General Scanning Hysteresis Model for Soil–Water Retention Curves
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 145, Issue 12
Abstract
Soil–water retention curve (SWRC) is a constitutive relation indispensable for analysis of fluid flow and moisture and stress distributions in unsaturated soils. Although the SWRC is traditionally formulated in the regime of positive matric suction, it is also relevant in the negative matric suction regime where pore water are pressurized. To date, no mathematical model is available for characterization of SWRC in both the positive and negative matric suction regimes. In this paper, the underlying mechanism for hydraulic hysteresis is analyzed especially in the regime of negative matric suction, and a novel SWRC scanning hysteresis model is developed for both the positive and negative matric suctions. To demonstrate the performance of the proposed model, the simulated results are compared with experimental data available in the literature, indicating that the new model can describe well the hydraulic hysteresis of unsaturated soils. The proposed model introduces only one parameter in order to describe the scanning hydraulic behavior and is general in the sense that the model can describe well the soil–water retention characteristics in both the positive and negative matric suction regimes.
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Acknowledgments
This research is supported by the US National Science Foundation (Grants No. CMMI 1233063 and CMMI 1230544) and the National Natural Science Foundation of China (Grant No. 41877269). The first author was supported by the Chinese Academy of Science as a visiting scholar in Colorado School of Mines. The authors also appreciate Dr. Chao Zhang and Dr. Godt W. Jonathan for their insightful comments on a draft of the manuscript.
References
Alsherif, N., A. Wayllace, and N. Lu. 2015. “Measuring the soil-water retention curve under positive and negative matric suction regimes.” Geotech. Test. J. 38 (4): 442–451. https://doi.org/10.1520/GTJ20140258.
Basile, A., G. Ciollaro, and A. Coppola. 2003. “Hysteresis in soil water characteristics as a key to interpreting comparisons of laboratory and field measured hydraulic properties.” Water Resour. Res. 39 (12): 1–12. https://doi.org/10.1029/2003WR002432.
Bishop, A. W. 1961. “The measurement of pore pressure in the triaxial test.” In Proc., Pore Pressure and Suction in Soils, 38–46. London: International Society of Soil Mechanics and Foundation Engineering.
Black, D. K., and K. L. Lee. 1973. “Saturating laboratory samples by back pressure.” J. Soil Mech. Found. Div. 99 (1): 75–93.
Chen, P., B. Mirus, N. Lu, and J. W. Godt. 2017. “Effect of hydraulic hysteresis on the stability of infinite slopes under steady infiltration.” J. Geotech. Geoenviron. Eng. 143 (9): 04017041. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001724.
Chen, P., and C. Wei. 2016. “Numerical procedure for simulating the two-phase flow in unsaturated soils with hydraulic hysteresis.” Int. J. Geomech. 16 (1): 04015030. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000505.
Chen, P., C. Wei, J. Liu, and T. Ma. 2013. “Strength theory model of unsaturated soils with suction stress concept.” J. Appl. Math. 2013: 10. https://doi.org/10.1155/2013/756854.
Chen, P., C. Wei, and T. Ma. 2015. “Analytical model of soil-water characteristics considering the effect of air entrapment.” Int. J. Geomech. 15 (6): 04014102. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000462.
Dafalias, Y. F. 1986. “Bounding surface plasticity. I: Mathematical foundation and hypoplasticity.” J. Eng. Mech. 112 (9): 966–987. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:9(966).
Feng, M., and D. G. Fredlund. 1999. “Hysteretic influence associated with thermal conductivity sensor measurements.” In Vol. 14 of Proc., Theory to the Practice of Unsaturated Soil Mechanics, 52nd Canadian Geotechnical Conf., 14–20. Vancouver, Canada: Canadian Geotechnical Society.
Grant, S. A., and A. Salehzadeh. 1996. “Calculations of temperature effects on wetting coefficients of porous solids and their capillary pressure function.” Water Resour. Res. 32 (2): 261–279. https://doi.org/10.1029/95WR02915.
Hammervold, W. L., Ø. Knutsen, J. E. Iversen, and S. M. Skjæveland. 1998. “Capillary pressure scanning curves by the micropore membrane technique.” J. Pet. Sci. Eng. 20 (3–4): 253–258. https://doi.org/10.1016/S0920-4105(98)00028-X.
Hassanizadeh, S. M., M. A. Celia, and H. K. Dahle. 2002. “Dynamic effect in the capillary pressure-saturation relationship and its impacts on unsaturated flow.” Vadose Zone J. 1 (1): 38–57. https://doi.org/10.2136/vzj2002.3800.
