Skip to main content
Log in

Unsaturated permeability of Gaomiaozi bentonite under partially free-swelling conditions

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

In the deep geological disposal of high-level radioactive wastes (HLW), Na-bentonite produced from Gaomiaozi (GMZ) deposit has been selected as a possible buffer and backfill material for the Beishan repository in China. A sealing buffer is manufactured with bentonite at its hygroscopic water content (initially unsaturated). After taking water from the surrounding geological medium, bentonite under totally free condition is used to seal the technological voids, and then the outer surrounding bentonite (affected by the water mostly) compresses the innermost bentonite under partially free-swelling condition. However, permeability of GMZ bentonite under the partially free-swelling condition is still unknown. In this article, using the instantaneous profile method, we present a laboratory test of the GMZ bentonite unsaturated hydraulic conductivity under partially free-swelling condition. Changes in the cross-sectional area and motion of the sensors (to measure temperature and relative humidity) were considered in computing the unsaturated permeability. Our experimental results show that before the finial hydration stage, although permeability increases locally at some suctions (due to saturation degree increase and bentonite swelling to some extent), unsaturated permeabilities decrease and become constant in general for the reasons as follows. Initially, water is tightly adsorbed to the clay sheet surface and then water film is adsorbed to the tightly adsorbed water which leads to the initial highest permeability, and then diffuse double-layer forces lead to water uptake between the hydrated montmorillonite unit layers which is partially restricted by the confining stress, while capillary water flows on the water adsorbed on the internal surface of the bentonite large pores. For the capillary water flow due to surface tension, complex microstructure evolution (e.g., mesoscopic swelling compacts the inter-aggregate pores due to hydration under the confining stress from the rubber tube) before the finial hydration stage leads to flux decrease if under a certain hydraulic gradient (i.e., permeability decreases). Results show that in the final hydration stage, permeability increases rapidly with decreasing suction, because large pore compacting is complete while saturation degree increases and bentonite swells to some extent. Results show that at the same suctions, the unsaturated permeabilities located at the sensor closest to the water injection device are the largest among the four sensors, which could be explained with “critical gradient” concept for unsaturated expansive clay or effect of hydraulic gradient from boundary water pressure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Agus SS, Leong EC, Rahardjo R (2003) A flexible wall permeameter for measurements of water and air coefficients of permeability of residual soils. Can Geotech J 40:559–574

    Google Scholar 

  2. Alonso EE, Vaunat J, Gens A (1999) Modelling the mechanical behaviour of expansive clays. Eng Geol 54:173–183

    Google Scholar 

  3. Bag R (2011) Coupled thermo-hydro-mechanical chemical behaviour of MX80 bentonite in geotechnical applications[D]Phd thesis, Cardiff University.

  4. Baker R, Frydman S (2009) Unsaturated soil mechanics: critical review of physical foundations. Eng Geol 106(1):26–39

    Google Scholar 

  5. Brooks RH, Corey AT (1964) Hydraulic properties of porous media. Hydrology Papers 3. Colorado State University, Fort Collins

    Google Scholar 

  6. Burdine NT (1953) Relative permeability calculations from pore size distribution data. Pet Trans AIME 198:71–78

    Google Scholar 

  7. Burdine NT, Gournay LS, Reichertz PP (1950) Pore size distribution of petroleum reservoir rocks. Pet Trans AIME 189:195–204

    Google Scholar 

  8. Cao J, Jung J, Song X, Bate B (2018) On the soil water characteristic curves of poorly graded granular materials in aqueous polymer solutions. Acta Geotech 13(1):103–116

    Google Scholar 

  9. Castellanos E, Villar MV, Romero E, Lloret A, Gens A (2008) Chemical impact on the hydro-mechanical behavior of high-density FEBEX bentonite. Phys Chem Earth 33:S516–S526

    Google Scholar 

  10. Chapuis RP (2012) Predicting the saturated hydraulic conductivity of soils: a review. Bull Eng Geol Environ 71(3):401–434

    Google Scholar 

  11. Chen B, Qian LX, Ye WM, Cui YJ, Wang J (2006) Soil–water characteristic curves of Gaomiaozi bentonite. Chin J Rock Mech Eng 25(4):788–793

    Google Scholar 

  12. Chin K-B, Leong E-C, Rahardjo H (2010) A simplified method to estimate the soil–water characteristic curve. Can Geotech J 47:138–1400

