Conceptual Hydraulic Conductivity Model for Unsaturated Soils at Low Degree of Saturation and Its Application to the Study of Capillary Barrier Systems
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 146, Issue 10
Abstract
Accurate modeling and prediction of the variation of the hydraulic conductivity of unsaturated soils at a very low degree of saturation has important implications in various engineering problems. Physical processes underlying the hydraulic behavior of unsaturated soils (retention behavior and variation of hydraulic conductivity) are first explained, and then a consistent set of new definitions for key transition hydraulic states is proposed. This lays the foundation for the presentation of a new predictive hydraulic conductivity model, accurate for the full range of degree of saturation and applicable to relatively coarse-grained soils (i.e., gravels, sands, and silts). The hydraulic conductivity is divided into two components—a bulk water component and a liquid film component—each of which varies with the degree of saturation or suction. The model is then validated against experimental data. Finally, the new hydraulic conductivity model is applied to the numerical study of the hydraulic behavior of capillary barrier systems (CBSs). The new model is able to predict the behavior of CBSs better than conventional models, and the numerical modeling highlights the role of liquid film flow, which is often neglected.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository online in accordance with funder data retention policies. The online repository is the institutional repository “Enlighten” of the University of Glasgow, and the data can be accessed using the following DOI: https://doi.org/10.5525/gla.researchdata.1018.
Acknowledgments
The authors wish to acknowledge the support of the European Commission via the Marie Skłodowska-Curie Innovative Training Networks (ITN-ETN) project Training Engineers and Researchers to Rethink geotechnical Engineering for a low carbon future (TERRE) (H2020-MSCA-ITN-2015-675762).
References
Akin, I. D., and W. J. Likos. 2017. “Implications of surface hydration and capillary condensation for strength and stiffness of compacted clay.” J. Eng. Mech. 143 (8): 04017054. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001265.
Baker, R. S., and D. Hillel. 1990. “Laboratory tests of a theory of fingering during infiltration into layered soils.” Soil Sci. Soc. Am. J. 54 (1): 20–30. https://doi.org/10.2136/sssaj1990.03615995005400010004x.
Bouwer, H. 1966. “Rapid field measurement of air entry value and hydraulic conductivity of soil as significant parameters in flow system analysis.” Water Resour. Res. 2 (4): 729–738. https://doi.org/10.1029/WR002i004p00729.
Brooks, R., and T. Corey. 1964. Vol. 3 of Hydraulic properties of porous media: Hydrology papers, 1–27. Fort Collins, CO: Colorado State Univ.
Burdine, N. T. 1953. “Relative permeability calculations from pore size distribution data.” J. Pet. Technol. 5 (3): 71–78. https://doi.org/10.2118/225-G.
Campbell, G. S., and S. Shiozawa. 1992. “Prediction of hydraulic properties of soils using particle-size distribution and bulk density data.” In Indirect methods for estimating the hydraulic properties of unsaturated soils, 317–328. Oakland, CA: Univ. of California.
Cass, A., G. S. Campbell, and T. L. Jones. 1984. “Enhancement of thermal water vapor diffusion in soil.” Soil Sci. Soc. Am. J. 48 (1): 25–32. https://doi.org/10.2136/sssaj1984.03615995004800010005x.
Fayer, M. J., and C. S. Simmons. 1995. “Modified soil water retention functions for all matric suctions.” Water Resour. Res. 31 (5): 1233–1238. https://doi.org/10.1029/95WR00173.
Fisher, R. A. 1926. “On the capillary forces in an ideal soil; correction of formulae given by WB Haines.” J. Agric. Sci. 16 (3): 492–505. https://doi.org/10.1017/S0021859600007838.
Fredlund, D. G., and A. Xing. 1994. “Equations for the soil-water characteristic curve.” Can. Geotech. J. 31 (4): 521–532. https://doi.org/10.1139/t94-061.
Gens, A. 2010. “Soil-environment interactions in geotechnical engineering.” Géotechnique 60 (1): 3. https://doi.org/10.1680/geot.9.P.109.
Haines, W. B. 1930. “Studies in the physical properties of soil. V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith.” J. Agric. Sci. 20 (1): 97–116.
Hillel, D., and R. S. Baker. 1988. “A descriptive theory of fingering during infiltration into layered soils.” Soil Sci. 146 (1): 51–56. https://doi.org/10.1097/00010694-198807000-00008.