Hopmans, W. J., and J. H. Danes. 1986. “Temperature dependence of soil water retention curves.” Soil Sci. Soc. Am. J. 50 (3): 562–567. https://doi.org/10.2136/sssaj1986.03615995005000030004x.
Khalili, N., M. A. Habte, and S. Zargarbashi. 2008. “A fully coupled flow deformation model for cyclic analysis of unsaturated soils including hydraulic and mechanical hysteresis.” Comput. Geotech. 35 (6): 872–889. https://doi.org/10.1016/j.compgeo.2008.08.003.
Khoury, N., R. Brooks, C. Khoury, and D. Yada. 2012. “Modeling resilient modulus hysteretic behavior with moisture variation.” Int. J. Geomech. 12 (5): 519–527. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000140.
Kool, J. B., and J. C. Parker. 1987. “Development and evaluation of closed-form expressions for hysteresis soil hydraulic properties.” Water Resour. Res. 23 (1): 105–114. https://doi.org/10.1029/WR023i001p00105.
Land, C. S. 1968. “Calculation of imbibition relative permeability for two- and three-phase flow from rock properties.” Soc. Pet. Eng. J. 8 (2): 149–156. https://doi.org/10.2118/1942-PA.
Lenhard, R. J., J. C. Parker, and J. J. Kaluarachchi. 1991. “Comparing simulated and experimental hysteretic two-phase transient fluid flow phenomena.” Water Resour. Res. 27 (8): 2113–2124. https://doi.org/10.1029/91WR01272.
Likos, W. J., and N. Lu. 2004. “Hysteresis of capillary stress in unsaturated granular soil.” J. Eng. Mech. 130 (6): 646–655. https://doi.org/10.1061/(ASCE)0733-9399.
Likos, W. J., N. Lu, and J. W. Godt. 2014. “Hysteresis and uncertainty in soil water-retention curve parameters.” J. Geotech. Geoenviron. Eng. 140 (4): 04013050. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001071.
Longeron, D., W. L. Hammervold, and S. M. Skjæveland. 1995. “Water-oil capillary pressure and wettability measurements using micropore membrane technique.” In Proc., Int. Meeting on Petroleum Engineering, 543–553. Richardson, TX: Society of Petroleum Engineering.
Lu, N., N. Alsherif, A. Wayllace, and J. W. Godt. 2015. “Closing the loop of the soil water retention curve.” J. Geotech. Geoenviron. Eng. 141 (1): 02814001. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001225.
Lu, N., M. Kaya, B. Collins, and J. Godt. 2013. “Hysteresis of unsaturated hydromechanical properties of a silty soil.” J. Geotech. Geoenviron. Eng. 139 (3): 507–510. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000786.
Lu, N., and W. J. Likos. 2004. Unsaturated soil mechanics. Hoboken, NJ: Wiley.
Lu, N., A. Wayllace, J. Carrera, and W. J. Likos. 2006. “Constant flow method for concurrently measuring soil-water characteristic curve and hydraulic conductivity function.” Geotech. Test. J. 29 (3): 1–12. https://doi.org/10.1520/GTJ12637.
Marinas, M., J. W. Roy, and J. E. Smith. 2013. “Changes in entrapped gas content and hydraulic conductivity with pressure.” Ground Water 51 (1): 41–50. https://doi.org/10.1111/j.1745-6584.2012.00915.x.
Morrow, N. R. 1975. “The effects of surface roughness on contact angle with special reference to petroleum recovery.” J. Can. Pet. Technol. 14 (4): 42–53. https://doi.org/10.2118/75-04-04.
Mualem, Y. 1984. “A modified dependent-domain theory of hysteresis.” Soil Sci. 137 (5): 283–291. https://doi.org/10.1097/00010694-198405000-00001.
Nimmo, J. R. 1992. “Semiemperical model of soil water hysteresis.” Soil Sci. Soc. Am. J. 56 (6): 1723–1730. https://doi.org/10.2136/sssaj1992.03615995005600060011x.
Parker, J. C., and R. J. Lenhard. 1987. “A model for hysteretic constitutive relations governing multiphase flow. 1: Saturation-pressure relations.” Water Resour. Res. 23 (12): 2187–2196. https://doi.org/10.1029/WR023i012p02187.
Parlange, J. Y. 1976. “Capillary hysteresis and relationship between drying and wetting curve.” Water Resour. Res. 12 (2): 224–228. https://doi.org/10.1029/WR012i002p00224.