    Google Scholar 

  13. Cui YJ, Loiseau C, Delage P (2002) Microstructure changes of a confined swelling soil due to suction controlled hydration. In: Jucá JFT, de Campos TMP, Marinho FAM (eds) Unsaturated soils. Proceedings of the 3rd international conference on unsaturated soils (UNSAT 2002), Recife, Brazil, vol 2. Swets and Zeitlinger, Lisse, pp 593–598

  14. Cui YJ, Tang AM, Loiseau C, Delage P (2008) Determining the unsaturated hydraulic conductivity of a compacted sand–bentonite mixture under constant-volume and free-swell conditions. Phys Chem Earth 33:462–471

    Google Scholar 

  15. Daniel DE (1982) Measurement of hydraulic conductivity of unsaturated soils with thermocouple psychrometers. Soil Sci Soc Am J 20(6):1125–1129

    Google Scholar 

  16. Darcy H (1856) Les fontaines publiques de la ville de Dijon. Dalmont, Paris

    Google Scholar 

  17. Delage P (2006) Some microstructure effects on the behaviour of compacted swelling clays used for engineered barriers. Chin J Rock Mech Eng 25(4):721–732

    Google Scholar 

  18. Delage P, Marcial D, Cui YJ, Ruiz X (2006) Ageing effects in a compacted bentonite: a microstructure approach. Géotechnique 56(5):291–304

    Google Scholar 

  19. Dieudonne A-C, Vecchia GD, Charlier R (2017) Water retention model for compacted bentonites. Can Geotech J 54:915–925

    Google Scholar 

  20. Dixon DA, Gray MN, Hnatiw D (1992) Critical gradients and pressures in dense swelling clays. Can Geotech J 29(6):1113–1119

    Google Scholar 

  21. Dolinar B (2015) Prediction of the soil–water characteristic curve based on the specific surface area of fine-grained soils. Bull Eng Geol Environ 74(3):697–703

    Google Scholar 

  22. Egloffstein TA (2001) Natural bentonites-influence of the ion exchange and partial desiccation on permeability and self-healing capacity of bentonites used in GCLs. Geotext Geomembr 19:427–444

    Google Scholar 

  23. Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. Wiley, New York

    Google Scholar 

  24. Fredlund DG, Xing AQ (1994) Equations for the soil–water characteristic curve. Can Geotech J 31(4):521–532

    Google Scholar 

  25. Fredlund DG, Xing AQ, Huang SY (1994) Predicting the permeability function for unsaturated soils using the soil–water characteristic curve. Can Geotech J 31(4):533–546

    Google Scholar 

  26. Gallipoli D, Wheeler SJ, Karstunen M (2003) Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique 53:105–112

    Google Scholar 

  27. Gens A, Alonso EE (1992) A framework for the behaviour of unsaturated expansive clays. Can Geotech J 29:1013–1032

    Google Scholar 

  28. Genuchten MTV (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(44):892–898

    Google Scholar 

  29. Goh SG, Rahardjo H, Leong EC (2015) Modification of triaxial apparatus for permeability measurement of unsaturated soils. Soils Found 55(1):63–73

    Google Scholar 

  30. Graham J, Oswell JM, Gray MN (1992) The effective stress concept in saturated sand-clay buffer. Can Geotech J 29:1033–1043

    Google Scholar 

  31. Green RE, Corey JC (1971) Calculation of hydraulic conductivity: a further evaluation of some predictive methods. Proc Soil Sci Soc Am 35:3–8

    Google Scholar 

  32. Grim RE (1968) Clay mineralogy. McGraw-Hill, New York

    Google Scholar 

  33. Hamilton JM, Daniel DE, Olson RE (1981) Measurement of hydraulic conductivity of partially saturated soils. In: Zimmie TF, Riggs CO (eds) Permeability and groundwater contaminant transport. ASTM Special Technical Publications, Philadelphia

    Google Scholar 

  34. Hoffmann C, Alonso EE, Romero E (2007) Hydro-mechanical behaviour of bentonite pellet mixtures. Phys Chem Earth 32:832–849

    Google Scholar 

  35. Huang GH, Zhang RD, Huang QZ (2006) Modeling soil water retention curve with a fractal method. Pedosphere 16(2):137–146

