Embankment 1,00,000 m³ excavation

Given

Embankment: $V = 1{,}00{,}000$ m³, $\gamma_d = 16$ kN/m³. Excavation site: $\gamma = 12$ kN/m³, $w = 15\%$, $G = 2.70$.

Dry weight needed in the embankment

$$W_s = 16 \times 100\,000 = 1.6 \times 10^{6}\ \text{kN}$$

Dry unit weight at the excavation site

$$\gamma_d = \frac{\gamma}{1+w} = \frac{12}{1.15} = 10.435\ \text{kN/m}^3$$

Volume to be excavated

$$V_{exc} = \frac{W_s}{\gamma_d} = \frac{1.6 \times 10^6}{10.435} = 1.533 \times 10^{5}\ \text{m}^3$$

Weight of soil to be excavated (moist)

$$W = \gamma \times V_{exc} = 12 \times 153\,333 = 1.84 \times 10^{6}\ \text{kN}$$

(check: $W_s(1+w) = 1.6 \times 10^6 \times 1.15 = 1.84 \times 10^6$ kN)

The specific gravity is not needed for this answer; it would only be used to find void ratios.

Answer: volume $\approx 1{,}53{,}333$ m³; weight $\approx 1.84 \times 10^{6}$ kN (dry weight $1.6 \times 10^{6}$ kN).