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Fractal characteristics of pore structure of compacted bentonite studied by ESEM and MIP methods

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Abstract

In this paper, we aim to clarify microstructure of bentonite from Cerny vrch deposit in the Czech Republic. We adopt results of ESEM and MIP experiments performed at various suctions along wetting and drying paths on bentonite samples compacted from powder to two different initial dry densities. The data were used for quantification of fractal dimension characteristics of pores of different sizes. Two different methods of calculating fractal dimension were used for MIP data, and one method was used for evaluation of ESEM images. Fractal dimensions obtained from MIP data, combined with the measured pore size density functions, allowed us to identify two different pore families: micropores and macropores. Macropores can be further subdivided into fine macropores and coarse macropores based on fractal analysis. The pore systems were further distinguished by different responses to suction changes and to compaction effort. In general, we observed slight increase in fractal dimension with increasing suction and with increasing dry density.

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References

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

    Article  Google Scholar 

  2. Beddoe RE, Lang K (1994) Effect of moisture on fractal dimension and specific surface of hardened cement paste by small-angle X-ray scattering. Cem Concr Res 24(4):605–612

    Article  Google Scholar 

  3. Burton GJ, Pineda JA, Sheng D, Airey D (2015) Microstructural changes of an undisturbed, reconstituted and compacted high plasticity clay subjected to wetting and drying. Eng Geol 193:363–373

    Article  Google Scholar 

  4. Cui ZD, Zhao LZ, Yuan L (2016) Microstructures of consolidated Kaolin clay at different depths in centrifuge model tests. Carbonates Evaporites 31(1):47–60

    Article  Google Scholar 

  5. Cuisinier O, Laloui L (2004) Fabric evolution during hydromechanical loading of a compacted silt. Can Geotech J 28:483–499

    Google Scholar 

  6. Dathe A, Eins S, Niemeyer J, Gerold G (2001) The surface fractal dimension of the soil–pore interface as measured by image analysis. Geoderma 103(1–2):203–229

    Article  Google Scholar 

  7. De Las Cuevas C (1997) Pore structure characterization in rock salt. Eng Geol 47(1–2):17–30

    Google Scholar 

  8. Delage P, Lefebvre G (1984) Study of the structure of a sensitive Champlain clay and of its evolution during consolidation. Can Geotech J 21(1):21–35

    Article  Google Scholar 

  9. Delage P, Audiguier M, Cui YJ, Howat MD (1996) Microstructure of a compacted silt. Can Geotech J 33:150–158

    Article  Google Scholar 

  10. Della VG, Jommi C, Romero E (2013) A fully coupled elastic–plastic hydromechanical model for compacted soils accounting for clay activity. Int J Numer Anal Methods Geomech 37(5):503–535

    Article  Google Scholar 

  11. Deng H, Hu X, Li HA, Luo B, Wang W (2016) Improved pore-structure characterization in shale formations with FESEM technique. J Nat Gas Sci Eng 35:309–319

    Article  Google Scholar 

  12. Farulla CA, Jommi C (2005) Suction controlled wetting–drying cycles on a compacted scaly clay. In: Proceedings of international conference on problematic soils, vol 25, p 27

  13. Flavio SA, Stefan L, Gregor PE (1998) Quantitative characterization of carbonate pore systems by digital image analysis. AAPG Bull 82(10):1815–1836

    Google Scholar 

  14. Florindo JB, Bruno OM (2014) Fractal descriptors based on the probability dimension: a texture analysis and classification approach. Pattern Recogn Lett 42:107–114

    Article  Google Scholar 

  15. Friesen WI, Mikula RJ (1987) Fractal dimensions of coal particles. J Colloid Interface Sci 120(1):263–271

    Article  Google Scholar 

  16. Gens A, Alonso EE (1992) A framework for the behaviour of unsaturated expansive clays. Can Geotech J 29(6):1013–1032

    Article  Google Scholar 

  17. Grau J, Méndez V, Tarquis AM, Diaz MC, Saa A (2006) Comparison of gliding box and box-counting methods in soil image analysis. Geoderma 134(3–4):349–359

    Article  Google Scholar 

  18. Hansen JP, Skjeltorp AT (1988) Fractal pore space and rock permeability implications. Phys Rev B 38(4):2635

    Article  Google Scholar 

  19. Hausmannova L, Vasicek R (2014) Measuring hydraulic conductivity and swelling pressure under high hydraulic gradients. Geol Soc Lond Spec Publ 400:293–301 (SP400-36)

    Article  Google Scholar 

  20. Hyslip JP, Vallejo LE (1997) Fractal analysis of the roughness and size distribution of granular materials. Eng Geol 48(3–4):231–244