    Google Scholar 

  36. Hueckel T, Loret B, Gajo A (2001) Expansive clays as two-phase, deformable reacting continua: concepts and modeling options. In: Maio CD, Hueckel T, Loret B (eds) Proceedings of the workshop on chemo-mechanical coupling in clays: from nano-scale to engineering applications. Balkema Publications, pp 105–120

  37. Hunt AG (2004) An explicit derivation of an exponential dependence of the hydraulic conductivity on relative saturation. Adv Water Resour 27(2):197–201

    Google Scholar 

  38. Hwang SI, Powers SE (2003) Lognormal distribution model for estimating soil water retention curves for sandy soils. Soil Sci 168(3):156–166

    Google Scholar 

  39. Hwang SI, Sang PH (2006) Estimating relative hydraulic conductivity from lognormally distributed particle-size data. Geoderma 133(3/4):421–430

    Google Scholar 

  40. Ichikawa Y, Kawamura K (2004) Secondary and tertial consolidation of bentonite clay: consolidation test, molecular dynamics simulation and multiscale homogenization analysis. Mech Mater 36(5):487–513

    Google Scholar 

  41. Indraratna B, Trani LDO (2010) The use of particle size distribution by surface area method in predicting the saturated hydraulic conductivity of graded granular soils. Géotechnique 60(12):957–962

    Google Scholar 

  42. Klute A (1965) Laboratory measurement of hydraulic conductivity of unsaturated soil. In: Black CA, Evans DD, White JL, Ensminger LE, Clark FE (eds) Methods of soil analysis. American Society of Agronomy, Madison, pp 253–261

    Google Scholar 

  43. Koch D (1994) Bentonitvergutete Abdichtungen. In: Burkhardt G, Egloffstein T (Hrsg) Alternative Abdichtungssysteme im Deponiebau und in der Altlastensicherung. Schriftenreihe Angewandte Geologie Karlsruhe, Band 30

  44. Komine H (2008) Theoretical equations on hydraulic conductivities of bentonite based buffer and backfill for underground disposal of radioactive wastes. J Geotech Geoenviron Eng 134(4):497–508

    Google Scholar 

  45. Kong Y-F, Song E-X (2015) A method for estimating soil–water characteristic curve from grain-size distribution. Rock Soil Mech 36(9):2487–2493 (in Chinese)

    Google Scholar 

  46. Kröhn K-P (2003) New conceptual models for the resaturation of bentonite. Appl Clay Sci 23(1–4):25–33

    Google Scholar 

  47. Kunze RJ, Uehara G, Graham K (1968) Factors important in the calculation of hydraulic conductivity. Soil Sci Soc Am J 32(6):760–765

    Google Scholar 

  48. Laird DA (1996) Model for crystalline swelling of 2:1 phyllosilicates. Clays Clay Miner 44(4):553–559

    Google Scholar 

  49. Leong EC, Rahardjo H (1997) Permeability function for unsaturated soils. J Geotech Geoenviron Eng 123(12):1118–1126

    Google Scholar 

  50. Li X, Zhang LM (2009) Characterization of the dual-structure pore-size distribution of soil. Can Geotech J 46:129–141

    Google Scholar 

  51. Likos WJ (2000) Total suction-moisture content characteristics for expansive soils. Ph.D. dissertation, Colorado School of Mines, Golden

  52. Liu YM, Wen ZJ (2003) An investigation of the physical properties of clayey materials used in nuclear waste disposal at great depth. Miner Rocks 23(4):42–45 (in Chinese)

    Google Scholar 

  53. Lloret A, Villar MV (2007) Advances on the knowledge of the thermo-hydro-mechanical behaviour of heavily compacted “FEBEX” bentonite. Phys Chem Earth 32:701–715

    Google Scholar 

  54. Loiseau C (2001) Transferts d’eau et couplages hydromécaniques dans les barrières ouvragées. Ph.D. thesis, CERMES/ENPC, France

  55. Loiseau C, Cui YJ, Delage P (2002) The gradient effect on the water flow through a compacted swelling soil. In: Proceedings of the 3rd international conference on unsaturated soils, UNSAT’2002 (1), Recife, Brazil, Balkema, pp 395–400

