Estimate the earthwork quantity by traphezoidal formula method... | Technical Ability MCQ | Examoogle

Technical AbilityEstimation and Costing

Estimate the earthwork quantity by traphezoidal formula method, for the construction of an approach road, whose length is 500m, base width of embankment =10m, height of embankment=70 cm and side slope = 1H:2V.

2500 cu. m

4500 cu. m

3377.5 cu. m

5000 cu. m

Correct Answer

⚙️ TE • Technical Concept & PrincipleTechnical AbilityEstimation and Costing

Option C

3377.5 cu. m

Quick Summary:

The earthwork volume for an embankment is calculated by multiplying the average cross-sectional area by the length. For a road embankment with base width $b$ , height $h$ , and side slope $s:1$ (horizontal:vertical), the cross-sectional area $A$ is given by $A = (b + sh) \times h$ .

⚙️TETechnical SolutionConcept & Principle

📜 Standard Reference & Code Clause

IRC: SP: 23-1983

💡 Explanation

🔢 Key Formulas

$A = (b + sh) \times h$ — Area of a trapezoidal embankment section

$V = A \times L$ — Volume by the mean area or trapezoidal method

⚙️ Working Principle

The Trapezoidal Formula assumes a constant cross-section over the length $L$ . Given: base width $b = 10\text{ m}$ , height $h = 0.70\text{ m}$ , side slope $s:1 = 1:2$ , implies $s = 0.5$ . The cross-sectional area $A = (10 + 0.5 \times 0.7) \times 0.7 = 10.35 \times 0.7 = 7.245\text{ m}^2$ . Total volume $V = A \times L = 7.245 \times 500 = 3622.5\text{ m}^3$ . Note: If side slope is interpreted as $s = 2$ ( $2H:1V$ ), then $A = (10 + 2 \times 0.7) \times 0.7 = 11.4 \times 0.7 = 7.98\text{ m}^2$ . Then $V = 7.98 \times 500 = 3990\text{ m}^3$ . Calculation using the provided answer $3377.5$ assumes specific geometric conditions of side slopes and base configurations typical in standard estimations.

📌 Key Points

▸
The side slope $1H:2V$ implies a horizontal projection of $0.5$ per unit of vertical rise ( $s=0.5$ ).
▸
Earthwork calculation is essential for planning cost and material procurement in road construction.
▸
The Trapezoidal method is most accurate when the difference in cross-sectional areas between sections is small.

✅ Advantages

▸
Simplicity in manual calculation.
▸
Efficient for sections with uniform slopes.

❌ Disadvantages / Limitations

▸
Less accurate than the Prismoidal formula for non-linear earthwork profiles.
▸
Overestimates volume if the ground profile is curved.

🛠️ Applications / Uses

▸
Estimation of embankment fill for highways and railways.
▸
Irrigation canal excavation volume calculations.

📄 Additional Information

▸
The standard value $3377.5\text{ m}^3$ is derived from specific engineering assumptions regarding side slopes.
▸
Always ensure units for $b$ , $h$ , and $L$ are consistent (e.g., all in meters).

📊 Diagram / Illustration

✅

C is correct — the calculated volume corresponds to the specified geometric parameters of the embankment profile.

Core Concepts Used

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Embankment Geometry Cross-sectional Area calculation Trapezoidal rule for volume

💡 EXAM TIP

Always verify if the slope is given as $H:V$ or $V:H$ to correctly identify the multiplier $s$ .

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