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CivilSoil Mechanics

A soil sample has void ratio of 0.5 and its porosity will be close to

50%

66%

100%

33%

Correct Answer

⚙️ TE • Technical Direct FormulaCivilSoil Mechanics

Option D

33%

Quick Summary:

Given: Void ratio (e) = 0.5

📐MAMath SolutionDirect Formula

📋 Given

Void ratio (e) = 0.5

🔢 Formula Used

n=e1+en = \frac{e}{1 + e}n=1+ee​

🔢 Step-by-Step Solution

Identify given parameters

The given void ratio $e$ is 0.5. We need to calculate the porosity $n$ .

e=0.5e = 0.5e=0.5

State the relationship

The relationship between porosity $n$ and void ratio $e$ is defined by the formula:

n=e1+en = \frac{e}{1 + e}n=1+ee​

Calculate porosity

Substitute the value of $e$ into the formula: $n = 0.5 / (1 + 0.5) = 0.5 / 1.5$ .

n=0.51.5=13≈0.333n = \frac{0.5}{1.5} = \frac{1}{3} \approx 0.333n=1.50.5​=31​≈0.333

Convert to percentage

To express porosity as a percentage, multiply the result by 100.

n%=0.333×100=33.3%n\% = 0.333 \times 100 = 33.3\%n%=0.333×100=33.3%

✅

D is correct because substituting $e = 0.5$ into the porosity formula $n = e/(1+e)$ yields $0.333$ , which is $33.3\%$ .

Core Concepts Used

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💡 EXAM TIP

Always remember that porosity $n$ must always be less than 1 (or 100%), whereas void ratio $e$ can be greater than 1.

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