Algebraic model for one-dimensional horizontal water flow with arbitrary initial soil water content
Lijun Su A B C D , Meng Li
B , Quanjiu Wang A C , Beibei Zhou A C , Yuyang Shan A C , Manli Duan C , Yan Sun A C and Songrui Ning A C
+ Author Affiliations
- Author Affiliations
A State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi’an University of Technology, Xi’an 710048, China.
B School of Science Xi’an University of Technology Xi’an, Shaanxi 710054, China.
C Institute of Water Resources and Hydroelectric Engineering, Xi’an University of Technology Xi’an 710048, China.
D Corresponding author. Email: sljun11@163.com
Soil Research 59(5) 511-524 https://doi.org/10.1071/SR20238
Submitted: 19 August 2020 Accepted: 24 January 2021 Published: 18 March 2021
Abstract
A simple analytical solution of the equation for the one-dimensional horizontal permeability of soil water is important for estimating the hydraulic properties of soil. Our main objective was to develop analytical solutions to the nonlinear Richards equation, with constant-saturation upper boundary and an arbitrary initial soil water content (SWC) for horizontal absorption. We estimated the infiltration rate based on the hypothesis proposed by Parlange and carried out a series of transformations based on the Brooks–Corey model to obtain a theoretical function of the one-dimensional movement of water in unsaturated soil under an arbitrary initial SWC. The algebraic analytical solutions were simple, and the selection of the initial SWC was arbitrary. We assumed three scenarios of linear distributions of initial SWC, and Hydrus-1D software was used to simulate horizontal infiltration. Based on the comparison of algebraic and numerical results, the corrected algebraic model was proposed and verified by the arbitrary initial water content conditions when the maximum SWC was less than the half of saturated water content. The proposed method provides a description of horizontal infiltration for the heterogeneous initial SWCs.
Keywords: algebraic analytical solution, Brooks–Corey model, cumulative infiltration, horizontal infiltration, Hydrus-1D, infiltration rate, Richards equation, unsaturated soil.
References
Basha HA (2011) Infiltration models for semi-infinite soil profiles. Water Resources Research 47, W08516| Infiltration models for semi-infinite soil profiles.Crossref | GoogleScholarGoogle Scholar |
Berardi M, Difonzo F, Notarnicola F, Vurro M (2019) A transversal method of lines for the numerical modeling of vertical infiltration into the vadose zone. Applied Numerical Mathematics 135, 264–275.
| A transversal method of lines for the numerical modeling of vertical infiltration into the vadose zone.Crossref | GoogleScholarGoogle Scholar |
Broadbridge P, White I (1987) Time to ponding: comparison of analytic, quasi-analytic, and approximate predictions. Water Resources Research 23, 2302–2310.
| Time to ponding: comparison of analytic, quasi-analytic, and approximate predictions.Crossref | GoogleScholarGoogle Scholar |
Broadbridge P, White I (1988) Constant rate rainfall infiltration: a versatile nonlinear model: 1. Analytic solution. Water Resources Research 24, 145–154.
| Constant rate rainfall infiltration: a versatile nonlinear model: 1. Analytic solution.Crossref | GoogleScholarGoogle Scholar |
Broadbridge P, Knight JH, Rogers C (1988) Constant rate rainfall infiltration in a bounded profile: Solutions of a nonlinear model. Soil Science Society of America Journal 52, 1526–1533.
| Constant rate rainfall infiltration in a bounded profile: Solutions of a nonlinear model.Crossref | GoogleScholarGoogle Scholar |
Broadbridge P, Edwards MP, Kearton JE (1996) Closed-form solutions for unsaturated flow under variable flux boundary conditions. Advances in Water Resources 19, 207–213.
| Closed-form solutions for unsaturated flow under variable flux boundary conditions.Crossref | GoogleScholarGoogle Scholar |
Brooks RH, Corey AJ (1964) ‘Hydraulic properties of porous media.’ (Colorado State Univ.: Fort Collins, CO, USA)
Carsel RF, Parrish RS (1988) Developing joint probability distributions of soil water retention characteristics. Water Resources Research 24, 755–769.
| Developing joint probability distributions of soil water retention characteristics.Crossref | GoogleScholarGoogle Scholar |
Chen JM, Tan YC, Chen CH, Parlange JY (2001) Analytical solutions for linearized Richards equation with arbitrary time-dependent surface fluxes. Water Resources Research 37, 1091–1093.
| Analytical solutions for linearized Richards equation with arbitrary time-dependent surface fluxes.Crossref | GoogleScholarGoogle Scholar |
Chen JM, Tan YC, Chen CH (2003) Analytical solutions of one-dimensional infiltration before and after ponding. Hydrological Processes 17, 815–822.
| Analytical solutions of one-dimensional infiltration before and after ponding.Crossref | GoogleScholarGoogle Scholar |
De Luca DLD, Cepeda JM (2016) Procedure to obtain analytical solutions of one-dimensional Richards’ equation for infiltration in two-layered soils. Journal of Hydrologic Engineering 21, 04016018
| Procedure to obtain analytical solutions of one-dimensional Richards’ equation for infiltration in two-layered soils.Crossref | GoogleScholarGoogle Scholar |
Hayek M (2016a) An exact explicit solution for the one-dimensional, transient, nonlinear Richards’ equation for modeling infiltration with special hydraulic functions. Journal of Hydrology 535, 662–670.
