Environmental Engineering Reference
In-Depth Information
18.2.8 Application: Numerical Simulations of Variably Saturated
Flow in a Soil Profile
Analysis of water flow in soils can be based on experimental exploration and/or
numerical simulation. Experimental studies yield valuable insight into the physi-
cal processes, but their implementation is often complicated, time consuming, and
costly. As an alternative, or a useful complement, numerical simulations of the water
regime can provide necessary information to analyse flow phenomena at a very high
spatio-temporal resolution and at reasonable cost. Also, simulations may be used
to plan and interpret experiments and to predict future flow behaviour for complex
conditions.
In the following examples, numerically simulated water flow will be discussed
for different conditions of increasing complexity. We start the discussion with one-
dimensional flow in a hypothetical single-layer (homogeneous) soil profile, and then
move to a two-layered soil. Note that we will not calculate water uptake by roots
explicitly, but rather apply a net rainfall rate, which is equal to the total rainfall
rate minus the actual evapotranspiration (runoff is assumed zero here, but could be
accounted for if needed).
The simulations for the hypothetical soil made use of the Van Genuchten-
Mualem hydraulic functions without hysteresis. Figure
18.7
shows the soil water
retention and hydraulic conductivity functions. All simulations were carried out
with the HYDRUS-1D finite element code (Šimunek et al.
2005
). As top bound-
ary condition for the hypothetical soil profile we implemented a constant rainfall
rate of 2
10
−
3
m/h). This value corresponds to one tenth of
the saturated hydraulic conductivity of the sand material. As bottom boundary we
assumed a groundwater table 4 m below surface. This condition is mathematically
implemented by fixing the pressure head equal to zero at the water table. As initial
condition for the pressure head we used
h
10
−
6
m/s (or 7.2
×
×
-
z
-4m,where
z
is the depth below
surface (the vertical axis is positive upward, with the reference depth z
=
0atthe
soil surface, see Fig.
18.8
). At the soil surface the pressure head initially is hence
0
=
−
=−
=−
−
−
=
0 m at the groundwa-
ter table. The soil profile was discretized into 0.05-m thick elements, which resulted
in 81 nodes for the one-dimensional simulation.
4
4 m, with
h
decreasing linearly to
h
(
4)
4
18.2.8.1 Single-Layer Soil
The numerically calculated infiltration process for a homogeneous sand is shown in
Fig.
18.9
in terms of pressure head (
h
z
) distributions
versus depth. At
t
< 0, the initial pressure head is equal to the height above the
water table, i.e.
h
−
z
) and water content (
θ
−
4 at the soil surface (also see
Fig.
18.8
). The corresponding water content profile has the same shape as the soil
water retention curve. At
t
> 0, water starts to infiltrate and the infiltration front
moves downward at a nearly constant rate. After 70 h following the start of the
infiltration, the water content in the profile reaches a steady-state value, while a
constant water flux is established in the entire soil profile.
=
0 at the water table and
h
=−
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