1. **Problem Statement:** Calculate the initial void ratio $e_0$ of a soil sample given the specific gravity $G_s = 2.67$, unit weight of water $\gamma_w = 1$, and dry unit weight $\gamma_d = 1.65$. 2. **Formula Used:** The initial void ratio is calculated by the formula: $$ e_0 = \frac{G_s \times \gamma_w}{\gamma_d} - 1 $$ This formula relates the specific gravity, unit weight of water, and dry unit weight to find the void ratio. 3. **Substitute the values:** $$ e_0 = \frac{2.67 \times 1}{1.65} - 1 $$ 4. **Calculate the fraction:** $$ e_0 = 1.618 - 1 $$ 5. **Final calculation:** $$ e_0 = 0.618 $$ 6. **Interpretation:** The initial void ratio of the soil is 0.618, which means the volume of voids is 61.8% of the volume of solids in the soil sample.