| An exact explicit solution for the one-dimensional, transient, nonlinear Richards’ equation for modeling infiltration with special hydraulic functions.Crossref | GoogleScholarGoogle Scholar |
Hayek M (2018) An efficient analytical model for horizontal infiltration in soils. Journal of Hydrology 564, 1120–1132.
| An efficient analytical model for horizontal infiltration in soils.Crossref | GoogleScholarGoogle Scholar |
Hogarth WL, Parlange JY (2000) Application and improvement of a recent approximate analytical solution of Richards’ Equation. Water Resources Research 36, 1965–1968.
| Application and improvement of a recent approximate analytical solution of Richards’ Equation.Crossref | GoogleScholarGoogle Scholar |
Huang RQ, Wu LZ (2012) Analytical solutions to 1-d horizontal and vertical water infiltration in saturated/unsaturated soils considering time-varying rainfall. Computers and Geotechnics 39, 66–72.
| Analytical solutions to 1-d horizontal and vertical water infiltration in saturated/unsaturated soils considering time-varying rainfall.Crossref | GoogleScholarGoogle Scholar |
Ma DH, Wang QJ, Shao MA (2009) Analytical method for estimating soil hydraulic parameters from horizontal absorption. Soil Science Society of America Journal 73, 727–736.
| Analytical method for estimating soil hydraulic parameters from horizontal absorption.Crossref | GoogleScholarGoogle Scholar |
Ma DH, Zhang JB, Lai JB, Wang QJ (2016) An improved method for determining Brooks–Corey model parameters from horizontal absorption. Geoderma 263, 122–131.
| An improved method for determining Brooks–Corey model parameters from horizontal absorption.Crossref | GoogleScholarGoogle Scholar |
Matthews C, Cook F, Knight J, Braddock R (2005) Handling the water content discontinuity at the interface between layered soils within a numerical scheme. Australian Journal of Soil Research 43, 945–955.
| Handling the water content discontinuity at the interface between layered soils within a numerical scheme.Crossref | GoogleScholarGoogle Scholar |
Menziani M, Pugnaghi S, Vincenzi S (2007) Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions. Journal of Hydrology 332, 214–225.
| Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions.Crossref | GoogleScholarGoogle Scholar |
Parlange JY (1971) Theory of water movement in soils: 1. One-dimensional absorption. Soil Science 111, 134–137.
| Theory of water movement in soils: 1. One-dimensional absorption.Crossref | GoogleScholarGoogle Scholar |
Parlange JY (1972) Theory of water movement in soils: 8. One-dimensional infiltration with constant flux at the surface. Soil Science 114, 1–4.
| Theory of water movement in soils: 8. One-dimensional infiltration with constant flux at the surface.Crossref | GoogleScholarGoogle Scholar |
Parlange JY, Barry DA, Parlange MB, Hogarth WL, Haverkamp R, Ross PJ, Ling L, Steenhuis TS (1997) New approximate analytical technique to solve Richards’ equation for arbitrary surface boundary conditions. Water Resources Research 33, 903–906.
| New approximate analytical technique to solve Richards’ equation for arbitrary surface boundary conditions.Crossref | GoogleScholarGoogle Scholar |
Parlange JY, Hogarth WL, Parlange MB, Haverkamp R, Barry DA, Ross PJ, Steenhuis TS (1998) Approximate analytical solution of the nonlinear diffusion equation for arbitrary boundary conditions. Transport in Porous Media 30, 45–55.
| Approximate analytical solution of the nonlinear diffusion equation for arbitrary boundary conditions.Crossref | GoogleScholarGoogle Scholar |
Philip JR (1957) The theory of infiltration: 2. The profile at infinity. Soil Science 83, 435–448.
| The theory of infiltration: 2. The profile at infinity.Crossref | GoogleScholarGoogle Scholar |
Philip JR (1969) Theory of infiltration. Advances in Hydroscience 5, 215–296.
| Theory of infiltration.Crossref | GoogleScholarGoogle Scholar |
Qiu QW, Zhan LT, Huang YY (2017) Analytical solutions for rainfall infiltration into monolithic covers considering arbitrary initial conditions. Chinese Journal of Geotechnical Engineering 39, 359–365.
| Analytical solutions for rainfall infiltration into monolithic covers considering arbitrary initial conditions.Crossref | GoogleScholarGoogle Scholar | [In Chinese with English abstract.]