Iden, S. C., and W. Durner. 2014. “Comment on ‘Simple consistent models for water retention and hydraulic conductivity in the complete moisture range’ by A. Peters.” Water Resour. Res. 50 (9): 7530–7534. https://doi.org/10.1002/2014WR015937.
Israelachvili, J. N. 2011. Intermolecular and surface forces. 3rd ed. San Diego: Academic Press.
Kemper, W. D. 1961. “Movement of water as effected by free energy and pressure gradients. I: Application of classic equations for viscous and diffusive movements to the liquid phase in finely porous media 1.” Soil Sci. Soc. Am. J. 25 (4): 255–260. https://doi.org/10.2136/sssaj1961.03615995002500040009x.
Khlosi, M., W. M. Cornelis, D. Gabriels, and G. Sin. 2006. “Simple modification to describe the soil water retention curve between saturation and oven dryness.” Water Resour. Res. 42 (11): W11501. https://doi.org/10.1029/2005WR004699.
Kosugi, K. I. 1996. “Lognormal distribution model for unsaturated soil hydraulic properties.” Water Resour. Res. 32 (9): 2697–2703. https://doi.org/10.1029/96WR01776.
Lebeau, M., and J. M. Konrad. 2010. “A new capillary and thin film flow model for predicting the hydraulic conductivity of unsaturated porous media.” Water Resour. Res. 46 (12): W12554.
Lu, N., and M. Khorshidi. 2015. “Mechanisms for soil-water retention and hysteresis at high suction range.” J. Geotech. Geoenviron. Eng. 141 (8): 04015032. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001325.
Lu, N., and W. J. Likos. 2006. “Suction stress characteristic curve for unsaturated soil.” J. Geotech. Geoenviron. Eng. 132 (2): 131–142. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(131).
Luckner, L., M. T. van Genuchten, and D. R. Nielsen. 1989. “A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface.” Water Resour. Res. 25 (10): 2187–2193. https://doi.org/10.1029/WR025i010p02187.
Mehta, B. K., S. H. O. Shiozawa, and M. Nakano. 1994. “Hydraulic properties of a sandy soil at low water contents.” Soil Sci. 157 (4): 208–214. https://doi.org/10.1097/00010694-199404000-00002.
Mualem, Y. 1976a. “A new model for predicting the hydraulic conductivity of unsaturated porous media.” Water Resour. Res. 12 (3): 513–522. https://doi.org/10.1029/WR012i003p00513.
Mualem, Y. 1976b. A catalogue of the hydraulic properties of unsaturated soils. Haifa, Israel: Technion Israel Institute of Technology, Technion Research and Development Foundation.
Nemes, A. D., M. G. Schaap, F. J. Leij, and J. H. M. Wösten. 2001. “Description of the unsaturated soil hydraulic database UNSODA version 2.0.” J. Hydrol. 251 (3–4): 151–162. https://doi.org/10.1016/S0022-1694(01)00465-6.
Olivella, S., J. Carrera, A. Gens, and E. E. Alonso. 1994. “Nonisothermal multiphase flow of brine and gas through saline media.” Transp. Porous Media 15 (3): 271–293. https://doi.org/10.1007/BF00613282.
Olivella, S., A. Gens, J. Carrera, and E. E. Alonso. 1996. “Numerical formulation for a simulator (CODE_BRIGHT) for the coupled analysis of saline media.” Eng. Comput. 13 (7): 87–112. https://doi.org/10.1108/02644409610151575.
Peters, A. 2013. “Simple consistent models for water retention and hydraulic conductivity in the complete moisture range.” Water Resour. Res. 49 (10): 6765–6780. https://doi.org/10.1002/wrcr.20548.
Peters, A. 2014. “Reply to comment by S. Iden and W. Durner on ‘Simple consistent models for water retention and hydraulic conductivity in the complete moisture range’.” Water Resour. Res. 50 (9): 7535–7539. https://doi.org/10.1002/2014WR016107.
Peters, A., and W. Durner. 2008. “A simple model for describing hydraulic conductivity in unsaturated porous media accounting for film and capillary flow.” Water Resour. Res. 44 (11): W11417. https://doi.org/10.1029/2008WR007136.
Philip, J. R., and D. A. De Vries. 1957. “Moisture movement in porous materials under temperature gradients.” Eos, Trans. Am. Geophys. Union 38 (2): 222–232. https://doi.org/10.1029/TR038i002p00222.
Rahardjo, H., V. A. Santoso, E. C. Leong, Y. S. Ng, and C. J. Hua. 2012. “Performance of an instrumented slope covered by a capillary barrier system.” J. Geotech. Geoenviron. Eng. 138 (4): 481–490. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000600.
