Problem Statement
Calculate the unit weights and specific gravities of solids for:
- (a) A soil composed of pure quartz
- (b) A soil composed of 60% quartz, 25% mica, and 15% iron oxide
Assume that both soils are saturated and have a voids ratio of 0.63. Take the average specific gravities as:
- Quartz: \( G = 2.66 \)
- Mica: \( G = 3.0 \)
- Iron Oxide: \( G = 3.8 \)
Solution
1. For Soil Composed of Pure Quartz
Specific gravity of quartz:
\( G = 2.66 \)
Saturated unit weight:
\( \gamma_{\text{sat}} = \frac{G + e}{1 + e} \cdot \gamma_w = \frac{2.66 + 0.63}{1 + 0.63} \cdot 9.81 = 19.8 \, \text{kN/m}^3 \)
2. For Soil Composed of Quartz, Mica, and Iron Oxide
Average specific gravity:
\( G_{\text{average}} = (2.66 \cdot 0.6) + (3.0 \cdot 0.25) + (3.8 \cdot 0.15) = 1.60 + 0.75 + 0.57 = 2.92 \)
Saturated unit weight:
\( \gamma_{\text{sat}} = \frac{G + e}{1 + e} \cdot \gamma_w = \frac{2.92 + 0.63}{1 + 0.63} \cdot 9.81 = 21.36 \, \text{kN/m}^3 \)
Results:
- Unit weight of pure quartz: \( 19.8 \, \text{kN/m}^3 \)
- Unit weight of composite soil: \( 21.36 \, \text{kN/m}^3 \)
- Specific gravity of composite soil: \( 2.92 \)
Explanation
- Saturated Unit Weight: This is calculated using the specific gravity of solids, voids ratio, and the unit weight of water.
- Composite Specific Gravity: Weighted averages are used to calculate the specific gravity of the composite soil based on its composition.
Physical Meaning
- Engineering Implications: The saturated unit weight is crucial in understanding the behavior of soils under load, particularly in saturated conditions.
- Practical Applications: Composite specific gravity is used in geotechnical calculations to evaluate the strength and stability of mixed soils.
