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 :
- 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, %
RECHARD R P, WILSON M L, SEVOUGIAN S D. Progression of performance assessment modeling for the Yucca Mountain disposal system for spent nuclear fuel and high-level radioactive waste [J]. Reliability Engineering and System Safety, 2014, 122: 96–123.
TSANG C F, BARNICHON J D, BIRKHOLZER J, et al. Coupled thermo-hydro-mechanical processes in the near field of a high-level radioactive waste repository in clay formations [J]. International Journal of Rock Mechanics and Mining Sciences, 2012, 49: 31–44.
WERSIN P, BIRGERSSON M. Reactive transport modelling of iron-bentonite interaction within the KBS-3H disposal concept: The Olkiluoto site as a case study [J]. Geological Society, London, Special Publications, 2014, 400(1): 237–250.
CUI S L, ZHANG H Y, ZHANG M. Swelling characteristics of compacted GMZ bentonite-sand mixtures as a buffer/backfill material in China [J]. Engineering Geology, 2012, 141/142: 65–73.
REID C, LUNN R, El MOUNTASSIR G, et al. A mechanism for bentonite buffer erosion in a fracture with a naturally varying aperture [J]. Mineralogical Magazine, 2015, 79(6): 1485–1494.
PUSCH R. Use of bentonite for isolation of radioactive waste products [J]. Clay Minerals, 1992, 27(3): 353–361.
RADHAKRISHNA H S, CHAN H T, CRAWFORD A M, et al. Thermal and physical properties of candidate buffer-backfill materials for a nuclear fuel waste disposal vault [J]. Canadian Geotechnical Journal, 1989, 26(4): 629–639.
XU Y F, SUN D A, YAO Y P. Surface fractal dimension of bentonite and its application to determination of swelling properties [J]. Chaos, Solitons and Fractals, 2004, 19(2): 347–356.
MOKNI N, BARNICHON J D, DICK P, et al. Effect of technological macro voids on the performance of compacted bentonite/sand seals for deep geological repositories [J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 88: 87–97.
YONG R N, BOONSINSUK P, WONG G. Formulation of backfill material for a nuclear fuel waste disposal vault [J]. Canadian Geotechnical Journal, 1986, 23(2): 216–228.
PUSCH R. Highly compacted sodium bentonite for isolating rock-deposited radioactive waste products [J]. Nuclear Technology, 1979, 45(2): 153–157.
KOMINE H, OGATA N. Predicting swelling characteristics of bentonites [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2004, 130(8): 818–829.
XU Y F, MATSUOKA H, SUN D A. Swelling characteristics of fractal-textured bentonite and its mixtures [J]. Applied Clay Science, 2003, 22(4): 197–209.
ALAWAJI H A. Swell and compressibility characteristics of sand-bentonite mixtures inundated with liquids [J]. Applied Clay Science, 1999, 15(3/4): 411–430.
ZHANG F, YE W M, CHEN Y G, et al. Influences of salt solution concentration and vertical stress during saturation on the volume change behavior of compacted GMZ01 bentonite [J]. Engineering Geology, 2016, 207: 48–55.
TANAI K, MATSUMOTO K. A study on extrusion behavior of buffer material into fractures using X-ray CT method [R]. Ibaraki-ken, Japan: Japan Atomic Energy Agency, 2008.
TANAI K, MATSUMOTO K. A study of extrusion behavior of buffer material into fractures [J]. Science & Technology Series, 2008, 334: 57–64.
MATSUMOTO K, FUJITA T. Extrusion and erosion of bentonite buffer (III) [R]. Ibaraki-ken, Japan: Japan Atomic Energy Agency, 2011.
MISSANA T, ALONSO U, ALBARRAN N, et al. Analysis of colloids erosion from the bentonite barrier of a high level radioactive waste repository and implications in safety assessment [J]. Physics and Chemistry of the Earth, Parts A/B/C, 2011, 36(17/18): 1607–1615.
KOMINE H, OGATA N. Prediction for swelling characteristics of compacted bentonite [J]. Canadian Geotechnical Journal, 1996, 33(1): 11–22.
KOMINE H, DE OGATA N. Experimental study on swelling characteristics of sand-bentonite mixture for nuclear waste disposal [J]. Soils and Foundations, 1999, 39(2): 83–97.
KOMINE H, OGATA N. New equations for swelling characteristics of bentonite-based buffer materials [J]. Canadian Geotechnical Journal, 2003, 40: 460–475.
BORRELLI R A, AHN J. Numerical modeling of bentonite extrusion and radionuclide migration in a saturated planar fracture [J]. Physics and Chemistry of the Earth, Part A/B/C, 2008, 33: S131–S141.
LIU L C, MORENO L, NERETNIEKS I. A dynamic force balance model for colloidal expansion and its DLVO-based application [J]. Langmuir, 2009, 25(2): 679–687.
LIU L C, MORENO L, NERETNIEKS I. A novel approach to determine the critical coagulation concentration of a colloidal dispersion with plate-like particles [J]. Langmuir, 2009, 25(2): 688–697.
PUSCH R. Stability of bentonite gels in crystalline rock—physical aspects [R]. Stockholm, Sweden: Swedish Nuclear Fuel and Waste Management Co., 1983.
PUSCH R. Clay colloids formation and release from MX-80 buffer [R]. Stockholm, Sweden: Swedish Nuclear Fuel and Waste Management Co., 1999.
PUSCH R. Microstructural evolution of buffers [J]. Engineering Geology, 1999, 54(1/2): 33–41.
SJÖBLOM R, KALBANTNER P, BJURSTRÖ M H, et al. Application of the general microstructural model to erosion phenomena — mechanisms for the chemical-hydrodynamic conversion of bentonite to a pumpable slurry in conjunction with retrieval [J]. Engineering Geology, 1999, 54(1/2): 109–116.
BAIK M H, CHO W J, HAHN P S. Erosion of bentonite particles at the interface of a compacted bentonite and a fractured granite [J]. Engineering Geology, 2007, 91: 229–239.
MORENO L, LIU L C, NERETNIEKS I. Erosion of sodium bentonite by flow and colloid diffusion [J]. Physics and Chemistry of the Earth, Parts A/B/C, 2011, 36(17/18): 1600–1606.
DAKSHANAMURTHY V. A New method to predict swelling using a hyperbolic equation [J]. Geotechnical Engineering, 1978, 9: 29–38.
CHAPUIS R P, AUBERTIN M. On the use of the Kozeny-Carman equation to predict the hydraulic conductivity of soils [J]. Canadian Geotechnical Journal, 2003, 40(4): 616–628.
KOMINE H. Predicting hydraulic conductivity of sand-bentonite mixture backfill before and after swelling deformation for underground disposal of radioactive wastes [J]. Engineering Geology, 2010, 114(3/4): 123–134.
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). https://doi.org/10.1007/s12204-021-2268-6
- free swell
- TU 443