Technical Papers
May 9, 2018

Assessing Hydraulic Hysteresis Models to Characterize Unsaturated Flow Behavior under Drying and Wetting Conditions

Publication: International Journal of Geomechanics
Volume 18, Issue 7

Abstract

A soil-water retention curve (SWRC) is one of the important constitutive laws for soil-water distribution and shear-strength assessment in unsaturated soil. A SWRC commonly shows the hysteretic behavior under drying and wetting conditions. Several mathematical models have been developed to describe hysteresis, including a model commonly presented in the literature and implemented into HYDRUS software. Recently, the authors developed a new hydraulic hysteresis model for which only one additional parameter was introduced to capture the effects of capillary and air-entrapment hysteresis. To confirm the capabilities of the two models in analyzing the unsaturated flow, the authors’ model was implemented with a numerical code using the FORTRAN language. The numerical codes including the authors’ model and the model in HYDRUS for hysteresis assessment were used to analyze the same transient unsaturated flow problems under drying and wetting conditions. By comparing the measured data to curves predicted by the two models, the results show that the hysteretic SWRC cannot be described correctly when the effects of hydraulic hysteresis are ignored under drying and wetting conditions. Moreover, the comparison between the results predicted by the two models shows that the authors’ model gave a robust performance for capturing hydraulic hysteresis behavior in unsaturated flow.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grants 41472286 and 41572293).

