---
title: "Embankment volume from void ratios"
subject: "Soil Mechanics"
chapter: 2
key: "semester_4/soil_mechanics:embankment-void-ratio-volume"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/embankment-void-ratio-volume
site: BCT Engineering
---

# Embankment volume from void ratios

Soil Mechanics · Chapter 2: Solids- Water –Air Relations and Index properties of soils

- Asked in: 2075 Baisakh, 3 marks
- Video: [The soil fill for a road embankment is to be compacted in place to a void ratio of 0.7. If the void](https://www.youtube.com/watch?v=GC0HXEdTLG8) — Unique Series - Civil Mantraa
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/embankment-void-ratio-volume
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-2

## Question

An embankment is made by compacting the soil. For compaction, 1,00,000 m³ of the soil is excavated from a borrow pit having void ratio equal to 0.8. Calculate the volume of the embankment if its void ratio after compaction is 0.6.

## Short answer

Equating solid volume, embankment volume = 88,889 m³.

## Answer

#### Principle
Compaction does not change the volume of solids. Only the void volume is reduced.

#### Given
Borrow pit: $V_1 = 1{,}00{,}000$ m³, $e_1 = 0.8$. Embankment: $e_2 = 0.6$.

#### Solution
$$
V = V_s(1+e) \Rightarrow V_s = \frac{V_1}{1+e_1} = \frac{100000}{1.8} = 55\,555.6\ \text{m}^3
$$
Volume of the compacted embankment:
$$
V_2 = V_s(1+e_2) = 55\,555.6 \times 1.6 = 88\,888.9\ \text{m}^3
$$

**Answer: volume of embankment $\approx 88\,889$ m³** (about 11,111 m³ less than excavated).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. During compaction of the borrow soil into an embankment, which quantity stays constant?
   A. Volume of solids
   B. Total volume
   C. Void ratio
   D. Volume of voids
   Answer: A. Compaction only squeezes out voids; the solids volume does not change. (Key point: Constant quantity in compaction)

2. With V = 1,00,000 m3 and e1 = 0.8, what is Vs?
   A. 80,000 m3
   B. 1,00,000 m3
   C. 55,556 m3
   D. 1,80,000 m3
   Answer: C. Vs = V/(1+e1) = 100000/1.8 = 55,556 m3. (Key point: Volume of solids)

3. What is the compacted embankment volume at e2 = 0.6?
   A. 60,000 m3
   B. 88,889 m3
   C. 1,00,000 m3
   D. 1,11,111 m3
   Answer: B. V2 = Vs(1+e2) = 55,556 x 1.6 = 88,889 m3. (Key point: Embankment volume)

## Related in Soil Mechanics

- [Embankment 1,00,000 m³ excavation](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aembankment-volume-weight-excavated) — Soil Mechanics, chapter 2
- [Borrow pit to embankment, water added](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aborrow-pit-embankment-water-added) — Soil Mechanics, chapter 2
- [Embankment 95% compaction, 950 cc mould](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aembankment-95-compaction-950cc-mould) — Soil Mechanics, chapter 5
- [Road base void ratio specification](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aroad-base-void-ratio-check) — Soil Mechanics, chapter 2
- [Phase diagrams before and after compaction](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aphase-diagram-compaction-consolidation) — Soil Mechanics, chapter 2
- [Phase diagram; void ratio, saturation](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aphase-diagram-void-ratio-saturation) — Soil Mechanics, chapter 2

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