A Soil Hydraulic Conductivity Equation Incorporating Adsorption and Capillarity
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 149, Issue 8
Abstract
A soil’s hydraulic conductivity is a highly nonlinear function of water content, decreasing many orders of magnitude from its saturated state to dry state. This nonlinearity is a macroscopic manifestation of microscopic soil properties of pore structure, pore connectivity, and mineral–water interaction. These microscopic soil properties are underpinned by two distinct soil–water interaction mechanisms: adsorption and capillarity. Herein, a soil hydraulic conductivity equation was developed by incorporating capillary pore flow and adsorptive film flow. The capillary pore flow is captured via a model of bundle of cylindrical capillaries, whereas the adsorptive film flow is established using a film thickness function incorporating adsorption mechanisms of the electric double layer, van der Waals, surface hydration, and cation hydration potentials. The transition between adsorptive film flow and capillary flow is delineated by a water cavitation probability function. The proposed soil hydraulic conductivity equation automatically can fulfill the five necessary physical constraints imposed by underlying soil–water interaction characteristics. The proposed hydraulic conductivity equation can capture the hydraulic conductivity data very well for a wide array of soils, and outperforms several established soil hydraulic models in full matric potential ranges, especially in the low matric potential range in which adsorptive film flow is dominant.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All experimental data are from the references listed in Table 3. All models and code generated or used during the study are available from the corresponding author.
Acknowledgments
This research was sponsored by the National Natural Science Foundation of China (Grant No. 52078208) for the contributions by Chao Zhang.
References
Becher, H. H. 1970. Eine methode zur messung der wasserleitfähigkeit von böden im ungesättigten zustand. Hannover, German: Technischen Universität, Fakultät für Gartenbau und Landeskultur.
Bharat, T. V., A. Srivastava, and Y. Gapak. 2021. “Prediction of wetting hydraulic characteristics of compacted bentonites in isochoric conditions.” J. Geotech. Geoenviron. Eng. 147 (8): 04021067. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002584.
Bird, R. B., W. E. Stewart, and E. N. Lightfoot. 1960. Transport phenomena. New York: Wiley.
Briggs, L. J. 1950. “Limiting negative pressure of water.” J. Appl. Phys. 21 (7): 721–722. https://doi.org/10.1063/1.1699741.
Brooks, R. H., and A. T. Corey. 1964. Hydraulic properties of porous medium. 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. Riverside, CA: Univ. of California.
Caupin, F., and E. Herbert. 2006. “Cavitation in water: A review.” C.R. Phys. 7 (9–10): 1000–1017. https://doi.org/10.1016/j.crhy.2006.10.015.
Chiu, T.-F., and C. D. Shackelford. 1998. “Unsaturated hydraulic conductivity of compacted sand-kaolin mixtures.” J. Geotech. Geoenviron. Eng. 124 (2): 160–170. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:2(160).
Dane, J. H., and C. G. Topp. 2020. Methods of soil analysis, part 4: Physical methods. New York: Wiley.
De Wit, C. T., and P. L. Arens. 1950. “Moisture content and density of some caly minerals and some remarks on the hydration pattern of clay.” In Proc., 4th Int. Congress of Soil Science Transactions, 59–62. Amsterdam, Netherlands: Hoitesema Brothers.
Durner, W., and H. Fluhler. 2005. “Soil hydraulic properties.” In Encyclopedia of hydrological sciences, edited by M. G. Anderson and J. J. McDonnell, 1103–1120. Hoboken, NJ: Wiley.
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.
Gardner, W. R. 1958. “Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table.” Soil Sci. 85 (4): 228–232. https://doi.org/10.1097/00010694-195804000-00006.
Gou, L., C. Zhang, S. Hu, R. Chen, and Y. Dong. 2022. “Semi-analytical solutions for soil consolidation induced by drying.” Acta Geotech. 18 (2): 739–755. https://doi.org/10.1007/s11440-022-01623-4.
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.
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.
Langmuir, I. 1938. “Repulsive forces between charged surfaces in water, and the cause of the Jones-Ray effect.” Science 88 (2288): 430–432. https://doi.org/10.1126/science.88.2288.430.
Leão, T. P., and M. Tuller. 2014. “Relating soil specific surface area, water film thickness, and water vapor adsorption.” Water Resour. Res. 50 (10): 7873–7885. https://doi.org/10.1002/2013WR014941.
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): 1–15. https://doi.org/10.1029/2010WR009092.
