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An earth embankment is to be constructed with compacted cohesion less soil. The volume of the embankment is 5000 m3 and the target dry unit weight is 16.2 kN/m3. Three nearly sites (see figure below) have been identified from where the required soil can be transported to the constructed site. The void ratios(e) of different sites are shown in the figure. Assume the specific gravity of soil to be 2.7 for all three sites. If the cost of transportation per km is twice the cost of excavation per m3 of borrow pits, which site would you choose as the most economic solution ?( use unit weight of water = 10 kN/m3)
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- Site X
- Site Y
- Site Z
- Any of the sites
Correct Option: B
V α l + e
| ∴ | = | = | = | |||||
| 1 + e | 1 + ex | 1 + ey | 1 + ez |
| γd = | 1 + e |
| ⇒ 16.2 = | 1 + e |
⇒ 1 + e = 1.67
∴ e = 0.67
| ∴ | = | = | = | |||||
| 1 + .67 | 1 + .6 | 1 + .64 | 1 + .7 |
| ⇒ Vx = | = 4790.4 m3 | 1.67 |
| Vy = | = 4910.18 m3 | 1.67 |
| Vz = | = 5089.8 m3 | 1.67 |
Let cost of excavation per unit m3 be C.
∴ Cost of excavating and transporting from each site
Cx = C × 4790.42 + (2 × C × 140) = 5070.4 C
Cy = C × 4910.18 + (2 × C × 80) = 5070.1 C
Cz = C × 5089.82 + (2 × C × 100) = 5289.8 C
