Sharif University of Technology Scientia Iranica 1026-3098 24 5 2017 10 01 Innovative Analytical Solutions to 1, 2 and 3D Water Infiltration into Unsaturated Soils for Initial-Boundary Value Problems 2346 2368 4161 10.24200/sci.2017.4161 EN Hamed Reza Zarif Sanayei Department of Civil and Environmental Engineering; Shiraz University, Iran G. R. Rakhshandehroo Department of Civil and Environmental Engineering, Shiraz University, Iran N. Talebbeydokhti Department of Civil and Environmental Engineering, Head of Environmental Research and Sustainable Development Center; Shiraz University, Iran 0000-0002-9322-2416 Journal Article 2016 01 10 Fluid infiltration into unsaturated soil is of vital significance from many perspectives. Mathematically, such transient infiltrations are described by Richards' equation; a nonlinear parabolic Partial Differential Equation (PDE) with limited analytical solutions in the literature. The current study uses separation of variables and Fourier series expansion techniques and presents new analytical solutions to the equation in one, two, and three dimensions subject to various boundary and initial conditions. Solutions for 1-D horizontal and vertical water infiltration are derived and compared to numerical finite difference method solutions, whereby both solutions are shown to coincide well with one another. Solutions to 2- and 3-D vertical water infiltration are derived for constant, no-flow, and sinusoidal boundary and initial conditions. Presented analytical solutions are such that both steady and unsteady solutions may be obtained from a single closed form solution. The solutions may be utilized to test numerical models that use different computational techniques https://scientiairanica.sharif.edu/article_4161_aba210701dfa4d6b971d241fb1fb5770.pdf