    Article  Google Scholar 

  21. Jommi C, Sciotti A (2003) A study of the microstructure to assess the reliability of laboratory compacted soils as reference material for earth constructions. In: Proceedings of the 2nd international conference on structural and construction engineering, vol 3, pp 2409–2415. Balkema

  22. Karperien A (2013) FracLac for ImageJ. Charles Sturt University, Dubbo

    Google Scholar 

  23. Katz A, Thompson AH (1985) Fractal sandstone pores: implications for conductivity and pore formation. Phys Rev Lett 54(12):1325

    Article  Google Scholar 

  24. Keiser L, Soreghan GS, Joo YJ (2014) Effects of drying techniques on grain-size analyses of fine-grained sediment. J Sediment Res 84(10):893–896

    Article  Google Scholar 

  25. Khoshghalb A, Pasha AY, Khalili N (2015) A fractal model for volume change dependency of the water retention curve. Géotechnique 65(2):141–146

    Article  Google Scholar 

  26. Komine H, Ogata N (1999) Experimental study on swelling characteristics of sand-bentonite mixture for nuclear waste disposal. Soils Found 39(2):83–97

    Article  Google Scholar 

  27. Korvin G (1992) Fractal models in the earth sciences. Elsevier Science Limited, Amsterdam

    Google Scholar 

  28. Li J, Yin ZY, Cui Y, Hicher PY (2017) Work input analysis for soils with double porosity and application to the hydromechanical modeling of unsaturated expansive clays. Can Geotech J 54(2):173–187

    Article  Google Scholar 

  29. Lin B, Cerato AB (2014) Applications of SEM and ESEM in microstructural investigation of shale-weathered expansive soils along swelling-shrinkage cycles. Eng Geol 177:66–74

    Article  Google Scholar 

  30. Liu X, Nie B (2016) Fractal characteristics of coal samples utilizing image analysis and gas adsorption. Fuel 182:314–322

    Article  Google Scholar 

  31. Liu K, Ostadhassan M, Zhou J, Gentzis T, Rezaee R (2017) Nanoscale pore structure characterization of the Bakken shale in the USA. Fuel 209:567–578

    Article  Google Scholar 

  32. 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

    Article  Google Scholar 

  33. Mahamud M, López Ó, Pis JJ, Pajares JA (2003) Textural characterization of coals using fractal analysis. Fuel Process Technol 81(2):127–142

    Article  Google Scholar 

  34. Manca D, Ferrari A, Laloui L (2016) Fabric evolution and the related swelling behaviour of a sand/bentonite mixture upon hydro-chemo-mechanical loadings. Géotechnique 66(1):41–57

    Article  Google Scholar 

  35. Mandelbrot BB (1977) Fractals: form, chance and dimension. Freeman, San Francisco

    MATH  Google Scholar 

  36. Mašín D (2013) Double structure hydromechanical coupling formalism and a model for unsaturated expansive clays. Eng Geol 165:73–88

    Article  Google Scholar 

  37. Mašín D (2017) Coupled thermohydromechanical double-structure model for expansive soils. ASCE J Eng Mech 143(9):04017067

    Article  Google Scholar 

  38. Monroy R, Zdravkovic L, Ridley A (2010) Evolution of microstructure in compacted London Clay during wetting and loading. Géotechnique 60(2):105–119

    Article  Google Scholar 

  39. Montes-H G (2005) Swelling–shrinkage measurements of bentonite using coupled environmental scanning electron microscopy and digital image analysis. J Colloid Interface Sci 284(1):271–277

    Article  Google Scholar 

  40. Niu WJ, Ye WM, Song X (2019) Unsaturated permeability of Gaomiaozi bentonite under partially free-swelling conditions. Acta Geotech. https://doi.org/10.1007/s11440-019-00788-9(in print)

    Article  Google Scholar 

  41. Přikryl R, Weishauptová Z (2010) Hierarchical porosity of bentonite-based buffer and its modification due to increased temperature and hydration. Appl Clay Sci 47(1–2):163–170

    Article  Google Scholar 

  42. Pyun SI, Rhee CK (2004) An investigation of fractal characteristics of mesoporous carbon electrodes with various pore structures. Electrochim Acta 49(24):4171–4180

    Article  Google Scholar 

  43. Rasband WS (2016) ImageJ. U. S. National Institutes of Health, Bethesda, Maryland, USA. https://imagej.nih.gov/ij/

  44. Romero MEE (1999) Characterisation and thermo-hydro-mechanical behaviour of unsaturated Boom clay: an experimental study. Universitat Politècnica de Catalunya, Barcelona