References

Baum, R. L., J. W. Godt, and W. Z. Savage. 2010. “Estimating the timing and location of shallow rainfall-induced landslides using a model for transient, unsaturated infiltration.” J. Geophys. Res. 115: 1–26. https://doi.org/10.1029/2009JF001321.
BeVille, S. H., B. B. Mirus, B. A. Ebel, G. G. Mader, and K. Loague. 2010. “Using simulated hydrologic response to revisit the 1973 Lerida Court landslide.” Environ. Earth Sci. 61 (6): 1249–1257. https://doi.org/10.1007/s12665-010-0448-z.
Bond, W. J., and N. Collis-George. 1981. “Ponded infiltration into simple soil systems: 1. The saturation and transition zones in the moisture content profiles.” Soil Sci. 131 (4): 202–209.https://doi.org/10.1097/00010694-198104000-00002.
Chen, P., B. Mirus, N. Lu, and J. W. Godt. 2017. “Effect of hydraulic hysteresis on 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: 1–11. 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.
Ebel, B. A., K. Loague, and R. I. Borja. 2010. “The impacts of hysteresis on variably saturated hydrologic response and slope failure.” Environ. Earth Sci. 61 (6): 1215–1225. https://doi.org/10.1007/s12665-009-0445-2.
Feng, M., and D. G. Fredlund. 1999. “Hysteretic influence associated with thermal conductivity sensor measurements.” In 52nd Canadian Geotechnical Conf., 651–657. Richmond, BC, Canada: Canadian Geotechnical Society.
Gillham, R. W., A. Klute, and D. F. Heermann. 1976. “Hydraulic properties of a porous medium measurement and empirical representation.” Soil Sci. Soc. Am. J. Abstr. 40 (2): 203–207. https://doi.org/10.2136/sssaj1976.03615995004000020008x.
Gillham, R. W., A. Klute, and D. F. Heermann. 1979. “Measurement and numerical simulation of hysteretic flow in a heterogeneous porous medium.” Soil Sci. Soc. Am. J. Abstr. 43 (6): 1061–1067. https://doi.org/10.2136/sssaj1979.03615995004300060001x.
Hoa, N. T., R. Gaudu, and C. Thirriot. 1977. “Influence of hysteresis effect on transient flows in saturated-unsaturated porous-media.” Water Resour. Res. 13 (6), 992–996. https://doi.org/10.1029/WR013i006p00992.
Huang, H.-C., Y.-C. Tan, C.-W. Liu, and C.-H. Chen. 2005. “A novel hysteresis model in unsaturated soil.” Hydrol. Processes 19 (8): 1653–1665. https://doi.org/10.1002/hyp.5594.
Kechavarzi, C., K. Soga, and T. H. Illangasekare. 2005. “Two-dimensional laboratory simulation of LNAPL infiltration and redistribution in the vadose zone.” J. Contam. Hydrol. 76 (Feb): 211–233. https://doi.org/10.1016/j.jconhyd.2004.09.001.
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 hystereses.” 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.
Khoury, C. N., and G. A. Miller. 2012. “Influence of hydraulic hysteresis on the shear strength of unsaturated soils and interfaces.” Geotech. Test. J. 35 (1): 135–149.
Kool, J. B., and J. C. Parker. 1987. “Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties.” Water Resour. Res. 23 (1): 105–114. https://doi.org/10.1029/WR023i001p00105.
Li, Y., P. Wu, Z. Xia, Q. Yang, G. Flores, H. Jiang, M. Kamon, and B. Yu. 2014. “Changes in residual air saturation after thorough drainage processes in an air-water fine sandy medium.” J. Hydrol. 519: 271–283. https://doi.org/10.1016/j.jhydrol.2014.07.019.
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.
Liu, C., and K. Muraleetharan. 2012. “Coupled hydro-mechanical elastoplastic constitutive model for unsaturated sands and silts. I: Formulation.” Int. J. Geomech. 12 (3): 239–247. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000146.
Lu, N., J. W. Godt, and D. T. Wu. 2010. “A closed-form equation for effective stress in unsaturated soil.” Water Resour. Res. 46 (5): W05515. https://doi.org/10.1029/2009WR008646.
Lu, N., M. Kaya, B. D. Collins, and J. W. 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.
Ma, T., C. Wei, H. Wei, and W. Li. 2016. “Hydraulic and mechanical behavior of unsaturated silt: Experimental and theoretical characterization.” Int. J. Geomech. 16 (6): D4015007. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000576.
Mualem, Y. 1976. “A new model for predicting hydraulic conductivity of unsaturated porous-media.” Water Resour. Res, 12 (3): 513–522. https://doi.org/10.1029/WR012i003p00513.
Mualem, Y., and G. Dagan. 1975. “A dependent domain model of capillary hysteresis.” Water Resour. Res. 11 (3): 452–460.https://doi.org/10.1029/WR011i003p00452.
Muraleetharan, K., and C. Wei. 2001. “U-DYSAC2: Dynamic unsaturated soil analysis code for 2-dimensional problems.” Technical Rep. Norman, OK: School of Civil Engineering and Environmental Science, Univ. of Oklahoma.
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.
Pasha, A. Y., A. Khoshghalb, and N. Khalili. 2017. “Hysteretic model for the evolution of water retention curve with void ratio.” J. Eng. Mech. 143 (7): 04017030. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001238.
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.
Pickens, J. F., and R. W. Gillham. 1980. “Finite element analysis of solute transport under hysteretic unsaturated flow conditions.” Water Resour. Res. 16 (6): 1071–1078. https://doi.org/10.1029/WR016i006p01071.
Poulovassilis, A. 1970. “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., and E. C. Childs. 1971. “The hysteresis of pore water: the non-independence of domains.” Soil Sci. 112 (5): 301–312. https://doi.org/10.1097/00010694-197111000-00002.
Scott, P. S., G. J. Farquhar, and N. Kouwen. 1983. “Hysteresis effects on net infiltration.” In Proc., National Conference on Advances in Infiltration, 163–170. St. Joseph, MI: American Society of Agricultural and Biological Engineers.
Seymour, R. M. 2000. “Air entrapment and consolidation occurring with saturated hydraulic conductivity changes with intermittent wetting.” Irrig. Sci. 20 (1): 9–14. https://doi.org/10.1007/PL00006716.
Sheng, D., and A.-N. Zhou. 2011. “Coupling hydraulic with mechanical models for unsaturated soils.” Can. Geotech. J. 48 (5): 826–840. https://doi.org/10.1139/t10-109.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna. 2012. The HYDRUS software package for simulating two- and three-dimensional movement of water, heat, and multiple solutes in variably-saturated media, version 2.0. Prague, Czech Republic: PC Progress.
Song, X., and R. I. Borja. 2014. “Mathematical framework for unsaturated flow in the finite deformation range.” Int. J. Numer. Methods Eng. 97 (9): 658–682. https://doi.org/10.1002/nme.4605.
Stonestrom, D. A., and J. Rubin. 1989. “Water-content dependence of trapped air in two soils.” Water Resour. Res. 25 (9): 1947–1958. https://doi.org/10.1029/WR025i009p01947.
Sun, D., D. Sheng, and S. W. Sloan. 2007. “Elastoplastic modelling of hydraulic and stress–strain behaviour of unsaturated soils.” Mech. Mater. 39 (3): 212–221. https://doi.org/10.1016/j.mechmat.2006.05.002.
Sun, D., W. 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. F. Feng, and S. Semprich. 2016. “Quasi-saturated zones induced by rainfall infiltration.” Transp. Porous Media 112 (1): 77–104. https://doi.org/10.1007/s11242-016-0633-y.
Tami, D., H. Rahardjo, and E.-C. Leong. 2004. “Effects of hysteresis on steady-state infiltration in unsaturated Slopes.” J. Geotech. Geoenviron. 130 (9): 956–967. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:9(956).
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. Th. 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.
Wei, C., and M. M. Dewoolkar. 2006. “Formulation of capillary hysteresis with internal state variables.” Water Resour. Res. 42 (7): W07405. https://doi.org/10.1029/2005WR004594.
Wheeler, S. J., R. S. Sharma, and M. S. R. Buisson. 2003. “Coupling of hydraulic hysteresis and stress- strain behaviour in unsaturated soils.” Géotechnique 53 (1): 41–54. https://doi.org/10.1680/geot.2003.53.1.41.
Yang, C., D. Sheng, and J. P. Carter. 2012. “Effect of hydraulic hysteresis on seepage analysis for unsaturated soils.” Comput. Geotech. 41 (Apr): 36–56.https://doi.org/10.1016/j.compgeo.2011.11.006.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 18Issue 7July 2018

History

Received: Sep 21, 2017
Accepted: Feb 2, 2018
Published online: May 9, 2018
Published in print: Jul 1, 2018
Discussion open until: Oct 9, 2018

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Assistant Professor, State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei, 430071, P. R. China. Email: [email protected]
Associate Professor, State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei, 430071, P. R. China (corresponding author). Email: [email protected]
Assistant Professor, State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei, 430071, P. R. China. Email: [email protected]

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