CONFINED FLOW AROUND AN IMPERMEABLE WALL

CONFINED FLOW AROUND AN IMPERMEABLE WALL

This document describes an example that has been used to verify the groundwater flowcapabilities of PLAXIS. The problem involves the confined flow under an impermeabledam around an impermeable wall.

Used version:

• PLAXIS 2D - Version 2011

• PLAXIS 3D - Version 2012

Input: Figure 1 shows the geometry and finite element mesh for the problem. Thegeometry is assumed to consist of a 10 m wide impermeable dam founded on a soil layerof 10.0 m thickness. The bottom of the soil layer is impermeable. A 5.0 m long wall isplaced under the dam. At one side of the dam the water level is 5.0 m and at the otherside the water level is 3.0 m. The wall is simulated by means of an impermeableinterface. The element mesh is locally refined around the wall by applying a Finenessfactor of 0.1 to cluster under the dam. Note that the model is extended by 1 m in they-direction in PLAXIS 3D. The permeability of soil is 1.0 m/day.

5 m5 m

5 m

5 m

5 m3 m

40 m

Figure 1 Problem geometry and boundary conditions

Figure 2 and Figure 3 show the finite element mesh used for the problem in PLAXIS 2Dand PLAXIS 3D respectively.

Figure 2 Finite element mesh (PLAXIS 2D)

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Figure 3 Finite element mesh (PLAXIS 3D)

Output: The steady state solution computed by PLAXIS 2D is presented in Figure 4 andFigure 5. The solution is obtained in a single iteration since the flow is confined. Figure 4shows the groundwater head contours in PLAXIS 2D, ranging from 5.0 m at the left handside to 3.0 m at the right hand side. Figure 5 shows a detail of the flow field around thewall. The total discharge is 0.8180 m3/day (per meter in the out of plane direction).

Figure 4 Contour lines of groundwater head (PLAXIS 2D)

Figure 5 Detail of flow field around the wall (PLAXIS 2D)

Figure 6 shows the groundwater head contours in PLAXIS 3D, ranging from 5.0 m at theleft hand side to 3.0 m at the right hand side. Figure 7 shows a detail of the flow fieldaround the wall. The total discharge is 0.8106 m3/day (per meter in the out of planedirection).

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CONFINED FLOW AROUND AN IMPERMEABLE WALL

Figure 6 Contour lines of groundwater head (PLAXIS 3D)

Figure 7 Detail of flow field around the wall (PLAXIS 3D)

Verification: Harr (1962) has given a closed form solution for the discharge of theproblem of confined flow around a wall for different geometrical ratios.

The solution is presented in Figure 8. In the situation described here (s/T = 0.5;b/T = 0.5) the solution is:

Q/k/∆h = 0.4

which gives a total discharge of 0.8 m3/day/m. The error in the numerical solution is 2.2%and 1.3% for PLAXIS 2D and PLAXIS 3D respectively.

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VALIDATION & VERIFICATION

Figure 8 (after Harr (1962))

REFERENCES

[1] Harr, M.E. (1962). Groundwater and seepage. McGraw-Hill, NY.

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