Post on 19-Mar-2018
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SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz) Page 1 of 9
Relief Well Spacing
1 Introduction
Relief wells are commonly installed on the downstream side of an earth dam to control the seepage and
pore-pressures (e.g. levee; Figure 1). A key design requirement for problems of this type is the required
well spacing.
Figure 1 Schematic of problem
The plan view option in SEEP/W can be used to explore the relative effect of well spacing on the seepage
and pore-pressures. The term relative is used here because the plan view simulation is not a true 3-
dimensional analysis. The plan view analysis is ideally used to simulate the flow in confined aquifers;
however, the problem shown in Figure 1 lends itself reasonably well to this type of analysis if a
simplifying assumption is made that the levee acts as a confining unit and the foundation soils act as an
‘aquifer’. Consequently, the plan view simulation can provide some useful information at considerably
less ‘cost’ in comparison to a true 3D analysis. This example demonstrates how the SEEP/W plan view
analysis can be used for this purpose.
2 Problem description
Figure 1 illustrates a case involving a 10 m thick foundation layer. The total head in the reservoir is 13 m
assuming that the datum is located at the bottom of the foundation layer. The ‘far-field’ total head some
distance down-slope of the levee is being controlled at 7 m by a natural stream which acts as a seepage
outlet. For the purpose of this example, it is assumed that pumping maintains the water level at 7 m in the
relief wells; the same elevation as the water in the outlet gulley.
7 m
13 m
7 m
Wells
Reservior
Natural outlet gulley
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SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz) Page 2 of 9
3 SEEP/W plan view definition
Figure 2 Plan view of SEEP/W configuration
Figure 2 shows the SEEP/W finite element mesh in plan-view. The mesh comprises a single region 50 m
along the levee with a line drawn along the toe (Draw | Line). The mesh is generated along the line
(Draw | Mesh (select the line) | Generate mesh along line) and points are added at equally spaced intervals
(Draw Points). As will be demonstrated, the points and the line (actually line segments after the points
are added) are necessary for the specification of the boundary conditions.
To use the Plan view in SEEP/W, it is necessary to represent the original ground surface (i.e. before the
levee was built) by specifying the x-y-z coordinates of three locations.
7 m
13 m
7 m
Wells
Reservior
-5 0 5 10 15 20 25 30 35 40 45 50 55
Dis
tance -
m
-5
0
5
10
15
20
25
30
35
40
45
50
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SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz) Page 3 of 9
The plan view option is selected using the Set Units and Scale command. After the Plan view is selected,
a Generate button appears. Clicking on the Generate button brings up the dialog box shown in Figure 3.
Figure 3 Plan view dialog box for mesh thickness generation
Points #1 and #2 define the left side of the plan view mesh and correspond to the position on the upstream
toe of the levee. Point #3 defines the lower-right corner of the plan view mesh and corresponds to the
position along the stream. The z-coordinate is considered to be the elevation of the ground surface; that
is, the top of the foundation layer. The ground surface is everywhere at the same elevation.
Clicking on the Generate button generates the appropriate thickness for all the elements in the mesh.
The reservoir is represented with a total head (H) boundary condition on the left equal to 13 m. The water
level in the outlet gulley is represented with H = 7 m. Three different scenarios are then investigated:
1. Without drainage: the case of having drainage controls is used as a basis for interpretation;
2. Collection trench: a drainage trench is simulated by applying H = 7 m to the line along the
downstream toe, and,
3. Variably spaced relief wells: the effect of relief wells is explored using a well spacing of 50 m, 25
m, 10 m, and 5 m.
For this illustrative example, the hydraulic conductivity has been set to 1 m/day, a value chosen simply
for convenient discussion purposes.
It is important to recognize that in a Plan view analysis only the specified saturated conductivity is used. Specifying
the K as a constant is consequently adequate in a Plan view analysis – no K function is required.
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4 Results and Discussion
4.1 Without drainage
The total quantity of seepage through the foundation is 60 m3/day without any drainage measures, as
shown by the two flux sections in Figure 4. The flux quantity Q can be verified by a simple calculation
because the gradient and cross-sectional area of the foundation unit are constants:
13 7/ (1) (50)(10) 0.12(500) 60
50Q k dH dl A m
3/day.
The equal spacing of the contours in Figure 4 is reflective of the constant gradient.
