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CivilSoil Mechanics

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The unit weight of soil mass is expressed in

$kg/m^2$

$kg/m^3$

$N/m^2$

$N/m^3$

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilSoil Mechanics

Option D

$N/m^3$

Quick Summary:

The unit weight of soil, often denoted by $\gamma$ , is defined as the weight of a soil mass per unit volume. In the SI system of units, weight is measured in Newtons (N) and volume is measured in cubic meters ( $m^3$ ), leading to the standard unit of $N/m^3$ .

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\gamma = \frac{W}{V}$ — Definition of unit weight

$\gamma = \rho \cdot g$ — Relation to mass density and gravity

⚙️ Working Principle

The unit weight of soil is the product of its bulk density ( $\rho$ ) and the acceleration due to gravity ( $g$ ). Since density is defined as mass per unit volume ( $kg/m^3$ ), multiplying by $g$ ( $m/s^2$ ) yields $kg \cdot m / (s^2 \cdot m^3)$ , which simplifies to $N/m^3$ based on Newton's Second Law ( $F = ma$ ).

📌 Key Points

▸
Unit weight is a vector quantity representing the force of gravity per unit volume.
▸
In geotechnical engineering, $\gamma_{sat}$ (saturated), $\gamma_{sub}$ (submerged), and $\gamma_d$ (dry) are common variants.
▸
The range for most common soils typically falls between $16 kN/m^3$ and $22 kN/m^3$ .

✅ Advantages

▸
Essential for calculating overburden pressure in soil strata.
▸
Critical parameter for determining slope stability and earth pressure.

❌ Disadvantages / Limitations

▸
Varies significantly with moisture content and void ratio.
▸
Requires careful sampling to avoid disturbance which affects density measurements.

🛠️ Applications / Uses

▸
Foundation design and settlement analysis.
▸
Slope stability assessment and earth retaining structure design.

📄 Additional Information

▸
Option B (kg/ $m^3)$ represents 'Density', which is mass per unit volume, not weight.
▸
Option A and C are incorrect as they represent pressure/stress (Force per unit area) or area-based weight, which are physically inconsistent with volumetric soil weight.

📊 Diagram / Illustration

✅

D is correct — The unit weight is expressed as weight per unit volume, which is $N/m^3$ in the SI system.

Core Concepts Used

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Phase relationships in soil Gravitational force Volumetric weight density

💡 EXAM TIP

Always distinguish between density ( $kg/m^3$ ) and unit weight ( $N/m^3$ ); examiners frequently swap these to test fundamental understanding.

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