Lenormand, R. 1990. “Liquids in porous media.” J. Phys.: Condens. Matter 2: SA79–SA88. https://doi.org/10.1088/0953-8984/2/S/008.
Low, P. F. 1959. “Viscosity of water in clay systems.” Clays Clay Miner. 170–182. https://doi.org/10.1346/CCMN.1959.0080116.
Low, P. F. 1976. “Viscosity of interlayer water in montmorillonite.” Soil Sci. Soc. Am. J. 40 (4): 500–505. https://doi.org/10.2136/sssaj1976.03615995004000040017x.
Lu, N. 2016. “Generalized soil water retention equation for adsorption and capillarity.” J. Geotech. Geoenviron. Eng. 142 (10): 04016051. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001524.
Lu, N., and W. J. Likos. 2004. Unsaturated soil mechanics. New York: Wiley.
Lu, N., W. J. Likos, S. Luo, and H. Oh. 2021. “Is the conventional pore water pressure concept adequate for fine-grained soils in geotechnical and geoenvironmental engineering?” J. Geotech. Geoenviron. Eng. 147 (10): 02521001. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002612.
Lu, N., and C. Zhang. 2019. “Soil sorptive potential: Concept, theory, and verification.” J. Geotech. Geoenviron. Eng. 145 (4): 4019006. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002025.
Lu, N., and C. Zhang. 2020. “Separating external and internal surface areas of soil particles.” J. Geotech. Geoenviron. Eng. 146 (2): 04019126. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002198.
Luo, S., W. J. Likos, and N. Lu. 2021. “Cavitation of water in soil.” J. Geotech. Geoenviron. Eng. 147 (8): 1–14. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002598.
Martin, R. T. 1960. “Adsorbed water on clay: A review.” Clays Clay Miner. 9 (1): 28–70. https://doi.org/10.1346/CCMN.1960.0090104.
Mathews, J., and R. L. Walker. 1970. Mathematical methods of physics. New York: WA Benjamin.
Meerdink, J. S., C. H. Benson, and M. V. Khire. 1996. “Unsaturated hydraulic conductivity of two compacted barrier soils.” J. Geotech. Eng. 122 (7): 565. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(565).
Mualem, Y. 1976a. A catalogue of the hydraulic properties of unsaturated soils. Haifa, Israel: Israel Institute of Technology.
Mualem, Y. 1976b. “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.
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.
Nguyen, H. T., S. Rahimi-Aghdam, and Z. P. Bažant. 2019. “Sorption isotherm restricted by multilayer hindered adsorption and its relation to nanopore size distribution.” J. Mech. Phys. Solids 127 (Aug): 111–124. https://doi.org/10.1016/j.jmps.2019.03.003.
Or, D., and M. Tuller. 1999. “Liquid retention and interfacial area in variably saturated porous media: Upscaling from single-pore to sample-scale model.” Water Resour. Res. 35 (12): 3591–3605. https://doi.org/10.1029/1999WR900262.
Or, D., and M. Tuller. 2000. “Flow in unsaturated fractured porous media: Hydraulic conductivity of rough surfaces.” Water Resour. Res. 36 (5): 1165–1177. https://doi.org/10.1029/2000WR900020.
Or, D., and M. Tuller. 2002. “Cavitation during desaturation of porous media under tension.” Water Resour. Res. 38 (5): 19-1–19–14. https://doi.org/10.1029/2001WR000282.
Pachepsky, Y., R. Scherbakov, G. Varallyay, and K. Rajkai. 1984. “On obtaining soil hydraulic conductivity curves from water retention curves.” [In Russian.] Pochvovedenie 10 (Mar): 60–72.
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.
Ponec, V., Z. Knor, and S. Cerny. 1974. Adsorption on solids. London: Butterworth.
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.
Saito, H., J. Šimůnek, and B. P. Mohanty. 2006. “Numerical analysis of coupled water, vapor, and heat transport in the vadose zone.” Vadose Zone J. 5 (2): 784–800. https://doi.org/10.2136/vzj2006.0007.
Scarfone, R., S. J. Wheeler, and M. Lloret-Cabot. 2020. “Conceptual hydraulic conductivity model for unsaturated soils at low degree of saturation and its application to the study of capillary barrier systems.” J. Geotech. Geoenviron. Eng. 146 (10): 04020106. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002357.
Schindler, U., K. Bohne, and R. Sauerbrey. 1985. “Comparison of different measuring and calculating methods to quantify the hydraulic conductivity of unsaturated soil.” Zeitschrift für Pflanzenernährung und Bodenkunde 148 (6): 607–617. https://doi.org/10.1002/jpln.19851480603.
