Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A hysteresis model for soil-water characteristic curve based on dynamic contact angle theory

  • Liu, Yan (Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University) ;
  • Li, Xu (Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University)
  • Received : 2020.10.30
  • Accepted : 2021.12.17
  • Published : 2022.01.25
⟨ Previous Next ⟩

Abstract

The steady state of unsaturated soil takes a long time to achieve. The soil seepage behaviours and hydraulic properties depend highly on the wetting/drying rate. It is observed that the soil-water characteristic curve (SWCC) is dependent on the wetting/drying rate, which is known as the dynamic effect. The dynamic effect apparently influences the scanning curves and will substantially affect the seepage behavior. However, the previous models commonly ignore the dynamic effect and cannot quantitatively describe the hysteresis scanning loops under dynamic conditions. In this study, a dynamic hysteresis model for SWCC is proposed considering the dynamic change of contact angle and the moving of the contact line. The drying contact angle under dynamic condition is smaller than that under static condition, while the wetting contact angle under dynamic condition is larger than that under static condition. The dynamic contact angle is expressed as a function of the saturation rate according to the Laplace equation. The model is given by a differential equation, in which the slope of the scanning curve is related to the slope of the boundary curve by means of contact angle. Empirical models can simulate the boundary curves. Given the two boundary curves, the scanning curve can be well predicted. In this model, only two parameters are introduced to describe the dynamic effect. They can be easily obtained from the experiment, which facilitates the calibration of the model. The proposed model is verified by the experimental data recorded in the literature and is proved to be more convenient and effective.

Keywords

Acknowledgement

The research described in this paper was financially supported by the Fundamental Research Funds for the Central Universities (2019JBM086).

