4.6 Darcy’s Law for Layered Soil
If saturated hydraulic conductivity can vary by orders of magnitude, then what does that mean for saturated flow through soil profiles, which consist of horizons with differing properties? Watch this video to learn how Darcy’s Law can be rearranged into a convenient form for solving saturated water flow problems for layered soil. For a soil with two distinct layers, the Darcy’s Law can be written as:
![\[ q = \frac{\Delta\Psi_t}{R_h_1+R_h_2} \]](https://open.library.okstate.edu/app/uploads/quicklatex/quicklatex.com-238c05e284356d8db86856cc77efa45e_l3.png "Rendered by QuickLaTeX.com")
(Eq. 4-4)
where Rh1 and Rh2 are the hydraulic resistances for layers 1 and 2, respectively. The hydraulic resistance of a soil layer is simply the thickness of the layer (L) divided by the hydraulic conductivity of the layer, Rh = L/K. For a soil consisting of more than two layers, additional hydraulic resistances can be added to the denominator of the equation above for each layer. This video shows an example of applying Darcy’s Law for layered soil to calculate flow through a soil profile with two distinctly different layers. Please take the time to watch the video as many times as necessary, following along with pencil and paper until you are confident you can solve this type of flow problem.
Darcy’s Law for layered soil allows us to estimate water flow rates for layered soils, which we are likely to encounter in the field. However, both forms of Darcy’s Law only apply to saturated water flow. Many times in the field we need to understand or estimate water flow rates when the soil is unsaturated. For example, infiltration into, redistribution through, and drainage from soil profiles all generally involve unsaturated soil. It would be 50 years after Darcy’s landmark paper before someone developed a relationship to predict water flow in unsaturated soil.
