Berner Nicolas
Brethaut Yoann
Gafsou Blaise
Lochmatter Samuel
LABORATORY 2
december, 12 2006
Vadoze Zone Hydrology
Introduction
In this laboratory, we have to determine the saturated hydraulic conductivity (Ks). The
hydraulic conductivity is the propriety of soil. This parameter describes how easily the water
can flow through the pores or the fractures of a particular soil. In our case, we have to
determine this coefficient when the soil is saturated with water.
To calculate Ks, we are using a method called the constant head method because we maintain
a head constant in the soil sample. It’s illustrated at the figure 1. We calculate the quantity of
water passing through the soil, measure different head values in the soil with piezometers and
the height of the sample and then with Darcy’s law, we can deduce Ks. Of course we measure
the flow when it’s steady. There is another method quite similar that we are not using for this
lab called the falling head method. In this case, the head is decreasing because the water
flowing through the soil is not replaced in the mariotte flask. We have to calculate only the
initial and the final depth of the ponded water and integrate the head in the time to obtain Ks.
First we calculate Ks for a single layer column with different heads an then we measure
another hydraulic conductivity (Ks) through a hydraulic head distribution within a two-layer
soil column.
We’ve done the experiment as described in the procedure and in the figure 1 in ANNEXE.
Plot of the calculated hydraulic conductivity Ks vs. Time for a one-layer soil column
Ks vs. time
0.70
Ks A 12
Ks A 23
0.60
Ks A 13
0.50
Ks [m/s]
Ks B 12
0.40
Ks B 23
0.30
Ks B 13
Ks C 12
0.20
Ks C 23
0.10
Ks C 13
0.00
18
38
62
85
107
127
150
172
196
219
Time [s]
1
Berner Nicolas
Brethaut Yoann
Gafsou Blaise
Lochmatter Samuel
LABORATORY 2
december, 12 2006
We have calculated the Ks coefficient three times for the one-layer soil column with different
height of the bubbling tube as describe in the tab following.
[cm]
height H(stock)
diameter
elevation
thickeness
H(sol)
z*(H1)
z(H2)
z(H3)
SAND
CLAY
41.5 17.5 51
51
6
6
6
6
8.5 8.5 8.5 8.5
20
2
10
18
20
2
10
18
20
2
10
18
9.5
2
5
8.2
* outlet piezometer's water, elevated from soil's base
For these three heights, we are able to determine several Ks between each piezometrical
measure’s point with Darcy’s law, as describe here :
Ks = - Jw * Δz / Δψh
where ψh = ψm + ψp + ψz = ψp + ψz .
We observe that the approximate value of Ks 23 is the same for the different ABC case. We
can do the same observation for Ks 13, but the concordance isn’t well as before. In fact, there
is a big difference between the three Ks 12.
By looking the previous graph, we remark a general trend : Ks 23 is smaller than Ks 12, so it
result that Ks 13 is situated between both.
Theoretically, we should obtain a same value for all this Ks, because we have
experimentations over an one-layer soil column, but we don’t.
A first global explanation is that there was air in the system for the two first experimentations,
so the continuity pressure wasn’t assured. Consequently, we cannot use the Darcy’s law with
our measurements, which aren’t more representative.
Another explanation could be our inability of good precision during measurement. The water
level is not easy to read exactly at 10 ml in the graduate cylinder, water outflow making move
level.
Secondly, Ks 12 is different than Ks 23 because we think that the piezometers gave us a
wrong value. It’s also possible that some preferential path have been formed in the section 12.
For the next graph, we determined the Ks effective using the following equation:
Keff = Σ Li / Σ ( Li / Ksi ).
We use Ks 12 and Ks 23 in this formula and the result should be equal to Ks 13. This relation
is respected : Ks eff = Ks 13 for the three experiment.
Because we don’t obtain the same result for Ks 12 and Ks 23 alone, we can suppose that the
piezometer 2 give us a wrong value, Ks eff calculated corresponding exactly to Ks 13. It
assumes that Ks 12 and Ks 23 are wrong calculated. However, when we determine Ks eff, this
false measurement at piezometer 2 disappears when we use Darcy’s law.
Once again, there isn’t a good exactitude between this three Ks, for the same reasons
probably, as previously said. In fact, analysing Ks eff of the first experimentation, we see a
big fluctuation of its value vs. time. It’s the sign there was air in the system and the inflow
2
Berner Nicolas
Brethaut Yoann
Gafsou Blaise
Lochmatter Samuel
LABORATORY 2
december, 12 2006
water pressure fluctuated. Ks eff of the two other heads are more constant during the time, it’s
probably another reason of their non-exactitude.
Ks eff vs. time
0.300
Ks A eff
0.250
Ks B eff
Ks [m/s]
0.200
0.150
Ks C eff
0.100
0.050
0.000
1
2
3
4
5
6
Time [s]
7
8
9
10
Plot of the calculated hydraulic conductivity Ks vs. Time for a two-layer soil column
We have calculated the Ks coefficient one time for the two-layer soil column with a single
height of the bubbling tube as describe in the tab before. Water took to much time to circule
trough this soil and we haven’t enough time to do other experimentation with this column.
Moreover, there was air in piezometer 3, so we cannot use its results for our calcul.
We have defined Ks 12 as describe here down.
First we determine the flux Jw, using the measurment of soil’s water outflow versus time.
Then using the Darcy’s law between point 1 and 2, we can calculate the Ks 12 coefficient.
As see before, unknown piezometer value in measure point 3 doesn’t let us define Ks 23 and
Ks 13 in the same way.
Because we have some value for the bubbling tube, height of soil column, atmospheric
pressure and water outflow, we are able to calculate the Ks eff coefficient, which should be
equals to the Ks 13 coefficient. Then we can define the Ks 23, using the Ks eff and Ks 1to3
relation. For this, we suppose that at the top of the soil column, the pressure equals to the
atmospheric pressure. Results are in the end, in the ANNEXE.
Plot a potential diagram of the two-layer experiment
Referencing to the graph in the ANNEXE, we can see that for the 3 first experiments, with a
one layer-soil column, the curve are nearly the same. But we don’t obtain perfect linear curve,
the measure at piezometer 2 were not very good, as describe before.
For the two soil-layer column, the pressure in the soil is much bigger. This is because there is
a small permeability. Moreover we note the large difference in potential between the two
soils. This is because their permeabilities are very different.
3
Berner Nicolas
Brethaut Yoann
Gafsou Blaise
Lochmatter Samuel
LABORATORY 2
december, 12 2006
Annexes
4