A Mathematical Model for Predicting Isothermal Soil Moisture Profiles Using Finite Difference Method

Authors: Kasthurirangan Gopalakrishnan, Anshu Manik

Abstract:

Subgrade moisture content varies with environmental and soil conditions and has significant influence on pavement performance. Therefore, it is important to establish realistic estimates of expected subgrade moisture contents to account for the effects of this variable on predicted pavement performance during the design stage properly. The initial boundary soil suction profile for a given pavement is a critical factor in determining expected moisture variations in the subgrade for given pavement and climatic and soil conditions. Several numerical models have been developed for predicting water and solute transport in saturated and unsaturated subgrade soils. Soil hydraulic properties are required for quantitatively describing water and chemical transport processes in soils by the numerical models. The required hydraulic properties are hydraulic conductivity, water diffusivity, and specific water capacity. The objective of this paper was to determine isothermal moisture profiles in a soil fill and predict the soil moisture movement above the ground water table using a simple one-dimensional finite difference model.

Keywords: Fill, Hydraulic Conductivity, Pavement, Subgrade.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332730

References:

[1] EPA Groundwater Primer. http://www.epa.gov/seahome/gwprimer.html. Software for Environmental Awareness. Accessed online on March 9, 2007.
[2] Environment Canada. http://www.mb.ec.gc.ca/index.en.html. Prairie and Northern Region Green Lane. Accessed online on March 9, 2007.
[3] M.D. Fredlund, G.W. Wilson, and D.G. Fredlund, ''Estimation of Hydraulic Properties of an Unsaturated Soil Using A Knowledge-Based System'', in Proc., Second International Conference on Unsaturated Soils, UNSAT'98, Beijing, China, 1998.
[4] D.G. Fredlund and H. Rahardjo. Soil Mechanics for Unsaturated Soils. John Wiley, New York, 1993.
[5] M.T. Van Genuchten, ''A closed form equation for predicting the hydraulic conductivity of unsaturated soils'', Soil Soc. Am. J., Vol. 44, 1980, pp. 892?898.
[6] D.G. Fredlund, S.K. Vanapalli, A. Xing, and D.E. Pufahl, ''Predicting the shear-strength function for unsaturated soils using the soil-water characteristic curve'', in: E.E. Alonzo, P. Delage (Eds.), Proc. of the First International Conference on Unsaturated Soils, vol. 1, Balkema Publishers, Rotterdam, 1995, pp. 63-69.
[7] K. Garbulewski and S. Zakowicz, ''Suction as an indicator of soil expansive potential'', in: E.E. Alonzo, P. Delage (Eds.), Proc. of the First International Conference on Unsaturated Soils, vol. 2, Balkema Publishers, Rotterdam, 1995, pp. 593-597.
[8] M.R. Sudhakar and K. Revanasiddappa, ''Role of matric suction in collapse of compacted clay soil'', J. Geotech. Geoenviron. Eng., ASCE, 126 (1), 2000, pp. 85-90.
[9] D.G Fredlund and A. Xing,''Equations for the soil-water characteristic curve'', Can. Geotech. J., 31 (3), 1994, pp. 521-532.
[10] D.G. Fredlund, A. Xing, and S. Huang, ''Predicting the permeability function for unsaturated soils using the soil-water characteristic curve'', Canadian Geotechnical Journal, 31(3), 1994, pp. 533-546.
[11] A. Casagrande, ''Seepage through Dams'', J. New England Water Works, Vol. 51, 1937, pp. 295-336.
[12] R.A. Freeze, ''Three-dimensional, Transient, Saturated-Unsaturated Flow in a Groundwater Basin'', Water Resources Research, 7(2), 1971, pp. 247-366.
[13] N.T.M. Thieu, M.D. Fredlund, D.G. Fredlund, and V.Q. Hung, ''Seepage Modeling in a Saturated/Unsaturated Soil System'', in Proc., International Conference on Management of the Land and Water Resources, MLWR, 2001, Hanoi, Vietnam.
[14] D. Dourado-Neto, D.R. Nielsen, J.W. Hopmans, and M.B. Parlange. Estimation of empirical parameters for soil-water retention curves - Computer Program, Univ. of Sao Paulo, Dep. of Agric., Brazil, and Univ. of California, Davis, Dep. of Land, Air, and Water Resources, Davis, CA.
[15] R.H. Brooks and A.T. Corey, ''Hydraulic properties of porous medium'', Colorado State University (Fort Collins), Hydrology Paper, Nr. 3, March 1964.
[16] F.J. Kastanek and D.R. Nielsen, ''Description of Soil Water Characteristics Using Cubic Spline Interpolation'', Soil Sci. Soc. Am. J., 65(2), 2001, pp. 279-283.
[17] V. Bagarello, M. Iovino, and G. Tusa, ''Factors affecting measurement of the near-saturated soil hydraulic conductivity'', Soil Sci. Soc. Am. J., 64, 2000, pp. 1203-1210.
[18] Q. Wang, M. Shao, and R. Horton, ''A Simple Method for Estimating Water Diffusivity of Unsaturated Soils'', Soil Sci. Soc. Am. J., 68(3), 2004, pp. 713-718.
[19] R.R. Bruce and A. Klute, ''The measurement of soil diffusivity'', Soil Sci. Soc. Am. Proc., 20, 1956, pp. 458-462.
[20] D. Kirkham and W.L. Powers, Advanced soil physics. Wiley Interscience, New York, 1972.
[21] D.K. Cassel, A.W. Warrick, D.R. Nielsen, and J.W. Bigger, ''Soil-water diffusivity values based upon time dependent soil-water content distributions'', Soil Sci. Soc. Am. Proc., 32, 1968, pp. 774-777.
[22] B.E. Clothier, D.R. Scotter, and A.E. Green, ''Diffusivity and one-dimensional absorption experiments'', Soil Sci. Soc. Am. J., 47, 1983, pp. 641-644.
[23] J.R. Philip, ''General method of exact solutions of the concentration-dependent diffusion equation'', Aust. J. Phys., 13, 1960, pp. 1-12.
[24] M. Shao and R. Horton, ''Soil water diffusivity determination by general similarity theory'', Soil Sci., 161, 1996, pp. 727-734.
[25] J.B. Passioura, ''Determining soil water diffusivities from one-step outflow experiments'', Aust. J. Soil Res., 15, 1976, pp. 1-8.
[26] S.C. Gupta, D.A. Farrell, and W.E. Larson, ''Determining effective soil water diffusivities from one-step outflow experiments'', Soil Sci. Soc. Am. Proc., 38, 1974, pp. 701-716.
[27] Parlange, J.-Y., ''Theory of water movement in soils: 1. One-dimensional absorption'', Soil Sci., 111, 1971, pp. 134-137.
[28] A. Klute, ''Some theoretical aspects of the flow of water in unsaturated soils'', Soil Sci. Soc. Proc., 16, 1952, pp. 144-148.
[29] J. Williams, R.E. Prebble, W.T. Williams, and C.T. Hignett, ''The influence of texture, structure and clay mineralogy on the soil moisture characteristic'', Australian J. Soil Res., 21, 1983, pp. 15-32.
[30] W.R. Gardener, ''Some steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water table'', Soil Science, 85, 1958, pp. 228-232.