Pham, H. Q., D. G. Fredlund, and S. L. Barbour. 2005. “A study of hysteresis models for soil-water characteristic curves.” Can. Geotech. J. 42 (6): 1548–1568. https://doi.org/10.1139/t05-071.
Poulovassilis, A. 1970a. “The effect of the entrapped air on the hysteresis curves of a porous body and on its hydraulic conductivity.” Soil Sci. 109 (3): 154–162. https://doi.org/10.1097/00010694-197003000-00003.
Poulovassilis, A. 1970b. “Hysteresis of pore water in granular porous bodies.” Soil Sci. 109 (1): 5–12. https://doi.org/10.1097/00010694-197001000-00002.
Sakaki, T., M. Komatsu, and R. Takeuchi. 2016. “Extending water retention curves to a quasi-saturated zone subjected to a high water pressure up to 1.5 megapascals.” Vadose Zone J. 15 (8): 1–7. https://doi.org/10.2136/vzj2015.12.0165.
Schuurman, I. E. 1966. “The compressibility of an air/water mixture and a theoretical relation between the air and water pressures.” Géotechnique 16 (4): 269–281. https://doi.org/10.1680/geot.1966.16.4.269.
Skjæveland, S. M., L. M. Siqveland, A. Kjosavik, W. L. Hammervold, and G. A. Virnovsky. 2000. “Capillary pressure correlation for mixed-wet reservoirs.” SPE Reservoir. Eval. Eng. 3 (1): 60–67. https://doi.org/10.2118/60900-PA.
Stonestrom, D. A., and J. Rubin. 1989. “Water-content dependence of trapped air in 2 soils.” Water Resour. Res. 25 (9): 1947–1958. https://doi.org/10.1029/WR025i009p01947.
Sun, D. A., W. J. Sun, and X. Li. 2010. “Effect of degree of saturation on mechanical behaviour of unsaturated soils and its elastoplastic simulation.” Comput. Geotech. 37 (5): 678–688. https://doi.org/10.1016/j.compgeo.2010.04.006.
Sun, D. M., Y. G. Zang, P. Feng, and S. Stephan. 2016. “Quasi-saturated zones induced by rainfall infiltration.” Transp. Porous Media 112 (1): 77–104. https://doi.org/10.1007/s11242-016-0633-.
Tami, D., H. Rahardjo, and E. C. Leong. 2004. “Effects of hysteresis on steady-state infiltration in unsaturated slopes.” J. Geotech. Geoenviron. Eng. 130 (9): 956–967. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:9(956).
Tian, H., C. Wei, H. Wei, R. Yan, and P. Chen. 2014. “An NMR-based analysis of soil-water characteristics.” Appl. Magn. Reson. 45 (1): 49–61. https://doi.org/10.1007/s00723-013-0496-0.
Vachaud, G., and J. L. Thony. 1971. “Hysteresis during infiltration and redistribution in a soil column at different initial water contents.” Water Resour. Res. 7 (1): 111–127. https://doi.org/10.1029/WR007i001p00111.
van Genuchten, M. T. 1980. “A closed form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Wardlaw, N. C., and R. P. Taylor. 1976. “Mercury capillary pressure curves and the interpretation of pore structure and capillary behaviour in reservoir rocks.” Bull. Can. Pet. Geol. 24 (2): 225–262.
Wayllace, A., and N. Lu. 2012. “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): 103–117. https://doi.org/10.1520/GTJ103596.
Wei, C., and M. M. Dewoolkar. 2006. “Formulation of capillary hysteresis with internal state variables.” Water Resour. Res. 42 (7): 1–16. https://doi.org/10.1029/2005WR004594.
Wildenschild, D., R. T. Armstrong, A. L. Herring, I. M. Young, and J. W. Carey. 2011. “Exploring capillary trapping efficiency as a function of interfacial tension, viscosity, and flow rate.” Energy Procedia 4: 4945–4952. https://doi.org/10.1016/j.egypro.2011.02.464.
Wildenschild, D., J. W. Hopmans, and J. Simunek. 2001. “Flow rate dependence of soil hydraulic characteristics.” Soil Sci. Soc. Am. J. 65 (1): 35–48. https://doi.org/10.2136/sssaj2001.65135x.
Zhang, C., Z. Liu, and P. Deng. 2016. “Contact angle of soil minerals: A molecular dynamics study.” Comput. Geotech. 75 (May): 48–56. https://doi.org/10.1016/j.compgeo.2016.01.012.
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Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Feb 8, 2018
Accepted: Aug 7, 2019
Published online: Oct 4, 2019
Published in print: Dec 1, 2019
Discussion open until: Mar 4, 2020
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