Soil phase relations: void ratio, porosity, water content and unit weight

Soil is made of three phases: solid particles, water and air. Phase relations link their volumes and weights, and nearly every soil mechanics problem starts here.

The basic definitions

Term	Definition
Void ratio, e	Vv / Vs
Porosity, n	Vv / V
Degree of saturation, S	Vw / Vv
Water content, w	Ww / Ws
Specific gravity, G	γs / γw

Void ratio and porosity are linked:

n = e1 + e e = n1 − n

The most useful relation

S e = w G

For a saturated soil S = 1, so e = wG. For a dry soil S = 0.

Unit weights

γ_d = G γ_w1 + e γ_sat = (G + e) γ_w1 + e

γ = (G + S e) γ_w1 + e γ' = γ_sat − γ_w

Dry unit weight from bulk unit weight and water content:

γ_d = γ1 + w

Worked example

A soil sample has γ = 19 kN/m³, w = 15% and G = 2.68. Take γ_w = 9.81 kN/m³.

γ_d = 191.15 = 16.52 kN/m³

e = G γ_wγ_d − 1 = 2.68 × 9.8116.52 − 1 = 0.59

S = w Ge = 0.15 × 2.680.59 = 0.68, so 68% saturated

Try it on our soil phase relations tool, which works out every parameter from any three you know.