Problem Statement (Civil Services Exam 1982)
The void ratio of borrow pit soil is 1.2. Determine:
- How many cubic meters of compacted fill can be placed in an embankment per 1000 m³ of borrow material.
- The percentage change in the degree of saturation if no water is added or lost during placement.
Solution
1. Volume of Compacted Fill
Given:
- Borrow pit void ratio, \( e_1 = 1.2 \)
- Embankment void ratio, \( e_2 = 0.7 \)
- Borrow material volume, \( V_1 = 1000 \, \text{m}^3 \)
Formula:
\( V_2 = V_1 \times \frac{1 + e_2}{1 + e_1} \)
Calculation:
\( V_2 = 1000 \times \frac{1 + 0.7}{1 + 1.2} = 1000 \times \frac{1.7}{2.2} \approx 772.73 \, \text{m}^3 \)
2. Percentage Change in Degree of Saturation
Relationship:
\( \frac{S_2}{S_1} = \frac{e_1}{e_2} \quad \text{(since \( w \) and \( G \) are constant)} \)
Calculation:
\( \% \text{ change} = \left( \frac{e_1}{e_2} – 1 \right) \times 100 = \left( \frac{1.2}{0.7} – 1 \right) \times 100 \approx 71.43\% \)
Results:
- Compacted fill volume: \( \approx 772.73 \, \text{m}^3 \)
- Degree of saturation increases by \( \approx 71.43\% \)
Explanation
Volume of Compacted Fill:
- The void ratio (\( e \)) is the ratio of the volume of voids to the volume of solids. During compaction, the void ratio decreases (\( e_2 < e_1 \)) as soil particles are packed more densely.
- The total volume of soil (\( V \)) is related to the void ratio by \( V = V_s(1 + e) \), where \( V_s \) is the constant volume of solids.
- Since \( V_s \) remains unchanged, the embankment volume \( V_2 \) is calculated using the ratio of void ratios.
Degree of Saturation:
- The degree of saturation (\( S \)) is the fraction of voids filled with water (\( S = \frac{V_w}{V_v} \)).
- With no change in water content (\( w \)) or specific gravity (\( G \)), the decrease in void ratio (\( e \)) increases \( S \), as the same water occupies a smaller void space.
Physical Meaning
1. Volume Reduction During Compaction:
- Compaction reduces air voids, decreasing the total volume of soil. This is critical for constructing stable embankments with minimal settlement.
- The borrow pit soil (loose) has higher voids, while the embankment (compacted) achieves higher density.
2. Saturation Increase:
- Even without adding water, the reduction in void space increases the degree of saturation. This affects soil permeability and strength.
- In practice, engineers monitor saturation to prevent liquefaction in saturated soils and ensure slope stability.
Exam Context (Civil Services 1982):
This problem tests understanding of soil mechanics fundamentals: void ratio, saturation, and their impact on geotechnical design. Such calculations are vital for infrastructure projects like dams, roads, and foundations.
