the chloride diffusivity in the capillary pore spaces. For this purpose, we employ advanced self-consistent homogenization theory as recently used for permeability upscaling, based on the resolution of the pore space as pore channels being oriented in all space directions, resulting in a quite compact analytical relation between porosity, pore diffusivity, and the overall diffusivity of the cement paste. This relation is supported by experiments and reconfirms the pivotal role that layered water most probably plays for the reduction of the pore diffusivity, with respect to the diffusivity found under the chemical condition of a bulk solution.Keywords Diffusion · Homogenization · Chlorides · Multiscale modeling · Layered water List of Symbols Mathematical operators divDivergence operator, applied to a vector field div Divergence operator, applied to a second-order tensor field grad Gradient operator on the microscopic observation scale of pore space

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“…Inside the RVE, microscopic ionic fluxes j fulfill the mass conservation law (Dormieux and Lemarchand 2001) …”

Section: Representative Volume Element For Diffusive Transport In Cemmentioning

confidence: 99%

Section: Representative Volume Element For Diffusive Transport In Cemmentioning

confidence: 99%

Section: Representative Volume Element For Diffusive Transport In Cemmentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

et al. 2017

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Computational Concrete Mechanics

Lackner

Mang

Pichler

2004

Encyclopedia of Computational Mechanics

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This chapter contains a report on recent developments in the field of computational concrete mechanics, introducing the multiscale concept for the simulation of cement‐based materials and, in the case of reinforced concrete (RC), of the steel–concrete interaction. In this concept, several scales of observation may be considered simultaneously in the numerical analysis. Alternatively, material properties, which serve as input for macroscopic analyses, are related to properties of material phases and their assemblage at finer scales of observation. The benefits of multiscale approaches in computational concrete mechanics are illustrated by two analyses of real‐life structures employing macroscopic material properties for plain and reinforced concrete related to finer scales of observation.

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Computational Concrete Mechanics

Lackner

Pichler

Traxl

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This chapter contains a report on recent developments in the field of computational concrete mechanics, introducing the multiscale concept for simulation of cement‐based materials and, in case of reinforced concrete Reinforced Concrete (RC), of the steel–concrete interaction. Within the framework of this concept, several scales of observation are considered simultaneously in the numerical analysis. Alternatively, material properties, which serve as input for macroscopic analyses, are related to properties of the material phases and their assemblage at finer scales of observation. The benefits of multiscale approaches in computational concrete mechanics are illustrated by the analysis of real‐life structures subjected to various loading conditions, including mechanical loading and thermal and chemical attacks. Macroscopic material properties for plain and reinforced concrete that are related to finer scales of observation are employed.

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Homogenization Approach of Advection and Diffusion in Cracked Porous Material

Cited by 52 publications

References 8 publications

Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

Computational Concrete Mechanics

Computational Concrete Mechanics

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