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Chemo-hydro-mechanical coupled consolidation for a poroelastic clay buffer in a radioactive waste repository

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Abstract

Salt rock or rock with salty ground water are often encountered as host media for the underground disposal of radioactive waste. The nuclear waste, contained in a metallic canister, is usually placed inside a tunnel or a shaft excavated in the rock deposit together with a buffer of compacted bentonite inserted between the host rock and the canister to provide hydro-mechanical sealing. Due to the very low permeability and rich clay content, the bentonite acts as an osmotic semi-permeable membrane under a gradient of concentration of salt dissolved in the ground water. In addition, chemically induced expansion or shrinkage of the bentonite is generated by changes in the concentration of dissolved salt. By including such important chemical aspects, the hydro-mechanical governing equations are derived for this particular boundary value problem within the framework of a linear Biot-like isotropic poroelastic consolidation. The equations are solved analytically and a parametric study is undertaken to highlight the influence of chemical osmosis and chemical deformation on the flow and mechanical response of the bentonite buffer.

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Abbreviations

Latin symbols :

 

\({c_{{\rm b}\ast}}\) :

Boundary chemical concentration

\({c_{\ast}}\) :

Chemical concentration

\({c_{0\ast}}\) :

Initial chemical concentration

D * :

Effective coefficient of diffusion of solute in pore fluid

J * :

Non-advective flux of solute

\({{k^\prime}_{{\rm h}\ast}}\) :

Coefficient of hydraulic permeability

\({{k^\prime}_{\pi \ast }}\) :

Coefficient of osmotic permeability

M s :

Solute molar mass

m v :

Coefficient of compressibility associated to a change of effective mean stress

m π :

Coefficient of compressibility associated to a change of osmotic pressure

n :

Porosity

n 0 :

Initial porosity

\({p_{{\rm b}\ast } }\) :

Boundary pore fluid pressure

p * :

Pore fluid pressure

R :

Universal gas constant equal to 8.314 J/(K mol)

r * :

Radial coordinate

R−A:

Electrostatic repulsive minus attractive stress

T :

Absolute temperature

u * :

Radial displacement

\({v_{\ast}^{\rm s}}\) :

Flux of solid phase

v * :

Flux of pore fluid

\({v_{{\rm h}\ast}}\) :

Flux of pore fluid – component due to hydraulic pressure gradient

\({v_{\pi \ast}}\) :

Flux of pore fluid – component due to osmotic pressure gradient

\({v_{{\rm c}\ast} }\) :

Flux of solute

Greek symbols :

 

\({\alpha _\ast }\) :

Coefficient of linear strain associated to a change of chemical concentration

\({\varepsilon _{v} }\) :

Volumetric strain

γ l :

Unit weight of pore fluid

\({\xi _\ast }\) :

Relative change of pore fluid density associated to a change of chemical concentration

μ:

Shear modulus

ν:

Poisson’s ratio

π:

Osmotic pressure

ρ:

Density of the pore fluid

\({\sigma _{{\rm r}\ast } }\) :

Total radial stress

\({\sigma _{\theta \ast } }\) :

Total tangential stress

\({\sigma _\ast }\) :

Total mean stress

σ:

Osmotic efficiency

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Authors and Affiliations

  1. Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia, Barcelona, Spain

    Guangjing Chen & Alberto Ledesma

  2. School of Engineering, Durham University, Durham, UK

    Domenico Gallipoli

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  1. Guangjing Chen
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  2. Domenico Gallipoli
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  3. Alberto Ledesma
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Correspondence to Guangjing Chen.

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Chen, G., Gallipoli, D. & Ledesma, A. Chemo-hydro-mechanical coupled consolidation for a poroelastic clay buffer in a radioactive waste repository. Transp Porous Med 69, 189–213 (2007). https://doi.org/10.1007/s11242-006-9083-2

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  • DOI: https://doi.org/10.1007/s11242-006-9083-2

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