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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Back to Practice Questions
CivilSoil Mechanics
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A soil sample has porosity of 20 % and its void ratio will be close to

A

2

B

8

C

1

D

25

Correct Answer

⚙️ TE • Technical Direct FormulaCivilSoil Mechanics
Option D

25

Quick Summary:

Given: Porosity (n) = 20% = 0.20

📐MAMath SolutionDirect Formula
📋 Given

Porosity (n) = 20% = 0.20

🔢 Formula Used

e=n1−ne = \frac{n}{1 - n}e=1−nn​

🔢 Step-by-Step Solution
1

Identify given parameters

The porosity nnn is given as 20%, which in decimal form is n=0.20n = 0.20n=0.20.

n=0.20n = 0.20n=0.20

2

State the relationship formula

The relationship between void ratio eee and porosity nnn is given by the formula e=n1−ne = \frac{n}{1-n}e=1−nn​.

e=n1−ne = \frac{n}{1 - n}e=1−nn​

3

Substitute and solve

Substituting n=0.20n = 0.20n=0.20 into the formula, we get e=0.201−0.20=0.200.80e = \frac{0.20}{1 - 0.20} = \frac{0.20}{0.80}e=1−0.200.20​=0.800.20​.

e=0.200.80=0.25e = \frac{0.20}{0.80} = 0.25e=0.800.20​=0.25

✅

D is correct because by substituting the porosity value of 0.2 into the conversion formula, we obtain a void ratio of 0.25.

Core Concepts Used
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Porosity Void Ratio Soil Phase Relationships
💡 EXAM TIP

Understanding the relationship between porosity and void ratio is foundational for calculating degree of saturation and unit weight of soils in later geotechnical chapters.

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