Criteria for Sketching Flownets:
A fl ownet is a graphical representation of a flow fi eld that satisfi es Laplace’s equation and comprises a family of fl ow lines and equipotential lines.
A fl ownet must meet the following criteria:
1. The boundary conditions must be satisfi ed.
2. Flow lines must intersect equipotential lines at right angles.
3. The area between fl ow lines and equipotential lines must be curvilinear squares. A curvilinear square has the property that an inscribed circle can be drawn to touch each side of the square and continuous bisection results, in the limit, in a point.
4. The quantity of fl ow through each fl ow channel is constant.
5. The head loss between each consecutive equipotential line is constant.
6. A fl ow line cannot intersect another flow line.
7. An equipotential line cannot intersect another equipotential line.
An infi nite number of fl ow lines and equipotential lines can be drawn to satisfy Laplace’s equation. However, only a few are required to obtain an accurate solution. The procedure for constructing a flownet is described next.
Flownet for Isotropic Soils:
1. Draw the structure and soil mass to a suitable scale.
2. Identify impermeable and permeable boundaries. The soil–impermeable boundary interfaces are fl ow lines because water can fl ow along these interfaces. The soil–permeable boundary interfaces are equipotential lines because the total head is constant along these interfaces.
3. Sketch a series of fl ow lines (four or fi ve) and then sketch an appropriate number of equipotential lines such that the area between a pair of fl ow lines and a pair of equipotential lines (cell) is approximately a curvilinear square. You would have to adjust the fl ow lines and equipotential lines to make curvilinear squares. You should check that the average width and the average length of a cell are approximately equal by drawing an inscribed circle. You should also sketch the entire flownet before making adjustments.
Flownet for a sheet pile.
The fl ownet in confi ned areas between parallel boundaries usually consists of fl ow lines and equipotential lines that are elliptical in shape and symmetrical (Figure ). Try to avoid making sharp transitions between straight and curved sections of fl ow and equipotential lines. Transitions should be gradual and smooth. For some problems, portions of the fl ownet are enlarged and are not curvilinear squares, and they do not satisfy Laplace’s equation. For example, the portion of the fl ownet below the bottom of the sheet pile in Figure does not consist of curvilinear squares. For an accurate fl ownet, you should check these portions to ensure that repeated bisection results in a point.
A few examples of fl ownets are shown in Figures shows a fl ownet for a sheet pile wall, Figure shows a fl ownet beneath a dam, and Figure shows a fl ownet in the backfill of a retaining wall. In the case of the retaining wall, the vertical drainage blanket of coarse-grained soil is used to transport excess porewater pressure from the backfi ll to prevent the imposition of a hydrostatic force on the wall. The interface boundary, AB (Figure ), is neither an equipotential line nor a flow line. The total head along the boundary AB is equal to the elevation head.