Soil Gravimetric Relationships Calculator
The relationships between phases (solids, water, air) are the starting point of any geotechnical analysis. This calculator converts between wet unit weight (γ), dry unit weight (γd), water content (w), specific gravity of solids (Gs), void ratio (e), porosity (n), and degree of saturation (S). Useful for interpreting Proctor tests, in-situ density, consolidation, triaxial tests, and for verifying the actual compaction of a fill relative to the maximum laboratory density.
What are gravimetric relationships?
Soil is a mixture of three phases: solid particles, water, and air. Gravimetric relationships express the proportions between them. Knowing any two variables from the set (γd, w, Gs, e, n, S) allows calculating the other four using exact identities. They are applied to interpret laboratory results, convert field density to relative compaction, analyze saturation below the water table, evaluate collapsibility in unsaturated soils, and as input for consolidation, liquefaction, and permeability analyses.
Applied formulas
Dry unit weight: γd = γ / (1 + w)
Void ratio: e = (Gs × γw / γd) − 1
Porosity: n = e / (1 + e)
Degree of saturation: S = (w × Gs) / e
Saturated unit weight: γsat = γw × (Gs + e) / (1 + e)
Submerged unit weight: γ' = γsat − γw
Where γw = 9.81 kN/m³ (unit weight of water), typical Gs 2.65-2.75.
Calculation example
| Parameter | Value |
|---|---|
| Wet unit weight (γ) | 19.2 kN/m³ |
| Water content (w) | 18.5 % |
| Specific gravity (Gs) | 2.70 |
First the dry unit weight: γd = 19.2 / (1 + 0.185) = 19.2 / 1.185 = 16.20 kN/m³. Then the void ratio: e = (2.70 × 9.81 / 16.20) − 1 = (26.49 / 16.20) − 1 = 1.635 − 1 = 0.635. Porosity becomes n = 0.635 / (1 + 0.635) = 0.388 or 38.8 %. Degree of saturation: S = (0.185 × 2.70) / 0.635 = 0.4995 / 0.635 = 0.787 or 78.7 %. Saturated unit weight γsat = 9.81 × (2.70 + 0.635) / 1.635 = 9.81 × 2.040 = 20.01 kN/m³, and submerged γ' = 20.01 − 9.81 = 10.20 kN/m³.
Result: γd = 16.20 kN/m³ · e = 0.64 · n = 38.8 % · S = 78.7 % · γsat = 20.0 kN/m³ · γ' = 10.2 kN/m³.
Interpretation of results
S = 78.7 % indicates a partially saturated soil, typical above the water table. With e = 0.64 it is in medium density (values 0.4-0.7 are common for compact sands and clays). If that sample were below the water table, γ' = 10.2 kN/m³ should be used to calculate effective stresses. Saturation above 95 % and e above 1.0 indicate very loose or soft soil, with high compressibility and potential consolidation problems.
Reference standards
- ASTM D854 — Specific Gravity of Solids (Pycnometer)
- ASTM D2216 — Laboratory Determination of Water Content
- ASTM D7263 — Density and Unit Weight of Intact Specimens
- ASTM D854 — Specific Gravity of Solids (Pycnometer)
- ASTM D2216 — Laboratory Determination of Water Content
Frequently asked questions
When do I use wet γ and when submerged γ?
Wet (or total) γ is used above the water table to calculate total stresses. Below the water table, γsat is used for total stresses and γ' = γsat − γw for effective stresses. Mixing them is a common error that overestimates or underestimates consolidation and bearing capacity calculations.
What typical Gs should I assume if I don't have a test?
For most granular soils and clays, Gs = 2.65 to 2.75. Pure siliceous sands 2.65; common clays 2.70-2.75; soils with high mica or organic content drop to 2.5-2.6; magnetite or heavy minerals can rise to 2.9 or more. If in doubt, measurement is mandatory.
Can I have S > 100 %?
No in a real soil. If the calculation gives S > 100 %, it means there is a test error: overestimated water content, incorrect Gs, or underestimated void ratio. First check the w and Gs measurements before accepting the result.
How do I go from compaction water content to the dry or wet side of the Proctor optimum?
With w and Gs you calculate e and S at that point. The dry side of the optimum typically has S between 70-85 % and the wet side between 85-95 %. On the Proctor curve, the "saturation line" (S = 100 %) is the theoretical upper limit and serves as a reference to verify that the curve is consistent.