The Chartership Forum

Soil Mechanics / module 14

Two-dimensional seepage and flow nets

Water seeping around walls and beneath dams: flow lines and equipotentials, the flow net as a graphical solution, the seepage flow rate, and the exit gradient that governs piping and heave.

What you will understand

  • Describe two-dimensional seepage with flow lines and equipotentials
  • Read a flow net as a mesh of curvilinear squares and count Nf and Nd
  • Derive and use the flow-net flow rate q = k·h·(Nf/Nd)
  • Find pore pressure at a point from the equipotential drops
  • Compute the exit gradient and the factor of safety against piping/heave

Lessons

  1. Flow lines and equipotentials

    From one-dimensional Darcy flow to a two-dimensional flow net.

  2. Using a flow net

    The seepage flow rate and pore pressure from the net.

  3. Exit gradient, piping and heave

    Where seepage emerges, and how it can lift or wash away the ground.

Module summary
  • Two-dimensional seepage is solved with a flow net of flow lines and equipotentials meeting at right angles.
  • Seepage flow rate q = k·h·(Nf/Nd); pore pressure at a point from the equipotential drops passed.
  • The exit gradient iexit = (h/Nd)/l governs piping/heave, compared with icr = (Gs − 1)/(1 + e) ≈ 1.
  • Factor of safety F = icr/iexit (commonly ≥ 3); lengthen the seepage path or add a filter to raise it.
Teaching basis and review status

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Check your understanding

Practice

A flow net has Nf = 3, Nd = 9, head loss h = 12 m and k = 5 × 10⁻⁷ m/s. What is the seepage flow rate per metre width, in m³/s/m?

Practice

With h = 8 m, Nd = 16 and an exit-square length l = 1.0 m, what is the exit gradient?

Check yourself

To increase the factor of safety against piping beneath a cutoff wall, you should: