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Relief Well Spacing


GEO-SLOPE International Ltd, Calgary, Alberta, Canada

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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.
Reservior Wells Natural outlet gulley 7m 13 m 7m

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 3dimensional 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.

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

Page 1 of 9

GEO-SLOPE International Ltd, Calgary, Alberta, Canada

www.geo-slope.com

3

SEEP/W plan view definition
Reservior Wells 7m 13 m 7m

50 45 40 35 30

Distance - m

25 20 15 10 5 0 -5 -5 0 5 10 15 20 25 30 35 40 45 50 55

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.

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

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GEO-SLOPE International Ltd, Calgary, Alberta, Canada

www.geo-slope.com

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.

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

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GEO-SLOPE International Ltd, Calgary, Alberta, Canada

www.geo-slope.com

4 4.1

Results and Discussion 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:
Q k dH / dl A (1) 13 7 (50)(10) 0.12(500) 60 m3/day. 50

The equal spacing of the contours in Figure 4 is reflective of the constant gradient.
50 45 40 35 30

10

9

Distance - m

12

60 m?/days

11

25 20 15 10 5 0 -5 -5 0 5

60 m?/days

8

10

15

20

25

30

35

40

45

50

7

55

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: (137) / 25 = 0.24. It is interesting to note that by installing the seepage control features the amount of seepage increases.

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

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GEO-SLOPE International Ltd, Calgary, Alberta, Canada
50 45 40 35 30

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25 20 15 10 5 0 -5 -5 0 5

10

15

20

25

30

35

40

5.0182e-013 m?/days
45

Distance - m

120 m?/days

50

55

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.

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

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GEO-SLOPE International Ltd, Calgary, Alberta, Canada

www.geo-slope.com

76.229 m?/days

Figure 6 Flow with 50 m well spacing

88.183 m?/days

Figure 7 Flow with 25 m well spacing

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

31.817 m?/days

43.771 m?/days

Page 6 of 9

GEO-SLOPE International Ltd, Calgary, Alberta, Canada

www.geo-slope.com

104.96 m?/days

Figure 8 Flow with 10 m well spacing

113.44 m?/days

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

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

6.5559 m?/days

15.044 m?/days

Page 7 of 9

GEO-SLOPE International Ltd, Calgary, Alberta, Canada

www.geo-slope.com

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 50 25 10 5 trench Percent passing wells 36 27 13 5 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.
3

2

Pressure Head (m)

1

Middle : 0 days

0

-1 Top : 0 days -2

-3 0 10 20 X (m) 30 40 50

Figure 10 Pressure profiles with a 50 m spacing

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

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GEO-SLOPE International Ltd, Calgary, Alberta, Canada

www.geo-slope.com

3

2

Pressure Head (m)

1

Middle : 0 days

0

-1 Top : 0 days -2

-3 0 10 20 X (m) 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 trenchcase. 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.

SEEP/W Example File: Relief Well Spacing.docx (pdf)(gsz)

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