GEO-SLOPE International Ltd, Calgary, Alberta, Canada Relief Well Spacing

Transcription

1 1 Introduction Relief Well Spacing 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 13 m 7 m 7 m 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 1 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 Page 1 of 9

2 3 SEEP/W plan view definition Reservior Wells 13 m 7 m 7 m Distance - m 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 5 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 Page 2 of 9

3 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 5 m, 25 m, 1 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 Page 3 of 9

4 4 Results and Discussion 4.1 Without drainage The total quantity of seepage through the foundation is 6 m 3 /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 are constant: 13 7 Q k dh / dl A (1) (5)(1).12(5) 6 5 m 3 /day. The equal spacing of the contours in Figure 4 is reflective of the constant gradient Distance - m m³/days 6 m³/days 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 =.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 Page 4 of 9

5 Distance - m m³/days 5.182e-13 m³/days 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: 5, 25, 1 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 Page 5 of 9

6 m³/days m³/days Figure 6 Flow with 5 m well spacing m³/days m³/days Figure 7 Flow with 25 m well spacing SEEP/W Example File: Relief well spacing.docx Page 6 of 9

7 14.96 m³/days m³/days Figure 8 Flow with 1 m well spacing m³/days m³/days Figure 9 Flow with 5 m well spacing The sum of the two flux sections in each of the cases is 12 m 3 /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 Page 7 of 9

8 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 12 m 3 /day, the results are as follows: Spacing - m Percent passing wells trench. 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 1 shows the pore-pressure for a profile though the drain and at the middle between two drains when the spacing is 5 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) Middle : days Top : days X (m) Figure 1 Pressure profiles with a 5 m spacing SEEP/W Example File: Relief well spacing.docx Page 8 of 9

9 3 2 Pressure Head (m) Middle : days Top : days X (m) 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 Page 9 of 9