GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com
Pond Infiltration and Watertable Mounding
1 Introduction The objective of this illustration is show how to model the filling of a pond with a liner. The zone below the liner remains unsaturated and the watertable deep in the profile mounds, due to percolation from the base of the pond. The modeling can help evaluate the effectiveness of lining the reservoir with a clay liner. Not only can the final, steady-state condition be established for both scenarios, but the rise in the watertable with time can be determined by conducting a transient analysis.
Feature Highlights Transient boundary conditions Watertable viewing over time Unit flux boundary conditions Unsaturated flow
2 Geometry and boundary conditions The containment facility is located on top of a hill, with a stream at the bottom of the embankment, as shown below. Since the change in the regional system needs to be evaluated with time, a transient analysis will be conducted.
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Figure 1 Problem configuration Before conducting a transient analysis, it is sometimes helpful to know the long-term, steady-state solution, so you know the conditions where the system is eventually going to stabilize. It can also be helpful as a point of reference to compare against your transient results, which can help you determine if the steady-state solution is reasonable or too far in the future to be considered obtainable. For both the steady-state and transient analyses, the pond is assumed to be filled and maintained at a depth of 1.25 m. Because it is anticipated that significant leakage will occur, it is reasonable to expect that a potential seepage face may develop along the edge of the embankment above the river’s edge. A potential seepage
SEEP/W Example File: Leakage from pond with clay liner.docx (pdf) (gsz) Page 1 of 5 GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com face type of boundary condition is applied to the slope of the embankment to appropriately capture the rising watertable. As with all transient analyses, the initial head conditions within the profile must first be determined. To develop the initial heads, the pond is assumed to be empty. The stream at the toe of the embankment is represented by total head = 4.5m boundary condition which is the elevation of the water in the stream. Once the initial conditions have been determined, and the steady-state location of the mounded watertable has been completed, a transient analysis can then be conducted, which will evaluate the impact the leakage from the pond has on the regional watertable with time.
3 Material properties Typical conductivity and volumetric water content functions are used for this illustrative example. The most important part of the material properties is the relative difference in the K between the native material and the liner clay. The K for the native soil is 0.1 m/day and for the liner it is 0.008 m/day; about a factor of 10 in the difference (one order of magnitude in difference).
4 Initial conditions The initial conditions (Figure 2) are assumed to be hydrostatic; that is, there is no flow in the system. This means the pore-pressure distribution with depth both above and below the watertable is linear.
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Figure 2 Initial hydrostatic conditions
5 Long term steady-state conditions Figure 3 shows the long term steady-state condition. Note that the watertable has mounded and a seepage face has developed on the slope just above the toe. Most importantly however is the leakage from the pond through an unsaturated zone. The leakage is sufficient to cause the watertable to rise but not sufficient to completely saturate the ground below the pond.
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Figure 3 Long term steady-state conditions
6 Mounding with time Now let us look at the mounding of the watertable with time after the pond has been filled. This requires a transient analysis. We’ll run the analysis over a period of 240 days with 30 time steps increasing exponentially with time. The first time step is 1 day and the results are saved every 3rd step. Figure 4 shows the rising watertable with time. By Day 240, the conditions have essentially reached the long term steady-state conditions.
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E 4 3 Figure 4 Mounding of the watertable with time 2 Figure 5 shows the conditions at the end of Day-15. Of interest is the observation that there has been leakage1 during this time but the watertable has as yet not begun to rise. The significance is that the leaking water has gone into storage – the soil has absorbed the water and is storing the water. This 0
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behavior is what the volumetric water content function is portraying. It describes the soils ability to store and release water.
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E 4 3 Figure 5 Conditions at the end of Day-15 2 1 7 0 Effect of a crack in the liner Of concern in the design and implementation of a clay liner like this is the possibility of crack or hole in the liner. There are several different ways that the effect of an opening in the liner can be modeled. One is to create a physical opening in the mesh. A simpler approach is to model the effect with a specified boundary condition. Re-call the fundamental FE equation: K H Q
And re-call that if Q is specified, H is computed, and if H is specified Q will be computed. If we specify a H-type boundary condition at the base of the linear and it is the same H as at the top of the liner, we are inferring that at the this location there was no head loss in the water getting across the liner – the same as if there was a physical opening. In this illustrative example the head at one point below the liner is assigned the same H as at the top of the liner. The resulting effect is shown in Figure 6. In dramatically alters the situation.
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E 4 3 2 Figure 6 Effect of an opening in the liner 1 0 It is important to remember that this is a 2D analysis and represents the results per unit distance into the page. In essence we have modeled a crack that extents along the length of the structure. This is unlikely in reality and needs to be considered in the interpretation of the results. While the actual leakage quantities may not be correct, this modeling nonetheless reveals the dramatic effect of a defect in the liner.
One of the beautiful things about numerical modeling is that the effect of physical components can modeled without including the actual physical component. The effect can often be modeled with a specified boundary condition making the model process easier.
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