Equivalent Horizontal Permeability of Layered Soil

Flow parallel to bedding runs through the layers side by side, so the discharges add and the equivalent permeability is the thickness-weighted arithmetic mean. Three metres of sand at 10⁻² cm/s over two metres of silt at 10⁻⁴ cm/s gives k_eq = (0.03 + 0.0002) ÷ 5 = 6.0×10⁻³ cm/s — the sand carries 99.3% of the flow and the silt might as well not be there.

The trap is using this for vertical flow. Perpendicular to the bedding the layers are in series, not parallel, and the equivalent permeability is the harmonic mean ΣH ÷ Σ(H/k), which for the same two layers is 5 ÷ (300 + 20 000) = 2.5×10⁻⁴ cm/s — twenty-four times smaller. Natural alluvial deposits routinely show horizontal-to-vertical ratios of 10 to 100 for exactly this reason, and getting the anisotropy backwards is how a dewatering scheme ends up pumping ten times more or less than planned. When you see a clay blanket over sand, remember that in the vertical direction the thinnest, least permeable layer dictates everything.