Relief Well Spacing Wells Natural outlet gulley 7 m 13 m 7 mdownloads.geo-slope.com/geostudioresources/examples/7/Relief Well... · SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

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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



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



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.



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



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



Figure 6 Flow with 50 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





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



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



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

Documents

Relief Well Spacing Wells Natural outlet gulley 7 m 13 m 7 mdownloads.geo-slope.com/geostudioresources/examples/7/Relief Well... · SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)