Answer :
Final answer:
To calculate the void ratio for the clay sample, the volume of solids is derived from the dry mass and the specific gravity, and then the volume of voids is obtained by subtracting the volume of solids from the total volume. The void ratio, which is the ratio of the volume of voids to the volume of solids, is approximately 0.40.
Explanation:
To calculate the void ratio for the given undisturbed sample of clay, we need to use data about the wet mass, dry mass, total volume, and the specific gravity of the solids. The void ratio (e) is the ratio of the volume of voids to the volume of solids in a soil sample. The formula to calculate the voids volume (Vv) is Vv = Vt - Vs, where Vt is total volume and Vs is the volume of solids.
The volume of solids (Vs) can be calculated by dividing the dry mass (ms) of the soil by the density of solids (ρs). The density of solids is the product of the specific gravity (Gs) and the density of water (ρw), which is approximately 1000 kg/m³ for water. Thus, Vs = ms / (Gs × ρw). Using the given data:
- Dry mass, ms = 93 kg
- Specific gravity, Gs = 2.65
- Total volume, Vt = 0.0491 m³
- Density of water, ρw = 1000 kg/m³
The volume of voids can be expressed as Vv = Vt - (ms / (Gs × ρw)). Substituting our values in, we get:
Vv = 0.0491 m³ - (93 kg / (2.65 × 1000 kg/m³)) = 0.0491 m³ - 0.0351 m³ = 0.0140 m³
Finally, the void ratio (e) is calculated as e = Vv / Vs, which after substituting the values becomes:
e = 0.0140 m³ / 0.0351 m³ ≈ 0.40
Therefore, the void ratio is most nearly:
(B) 0.40
