Skip to main content

Embankment volume from void ratios

Short answer

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

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.

Principle

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

Given

Borrow pit: V1=1,00,000V_1 = 1{,}00{,}000 m³, e1=0.8e_1 = 0.8. Embankment: e2=0.6e_2 = 0.6.

Solution

V=Vs(1+e)⇒Vs=V11+e1=1000001.8=55 555.6 m3V = 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:

V2=Vs(1+e2)=55 555.6×1.6=88 888.9 m3V_2 = V_s(1+e_2) = 55\,555.6 \times 1.6 = 88\,888.9\ \text{m}^3

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

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Soil Mechanics chapter 2 questions →