Void ratio from saturation condition: A saturated soil has water content w = 40% and specific gravity of solids G = 2.7. Determine the void ratio e (assume full saturation).

Introduction / Context:
For fully saturated soils, a very useful identity links void ratio e, water content w, and specific gravity G. This provides a quick check on laboratory data and helps initialize consolidation and seepage analyses.

Given Data / Assumptions:

• Saturation: S_r = 1.0 (fully saturated).
• Water content w = 40% = 0.40 (decimal).
• Specific gravity of solids G = 2.7.

Concept / Approach:
Under full saturation, the fundamental phase-relationship reduces to e = w * G (with w in decimal form). This comes from S_r = (w * G)/e and S_r = 1 at saturation, giving e = w * G directly.

Step-by-Step Solution:

Verification / Alternative check:
Porosity n = e / (1 + e) = 1.08 / 2.08 ≈ 0.519 (~52%), a realistic value for saturated fine-grained soils at this water content and mineral density.

Why Other Options Are Wrong:

• 0.40 or 0.52 or 0.80: Do not satisfy e = w * G for the given data.
• “None of these”: incorrect because a valid computed value exists in the options.

Common Pitfalls:
Using w as a percent without converting to decimal; confusing G (dimensionless) with unit weights.

Final Answer:
1.08