Sheet pile flow net; graded filter

Flow net under a sheet pile

A flow net for seepage under a sheet pile wall (confined flow) is drawn by trial and error.

 upstream ~~~~~|S|~~~~~ downstream
 h1 ▽__________| |__________▽ h2
   ..flow lines..|..flow lines..
 ----equipotentials cross at 90°-----
 =========== impervious layer ===========

Steps:

1. Draw the section to a convenient scale: sheet pile, ground levels, water levels and the impervious base.
2. Identify the boundary conditions. The upstream soil surface (bed) and the downstream surface are equipotential lines. The surface of the sheet pile and the impervious base are flow lines.
3. Sketch 3 to 4 flow lines, smooth curves starting perpendicular to the upstream equipotential, bending round the pile tip, and ending perpendicular to the downstream equipotential. The line nearest the pile follows the pile; the lowest follows the impervious layer.
4. Sketch equipotential lines to cut the flow lines at right angles so that each field is nearly a square (a circle can be inscribed in each).
5. Adjust the lines by trial until all fields are curvilinear squares.
6. Count $N_f$ (flow channels) and $N_d$ (equipotential drops). Discharge: $q = k\,h\,\dfrac{N_f}{N_d}$ per metre length, with $h = h_1 - h_2$.

Graded filter design

A filter between the base soil and a coarse drain lets water pass but holds back soil particles (piping prevention). For a big grain-size jump, several layers of increasing size are used, each protecting the previous one.

 base soil | filter 1 | filter 2 | coarse drain
  fine     |  finer   | coarser  | stone/pipe
 -------------------------------------------->
          direction of seepage

Terzaghi's criteria, for each filter and the layer it protects:

• Piping: $\dfrac{D_{15}(\text{filter})}{D_{85}(\text{soil})} \le 4 \text{ to } 5$
• Permeability: $\dfrac{D_{15}(\text{filter})}{D_{15}(\text{soil})} \ge 4 \text{ to } 5$
• $\dfrac{D_{50}(\text{filter})}{D_{50}(\text{soil})} \le 25$, and the grading curve of the filter roughly parallel to that of the soil.

Procedure: plot the grading curve of the base soil; find $D_{85}$ and $D_{15}$; fix the grading band of the first layer from the criteria; repeat with the first layer as the "soil" for the next layer until the last layer is coarse enough for the drain. Each layer should have a minimum thickness (about 15 to 30 cm) and contain few fines.