Void ratio–porosity relationship: Which expression correctly relates porosity n to void ratio e for a soil mass?

Introduction / Context:

Porosity n and void ratio e are closely related measures of the void content in soils. Converting between them is routine when interpreting laboratory results and specifying compaction targets or saturation levels in geotechnical design.

Given Data / Assumptions:

• Definitions: e = Vv / Vs and n = Vv / Vt, where Vv is void volume, Vs is volume of solids, and Vt = Vv + Vs is total volume.

Concept / Approach:

Starting with the definitions, express n in terms of e: n = Vv / (Vv + Vs) and e = Vv / Vs. Substitute Vv = e * Vs into the expression for n to obtain the algebraic relationship.

Step-by-Step Solution:

Verification / Alternative check:

Invert the relation to get the equivalent expression e = n / (1 - n), confirming consistency and enabling conversion either way as needed.

Why Other Options Are Wrong:

• n = e / (1 - e) and e = n / (1 + n) are algebraically incorrect.
• n = 1 / (1 + e) confuses porosity with the solid fraction.
• e = 1 / (1 - n) omits scaling by n and is dimensionally inconsistent.

Common Pitfalls:

• Mistaking porosity for percent voids; always convert to a fraction before using the relation.

Final Answer:

n = e / (1 + e)