Index properties — convert porosity to void ratio If a soil sample has porosity n = 20%, what is the corresponding void ratio e?

Introduction / Context:
Porosity n and void ratio e are two ways to express the fraction of voids in a soil. They are related but not equal. Converting between them is frequently required in geotechnical calculations involving volume change, permeability, and compaction.

Given Data / Assumptions:

• Porosity n = 20% = 0.20 (dimensionless).
• Standard definitions: e = Vv/Vs and n = Vv/Vt.
• Relationships hold for any two-phase soil, neglecting compressibility during conversion.

Concept / Approach:
The relationship is n = e / (1 + e) ⇔ e = n / (1 − n). This derives from Vt = Vv + Vs and the definitions of e and n. Substituting the given n yields e directly.

Step-by-Step Solution:
1) Write e = n / (1 − n).2) Substitute n = 0.20 → e = 0.20 / 0.80.3) Compute: e = 0.25.4) Choose 0.25.

Verification / Alternative check:
Back-substitute: n = e/(1 + e) = 0.25/1.25 = 0.20 = 20%, confirming correctness.

Why Other Options Are Wrong:
0.20 confuses porosity with void ratio; 0.80 and 1.00 are inconsistent with the conversion; 0.25 is the only correct value.

Common Pitfalls:
Using percentages without converting to decimals; mixing up e and n definitions; rounding prematurely.

Final Answer:
0.25