Polder Dyke Seepage

What is modelled

Water flows through soil in proportion to the head gradient (Darcy's law). Through the body of a dyke on an impervious base the flow follows a parabolic water line (Dupuit). Under the dyke the water goes through the sand layer, and if the path is short the flow can carry sand grains out at the toe and eat a pipe back toward the river. The Lane creep method compares the weighted length of the path with a length needed by the soil.

Equations

• Dupuit discharge q = k (h12 − h22) / (2L), water line h(x) = √(h12 − (h12 − h22) x/L).
• Confined layer q = k T ΔH / path.
• Lane path Lw = ΣLv + ⅓ ΣLh, required CL ΔH.
• Critical exit gradient about 1 for sand of usual density.

Checks run in the page

• The Dupuit discharge integrated along the dyke back to the ditch level.
• The same discharge at every station of the water line.
• A successive over-relaxation solution of 2D flow under the dyke.
• The Lane creep path and the shortest sheet pile that satisfies it.

Honest simplifications

The Dupuit parabola assumes nearly horizontal flow and ignores the seepage face at the toe, the dyke is homogeneous and rests on an impervious base apart from the sand layer, the layers are treated separately, and the creep rule is an empirical screening method, not a design calculation. Real dyke safety needs slope stability, filters and drainage as well.

• Press High flood, sandy base: the creep safety factor falls below 1.
• Press Same flood, sheet pile added and compare the under-seepage.
• Press Leaky sand dyke and watch the water line stay high inside the dyke.