Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Index properties of soils
Question Statement:
A sample of wet sandy-clay loam soil of mass 135 kg is collected for laboratory tests. The wet density, water content (weight basis) and specific gravity of solids of this soil sample are 1.8 g·cm⁻³, 18%, and 2.7, respectively. The dry density (in g·cm⁻³) and porosity (in per cent) of the soil sample, respectively, are
Options:
(A) 1.53 and 43.50
(B) 1.53 and 77.00
(C) 1.65 and 43.50
(D) 1.65 and 77.00
Official Answer Key:
A
Step-by-Step Solution & Explanation
Dry density ρ_d = ρ_wet/(1+w) = 1.8/1.18 = 1.5254 ≈ 1.53 g/cm³. Void ratio e = (Gs·ρ_water/ρ_d) − 1 = (2.7×1/1.5254) − 1 = 1.7699 − 1 = 0.7699. Porosity n = e/(1+e) = 0.7699/1.7699 = 0.435 = 43.5%, matching (A). (The 135 kg total mass is a distractor, not needed for these ratio-based properties.)
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