An aquifer is called an unconfined or phreatic aquifer if its upper surface (water level) is accessible to the atmosphere through permeable material. In contrast to a confined aquifer, the groundwater level in an unconfined aquifer does not have a superimposed impermeable rock layer to separate it from the atmosphere.
To simplify the problem of unconfined flow and to make it analytically writeable, Dupuit (1857) used the following assumptions, now commonly referred to as Dupuitassumptions, in connection with unconfined aquifers:
Using the assumptions of Dupuit, Forchheimer (1898) developed a differential equation for the unconfined steadystate case, and Boussinesq introduced the unconfined transient groundwater flow equation in 1904:
$$ \begin{eqnarray} \frac{∂}{∂x}(h\frac{∂h}{∂x})+\frac{∂}{∂y}(h\frac{∂h}{∂y}) = \frac{S_y}{K}\frac{∂h}{∂t} \label{Boussinesq} \end{eqnarray} $$
where $h[m]$ is the hydraulic head, $S_y$ is the specific yield and $K$ is the hydraulic conductivity. The Specific Yield $S_y$, also known as the drainable porosity, is a quantity that is smaller or equal to the effective porosity in a coarse and porous medium. $S_y$ indicates the volumetric water content that can flow out from the material under the influence of gravity.
The examples shown here are horizontal 2D models parameterized by hydraulic head $h[m]$.
Since the formulation within OGS is basically based on pressure ($P$) and permeability ($k$), the following relationships must be considered during parameterization in order to be able to work headbased and with hydraulic conductivity ($K$):
$$ \begin{eqnarray} P= ρ g h \label{Pressure vs. head} \end{eqnarray} $$
$$ \begin{eqnarray} K= \frac{kgh}{μ} \label{K & k} \end{eqnarray} $$
For the model parameterization this means:
Note: in such a case, the result is also an output of hydraulic head in [m] and not Pressure in [Pa].
The following simple examples, which have been compared with MODFLOW simulations, shall verify the result and demonstrate the basic parameterization.
The basic scenario for the twodimensional unconfined aquifer:
For more information see e.g.
This article was written by Thomas Kalbacher. If you are missing something or you find an error please let us know.
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Last revision: November 22, 2022
Commit: [PL/THM] Implement freezing for temperature eq. 68ebbec
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