Approach to Estimate Hydraulic Conductivity Function from Soil–Water Retention Curve for Noncohesive Soils
Publication: Journal of Materials in Civil Engineering
Volume 33, Issue 10
Abstract
Pavement materials are prone to damage due to mechanical loadings and rainfall infiltration. The rainfall initiates moisture movement within the layers and accelerates the damaging rate. A better understanding of the moisture flow and damage can be achieved by rigorous and efficient modeling. The hydraulic conductivity function (HCF) is one of the essential soil properties for numerical seepage modeling. Due to the difficulty in direct HCF measurements, it is generally predicted empirically or statistically by integration along the soil-water retention curve (SWRC) based on the fundamentals of fluid flow in porous media. This paper presents an analytical approach to predict the HCF from experimentally obtained data of an SWRC for noncohesive soils. The model is derived based on the Hagen-Poiseuille law and Darcy law and considered the pore size distribution, porosity, and geometry of the soil grains as inputs. The pore size distribution is considered analogous to a normalized SWRC based on the fundamentals of the capillary theory. The proposed model is validated based on a large number of published experimental data of SWRC and HCF, illustrating the robustness of the model. Additionally, the application of the model is presented for the pavement drainage design.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The work described in this paper is financially supported the by Prime Minister’s Fellowship Scheme for Doctoral Research, a public-private partnership between the Science and Engineering Research Board, Department of Science & Technology, Government of India, and the Confederation of Indian Industry with industry partner Maccaferri Environmental Solutions Pvt. Ltd., India.
References
ARA (Applied Research Associates). 2004. Guide for mechanical-empirical design of new and rehabilitated pavement structures. Washington, DC: Transportation Research Board.
Ariza, P., and B. Birgisson. 2002. Evaluation of water flow through pavement systems. St. Paul, MN: Minnesota DOT.
Barber, E. S., and C.-L. Sawyer. 1952. “Highway subdrainage.” Public Roads 26 (12): 251–268.
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 calculation size distribution data.” Trans. Am. Inst. Min. Metall. Pet. Eng. 198: 71–78. https://doi.org/10.2118/225-G.
Carman, P. C. 1956. Flow of gases through porous media. London: Butterworths Scientific Publications.
Casagrande, A., and W. L. Shannon. 1952. “Base course drainage for airport pavements.” Proc. Am. Soc. Civ. Eng. 117 (1): 792–814. https://doi.org/10.1061/TACEAT.0006654.
Cedergren, H. R. 1974. Drainage of highway and airfield pavements. New York: Wiley.
Childs, E. C., and N. Collis-George. 1950. “The permeability of porous materials.” Proc. R. Soc. London, Ser. A. Math. Phys. Sci. 201 (1066): 392–405. https://doi.org/10.1098/rspa.1950.0068.
Dempsey, B. J., and A. A. Elzeftay. 1975. Moisture movement and moisture equilibria in pavement systems. Chicago: Illinois Cooperative Highway Research Program.
FHWA (Federal Highway Administration). 1999. Pavement subsurface drainage design. Washington, DC: DOT.
FHWA (Federal Highway Administration). 2001. Drainage requirements in pavements (DRIP). Washington, DC: DOT.
Forsyth, R. A., G. K. Wells, and J. H. Woodstrom. 1987. The economic impact of the pavement subsurface drainage. Washington, DC: Transportation Research Board.
Fredlund, D. G., and A. Xing. 1994. “Equations for the soil-water characteristic curve.” Can. Geotech. 31: 521–532. https://doi.org/10.1139/t94-061.
Fredlund, D. G., A. Xing, and S. Huang. 1994. “Predicting the hydraulic function for unsaturated soils using the soil-water characteristic curve.” Can. Geotech. 31: 533–546. https://doi.org/10.1139/t94-062.
Freeze, R. A., and J. A. Cherry. 1979. Groundwater. Englewood Cliffs, NJ: Prentice-Hall.
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.
Gates, J. I., and W. T. Lietz. 1950. “Relative permeabilities of California cores by the capillary pressure method.” In Drilling, and production practice. Washington, DC: American Petroleum Institute. https://doi.org/10.1097/00010694-195804000-00006.
Gottardi, G., and M. Venutalli. 1993. “RICHARDS: Computer programme for the numerical simulation of one-dimensional infiltration into unsaturated soil.” Comput. Geosci. 19 (9): 1239–1266. https://doi.org/10.1016/0098-3004(93)90028-4.
Hall, K., and C. Correa. 2003. Effects of subsurface drainage on performance of asphalt and concrete pavements. Washington, DC: Transportation Research Board.
Hassan, H. F., and T. D. White. 1998. “Measuring and modeling performance of pavement subdrainage systems.” In Proc., TRB 77th Annual Meeting. Washington, DC: Transportation Research Board.
Hassan, H. F., and T. D. White. 2001. “Modeling pavement subdrainage systems.” Transp. Res. Rec. 1772 (1): 137–142. https://doi.org/10.3141/1772-16.
Hazen, A., 1892. “Some physical properties of sands and gravels, with special reference to their use in filtration.” In Proc., 24th Annual Report, Massachusetts State Board of Health, 539–556. https://doi.org/10.4159/harvard.9780674600485.c25.
Hu, R., Y. F. Chen, H. H. Liu, and C. B. Zhou. 2013. “A water retention curve and unsaturated hydraulic conductivity model for deformable soils: Consideration of the change in pore-size distribution.” Géotechnique 63 (16): 1389–1405. https://doi.org/10.1680/geot.12.P.182.
