DEPARTMENT OF CIVIL ENGINEERING
Groundwater Hydrology and Pollution
Group Lab Work Project
by: Alemayehu Yetayew
Tanimola Mutiu-olaitan
DEPARTMENT OF CIVIL ENGINEERING
Introduction

The objective for this Group Laboratory project is:

to determine the Hydraulic Conductivity(K) of the
sand in the Drainage and seepage tank in the
Hydraulics lab.
to compare the results of the actual groundwater flow
in the Lab versus the finite difference method used
for modeling the groundwater flow by an excel.

DEPARTMENT OF CIVIL ENGINEERING
Introduction



The hydraulic conductivity(K) of any soil type can be
measured in Laboratory if we know the velocity of
the groundwater flow in that soil between two points.
The Darcy pore velocity can be equated with the
distance per time travel of the groundwater flow
between two known points to solve for the K.
We used the Drainage and Seepage Tank in the
Hydraulics Lab to measure the K value of coarse
sand.
DEPARTMENT OF CIVIL ENGINEERING
Laboratory Procedure for estimating K
1.
2.
We divide the length of the glass into 23 elements
and its height into 10 elements to make a 2X2
square inches of finite element.
We put a constant water discharge between two
sides of the tank to make it in steady state.
DEPARTMENT OF CIVIL ENGINEERING
Laboratory Procedure for estimating K
3.
4.
We draw the water table between the inlet and outlet
points of the water from the tank to measure the
different hydraulic heads at each of the finite
elements.
To measure the distance travel per time(velocity) of
the water between two particular finite elements
(points) in the sand we used dyes as a tracer.
DEPARTMENT OF CIVIL ENGINEERING
Laboratory Procedure for estimating K
DEPARTMENT OF CIVIL ENGINEERING
Laboratory Procedure for estimating K
5.
6.
7.
We pick four points in the X-direction and
record the dye’s travel time versus the distance
between each point and their hydraulic head
from the water table line.
To get the Velocity of the groundwater model
flow in the sand; we divide the distance b/n
each points to the time taken by the dye to
reach each points respectively. This is the
Darcy’s pore-velocity in the sand.
We equate the above result with Darcy’s
equation to solve for the Hydraulic
Conductivity(K).
DEPARTMENT OF CIVIL ENGINEERING
Laboratory Procedure for estimating K
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference



Head
We measured the actual hydraulic head of each
element to our best accuracy from the water table
line we plotted during the groundwater flow.( Note:
we were not able to consider the elements which
the water table line didn’t pass in full. So we made
these element’s values as zero.)
Then graphed the measured data using excel
sheet.
We tried to use finite difference modeling technique
to compare the results by restricting the inlet and
outlet head as the measured data from the Lab.
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
Hi,j= (Hi-1,j + Hi+1,j + Hi,j-1 + Hi,j+1)/4
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
Hi,j= (Hi-1,j + Hi+1,j + Hi,j-1 + Hi,j+1)/4
Modeling Actual Groundwater Flow Datas from Laboratory
14
12
10
Head; in
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
Series1
8
Series2
6
Series3
Series4
4
Series5
2
Series6
Series7
0
1
2
3
4
5
6
7
8
9
10 11 12
13 14 15
16 17
18
19
20
21
22
23
24
Groundwater Flow Model Under a Dam
14
12
10
Head; in
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
8
Series1
6
Series2
4
Series3
2
Series4
Series5
0
1 2
3 4
5 6
7 8
9
Series6
Series7
10 11
12 13
14 15
16
17
18
19
20
21
22
23
24
When we compare the actual Vs the
model graph; there was 15% difference
between the two data.
 Where does it come from?

%Difference b/n the Measured Vs
Modeled Head
%error
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
20
Series1
15
Series2
10
Series3
5
Series4
0
Series5
1 2 3 4
5 6 7 8
9 10 11 12
13 14
Series6
15 16 17
18 19 20
21 22 23
24
Series7
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
Velocity
 Next, we tried to calculate the Darcy’s
pore velocity in X-direction through
each element:
V=-K*(H2-H1)/(Ф*(X2-X1))
for the actual recorded data and the
model; and we come up with two
similar graphs but not exact.
Lab Actual Velocity in X-Direction Vs Distance Travel
0.5
0.45
0.4
Velocity; in/sec
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
0.35
Series1
0.3
Series2
0.25
Series3
0.2
Series4
0.15
Series5
0.1
Series6
0.05
Series7
0
1
2
3
4
5
6
7
8
9
10 11 12
13 14
15
16
17
18
19
20
21
22
23
Model Velocity in X-direction Vs Distance Travel
0.25
0.2
Velocity; in/sec
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
Series1
0.15
Series2
Series3
0.1
Series4
Series5
0.05
Series6
Series7
0
1
2
3
4
5
6
7
8
9
10 11 12
13 14
15
16
17
18
19
20
21
22
23
Model Velocity in Y-Direction Vs Distance Travel
0.06
0.04
0.02
Velocity; in/sec
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
0
-0.02
Series1
-0.04
Series2
-0.06
Series3
-0.08
Series4
-0.1
Series5
-0.12
-0.14
Series6
1
2
3
4
5
6
7
8
9
10 11 12
13 14 15
16 17
18
19
20
21
22
23
DEPARTMENT OF CIVIL ENGINEERING

