Numerical Study of Sodium Bentonite Extrusion into a Planar Fracture


As a candidate buffer/backfill material for high-level radioactive waste geological repositories, bentonite has numerous favorable properties, such as low permeability, high expansibility, and a high sorption capacity for radionuclides. The radionuclide-isolating performance of a buffer is strongly influenced by its extrusion. In this study, the bentonite extrusion process is explored: its basic mechanism can be considered free swelling of the bentonite. A 2D extrusion model of bentonite that is based on the 1D free swelling model of bentonite is presented. A numerical method is proposed to investigate the extrusion process of Na-bentonite into fractures over time under no-seepage conditions based on the free swelling model. The influences of the electrolyte concentration and dry density on the extrusion depth and mass of the bentonite are discussed, and the distribution of montmorillonite inside the bentonite is analysed. The rationale of the proposed bentonite extrusion model is then illustrated in comparison with the results of the bentonite extrusion test.

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a :

Fracture aperture, mm

c :

Electrolyte concentration of the solution, mmol/L

f :

Friction coefficient, g/h

F s :

Resultant of the gravity of the particles and the floatage of the solution to the particles, N

m z :

Mass of the bentonite in the fracture, g

r :

Polar radius, mm

s :

Extrusion depth of bentonite, mm

t :

Time, h

β :

Proportion coefficient, mm/h1/2


Sum of energy of montmorillonite particles arising from thermal motion, van der Waals force and electrostatic force, J

θ :

Polar angle, (°)

ρ d :

Dry density of bentonite, g/cm3

ρ m :

Density of montmorillonite, g/cm3

ϕ :

Volume fraction of montmorillonite particles, %

ϕ 0 :

Initial volume fraction of the montmorillonite in the inner boundary, %

ϕ mb :

Volume fraction of the montmorillonite in the bentonite, %


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Corresponding author

Correspondence to Yongfu Xu 徐永福.

Additional information

Foundation item

the National Natural Science Foundation of China (Nos. 41630633 and 41877211)

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Liu, M., Li, X. & Xu, Y. Numerical Study of Sodium Bentonite Extrusion into a Planar Fracture. J. Shanghai Jiaotong Univ. (Sci.) (2021).

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Key words

  • bentonite
  • extrusion
  • buffer
  • free swell

CLC number

  • TU 443

Document code

  • A