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CivilSoil Mechanics

If the volume of voids is equal to the volume of soil solids, then the values of porosity and void ratio are respectively

and 0.5

and 1

and 0.5

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilSoil Mechanics

Option B

and 1

Quick Summary:

Given that the volume of voids ( $V_v$ ) is equal to the volume of solids ( $V_s$ ), we have the condition $V_v = V_s$ . Using this, the void ratio ( $e$ ) is calculated as the ratio of $V_v$ to $V_s$ , which equals 1, and porosity ( $n$ ) is calculated as the ratio of $V_v$ to the total volume ( $V_T = V_v + V_s$ ), resulting in 0.5.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$e = \frac{V_v}{V_s}$ — Void Ratio

$n = \frac{V_v}{V_T} = \frac{e}{1+e}$ — Porosity

$n = \frac{V_v}{V_v + V_s}$ — Porosity based on volumes

⚙️ Working Principle

In soil mechanics, void ratio ( $e$ ) relates the void space to the solid particles: $e = V_v / V_s$ . Since $V_v = V_s$ , $e = V_v / V_v = 1$ . Porosity ( $n$ ) relates the void space to the total volume: $n = V_v / (V_v + V_s)$ . Substituting $V_s$ with $V_v$ , we get $n = V_v / (V_v + V_v) = V_v / (2V_v) = 0.5$ .

📌 Key Points

▸
Void ratio ( $e$ ) is the ratio of the volume of voids to the volume of soil solids.
▸
Porosity ( $n$ ) is the ratio of the volume of voids to the total volume of the soil mass.
▸
The range of $e$ is $0 < e < \infty$ , whereas $0 < n < 1$ .
▸
A condition where $V_v = V_s$ implies a very loose soil structure.

✅ Advantages

▸
Mathematically clear relationship
▸
Fundamental for permeability and settlement calculations

🛠️ Applications / Uses

▸
Soil classification
▸
Compressibility analysis
▸
Shear strength determination

📄 Additional Information

▸
Void ratio is dimensionless and typically greater than zero for soils.
▸
Porosity is expressed as a fraction or percentage; it must always be less than 1 (100%).

📊 Diagram / Illustration

✅

C is correct — When $V_v = V_s$ , the void ratio $e = 1$ and porosity $n = 0.5$ .

Core Concepts Used

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Phase relationships in soil Definition of void ratio Definition of porosity

💡 EXAM TIP

Always remember the relation $n = e / (1+e)$ . If you are given $e$ , you can quickly find $n$ without calculating volumes separately.

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