References

  1. Albers, B. (2014), "Modeling the hysteretic behavior of the capillary pressure in partially saturated porous media: A review", Acta Mech., 225(8), 2163-2189. https://doi.org/10.1007/s00707-014-1122-4.
  2. Alves, R.D., Gitirana Jr., G. and Vanapalli, S.K. (2020), "Advances in the modeling of the soil-water characteristic curve using pore-scale analysis", Comput. Geotech., 127(4), 103766. https://doi.org/10.1016/j.compgeo.2020.103766.
  3. Azizi, A., Jommi, C. and Musso, G. (2017). "A water retention model accounting for the hysteresis induced by hydraulic and mechanical wetting-drying cycles", Comput. Geotech., 87(1), 86-98. https://doi.org/10.1016/j.compgeo.2017.02.003.
  4. Camps-Roach, G., O'Carroll, D.M., Newson, T.A., Sakaki, T. and Illangasekare, T.H. (2010), "Experimental investigation of dynamic effects in capillary pressure: Grain size dependency and upscaling", Water Resour. Res., 46(8), W08544. https://doi.org/10.1029/2009WR008881.
  5. Chen, H., Chen, K., Yang, M. and Xu, P. (2020a), "A fractal capillary model for multiphase flow in porous media with hysteresis effect", Int. J. Multip. Fl., 125(1), 103208. https://doi.org/10.1016/j.ijmultiphaseflow.2020.103208.
  6. Chen, H., Chen, K. and Yang, M. (2020b), "A new hysteresis model of the water retention curve based on pore expansion and contraction", Comput. Geotech., 121(12), 103482. https://doi.org/10.1016/j.compgeo.2020.103482.
  7. Chen, R., Liu, P., Liu, X., Wang, P. and Kang, X. (2019), "Porescale model for estimating the bimodal soil-water characteristic curve and hydraulic conductivity of compacted soils with different initial densities", Eng. Geol., 260, 105199. https://doi.org/10.1016/j.enggeo.2019.105199.
  8. Das, D.B. and Mirzaei, M. (2013), "Experimental measurement of dynamic effect in capillary pressure relationship for two-phase flow in weakly layered porous media", Aiche J., 59(5), 1723-1734. http://doi.org/10.1002/aic.13925.
  9. Diamantopoulos, E. and Durner, W. (2012), "Dynamic nonequilibrium of water flow in porous media: A review", Vadose Zone J., 11(3), vzj2011.0197. http://doi.org/10.2136/vzj2011.0197.
  10. Eral, H.B., Mannetje, D.T. and Oh, J.M. (2013), "Contact angle hysteresis: a review of fundamentals and applications", Colloid Polym. Sci., 291(2), 247-260. http://doi.org/10.1007/s00396-012-2796-6.
  11. Friedman, S.P. (1999), "Dynamic contact angle explanation of flow rate-dependent saturation-pressure relationships during transient liquid flow in unsaturated porous media", J. Adhes. Sci. Technol., 13(12), 1495-1518. http://doi.org/10.1163/156856199X00613.
  12. Gallipoli, D., Bruno, A.W., D'Onza, F. and Mancuso, C. (2015), "A bounding surface hysteretic water retention model for deformable soils", Geotechnique, 65(10), 793-804. http://doi.org/10.1680/jgeot.14.P.118.
  13. Gao, Y. and Sun, D. (2017), "Soil-water retention behavior of compacted soil with different densities over a wide suction range and its prediction", Comput. Geotech., 91(1), 17-26. https://doi.org/10.1016/j.compgeo.2017.06.016.
  14. Good, R.J. (1992), "Contact angle, wetting, and adhesion: a critical review", J. Adhes. Sci. Technol., 6(12), 1269-1302. https://doi.org/10.1163/156856192X00629.
  15. Hassanizadeh, S.M. and Gray, W.G. (1993), "Thermodynamic basis of capillary pressure in porous media", Water Resour. Res., 29(10), 3389-3405. http://doi.org/10.1029/93WR01495.
  16. Hassanizadeh, S.M., Celia, M.A. and Dahle, H.K. (2002), "Dynamic effect in the capillary pressure-saturation relationship and its impacts on unsaturated flow", Vadose Zone J., 1(1), 38-57. http://doi.org/10.2136/vzj2002.3800.
  17. Hu, R., Chen, Y.F., Liu, H.H. and Zhou, C.B. (2013), "A water retention curve and unsaturated hydraulic conductivity model for deformable soils: Consideration of the change in pore-size distribution", Geotechnique, 63(16), 1389-1405. https://doi.org/10.1680/geot.12.P.182
  18. Jaynes, D.B. (1984), "Comparison of soil-water hysteresis models", J. Hydrol., 75(1), 287-299. https://doi.org/10.1016/0022-1694(84)90054-4.
  19. Li, X.S. (2005), "Modelling of hysteresis response for arbitrary wetting/drying paths", Comput. Geotech., 32(2), 133-137. https://doi.org/10.1016/j.compgeo.2004.12.002.
  20. Likos, W.J., Lu, N. and Godt, J.W. (2014), "Hysteresis and uncertainty in soil water-retention curve parameters", J. Geotech. Geoenviron., 140(4), 04013050. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001071.
  21. Liu, Z., Yu, X. and Wan, L. (2013), "Influence of contact angle on soil-water characteristic curve with modified capillary rise method", Transport. Res. Rec., 2349(1), 32-40. https://doi.org/10.3141/2349-05.