    Google Scholar 

  45. Romero E, Simms PH (2008) Microstructure investigation in unsaturated soils: a review with special attention to contribution of mercury intrusion porosimetry and environmental scanning electron microscopy. Geotech Geol Eng 26:705–727

    Article  Google Scholar 

  46. Romero E, Della VG, Jommi C (2011) An insight into the water retention properties of compacted clayey soils. Géotechnique 61(4):313

    Article  Google Scholar 

  47. Sánchez M, Gens A, Villar MV, Olivella S (2016) Fully coupled thermo-hydro-mechanical double-porosity formulation for unsaturated soils. Int J Geomech 16(6):D4016015

    Article  Google Scholar 

  48. Schepers HE, Van Beek JH, Bassingthwaighte JB (1992) Four methods to estimate the fractal dimension from self-affine signals (medical application). IEEE Eng Med Biol Mag 11(2):57–64

    Article  Google Scholar 

  49. Seiphoori A, Ferrari A, Laloui L (2014) Water retention behaviour and microstructural evolution of MX-80 bentonite during wetting and drying cycles. Géotechnique 64(9):721–734

    Article  Google Scholar 

  50. Stastka J, Smutek J (2015) Experimental works with bentonite pellets at the CEG. In: LUCOEX conference and workshop—full-scale demonstration tests in technology development of repositories for disposal of radioactive waste, Oskarshamn, Sweden, pp 179–184

  51. Sun H, Mašín D, Najser J, Neděla V, Navrátilová E (2019) Bentonite microstructure and saturation evolution in wetting–drying cycles evaluated using ESEM, MIP and WRC measurements. Géotechnique 69(8):713–726

    Article  Google Scholar 

  52. Turcotte DL (2002) Fractals in petrology. Lithos 65(3–4):261–271

    Article  Google Scholar 

  53. Vallejo LE (1996) Fractal analysis of the fabric changes in a consolidating clay. Eng Geol 43(4):281–290

    Article  Google Scholar 

  54. Wang Q, Cui YJ, Tang AM, Li XL, Ye WM (2014) Time- and density-dependent microstructure features of compacted bentonite. Soils Found 54(4):657–666

    Article  Google Scholar 

  55. Watt GR, Griffin BJ, Kinny PD (2000) Charge contrast imaging of geological materials in the environmental scanning electron microscope. Am Miner 85(11–12):1784–1794

    Article  Google Scholar 

  56. Wong PZ, Howard J (1986) Surface roughening and the fractal nature of rocks. Phys Rev Lett 57:637–642

    Article  Google Scholar 

  57. Xiang G, Xu Y, Xie S, Fang Y (2017) A simple method for testing the fractal dimension of compacted bentonite immersed in salt solution. Surf Rev Lett 24(03):1750040

    Article  Google Scholar 

  58. Xu Y (2018) The fractal evolution of particle fragmentation under different fracture energy. Powder Technol 323:337–345

    Article  Google Scholar 

  59. Xu Y (2018) Shear strength of granular materials based on fractal fragmentation of particles. Powder Technol 333:1–8

    Article  Google Scholar 

  60. Xu Y (2018) Fractal model for the correlation relating total suction to water content of bentonites. Fractals 26(03):1850028

    Article  Google Scholar 

  61. Yang F, Ning Z, Liu H (2014) Fractal characteristics of shales from a shale gas reservoir in the Sichuan Basin, China. Fuel 115:378–384

    Article  Google Scholar 

  62. Zhang B, Li S (1995) Determination of the surface fractal dimension for porous media by mercury porosimetry. Ind Eng Chem Res 34(4):1383–1386

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This project receives funding from the Euratom Research and Training Programme 2014–2018 under grant agreement No. 745942. The first author acknowledges support by the grants Nos. 846216 and 1476119 of the Charles University Grant Agency. Institutional support by Center for Geosphere Dynamics (UNCE/SCI/006) is greatly appreciated.

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Authors and Affiliations

  1. Faculty of Science, Charles University, Albertov 6, 128 43, Prague, Czech Republic

    Haiquan Sun, David Mašín & Jan Najser

  2. Institute of Scientific Instruments, The Czech Academy of Sciences, Královopolská 147, 612 64, Brno, Czech Republic

    Vilém Neděla & Eva Navrátilová

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  1. Haiquan Sun
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Correspondence to David Mašín.

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Sun, H., Mašín, D., Najser, J. et al. Fractal characteristics of pore structure of compacted bentonite studied by ESEM and MIP methods. Acta Geotech. 15, 1655–1671 (2020). https://doi.org/10.1007/s11440-019-00857-z

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