Reinson, J. R., D. G. Fredlund, and G. W. Wilson. 2005. “Unsaturated flow in coarse porous media.” Can. Geotech. J. 42 (1): 252–262. https://doi.org/10.1139/t04-070.
Richards, B. G. 1965. “Measurement of the free energy of soil moisture by the psychrometric technique using thermistors.” In Moisture equilibria and moisture changes in soils beneath covered areas, edited by G. D. Aitchison, 35–46. Sydney, Australia: Butterworths & Co.
Rossi, C., and J. R. Nimmo. 1994. “Modeling of soil water retention from saturation to oven dryness.” Water Resour. Res. 30 (3): 701–708. https://doi.org/10.1029/93WR03238.
Scarfone, R., M. Lloret-Cabot, and S. J. Wheeler. 2018. “Numerical modelling of water breakthrough in coarse soils initially at very low degree of saturation.” In Proc., 7th Int. Conf. on Unsaturated Soils. Scotland, UK: Enlighten Publications.
Schubert, H., W. Herrmann, and H. Rumpf. 1975. “Deformation behaviour of agglomerates under tensile stress.” Powder Technol. 11 (2): 121–131. https://doi.org/10.1016/0032-5910(75)80037-4.
Stormont, J. C., and C. E. Anderson. 1999. “Capillary barrier effect from underlying coarser soil layer.” J. Geotech. Geoenviron. Eng. 125 (8): 641–648. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:8(641).
Stormont, J. C., and C. E. Morris. 1998. “Method to estimate water storage capacity of capillary barriers.” J. Geotech. Geoenviron. Eng. 124 (4): 297–302. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:4(297).
Tami, D., H. Rahardjo, E. C. Leong, and D. G. Fredlund. 2004. “Design and laboratory verification of a physical model of sloping capillary barrier.” Can. Geotech. J. 41 (5): 814–830. https://doi.org/10.1139/t04-036.
Tokunaga, T. K. 2009. “Hydraulic properties of adsorbed water films in unsaturated porous media.” Water Resour. Res. 45 (6), https://doi.org/10.1029/2009WR007734.
Tuller, M., and D. Or. 2001. “Hydraulic conductivity of variably saturated porous media: Film and corner flow in angular pore space.” Water Resour. Res. 37 (5): 1257–1276. https://doi.org/10.1029/2000WR900328.
Vanapalli, S. K., D. G. Fredlund, and D. E. Pufahl. 1999. “The influence of soil structure and stress history on the soil–water characteristics of a compacted till.” Géotechnique 49 (2): 143–159. https://doi.org/10.1680/geot.1999.49.2.143.
Vanapalli, S. K., W. S. Sillers, and M. D. Fredlund. 1998. “The meaning and relevance of residual state to unsaturated soils.” In Vol. 1 of Proc., 51st Canadian Geotechnical Conf., 101–108. State College, PA: Pennsylvania State Univ.
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.
Wheeler, S. J., and D. Karube. 1996. “Constitutive modelling.” In Vol. 3 of Proc., 1st Int. Conf. on Unsaturated Soils, 1123–1356. Rotterdam, Netherlands: A.A. Belkema.
Yang, H., H. Rahardjo, and E. C. Leong. 2006. “Behavior of unsaturated layered soil columns during infiltration.” J. Hydrol. Eng. 11 (4): 329–337. https://doi.org/10.1061/(ASCE)1084-0699(2006)11:4(329).
Yang, H., H. Rahardjo, E. C. Leong, and D. G. Fredlund. 2004. “A study of infiltration on three sand capillary barriers.” Can. Geotech. J. 41 (4): 629–643. https://doi.org/10.1139/t04-021.
Zhan, T. L., and C. W. Ng. 2004. “Analytical analysis of rainfall infiltration mechanism in unsaturated soils.” Int. J. Geomech. 4 (4): 273–284. https://doi.org/10.1061/(ASCE)1532-3641(2004)4:4(273).
Zhang, Z. F. 2011. “Soil water retention and relative permeability for conditions from oven-dry to full saturation.” Vadose Zone J. 10 (4): 1299–1308. https://doi.org/10.2136/vzj2011.0019.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 146 • Issue 10 • October 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jul 16, 2019
Accepted: May 26, 2020
Published online: Jul 29, 2020
Published in print: Oct 1, 2020
Discussion open until: Dec 29, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.