Abstract
To understand better the influence of soil-water characteristic hysteresis on rainfall infiltration and pore-water pressure distributions in unsaturated soils, an analytical solution to the one-dimensional governing partial differential equation considering hysteresis is derived using a Fourier integral transformation. The analytical solution considers time-dependent and arbitrary initial pore-water pressure distributions, as well as a time-varying rainfall flux process at the ground surface. An exponential function is used to represent the hysteretic Soil-Water Characteristic Curve (SWCC) and the relationship between hydraulic conductivity and pore-water pressure. The calculated results demonstrate that the critical point, the intersection between wetting and drying domains in one-dimensional unsaturated seepage, is influenced by many factors. The hysteresis in soil-water characteristics is an important factor in infiltration process influencing the pore-water pressure profiles in unsaturated soils. The effects of hysteretic parameters on pore-water pressure profiles are also analyzed. The value of α in the hysteresis model is found to be the most significant factor influencing the pore pressure distributions.
Similar content being viewed by others
References
Basha, H. A. (1999). “Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface.” Water Resources Research, Vol. 35, No. 1, pp. 75–83.
Basha, H. A. (2000). “Multidimensional linearized nonsteady infiltration toward a shallow water table.” Water Resources Research, Vol. 36, No. 9, pp. 2567–2573.
Batu, V. (1983). “Time-dependent linearized two-dimensional infiltration and evaporation from nonuniform and periodic strip sources.” Water Resources Research, Vol. 19, No. 6, pp. 1523–1529.
Broadbridge, P. and White, I. (1988). “Constant rate rainfall infiltration: A versatile nonlinear model. I. Analytical solution.” Water Resources Research, Vol. 24, No. 1, pp. 145–154.
Brooks, R. H. and Corey, A. T. (1964). “Hydraulic properties of porous media.” Hydrology, Paper No. 3. Colorado State University, Fort Collins, Colorado.
Chen, J. M., Tan, Y. C., and Chen, C. H. (2001). “Multidimensional infiltration with arbitrary surface fluxes.” Journal of Irrigation and Drainage Engineering (ASCE), Vol. 127, No. 6, pp. 370–377.
Dane, J. H. and Wierenga, P. J. (1975). “Effect of hysteresis on the prediction of infiltration, redistribution and drainage of water in layered soil.” Journal of Hydrology, Vol. 25, Nos. 3–4, pp. 229–242.
Fredlund, D. G. and Rahardjo, H. (1993). Soil mechanics for unsaturated soils, John Wiley & Sons, New York.
Gillham, R. W., Klute, A., and Heerman, D. F. (1976). “Hydraulic properties of a porous medium: Measurement and empirical representation.” Soil Science Society American Journal, Vol. 40, No. 2, pp. 203–207.
Haines, W. B. (1930). “Studies in the physical properties of soil — V: The hysteresis effect in capillary properties and the modes of water distribution associated therewith.” Journal of Agricultural Science, Vol. 20, pp. 97–116.
Hank, R. J., Klute, A., and Bresler, E. (1969). “A numerical method for estimating infiltration redistribution, drainage, and evaporation of water from soil.” Water Resources Research, Vol. 13, pp. 992–998.
Hillel, D. (1998). Environmental soil physics, Academic, New York.
Hills, R. G. B., Hudson, I. P., and Wierenga, P. J. (1989). “Modeling onedimensional infiltration into very dry soils.” Water Resources Reseach, Vol. 25, No. 6, pp. 1271–1282.
Hogarth, W., Hopmans, J., Parlange, J. Y., and Haverkamp, R. (1988). “Application of a simple soil-water hysteresis model.” Journal of Hydrology, Vol. 98, Nos. 1–2, pp. 21–29.
Jaynes, D. B. (1985). “Comparison of soil-water hysteresis models.” Journal of Hydrology, Vol. 75, Nos. 1–4, pp. 287–299.
Kacimov, A. R. and Yakimov, N. D. (1998). “Nonmonotonic moisture profile as a solution of Richards’ equation for soils with conductivity hysteresis.” Advances in Water Resources, Vol. 21, No. 8, pp. 691–696.
Kawai, K., Karube, D., and Kato, S. (2000). “The model of water retention curve considering effects of void ratio.” Proceedings Asian Conference on Unsaturated Soils, pp. 329–334.
Klausner, Y. (1991). Fundamentals of continuum mechanics of soils, Springer-Verlag, New York.
Kool, J. B. and Parker, J. C. (1987). “Development and evaluation of closed-form expressions for hysteretic hydraulic properties.” Water Resources Research, Vol. 23, No. 1, pp. 105–114.
Li, X. S. (2005). “Modelling of hysteresis response for arbitrary wetting/drying paths.” Computers and Geotechnics, Vol. 32, No. 2, pp. 133–137.
Likos, W. J. and Lu, N. (2004). “Hysteresis of capillary stress in unsaturated granular soil.” Journal of Engineering Mechanics, ASCE, Vol. 130, No. 6, pp. 646–655.
Min, T. K. and Phan, T. H. (2010). “Prediction of hysteretic behavior for unsaturated sands using the elasto-plastic constitutive relations.” KSCE Journal of Civil Engineering, Vol. 14, No. 3, pp. 299–305.
