Permeability of Soil Notes

Last reviewed 16 Sept 2026 · 5 min read

Permeability

Permeability is the ease with which water flows through the interconnected voids of a soil. It controls:

seepage through and under dams, levees and sheet piles, and uplift pressures,
rate of consolidation settlement of clay layers,
drainage of excavations, roads and retaining walls,
yield of wells and dewatering design.

Darcy's law

For laminar flow through saturated soil:

v = k i, q = k i A

$v$ = discharge (superficial) velocity — discharge divided by the total cross-sectional area; $i = h / L$ = hydraulic gradient; $k$ = coefficient of permeability (hydraulic conductivity), in m/s or cm/s.

The actual average velocity through the pores is the seepage velocity:

v_{s} = \frac{v}{n} (> v, since flow passes only through voids)

Darcy's law holds when flow is laminar — true for silts, clays and most sands; it may not hold for coarse gravels at high gradients (turbulent flow).

Typical permeability

Soil	$k$ (m/s), order of magnitude	Drainage
Clean gravel	$1 0^{- 1}$ to $1 0^{- 3}$	Very good
Clean coarse to medium sand	$1 0^{- 3}$ to $1 0^{- 5}$	Good
Fine sand, silty sand	$1 0^{- 5}$ to $1 0^{- 7}$	Fair
Silt	$1 0^{- 7}$ to $1 0^{- 9}$	Poor
Clay	below $1 0^{- 9}$	Practically impervious

Factors affecting permeability

The Kozeny–Carman expression shows the main influences:

k = C \frac{γ _{w}}{μ} \frac{e ^{3}}{1 + e} D^{2}

Grain size — $k \propto D^{2}$ (Hazen uses $D_{10}$ ).
Void ratio — $k$ rises sharply with $e$ ( $e^{3} / (1 + e)$ ).
Properties of pore fluid — $k \propto γ_{w} / μ$ ; warm water (lower viscosity) flows faster. Standard results are reported at 27 °C in Indian practice: $k_{27} = k_{T} μ_{T} / μ_{27}$ .
Shape and arrangement of particles, soil structure — flocculated clays are more permeable than dispersed ones at the same void ratio.
Degree of saturation — entrapped air reduces $k$ .
Adsorbed water in clays reduces the effective pore space.
Stratification — horizontal permeability usually far exceeds vertical.
Impurities / fines clog pores.

Hazen's empirical relation (clean uniform sands)

k = C D_{10}^{2} (k in cm/s, D_{10} in cm, C \approx 100 to 150)

Laboratory tests

Constant-head test (coarse-grained soils)

Water flows under a steady head $h$ through a sample of length $L$ and area $A$ ; volume $Q$ is collected in time $t$ :

k = \frac{Q L}{A h t}

Falling-head (variable-head) test (fine-grained soils)

Water from a standpipe of area $a$ falls from $h_{1}$ to $h_{2}$ in time $t$ :

k = \frac{a L}{A t} ln \frac{h _{1}}{h _{2}} = \frac{2.303 a L}{A t} lo g_{10} \frac{h _{1}}{h _{2}}

(Very low permeabilities are also found indirectly from consolidation test data: $k = c_{v} m_{v} γ_{w}$ .)

Field pumping tests

Laboratory samples may not represent stratification and fissures; pumping-out tests measure average field permeability. Water is pumped at a steady rate $q$ and water levels are observed in two observation wells at radii $r_{1}$ and $r_{2}$ .

FormulaSteady pumping

Unconfined aquifer (water table aquifer), heights of water above the impervious base $h_{1}$ , $h_{2}$ :

k = \frac{q ln ( r _{2} / r _{1} )}{π ( h _{2}^{2} - h _{1}^{2} )} = \frac{2.303 q lo g _{10} ( r _{2} / r _{1} )}{π ( h _{2}^{2} - h _{1}^{2} )}

Confined aquifer of thickness $b$ (piezometric heads $h_{1}$ , $h_{2}$ ):

k = \frac{q ln ( r _{2} / r _{1} )}{2 π b ( h _{2} - h _{1} )}

Other field tests: pumping-in tests in bore holes, packer tests in rock.

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Permeability of Soil