Richards LA (1931) Capillary conduction of liquids through porous medium Physics. Physics 1, 318–333.
| Capillary conduction of liquids through porous medium Physics.Crossref | GoogleScholarGoogle Scholar |
Sanayei HRZ, Rakhshandehroo GR, Talebbeydokhti N (2017) Innovative analytical solutions to 1, 2, and 3D water infiltration into unsaturated soils for initial-boundary value problems. Scientia Iranica 24, 2346–2368.
| Innovative analytical solutions to 1, 2, and 3D water infiltration into unsaturated soils for initial-boundary value problems.Crossref | GoogleScholarGoogle Scholar |
Sanayei HRZ, Talebbeydokhti N, Rakhshandehroo GR (2019) Analytical Solutions for Water Infiltration into Unsaturated-Semi-Saturated Soils Under Different Water Content Distributions on the Top Boundary. Civil Engineering (Shiraz) 43, 747–760.
| Analytical Solutions for Water Infiltration into Unsaturated-Semi-Saturated Soils Under Different Water Content Distributions on the Top Boundary.Crossref | GoogleScholarGoogle Scholar |
Šimůnek J, Genuchten MTV, Šejna M (2008) Development and applications of the HYDRUS and STANMOD software packages, and related codes. Vadose Zone Journal 7, 587–600.
| Development and applications of the HYDRUS and STANMOD software packages, and related codes.Crossref | GoogleScholarGoogle Scholar |
Šimůnek J, Genuchten MTV, Šejna M (2012) HYDRUS: Model use, calibration and validation. Transactions of the Asabe 55, 1261–1274.
Šimůnek J, Jacques D, Langergraber G, Bradford SA, Šejna M, Genuchten MTV (2013) Numerical modeling of contaminant transport with HYDRUS and its specialized modules. Journal of the Indian Institute of Science 93, 265–284.
Srivastava R, Yeh TCJ (1991) Analytical solutions for one-dimensional, transient infiltration toward the water table in homogeneous and layered soils. Water Resources Research 27, 753–762.
| Analytical solutions for one-dimensional, transient infiltration toward the water table in homogeneous and layered soils.Crossref | GoogleScholarGoogle Scholar |
Su LJ, Yang X, Wang QJ, Qin XQ, Zhou BB, Shan YY (2018b) Functional extremum solution and parameter estimation for one-dimensional vertical infiltration using the Brooks–Corey model. Soil Science Society of America Journal 82, 1319–1332.
| Functional extremum solution and parameter estimation for one-dimensional vertical infiltration using the Brooks–Corey model.Crossref | GoogleScholarGoogle Scholar |
Sun CS, Qin XJ, Huang XL (2019) Analytical solution of infiltration process in unsaturated soil considering arbitrary initial condition. Yangtze River 50, 182–186.
| Analytical solution of infiltration process in unsaturated soil considering arbitrary initial condition.Crossref | GoogleScholarGoogle Scholar | [In Chinese with English abstract.]
Teng JD, Zhang X, Zhang S, Zhao CJ, Sheng DC (2019) An analytical model for evaporation from unsaturated soil. Computers and Geotechnics 108, 107–116.
| An analytical model for evaporation from unsaturated soil.Crossref | GoogleScholarGoogle Scholar |
Tracy FT (2007) Three-dimensional analytical solutions of Richards’ equation for a box-shaped soil sample with piecewise-constant head boundary conditions on the top. Journal of Hydrology 336, 391–400.
| Three-dimensional analytical solutions of Richards’ equation for a box-shaped soil sample with piecewise-constant head boundary conditions on the top.Crossref | GoogleScholarGoogle Scholar |
Triadis D, Broadbridge P (2010) Analytical model of infiltration under constant-concentration boundary conditions. Water Resources Research 46, 91–103.
| Analytical model of infiltration under constant-concentration boundary conditions.Crossref | GoogleScholarGoogle Scholar |
Wang Q, Horton R, Shao M (2003b) Algebraic model for one-dimensional infiltration and soil water distribution. Soil Science 168, 671–676.
| Algebraic model for one-dimensional infiltration and soil water distribution.Crossref | GoogleScholarGoogle Scholar |
Wang Q, Shao M, Horton R (2004) A simple method for estimating water diffusivity of unsaturated soils. Soil Science Society of America Journal 68, 713–718.
| A simple method for estimating water diffusivity of unsaturated soils.Crossref | GoogleScholarGoogle Scholar |
Warrick AW, Lomen DO, Yates SR (1985) A generalized solution to infiltration. Soil Science Society of America Journal 49, 34–38.
| A generalized solution to infiltration.Crossref | GoogleScholarGoogle Scholar |
Warrick AW, Lomen DO, Islas A (1990) An analytical solution to Richards’ equation for a draining soil profile. Water Resources Research 26, 253–258.
| An analytical solution to Richards’ equation for a draining soil profile.Crossref | GoogleScholarGoogle Scholar |
Warrick AW, Islas A, Lomen DO (1991) An analytical solution to Richards’ equation for time-varying infiltration. Water Resources Research 27, 763–766.
| An analytical solution to Richards’ equation for time-varying infiltration.Crossref | GoogleScholarGoogle Scholar |
Zlotnik VA, Wang T, Nieber JL, Šimunek J (2007) Verification of numerical solutions of the Richards equation using a traveling wave solution. Advances in Water Resources 30, 1973–1980.
| Verification of numerical solutions of the Richards equation using a traveling wave solution.Crossref | GoogleScholarGoogle Scholar |