Mualem, Y. (1974). “A conceptual model of hysteresis.” Water Resources Research, Vol. 10, No. 3, pp. 514–520.
Mualem, Y. (1984). “Prediction of the soil boundary wetting curve.” Soil Science, Vol. 137, No. 6, pp. 379–389.
Nimmo, J. R. (1992). “Semi-empirical model of soil water hysteresis.” Soil Science Society of America Journal, Vol. 56, No. 6, pp. 1723–1730.
Ozisik, M. (1989). Boundary value problems of heat conduction, Dover, New York, pp. 85–87.
Parlange, J. Y. (1972). “Theory of water movement in soils: VIII. One dimensional infiltration with constant flux at the surface.” Soil Science, Vol. 114, No. 4, pp. 1–4.
Parlange, J. Y. (1976). “Capillary hysteresis and the relationship between drying and wetting curves.” Water Resources Research, Vol. 12, No. 2, pp. 224–228.
Pedroso, D. M. and Williams, D. J. (2010). “A novel approach for modelling soil-water characteristic curves with hysteresis.” Computers and Geotechnics, Vol. 37, No. 3, pp. 374–380.
Pham, H. Q., Fredlund, D. G., and Barbour, S. L. (2003). “A practical hysteresis model for the soil-water characteristic curve for soils with negligible volume change.” Geotechnique, Vol. 53, No. 2, pp. 293–298.
Philip, J. R. (1964). “Similarity hypothesis for capillary hysteresis in porous materials.” Journal of Geophysical Research, Vol. 69, No. 8, pp. 1553–1562.
Philip, J. R. and Knight, J. H. (1974). “On solving the unsaturated flow equation: III. New quasi-analytical technique.” Soil Science, Vol. 117, pp. 1–13.
Richards, L. A. (1931). “Capillary conduction of liquids through porous mediums.” Physics (N.Y.), Vol. 1, No. 5, pp. 318–333.
Russo, D., Jury, W. A., and Butters, G. L. (1989). “Numerical analysis of solute transport during transient irrigation. 1. The effect of hysteresis and profile heterogeneity.” Water Resources Research, Vol. 25, No. 10, pp. 2109–2118.
Sander, G. C., Cunning, I. F., Hogarth, W. L., and Parlange, J. Y. (1991). “Exact solution for nonlinear, non-hysteretic redistribution in vertical soil of finite depth.” Water Resources Research, Vol. 27, No. 7, pp. 1529–1536.
Sander, G. C., Parlange, J. Y., Kuhnel, V., Hogarth, W. L., Lockington, D., and O’Kane, J. P. J. (1988). “Exact nonlinear solution for constant flux infiltration.” Journal of Hydrology, Vol. 97, No. 4, pp. 341–346.
Sheng, D., Fredlund, D. G., and Gens, A. (2008). “A new modelling approach for unsaturated soils using independent stress variables.” Canadian Geotechnical Journal, Vol. 45, No. 4, pp. 511–534.
Si, B. C. and Kachanoski, R. G. (2000). “Unified solution for infiltration and drainage with hysteresis: Theory and field test.” Soil Science Society of America Journal, Vol. 64, No. 1, pp. 30–36.
Srivastava, R. and Yeh, T. C. J. (1991). “Analytical solutions for onedimension, transient infiltration toward the water table in homogeneous and layered soils.” Water Resources Research, Vol. 27, No. 5, pp. 753–762.
Staple, W. J. (1969). “Comparison of computed and measured moisture redistribution following infiltration.” Soil Science Society of America Proceedings, Vol. 33, No. 6, pp. 840–847.
Tan, Y. C., Ma, K. C., Chen, C. H., Ke, K. Y., and Wang, M. T. (2009). “A numerical model of infiltration processes for hysteretic flow coupled with mass conservation.” Irrigation and Drainage, Vol. 58, No. 3, pp. 366–380.
Topp, G. C. (1971). “Soil-water hysteresis: The domain theory extended to pore interaction conditions.” Soil Science Society of America Proceedings, Vol. 35, No. 2, pp. 219–225.
Van Genuchten, M. T. (1980). “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Science Society of America Journal, Vol. 44, No. 5, pp. 892–898.
Warrick, A. W., Islas, A., and Lomen, D. O. (1991). “An analytical solution to Richards’ equation for time-varying infiltration.” Water Resources Research, Vol. 27, No. 5, pp. 763–766.
Warrick, A. W., Lomen, D. O., and Islas, A. (1990). “An analytical solution to Richards’ equation for a draining soil profiles.” Water Resources Research, Vol. 26, No. 2, pp. 253–258.
White, I., Smiles, D. E., and Peroux, K. M. (1979). “Absorption of water by soil: The constant flux boundary condition.” Soil Science Society of America Journal, Vol. 43, No. 4, pp. 659–664.
Wu, L. Z. and Zhang, L. M. (2009). “Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 33, No. 6, pp. 773–790.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, L.Z., Huang, R.Q. & Xu, Q. Incorporating hysteresis in one-dimensional seepage modeling in unsaturated soils. KSCE J Civ Eng 16, 69–77 (2012). https://doi.org/10.1007/s12205-012-1377-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-012-1377-z