The Chartership Forum

Soil Mechanics / Water in soil and Darcy's law

Layered soils and permeability tests

Flow along the layers versus across them, and how k is measured.

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Why this matters

Natural ground is layered, and the layers usually have very different permeabilities. Whether water flows along the layers or across them changes the effective permeability enormously — and which layer controls it.

For flow parallel to the layers (horizontal), each layer sees the same gradient and the flows add, so the most permeable layer dominates:

kh=∑kiHi∑Hi.k_h = \dfrac{\sum k_i H_i}{\sum H_i}.

For flow normal to the layers (vertical), each layer passes the same flow and the head losses add, so the least permeable layer dominates:

kv=∑Hi∑(Hi/ki).k_v = \dfrac{\sum H_i}{\sum (H_i/k_i)}.

The horizontal (parallel) value is always greater than or equal to the vertical (series) value. A single thin clay layer can throttle vertical flow through an otherwise permeable deposit.

Check yourself

A deposit is 2 m of sand (k = 10⁻⁴ m/s) over 1 m of clay (k = 10⁻⁶ m/s). For VERTICAL flow through both, roughly what is the equivalent permeability?

Summary

  • Parallel (horizontal) flow: kh = Σ(ki Hi)/ΣHi — the most permeable layer dominates.
  • Normal (vertical) flow: kv = ΣHi / Σ(Hi/ki) — the least permeable layer dominates.
  • kh ≥ kv always; a thin clay throttles vertical flow.
  • Constant-head tests suit permeable soils; falling-head tests suit finer soils.