Saturated Unit Weight
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
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Take a unit volume of solids: it weighs Gs·γw and occupies 1, while the voids occupy e and — if saturated — hold e·γw of water. Total weight (Gs + e)γw over total volume (1 + e) gives the saturated unit weight directly. For Gs = 2.68, e = 0.70 and γw = 9.81 kN/m³ that is (3.38 × 9.81) ÷ 1.70 = 19.50 kN/m³. In imperial units Gs = 2.65 with e = 0.55 and γw = 62.4 pcf gives (3.20 × 62.4) ÷ 1.55 = 128.8 pcf.
The trap is applying γsat above the water table. Soil there is moist, not saturated, and its unit weight is lower — using γsat for a whole profile overstates total stress and, worse, understates the effective stress ratio the strength depends on. The second trap is arithmetic laziness: γsat is not γd + γw. A denser soil holds less water, so as e falls γsat rises while the water carried per unit volume falls. Run the numbers at e = 0.4 and e = 1.0 and watch the two effects part company.
- = Saturated unit weight
- = Specific gravity of solids
- = Void ratio
- = Unit weight of water
- Saturated unit weight — Submerged (Buoyant) Unit Weight, Dry Unit Weight from Moist Unit Weight
- Specific gravity of solids — Degree of Saturation (Se = wGs), Dry Unit Weight from Gs and Void Ratio
- Void ratio — Void Ratio and Porosity (e = n/(1 − n)), Degree of Saturation (Se = wGs)
- Unit weight of water — Dry Unit Weight from Gs and Void Ratio, Pore Water Pressure (u = γw zw)