Modeling the measured data Vs the
Finite Difference
We use Option 2 to model the resultant
velocity from the X & Y-Directions using
the formula:
VR=SQRT(VX + VY)
and the resultant velocity direction was
governed by the sign of the Y-component
velocity as the X-component is always
positive!!!!
Resultant Velocity Vs Distance
0.6
Resultant Velocity; in/sec
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
0.4
0.2
Series1
0
Series2
Series3
-0.2
Series4
Series5
-0.4
Series6
-0.6
1
2
3
4
5
6
7
8
9
10 11 12
13 14
15
16
17
18
19
20
21
22
23
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference

In the actual data velocity graph, there
was a rapid change in velocity(distance
gradient) at the end. Where does it
come from?
Our guess is that - since we didn’t
follow the seepage line up to the end to
draw our water table line(instead finish
it at the water level of the other side);
this might cause the discrepancy.
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
Flux Plane
 To estimate the Flux at each element;
we used the following formula:
Q=-K((H2+H1)/2)*b*(H2-H1)/(Ф*ΔX)
where,b – is the width of the
seepage tank.
 Using the values from the formula; two
graphs are drawn for actual data and
the model one.
Actual Flux Plane in Lab Vs Grid Node
2
1.8
Flux Plane;(in3/sec)
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
1.6
1.4
Series1
1.2
Series2
1
Series3
0.8
Series4
0.6
Series5
0.4
0.2
Series6
0
Series7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Model Flux Plane Vs Grid Node
1.2
1
Flux Plane; (in3/sec)
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
0.8
Series1
Series2
0.6
Series3
Series4
0.4
Series5
0.2
Series6
Series7
0
1
2
3
4
5
6
7
8
9
10 11
12 13
14
15
16
17
18
19
20
21
22
23
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
Well; the Flux plane is taken as a good
parameter to check whether our model
is bad, good or very good; or………
 Then we take the summation of all the
flux planes at a cross-section across
the whole distance and observe if there
is a discrepancy or not……….Then the
result comes out to be….…..see excel
sheet!!!!!!

DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference

There is some discrepancy as we go
further towards the end;
this comes from the difficulty to take the
right head measurements at the different
cells which were labeled as zero head; in
actual case there should be some values
corresponding to the cells.
DEPARTMENT OF CIVIL ENGINEERING
Modeling the measured data Vs the
Finite Difference
SO WHAT DO U THINK OF THE MODEL?
DEPARTMENT OF CIVIL ENGINEERING
Results

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

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

Hydraulic Conductivity, k=0.198 in/sec;
Discharge=Volume / Time taken to fill flask.
Volume=3.93 lit
Time=4min,12sec
Q=V/t=3.93lit/252sec=0.016lit/sec;
Average Discharge from Model Flux=0.019lit/sec;
Porosity, Ф=40%;
Travel Time= 5min
Distance= 44 in;
Average Velocity= Distance/ Time
=40in/5min
=8in/min.
We use 40in as a distance because the dye started from
the second element.
DEPARTMENT OF CIVIL ENGINEERING
Conclusion
(What we learned from this project)
We know how to calculate the K(very
interesting physical property for Hydrogeologists and Engineers) in the
Laboratory for any soil type we may
encounter in the field.
 We made proof that the flow lines are
perpendicular to the equipotential lines
wherever they flow in the sand by using
the dyes.

DEPARTMENT OF CIVIL ENGINEERING
Conclusion
(What we learned from this project)
 We understand that the Darcy’s velocity
increases under a cut-off due to higher
change in head between the two sides
of the pile-sheet.
 If we know two things i.e the hydraulic
heads at two sides of a mountain or
groundwater flow between 2 points and
the K value for the soil; we can
estimate the hydraulic head at every
point by using the finite difference
model. (Interesting!!!!!)
DEPARTMENT OF CIVIL ENGINEERING
Conclusion
(What we learned from this project)

We also understood that it is pretty much
difficult to model the actual thing
happening in the ground with a software
as there was a maximum of 15%
discrepancy between the two.( This
discrepancy can be decreased by taking
smaller values of ΔX in the flow direction.)
DEPARTMENT OF CIVIL ENGINEERING
FINALLY
We thank Dr. Walton for
giving us the chance to
know those points in this
class!!!!!!

“Alex and Ola”