Index properties — convert void ratio to porosity A soil has a void ratio e = 0.5. The porosity n (in %) will be approximately:

Introduction / Context:Void ratio e and porosity n are related measures of the void content in soils. Converting properly between them is fundamental in geotechnical computations, such as evaluating compaction, compressibility, and permeability changes.

Given Data / Assumptions:

• Void ratio e = 0.5 (dimensionless).
• Definitions: e = Vv/Vs, n = Vv/Vt, with Vt = Vv + Vs.
• Standard relationship between e and n applies.

Concept / Approach:The conversion formula is n = e / (1 + e). This follows from substituting the definitions and eliminating Vv and Vs using Vt.

Step-by-Step Solution:1) Compute n = e / (1 + e) = 0.5 / 1.5.2) n = 0.3333…3) Express as percent: n ≈ 33%.4) Choose option 33%.

Verification / Alternative check:Back-conversion: e = n/(1 − n) with n = 0.333 gives e ≈ 0.5, confirming consistency.

Why Other Options Are Wrong:50% corresponds to e = 1.0; 66% implies e ≈ 2.0; 100% is impossible physically for soil skeletons in normal states.

Common Pitfalls:Confusing e with n; using percent values directly without converting to fractions before substitution.

Final Answer:33%