  22. Liu, Z., Yu, X. and Wan, L. (2016), "Capillary rise method for the measurement of the contact angle of soils", Acta Geotech., 11(1), 21-35. https://doi.org/10.1007/s11440-014-0352-x.
  23. Milatz, M., Torzs, T., Nikooee, E., Hassanizadeh, S.M. and Grabe, J. (2018), "Theoretical and experimental investigations on the role of transient effects in the water retention behaviour of unsaturated granular soils", Geomech. Energy Envir., 15, 54-64. https://doi.org/10.1016/j.gete.2018.02.003
  24. Mualem, Y. (1974), "a conceptual model of hysteresis", Water Resour. Res., 10(3), 514-520. http://doi.org/10.1029/wr010i003p00514.
  25. Niu, G., Shao, L., Sun, D. and Guo, X. (2020), "A simplified directly determination of soil-water retention curve from pore size distribution", Geomech. Eng., 20(5), 411-420. http://doi.org/10.12989/gae.2020.20.5.411.
  26. O'Carroll, D.M., Phelan, T.J. and Abriola, L.M. (2005), "Exploring dynamic effects in capillary pressure in multistep outflow experiments", Water Resour. Res., 41(11), W11419. http://doi.org/10.1029/2005WR004010.
  27. Otalvaro, I.F., Neto, M.P.C., Delage, P. and Caicedo, B. (2016), "Relationship between soil structure and water retention properties in a residual compacted soil", Eng. Geol., 205, 73-80. https://doi.org/10.1016/j.enggeo.2016.02.016.
  28. Pham, H.Q., Fredlund, D.G. and Barbour, S.L. (2005), "A study of hysteresis models for soil-water characteristic curves", Can. Geotech. J., 42(6), 1548-1568. http://doi.org/10.1139/t05-071.
  29. Rafraf, S., Guellouz, L., Guiras, H. and Bouhlila, R. (2016), "A new model using dynamic contact angle to predict hysteretic soil water retention curve", Soil Sci. Soc. Am. J., 80(6), 1433-1442. http://doi.org/10.2136/sssaj2016.01.0006.
  30. Rahardjo, H., Meilani, I., Leong, E.C. and Rezaur, R.B. (2009), "Shear strength of compacted soil under infiltration condition" Geomech. Eng., 1(1), 35-52. http://doi.org/10.12989/gae.2009.1.1.035.
  31. Rasool, A.M. and Kuwano, J. (2020), "Ffect of constant loading on unsaturated soil under water infiltration conditions", Geomech. Eng., 20(3), 221-232. http://doi.org/10.12989/gae.2020.20.3.221.
  32. Sakaki, T., O'Carroll, D.M. and Illangasekare, T.H. (2010), "Direct quantification of dynamic effects in capillary pressure for drainage-wetting cycles", Vadose Zone J., 9(2), 424-437. http://doi.org/10.2136/vzj2009.0105.
  33. Smiles, D.E., Vachaud, G. and Vauclin, M. (1971), "A test of the uniqueness of the soil moisture characteristic during transient, nonhysteretic flow of water in a rigid soil1", Soil Sci. Soc. Am. J., 35(4), 534-539. http://doi.org/10.2136/sssaj1971.03615995003500040018x.
  34. Topp, G.C., Klute, A. and Peters, D.B. (1967), "Comparison of water content-pressure head data obtained by equilibrium, steady-state, and unsteady-state methods", Soil Sci. Soc. Am. J., 31(3), 312-314. http://doi.org/10.2136/sssaj1967.03615995003100030009x.
  35. Viaene, P., Vereecken, H., Diels, J. and Feyen, J. (1994), "A statistical analysis of six hysteresis models for the moisture retention characteristic", Soil Sci., 157(6), 345-355. http://doi.org/10.1097/00010694-199406000-00003.
  36. Wana-etyem, C. (1982), "Static and dynamic water content-pressure head relations of porous media", Ph.D. Dissertation, Colorado State University, Colorado.
  37. Wei, C.F. and Dewoolkar, M.M. (2006), "Formulation of capillary hysteresis with internal state variables", Water Resour. Res., 42 (7), W07405. http://dx.doi.org/10.1029/2005wr004594
  38. Wheeler, S.J., Sharma, R.S. and Buisson, M.S.R. (2003), "Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils", Geotechnique, 53(1), 41-54. http://doi.org/10.1680/geot.53.1.41.37252.
  39. Zhou, A. (2013), "A contact angle-dependent hysteresis model for soil-water retention behaviour", Comput. Geotech., 49, 36-42. https://doi.org/10.1016/j.compgeo.2012.10.004.
  40. Zhou, A.N., Sheng, D. and Carter, J.P. (2012), "Modelling the effect of initial density on soil-water characteristic curves", Geotechnique, 62(8), 669-680. https://doi.org/10.1680/geot.10.P.120.
  41. Zhou, C. and Ng, C.W.W. (2014), "A new and simple stress-dependent water retention model for unsaturated soil", Comput. Geotech., 62, 216-222. https://doi.org/10.1016/j.compgeo.2014.07.012.
  42. Zhuang, L., Hassanizadeh, S.M., Qin, C. and de Waal, A. (2017), "Experimental investigation of hysteretic dynamic capillarity effect in unsaturated flow", Water Resour. Res., 53(11), 9078-9088. http://doi.org/10.1002/2017WR020895.