Module 7 · Lesson 7.3

Layered soils and permeability tests

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

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:

k_{h} = \frac{\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:

k_{v} = \frac{\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: k_h = Σ(k_i H_i)/ΣH_i — the most permeable layer dominates.
Normal (vertical) flow: k_v = ΣH_i / Σ(H_i/k_i) — the least permeable layer dominates.
k_h ≥ k_v always; a thin clay throttles vertical flow.
Constant-head tests suit permeable soils; falling-head tests suit finer soils.

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This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint