13.2.4 Seepage Faces

To describe the occurrence of seepage faces in groundwater flow analysis you may apply boundary elements of the `groundwater flow' type which enable changes of boundary conditions from insulated to prescribed hydraulic head and vice versa [Vol. Element Library]. The boundary elements form a resistance layer with zero thickness and must be placed in the area where occurrence of the seepage face is allowed. The prescribed hydraulic head is forced upon the boundary by using a penalty method. For the boundary elements you may specify the conduction coefficient as follows.

    (syntax)

BOUNCO

kp is the permeablity of a resistance layer between environment and boundary, divided by the physical thickness of the layer. A typical unit is s^-1 . Alternatively it can be used as a penalty conduction coefficient K_p [ K_p = 1 ] between environment and boundary: a very large value for `open' conditions and a zero value for `closed' conditions. If the penalty value becomes too large, the system conductivity matrix will become ill-conditioned.

To illustrate the analysis of a seepage face we consider an edge of a soil domain above a free water surface as shown in Figure 13.1.^13.1

Figure 13.1: Seepage face

The seeping part of the edge must have a prescribed pressure head equal to zero. No flux runs through the part of the edge above the seepage point S. At the start of the Finite Element Analysis, the position of the seepage point is unknown. DIANA applies an iterative procedure to determine the correct boundary conditions for the seepage face, i.e., in the groundwater flow boundary elements.

After an iteration which does not reach an accurate solution, four parts may be distinguished on the edge above the free water surface [Fig.13.1].

1. A part where a flux occurred in the previous iteration and which still satisfies the condition that the internal pressure head is greater than the external pressure head. In this part of the boundary the pressure remains prescribed: $\phi_{{\mathrm{p}}}^{}$ = 0 .

2. A part where no flux occurred in the previous iteration and which still satisfies the condition that the internal pressure head is less than the external pressure head. This part remains fully insulated: q = 0 .

3. A part where no flux occurred in the previous iteration and where the condition that the internal pressure head is less than the external pressure head is no longer satisfied. On this part of the boundary DIANA now allows a flux to occur, starting at the lower point. It is essential that this change occurs gradually: per iteration the conduction of only one boundary element can change.

4. A part where flux occurred in the previous iteration and where the condition that the internal pressure head is greater than the external pressure head is no longer satisfied. DIANA fully insulates the integration points for the elements on this part of the boundary: q = 0 .

Please note that in transient analysis , the external hydraulic head can be time-dependent, which will result in an adapted position of the top and the bottom of the seepage face.