Huyghe, J. M., E. Nikooee, and S. M. Hassanizadeh. 2017. “Bridging effective stress and soil water retention equations in deforming unsaturated porous media: A thermodynamic approach.” Transp. Porous Media 117 (3): 349–365. https://doi.org/10.1007/s11242-017-0837-9.
Jaafar, R., and W. J. Likos. 2014. “Pore-scale model for estimating saturated and unsaturated hydraulic conductivity from grain size distribution.” J. Geotech. Geoenviron. Eng. 14 (2): 1–12. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001031.
Kalore, S. A., G. L. Sivakumar Babu, and R. B. Mallick. 2019. “Design approach for drainage layer in pavement subsurface drainage system considering unsaturated characteristics.” Transp. Geotech. 18 (Mar): 57–71. https://doi.org/10.1016/j.trgeo.2018.11.004.
Kovacs, G. 1981. Seepage hydraulics. Amsterdam, Netherlands: Elsevier Scientific.
Kresic, N. 1998. Quantitative solutions in hydrogeology and groundwater modeling. Boca Raton, FL: CRC Press.
Kunze, R. J., G. Uehara, and K. Graham. 1968. “Factors important in the calculation of hydraulic conductivity.” Soil Sci. Soc. Am. 32 (6): 760–765. https://doi.org/10.2136/sssaj1968.03615995003200060020x.
Leij, F. J., W. J. Alves, M. Th. van Genuchten, and J. R. Williams. 1996. Unsaturated soil hydraulic database, UNSODA 1.0 user’s manual. Washington, DC: USEPA.
Mallick, R. B., and T. El-Korchi. 2009. Pavement engineering principles and practice. Boca Raton, FL: CRC Press.
Marshall, T. J. 1958. “A relation between permeability and size distribution of pores.” J. Soil Sci. 9 (1): 1–8. https://doi.org/10.1111/j.1365-2389.1958.tb01892.x.
Millington, R. J., and J. P. Quirk. 1959. “Permeability of porous media.” Nature 183 (4658): 387–388. https://doi.org/10.1038/183387a0.
Moulton, L. K. 1980. Highway subdrainage design manual. McLean, VA: Federal Highway Administration.
Mualem, Y. 1976. “A new model for predicting the hydraulic conductivity of unsaturated porous media.” Water Resour. Res. 12 (3): 593–622.
Odong, J. 2007. “Evaluation of empirical formulae for determination of hydraulic conductivity based on grain-size analysis.” J. Am. Sci. 3 (3): 54–60.
Pasha, A. Y., A. Khoshghalb, and N. Khalili. 2016. “Pitfalls in interpretation of gravimetric water content–based soil-water characteristic curve for deformable porous media.” Int. J. Geomech. 16 (6): D4015004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000570.
Rose, W. 1949. “Theoretical generalizations leading to the evaluation of relative permeability.” Trans. AIME 186 (1): 325. https://doi.org/10.2118/949325-G.
Slichter, C. S. 1898. “Theoretical investigation of the motion of ground waters.” In Proc., 19th Annual Report, Part II, 295–384. Washington, DC: USGS.
Tavakoli Dastjerdi, M. H., G. Habibagahi, and E. Nikooee. 2014. “Effect of confining stress on soil water retention curve and its impact on the shear strength of unsaturated soils.” Vadose Zone J. 13 (5): 1–11. https://doi.org/10.2136/vzj2013.05.0094.
Vanapalli, S. K., D. E. Pufahl, and D. G. Fredlund. 1998. “The meaning and relevance of residual state to unsaturated soils.” In Proc., 51st Canadian Geotechnical Conf., 101–108. Surrey, BC, Canada: Canadian Geotechnical Society.
Van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Vukovic, M., and A. Soro. 1992. Determination of hydraulic conductivity of porous media from grain-size composition. Littleton, CO: Water Resources Publications.
White, F. M. 1999. Fluid mechanics. 4th ed. Boston: McGraw-Hill.
Wijaya, M., and E. C. Leong. 2016. “Equation for unimodal and bimodal soil-water characteristic curves.” Soils Found. 56 (2): 291–300. https://doi.org/10.1016/j.sandf.2016.02.011.
Wyllie, M. R. J., and M. B. Spangler. 1952. “Applications of electrical resistivity measurement to problems of fluid flow in porous media.” AAPG Bull. 36 (2): 359.
Zhai, Q., and H. Rahardjo. 2015. “Estimation of permeability function from the soil-water characteristic curve.” Eng. Geol. 199 (Dec): 148–156. https://doi.org/10.1016/j.enggeo.2015.11.001.
Zhang, F., and D. G. Fredlund. 2015. “Examination of the estimation of relative permeability for unsaturated soils.” Can. Geotech. J. 52 (12): 2077–2087. https://doi.org/10.1139/cgj-2015-0043.
Zhou, W. H., K. V. Yuen, and F. Tan. 2014. “Estimation of soil-water characteristic curve and relative permeability for granular soils with different initial dry densities.” Eng. Geol. 179 (Sep): 1–9. https://doi.org/10.1016/j.enggeo.2014.06.013.
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Published In
Journal of Materials in Civil Engineering
Volume 33 • Issue 10 • October 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Sep 14, 2020
Accepted: Mar 2, 2021
Published online: Jul 30, 2021
Published in print: Oct 1, 2021
Discussion open until: Dec 30, 2021
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