UNCONFINED FLOW THROUGH AN EARTH DAM

UNCONFINED FLOW THROUGH AN EARTH DAM

This document verifies that groundwater flow principles are correctly implemented inPLAXIS. The water flow through an earth dam with drain in the downstream toe isstudied. The flow in such a case is unconfined due to the unknown phreatic level and theunknown area of the seepage surface. This constitutes a problem which can be solvedby the flow net method (Lambe & Whitman, 1979).

Used version:

• PLAXIS 2D - Version 2018.0

• PLAXIS 3D - Version 2018.0

Geometry: On the upstream side, the water is at the reservoir level, at 12.19 m, whichresults in an equipotential line along AB with total head equal to 12.19 m. On thedownstream side, the water is at the ground surface level which results in anequipotential line with a total head equal to 0 m. The equipotentials and the stream linesdetermined by the flow net method are presented in Figure 1 (Lambe & Whitman, 1979).

Figure 1 Earth dam geometry and groundwater equipotentials and stream lines

The model geometry (including coordinates) and the groundwater flow boundaryconditions used in PLAXIS 2D are illustrated in Figure 2. The bottom flow boundary is setto be Closed, while every other is set to be Open.

In PLAXIS 3D, the model is extended by 1 m in the y-direction, as depicted in Figure 3.Both groundwater flow boundaries in y-direction as well as the bottom boundary are setto be Closed. Every other flow boundary is set to Open.

In addition to the global model conditions, an inclined water level is used to generate thehydraulic head of 12.19 m at the left side and 0.0 m at the right side. The internal part ofthis water level has no meaning and it will be overwritten by the results of thegroundwater flow analysis.

Materials: The Rock at the toe is simulated by using a relatively high coefficient ofpermeability (1 m/s). The Standard hydraulic model (Coarse material) is used to modelthe unsaturated flow in all layers. The adopted material parameters are:

Soil: Linear elastic Drained E ' = 1 kN/m2 k = 1.52 ×10−4 m/s

Rock toe: Linear elastic Drained E ' = 1 kN/m2 k = 1 m/s

Meshing: In both PLAXIS 2D and PLAXIS 3D models, the Very fine option is selected

PLAXIS 2018 | Validation & Verification 1

VALIDATION & VERIFICATION

h = 12.19m(19.87,12.79) (24.38,12.79)

(38.53,3.61)

(43.95,0)(34.62,0)Closed (impervious)(0,0)

Figure 2 Model geometry, finite element mesh (15-noded) and groundwater flow boundaryconditions (PLAXIS 2D)

Closed (impervious)

1.0m

Figure 3 Model geometry, finite element mesh (10-noded) and groundwater flow boundaryconditions (PLAXIS 3D)

for the Element distribution. The geometry line/surface which separate the Soil from theRock toe and the top geometry line/surface at the crest of the dam are refined with aCoarseness factor of 0.2. The resulting mesh is presented in Figures 2 and 3.

Calculations: The calculations are performed using the Flow only mode with Steadystate groundwater flow as the Pore pressure calculation type.

Output: The resulting phreatic line and the active pore pressures are presented inFigures 4 and 5 for PLAXIS 2D and PLAXIS 3D respectively. In PLAXIS 3D a verticalcross-section at the middle of the model (y=0.5 m) is considered.

Verification: The total discharge calculated by the flow net method equals Q=5.36·10-4

m3/s/m.

In PLAXIS, the total discharge through the dam is determined via a vertical cross-sectionat the middle of the dam. Comparison of the results obtained from PLAXIS and the flownet method is presented in Table 1. It is concluded that the results are in good agreement.

Table 1 Comparison between total discharge obtained from PLAXIS and the flow net method

Total discharge (m3/s/m) Error (%)

Lambe and Whitman PLAXIS 2D PLAXIS 3D PLAXIS 2D PLAXIS 3D

5.36·10-4 5.44·10-4 5.44·10-4 1.7 1.7

2 Validation & Verification | PLAXIS 2018

UNCONFINED FLOW THROUGH AN EARTH DAM

Figure 4 Phreatic line and active pore pressures (PLAXIS 2D)

Figure 5 Phreatic line and active pore pressures (PLAXIS 3D, vertical cross-section at y=0.5 m)

REFERENCES

[1] Lambe, T.W., Whitman, R.V. (1979). Soil Mechanics. John Wiley and Sons.

PLAXIS 2018 | Validation & Verification 3