Soil Void Ratio Calculator (Porosity, Saturation & Unit Weights)
Calculate a soil’s void ratio, porosity, degree of saturation, dry, saturated and submerged unit weight from its moisture content, specific gravity Gs and bulk or dry unit weight — soil phase relationships.
How it works
γd = γ/(1 + w) · e = Gs·γw/γd − 1 · n = e/(1 + e) · S = w·Gs/e · γsat = (Gs + e)·γw/(1 + e) · γ′ = γsat − γw · air content = n(1 − S) · γw = 9.81 kN/m³ = 62.4 pcf.
A soil sample is solids, water and air. Phase relationships tie the volumes and weights together so that three measured quantities — usually the moisture content (oven drying, ASTM D2216), the specific gravity of the solids (ASTM D854) and the unit weight from a tube sample or field density test — give everything else. The key identity S·e = w·Gs links saturation, void ratio and water content. Void ratio feeds consolidation settlement, porosity feeds seepage and storage calculations, and the saturated and submerged unit weights are needed for effective-stress calculations below the water table.
Worked example
A sample weighs 19 kN/m³ at 18% moisture with Gs = 2.70. γd = 19/1.18 = 16.10 kN/m³, so e = 2.70 × 9.81/16.10 − 1 = 0.645. Porosity n = 0.645/1.645 = 39.2% and S = 0.18 × 2.70/0.645 = 75.4%. Fully saturated it would weigh (2.70 + 0.645)/1.645 × 9.81 = 19.95 kN/m³, or 10.14 kN/m³ submerged.
Sources: FHWA — Soils and Foundations Reference Manual Vol. I, §4 (soil phase relationships) · Void ratio
Frequently asked questions
What is the difference between void ratio and porosity?
Void ratio e is the volume of voids divided by the volume of solids; porosity n is the volume of voids divided by the total volume. They carry the same information: n = e/(1 + e) and e = n/(1 − n). Void ratio is preferred in geotechnics because the solids volume does not change as the soil compresses.
What are typical void ratios?
Dense sand and gravel 0.3–0.5, loose sand 0.6–0.8, stiff clay 0.5–0.9, soft clay 0.9–1.5 and organic clay or peat from 2 up to 10 or more.
Why can the degree of saturation come out above 100%?
Only because of inconsistent inputs — a unit weight too high for the moisture content, or the wrong Gs. Measurement errors of a few percent in moisture content or density easily push a nearly saturated clay over 100%, so the calculator flags it.
What is the submerged unit weight used for?
Below the water table the soil is buoyed up, so vertical effective stress grows with γ′ = γsat − γw rather than the full unit weight. It is used for bearing capacity, earth pressure and consolidation stresses in saturated soil.
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This calculator is for educational purposes. Double-check important results before acting on them.