Silva, O., and J. Grifoll. 2007. “A soil-water retention function that includes the hyper-dry region through the BET adsorption isotherm.” Water Resour. Res. 43 (11): 1–13. https://doi.org/10.1029/2006WR005325.
Šimůnek, J. 2005. “Encyclopedia of hydrological sciences.” In Models of water flow and solute transport in the unsaturated zone. Chichester, UK: Wiley.
Srivastava, R., and T.-C. J. Yeh. 1991. “Analytical solutions for one-dimensional, transient infiltration toward the water table in homogeneous and layered soils.” Water Resour. Res. 27 (5): 753–762. https://doi.org/10.1029/90WR02772.
Tokunaga, T. K. 2009. “Hydraulic properties of adsorbed water films in unsaturated porous media.” Water Resour. Res. 45 (6): 1–9. https://doi.org/10.1029/2009WR007734.
Tokunaga, T. K. 2011. “Physicochemical controls on adsorbed water film thickness in unsaturated geological media.” Water Resour. Res. 47 (8): 1–12. https://doi.org/10.1029/2011WR010676.
Toledo, P. G., R. A. Novy, H. T. Davis, and L. E. Scriven. 1990. “Hydraulic conductivity of porous media at low water content.” Soil Sci. Soc. Am. J. 54 (3): 673–679. https://doi.org/10.2136/sssaj1990.03615995005400030007x.
Tuli, A., and J. W. Hopmans. 2003. “Presenting essential soil science from Blackwell Publishing.” Eur. J. Soil Sci. 54 (3): 648. https://doi.org/10.1046/j.1365-2389.2003.00551.x.
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.
Tuller, M., and D. Or. 2005. “Water films and scaling of soil characteristic curves at low water contents.” Water Resour. Res. 41 (9): 1–6. https://doi.org/10.1029/2005WR004142.
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.
Wan, J., and T. K. Tokunaga. 1997. “Film straining of colloids in unsaturated porous media: Conceptual model and experimental testing.” Environ. Sci. Technol. 31 (8): 2413–2420. https://doi.org/10.1021/es970017q.
Wang, Y., J. Ma, and H. Guan. 2016. “A mathematically continuous model for describing the hydraulic properties of unsaturated porous media over the entire range of matric suctions.” J. Hydrol. 541 (Jun): 873–888. https://doi.org/10.1016/j.jhydrol.2016.07.046.
Yu, L., and N. C. Wardlaw. 1986. “Mechanisms of nonwetting phase trapping during imbibition at slow rates.” J. Colloid Interface Sci. 109 (2): 473–486. https://doi.org/10.1016/0021-9797(86)90325-5.
Zhang, C., L. Gou, S. Hu, and N. Lu. 2022. “A thermodynamic formulation of water potential in soil.” Water Resour. Res. 58 (9): 1–20. https://doi.org/10.1029/2022WR032369.
Zhang, C., and N. Lu. 2018. “What is the range of soil water density? Critical reviews with a unified model.” Rev. Geophys. 56 (3): 532–562. https://doi.org/10.1029/2018RG000597.
Zhang, C., and N. Lu. 2019. “Augmented Brunauer–Emmett–Teller equation for water adsorption on soils.” Vadose Zone J. 18 (1): 1–12. https://doi.org/10.2136/vzj2019.01.0011.
Zhang, C., and N. Lu. 2020a. “Soil sorptive potential: Its determination and predicting soil water density.” J. Geotech. Geoenviron. Eng. 146 (1): 04019118. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002188.
Zhang, C., and N. Lu. 2020b. “Unified effective stress equation for soil.” J. Eng. Mech. 146 (2): 04019135. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001718.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 149 • Issue 8 • August 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Oct 4, 2022
Accepted: Mar 21, 2023
Published online: May 25, 2023
Published in print: Aug 1, 2023
Discussion open until: Oct 25, 2023
ASCE Technical Topics:
- Adsorption
- Chemical processes
- Chemistry
- Engineering fundamentals
- Environmental engineering
- Geomechanics
- Geotechnical engineering
- Hydration
- Hydraulic conductivity
- Hydraulic models
- Laminating
- Materials engineering
- Materials processing
- Models (by type)
- Saturated soils
- Soft soils
- Soil dynamics
- Soil mechanics
- Soil properties
- Soil water
- Soil-structure interaction
- Soils (by type)
- Sorption
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.