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CivilSoil Mechanics

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The relation between the air content and degree of saturation is

$a_c = 1 + S_r$

$a_c = 1 - S_r$

$a_c = 1 / S_r$

none of these

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilSoil Mechanics

Option B

$a_c = 1 - S_r$

Quick Summary:

In soil mechanics, the total volume of voids ( $V_v$ ) in a soil mass is composed of the volume of water ( $V_w$ ) and the volume of air ( $V_a$ ). Since the sum of the degree of saturation ( $S_r$ ) and air content ( $a_c$ ) represents the total volume of voids relative to the volume of voids itself, their sum must equal unity (100%).

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$S_r = \frac{V_w}{V_v}$ — Degree of saturation

$a_c = \frac{V_a}{V_v}$ — Air content

$S_r + a_c = 1$ — Fundamental soil phase relation

⚙️ Working Principle

The degree of saturation ( $S_r$ ) is defined as the ratio of the volume of water to the volume of voids ( $S_r = V_w/V_v$ ). The air content ( $a_c$ ) is defined as the ratio of the volume of air to the volume of voids ( $a_c = V_a/V_v$ ). Given that $V_v = V_w + V_a$ , dividing by $V_v$ yields $\frac{V_w}{V_v} + \frac{V_a}{V_v} = \frac{V_v}{V_v}$ , which simplifies to $S_r + a_c = 1$ .

📌 Key Points

▸
Air content ( $a_c$ ) is the ratio of volume of air to volume of voids.
▸
Degree of saturation ( $S_r$ ) is the ratio of volume of water to volume of voids.
▸
The sum of air content and degree of saturation always equals 1.
▸
Air content is not to be confused with 'percentage air voids' ( $n_a$ ), which relates $V_a$ to the total volume of soil $V$ .

✅ Advantages

▸
Simplifies phase volume calculations
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Provides a quick check for soil saturation states

🛠️ Applications / Uses

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Compaction control of earth embankments
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Determining air-void ratios in unsaturated soils

📄 Additional Information

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For fully saturated soil, $S_r = 1$ , thus $a_c = 0$ .
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For completely dry soil, $S_r = 0$ , thus $a_c = 1$ .
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Option A is incorrect as it implies air content increases with saturation.

📊 Diagram / Illustration

✅

B is correct — The air content is defined as the fraction of void space occupied by air, and since the remaining void space is occupied by water, $a_c = 1 - S_r$ .

Core Concepts Used

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Soil Phase Diagram Void Ratio Degree of Saturation

💡 EXAM TIP

Remember that $a_c$ is defined relative to volume of voids, whereas percentage air voids ( $n_a$ ) is defined relative to the total soil volume; always check the denominator in your definitions.

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