Figure 4 Flow situation with no wells
5 Collection trench
The installation of a free draining collection trench would permit the water level to be maintained at an
elevation of about 7 m. Essentially the same flow system would develop if the wells were spaced closely.
This case and the previous case could both be simulated using a 2-dimensional analysis.
Figure 5 shows the total head contours and fluxes at two sections. There is no flow beyond the trench, as
indicated by the lack of head contours, for two reasons: 1) all of the seepage from the reservoir is
collected by the trench; and 2) the water elevation in the trench is the same as the outlet gulley (i.e. there
is no flow from the outlet gulley towards the trench).
The total flow quantity is now twice the value reported previously because the gradient has doubled: (13-
7) / 25 = 0.24.
It is interesting to note that by installing the seepage control features the amount of seepage increases.
7
8
9
1
0
1
1
1
2
6
0 m
³/d
ays
6
0 m
³/d
ays
-5 0 5 10 15 20 25 30 35 40 45 50 55
Dis
tance -
m
-5
0
5
10
15
20
25
30
35
40
45
50
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SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz) Page 5 of 9
Figure 5 Flow with an open collection trench
6 Variably spaced relief wells
The effect of relief wells of variable spacing can be explored by applying H = 7 m at the well locations
(i.e. Points) for the cases of: 50, 25, 10 and 5 m spacing. The resulting fluxes at two locations and the
total head contours are shown in Figure 6 through Figure 9, respectively.
1
20
m³/
da
ys
5
.01
82
e-0
13
m³/
da
ys
-5 0 5 10 15 20 25 30 35 40 45 50 55
Dis
tance -
m
-5
0
5
10
15
20
25
30
35
40
45
50
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SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz) Page 6 of 9
Figure 6 Flow with 50 m well spacing
Figure 7 Flow with 25 m well spacing
7
6.2
29
m³/
da
ys
4
3.7
71
m³/
da
ys
8
8.1
83
m³/
da
ys
3
1.8
17
m³/
da
ys
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SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz) Page 7 of 9
Figure 8 Flow with 10 m well spacing
Figure 9 Flow with 5 m well spacing
The sum of the two flux sections in each of the cases is 120 m3/day. The difference between the two flux
sections is the amount captured by the wells. This can be verified by using the View Results Information
1
04
.96
m³/
da
ys
1
5.0
44
m³/
da
ys
1
13
.44
m³/
da
ys
6
.55
59
m³/
da
ys
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SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz) Page 8 of 9
command and clicking on the Point at the well. This will give the amount of flow out of the system at the
well.
The amount depicted by the right most flux section is the amount of flow that bypasses the wells. If this
amount is taken as a percentage of the total 120 m3/day, the results are as follows:
Spacing - m Percent passing wells
50 36
25 27
10 13
5 5
trench 0.0
7 Commentary
It is interesting to note that even a wide spacing between the relief wells has a significant impact on the
amount of flow through the foundation. However, the pore-pressure profile between the drains (along the
bottom of the model) is hardly affected. Figure 10 shows the pore-pressure for a profile though the drain
and at the middle between two drains when the spacing is 50 m. Conversely, the pressure profiles are
nearly identical when the spacing is 5 m as shown in Figure 11– the only difference is right at the well.
Figure 10 Pressure profiles with a 50 m spacing
Middle : 0days
Top : 0 days
Pre
ssure
Head
(m
)
X (m)
-1
-2
-3
0
1
2
3
0 10 20 30 40 50
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SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz) Page 9 of 9
Figure 11 Pressure profiles with a 5 m spacing
Perhaps the most significant observation is that with a 5 m spacing the results are very close to the trench-
case. The implication is that a conventional 2D vertical section analysis would be a realistic
representation of the actual conditions in the field. Such a conventional 2D analysis could of course
capture more of the complexity of a cross-section such as flow through the levee itself.
The results of the plan view analysis are best viewed as relative values for various spacing. Actual
seepage quantities would be better represented by a conventional 2D analysis.
8 Concluding remark
This example shows how SEEP/W can be used to approximate the effect of relief well spacing along a
linear structure such as a levee or irrigation canal.
Middle : 0days
Top : 0 days
Pre
ssure
Head
(m
)
X (m)
-1
-2
-3
0
1
2
3
0 10 20 30 40 50