Porosity from densities and Gs A soil has dry density ρd = 1.60 g/cm³, bulk density ρ = 1.84 g/cm³, and specific gravity of solids Gs = 2.56. Determine the porosity n.

Introduction / Context:Porosity n is the ratio of void volume to total volume. With dry density and Gs known, n follows directly from a standard relationship derived from the volumes of solids and voids.

Given Data / Assumptions:

• ρd = 1.60 g/cm³ (dry).
• Gs = 2.56; ρw = 1 g/cm³.
• Isothermal conditions; no chemical changes.

Concept / Approach:

The relation between dry density and porosity is: ρd = (Gs * ρw) * (1 − n) ⇒ n = 1 − (ρd / (Gs * ρw)) Bulk density is not needed for n in this formula (it can be used to cross-check water content).

Step-by-Step Solution:

Verification / Alternative check:

Alternatively, find void ratio e = ρs/ρd − 1 = 2.56/1.60 − 1 = 0.60; then n = e/(1 + e) = 0.60/1.60 = 0.375.

Why Other Options Are Wrong:

0.370 and 0.380 are near-misses; 0.390 and 0.360 deviate further. The exact computed value is 0.375.

Common Pitfalls:

Using bulk density instead of dry density; mixing units; rounding too early.

Final Answer:

0.375