Problem Statement
The in-situ percentage voids of a sand deposit is 34%. To determine the density index, dried sand from the stratum was first filled loosely in a 1000 cm3 mould and then vibrated to achieve maximum density. The loose dry mass in the mould was 1610 g, and the dense dry mass at maximum compaction was found to be 1980 g. Determine the density index if the specific gravity of the sand particles is 2.67.
Solution
1. Void Ratio
Void ratio:
\( e = \frac{n}{1 – n} = \frac{0.34}{1 – 0.34} = 0.515 \)
2. Dry Unit Weights
Maximum dry unit weight:
\( (\gamma_d)_{\text{max}} = \frac{1980}{1000} \cdot 9.81 = 19.42 \, \text{kN/m}^3 \)
Minimum dry unit weight:
\( (\gamma_d)_{\text{min}} = \frac{1610}{1000} \cdot 9.81 = 15.79 \, \text{kN/m}^3 \)
3. Maximum and Minimum Void Ratios
Maximum void ratio:
\( e_{\text{max}} = \frac{G \cdot \gamma_w}{(\gamma_d)_{\text{min}}} – 1 = \frac{2.67 \cdot 9.81}{15.79} – 1 = 0.659 \)
Minimum void ratio:
\( e_{\text{min}} = \frac{G \cdot \gamma_w}{(\gamma_d)_{\text{max}}} – 1 = \frac{2.67 \cdot 9.81}{19.42} – 1 = 0.349 \)
4. Density Index
Density index:
\( I_D = \frac{e_{\text{max}} – e}{e_{\text{max}} – e_{\text{min}}} = \frac{0.659 – 0.515}{0.659 – 0.349} = 0.465 = 46.5\% \)
Results:
- Void Ratio: 0.515
- Maximum Dry Unit Weight: 19.42 kN/m3
- Minimum Dry Unit Weight: 15.79 kN/m3
- Maximum Void Ratio: 0.659
- Minimum Void Ratio: 0.349
- Density Index: 46.5%
Explanation
- Void Ratio: The void ratio represents the ratio of the volume of voids to the volume of solids in the sand.
- Dry Unit Weights: These are calculated based on the mass of loose and dense sand in the mould and help to find the range of void ratios.
- Density Index: The density index indicates the relative compaction of the sand compared to its loosest and densest states, providing a measure of compaction efficiency.
Physical Meaning
- Engineering Applications: The density index is a critical parameter in geotechnical design, particularly for evaluating the stability and load-bearing capacity of sand deposits.
- Practical Significance: It helps in determining the compaction quality of sandy soils and in ensuring the safety and durability of structures built on sand foundations.
