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Equivalent Vertical Permeability

Hardpermeabilitylayered soil
A 2 m thick sand layer with hydraulic conductivity 5 × 10⁻⁴ m/s overlies a 1 m thick clay layer with hydraulic conductivity 1 × 10⁻⁷ m/s. For vertical flow through both layers, the equivalent hydraulic conductivity is most nearly:
  1. A1.5 × 10⁻⁷ m/s
  2. B3.0 × 10⁻⁷ m/s
  3. C3.3 × 10⁻⁴ m/s
  4. D5.0 × 10⁻⁴ m/s
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Answer: B. 3.0 × 10⁻⁷ m/s

Vertical flow passes through the layers in series, so the equivalent conductivity is the harmonic form keq = ΣH/Σ(H/k) = 3/[(2/5×10⁻⁴) + (1/1×10⁻⁷)] = 3/(4,000 + 10,000,000) ≈ 3.0 × 10⁻⁷ m/s. The thin clay layer dominates completely. Averaging the two conductivities arithmetically would give 3.3 × 10⁻⁴ and describes horizontal flow instead, where the layers act in parallel.
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