  56. Lu N (2008) Is matric suction a stress variable? J Geotech Geoenviron Eng 134(7):899–905

    Google Scholar 

  57. Lu N, Likos WJ (2004) Unsaturated soil mechanics. Wiley, New York

    Google Scholar 

  58. Lu N, Wayllace A, Carrera J, Likos WJ (2006) Constant flow method for concurrently measuring soil–water characteristic curve and hydraulic conductivity function. J Geotech Test 29(3):256–266

    Google Scholar 

  59. Marshall TJ (1958) A relation between permeability and size distribution of pores. J Soil Sci 9:1–8

    Google Scholar 

  60. Masrouri F, Bicalho KV, Kawai K (2008) Laboratory hydraulic testing in unsaturated soils. Geotech Geol Eng 26(6):691–704

    Google Scholar 

  61. Massey B, Ward-Smith J (2006) Mechanics of fluids. Taylor and Francis, Milton Park

    Google Scholar 

  62. McQueen IS, Miller RF (1974) Approximating soil moisture characteristics from limited data: empirical evidence and tentative model. Water Resour Res 10(3):521–527

    Google Scholar 

  63. Mitchell JK (1993) Fundamentals of soil behaviour. Wiley, New York

    Google Scholar 

  64. Mualem Y (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour Res 12(3):513–522

    Google Scholar 

  65. Müller HR, Garitte B, Vogt T, Köhler S, Sakaki T, Weber H, Spillmann T, Hertrich M, Becker JK, Giroud N, Cloet V, Diomidis N, Vietor T (2017) Implementation of the full-scale emplacement (FE) experiment at the Mont Terri rock laboratory. Swiss J Geosci 110:287–306

    Google Scholar 

  66. Navarro V, Morena GDL, Yustres Á, González-Arteaga J, Asensio L (2017) Predicting the swelling pressure of MX-80 bentonite. Appl Clay Sci 149:51–58

    Google Scholar 

  67. Nguyen XP, Cui YJ, Tang AM, Deng YF, Li XL, Wouters L (2013) Effects of pore water chemical composition on the hydro-mechanical behavior of natural stiff clays. Eng Geol 166:52–64

    Google Scholar 

  68. Niu WJ (2008) Study on unsaturated permeability of densely compacted bentonite under free swelling conditions. Ph.D.-thesis, Tongji University, Shanghai (in Chinese)

  69. Niu WJ (2012) Influences of microstructure variations on intrinsic permeability of compacted bentonite with Newton’s viscosity coefficient. Int J Mech Syst Eng 2(3):101–107

    Google Scholar 

  70. Norrish K (1954) The swelling of montmorillonite. Discuss Faraday Soc 18(18):120–134

    Google Scholar 

  71. Or D, Tuller M (2002) Cavitation during desaturation of porous media under tension. Water Resour Res 38:1–4

    Google Scholar 

  72. Pusch R (1999) Microstructural evolution of buffers. Eng Geol 54:33–41

    Google Scholar 

  73. Pusch R (2001) The microstructure of MX-80 clay with respect to its bulk physical properties under different environmental conditions. Technical Report, TR-01-08

  74. Pusch R, Karnland O, Hokmark H (1990) GMM - a general microstructural model for qualitative and quantitative studies of smectite clays. Swedish Nuclear Fuel and Waste Management Company, Stockholm, Sweden

    Google Scholar 

  75. Romero E, Gens A, Lloret A (1999) Water permeability, water retention and microstructure of unsaturated compacted Boom clay. Eng Geol 54:117–127

    Google Scholar 

  76. Romero E, Gens A, Lloret A (2001) Temperature effects on the hydraulic behaviour of an unsaturated clay. Geotech Geol Eng 19:311–332

    Google Scholar 

  77. Schanz T, Tripathy S (2009) Swelling pressure of a divalent-rich bentonite: diffuse double-layer theory revisited. Water Resour Res 45:12. https://doi.org/10.1029/2007wr006495

    Article  Google Scholar 

  78. Song X (2017) Transient bifurcation condition of partially saturated porous media at finite strain. Int J Numer Anal Meth Geomech 41(1):135–156

    Google Scholar 

  79. Song X, Borja RI (2014a) Finite deformation and fluid flow in unsaturated soils with random heterogeneity. Vadose Zone J 13(5):1–11

    Google Scholar 

  80. Song X, Borja RI (2014b) Mathematical framework for unsaturated flow in the finite deformation range. Int J Numer Anal Meth Eng 97(9):658–682

    MathSciNet  MATH  Google Scholar 

  81. Song X, Ye M, Wang K (2017) Strain localization in a solid-water-air system with random heterogeneity via stabilized mixed finite elements. Int J Numer Anal Meth Geomech 112 (13):1926–1950

    MathSciNet  Google Scholar 

  82. Song X, Wang K, Ye M (2018a) Localized failure in unsaturated soils under non-isothermal conditions. Acta Geotech 13(1):73–85

    Google Scholar 

  83. Song X, Wang K, Bate B (2018b) A hierarchical thermo-hydro-plastic constitutive model for unsaturated soils and its numerical implementation. Int J Numer Anal Meth Geomech 42(15):1785–1805

    Google Scholar 

  84. Stewart DI, Studds PG, Cousens TW (2003) The factors controlling the engineering properties of bentonite-enhanced sand. Appl Clay Sci 23(1–4):97–110

    Google Scholar 

  85. Suits LD, Sheahan TC, Wayllace A, Lu N (2011) A transient water release and imbibitions method for rapidly measuring wetting and drying soil water retention and hydraulic conductivity functions. Geotech Test J 35(1):103596

    Google Scholar 

  86. Suzuki S, Prayongphan S, Ichikawa Y, Chae BG (2005) In situ observations of the swelling of bentonite aggregates in NaCl solution. Appl Clay Sci 29(2):89–98

    Google Scholar 

  87. Tang AM, Cui YJ (2011) Controlling suction by vapour equilibrium technique at different temperatures and its application in determining the water retention properties of MX80 clay. Can Geotech J 42(1):287–296

    Google Scholar 

  88. Tang AM, Cui YJ, Qian LX, Delage P, Ye WM (2010) Calibration of the osmotic technique of controlling suction with respect to temperature using a miniature tensiometer. Can Geotech J 47(3):359–365

    Google Scholar 

  89. van Olphen H (1991) An introduction to clay colloid chemistry, 2nd edn. Krieger Publishing Co., Florida

    Google Scholar 

  90. Vardhan H, Garg A, Li JH, Garg A (2016) Measurement of stress dependent permeability of unsaturated clay. Measurement 91:371–376

    Google Scholar 

  91. Vecchia GD, Dieudonné A-C, Jommi C, Charlier R (2015) Accounting for evolving pore size distribution in water retention models for compacted clays. Int J Numer Anal Methods Geomech 39:702–723

    Google Scholar 

  92. Villar MV, Lloret A (2008) Influence of dry density and water content on the swelling of a compacted bentonite. Appl Clay Sci 39:38–49

    Google Scholar 

  93. Villar MV, Martín PL, Barcala JM (2005) Modification of physical, mechanical and hydraulic properties of bentonite by thermo-hydraulic gradients. Eng Geol 81:284–297

    Google Scholar 

  94. Von Helmholtz R (1886) Untersuchungen über Dämpfe und Nebel, besonders über solche von Lösungen (Investigations of vapors and mists, especially of such things from solutions). Ann der Physik 263(4):508–543 [On pages 523–525, Robert von Helmholtz converts Kelvin’s equation to the form that appears here (which is actually the Ostwald–Freundlich equation)]

    Google Scholar 

  95. Wang J, Su R, Chen W, Guo YH, Jin YX, Wen ZJ, Liu YM (2006) Deep geological disposal of high-level radioactive wastes in China. Chin J Rock Mech Eng 25(4):649–658

    Google Scholar 

  96. Wang Q, Cui YJ, Tang AM, Barnichon J-D, Saba S, Ye W-M (2013) Hydraulic conductivity and microstructure changes of compacted bentonite/sand mixture during hydration. Eng Geol 164:67–76

    Google Scholar 

  97. Wang Q, Tang AM, Cui YJ, Delage P, Barnichon J-D, Ye WM (2013) The effects of technological voids on the hydro-mechanical behaviour of compacted bentonite-sand mixture. Soils Found 53(2):232–245

    Google Scholar 

  98. Wang XR, Shao H, Wang WQ, Hesser J, Kolditz O (2015) Numerical modeling of heating and hydration experiments on bentonite pellets. Eng Geol 198:94–106

    Google Scholar 

  99. Watson KK (1966) An instantaneous profile method for determining the hydraulic conductivity of unsaturated porous materials. Water Resour Res 2(4):709–715

