Darcy's law and how permeability is measured

Water moves through the connected pores of soil. How easily it moves is the soil's permeability, and it controls seepage under dams, dewatering of excavations and how fast clay consolidates.

Darcy's law

For laminar flow, discharge is proportional to the hydraulic gradient:

q = k i A i = hL

k is the coefficient of permeability (m/s), i the hydraulic gradient, h the head lost over length L, and A the gross area.

The discharge velocity is v = k i. The water actually moves faster, through the pores only, at the seepage velocity:

v_s = vn

Typical values of k

Soil	k (m/s)
Clean gravel	10⁻² and above
Clean sand	10⁻³ to 10⁻⁵
Silt	10⁻⁵ to 10⁻⁷
Clay	10⁻⁹ and below

Constant head test (coarse soils)

Water flows through the sample under a steady head h, and volume Q is collected in time t:

k = Q LA h t

Falling head test (fine soils)

The head falls in a standpipe of area a from h₁ to h₂ in time t:

k = 2.303 a LA t log₁₀ h₁h₂

Factors that change k

Grain size has the biggest effect. Allen Hazen's rule for clean sands is k = C D₁₀², with D₁₀ the effective size. Void ratio, water viscosity (temperature), soil structure and entrapped air also matter.