Transport in Porous Media

, Volume 69, Issue 2, pp 189–213 | Cite as

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

  • Guangjing ChenEmail author
  • Domenico Gallipoli
  • Alberto Ledesma
Original Paper


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.


Chemical osmosis Chemical consolidation Radioactive waste repository Poroelastic Chemical concentration 


Latin symbols


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

Boundary chemical concentration


Chemical concentration


Initial chemical concentration


Effective coefficient of diffusion of solute in pore fluid


Non-advective flux of solute

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

Coefficient of hydraulic permeability

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

Coefficient of osmotic permeability


Solute molar mass


Coefficient of compressibility associated to a change of effective mean stress


Coefficient of compressibility associated to a change of osmotic pressure




Initial porosity

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

Boundary pore fluid pressure


Pore fluid pressure


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


Radial coordinate


Electrostatic repulsive minus attractive stress


Absolute temperature


Radial displacement

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

Flux of solid phase


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


Shear modulus


Poisson’s ratio


Osmotic pressure


Density of the pore fluid

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

Total radial stress

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

Total tangential stress

\({\sigma _\ast }\)

Total mean stress


Osmotic efficiency


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Guangjing Chen
    • 1
    Email author
  • Domenico Gallipoli
    • 2
  • Alberto Ledesma
    • 1
  1. 1.Department of Geotechnical Engineering and GeosciencesTechnical University of CataloniaBarcelonaSpain
  2. 2.School of EngineeringDurham UniversityDurhamUK

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