    MathSciNet  Google Scholar 

  100. Wen ZJ (2006) Physical property of China’s buffer material for high-level radioactive waste repositories. Chin J Rock Mech Eng 25(4):794–800

    Google Scholar 

  101. Xiong QR, Baychev TG, Jivkov AP (2016) Review of pore network modelling of porous media: experimental characterisations, network constructions and applications to reactive transport. J Contam Hydrol 192:101–117

    Google Scholar 

  102. Xu YF (2004) Calculation of unsaturated hydraulic conductivity using a fractal model for the pore-size distribution. Comput Geotech 31:549–557

    Google Scholar 

  103. Ye WM, Cui YJ, Qian LX, Chen B (2009) An experimental study of the water transfer through confined compacted GMZ bentonite. Eng Geol 108:169–176

    Google Scholar 

  104. Ye WM, Qian LX, Chen B, Yu C (2009) Characteristics of micro-structure of densely compacted Gaomiaozi bentonite. J Tongji Univ (Nat Sci) 37(1):31–35

    Google Scholar 

  105. Ye WM, Wan M, Chen B, Chen YG, Cui YJ, Wang J (2012) Temperature effects on the unsaturated permeability of the densely compacted GMZ01 bentonite under confined conditions. Eng Geol 126:1–7

    Google Scholar 

  106. Ye WM, Wan M, Chen B, Chen YG, Cui YJ (2013) Temperature effects on the swelling pressure and saturated hydraulic conductivity of the compacted GMZ01 bentonite. Environ Earth Sci 68:281–288

    Google Scholar 

  107. Ye WM, Zhang F, Chen B, Chen YG, Wang Q, Cui YJ (2014) Effects of salt solutions on the hydro-mechanical behaviour of compacted GMZ01 bentonite. Environ Earth Sci 72:2621–2630

    Google Scholar 

  108. Ye WM, Borrell NC, Zhu JY, Chen B, Chen YG (2014) Advances on the investigation of the hydraulic behavior of compacted GMZ bentonite. Eng Geol 169:41–49

    Google Scholar 

  109. Ye WM, Wan M, Chen B, Chen YG, Cui YJ, Wang J (2014) An unsaturated hydraulic conductivity model for compacted GMZ01 bentonite with consideration of temperature. Environ Earth Sci 71:1937–1944

    Google Scholar 

  110. Yilmaz G, Yetimoglu T, Arasan S (2008) Hydraulic conductivity of compacted clay liners permeated with inorganic salt solutions. Waste Manag Res 26:464–473

    Google Scholar 

  111. Yong RN (1999) Soil suction and soil–water potentials in swelling clays in engineered clay barriers. Eng Geol 54:3–13

    Google Scholar 

  112. Yu C (2006) Volume change behavior and micro-structure mechanism of unsaturated Gaomiaozi bentonite. Master Dissertation, Tongji University, Shanghai (in Chinese)

  113. Yuan C, Chareyre B, Darve F (2016) Pore-scale simulations of drainage in granular materials: finite size effects and the representative elementary volume. Adv Water Resour 95:109–124

    Google Scholar 

  114. Zhang FX, Fredlund DG (2015) Examination of the estimation of relative permeability for unsaturated soils. Can Geotech J 52:2077–2087

    Google Scholar 

  115. Zhang S, Zhang Y, Wang B (2017) Evolution of the effective permeability for transient and pore-scale two-phase flow in real porous media. Int J Heat Mass Transf 113:1093–1105

    Google Scholar 

  116. Zhou AN, Huang RQ, Sheng DC (2016) Capillary water retention curve and shear strength of unsaturated soils. Can Geotech J 53(6):974–987

    Google Scholar 

  117. Zou YZ (2012) A macroscopic model for predicting the relative hydraulic permeability of unsaturated soils. Acta Geotech 7:129–137

    Google Scholar 

Download references

Acknowledgements

The project was supported by the National Natural Science Foundation of China (No. 40572161). We thank the anonymous reviewers for their insightful comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wen-Jie Niu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Niu, WJ., Ye, WM. & Song, X. Unsaturated permeability of Gaomiaozi bentonite under partially free-swelling conditions. Acta Geotech. 15, 1095–1124 (2020). https://doi.org/10.1007/s11440-019-00788-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-019-00788-9

Keywords

Navigation