Sandy soil in a borrow pit has a unit weight of solids as 26.3 kN/m3, water content equal to 11%, and bulk unit weight equal to 16.4 kN/m3. How many cubic metres of compacted fill could be constructed of 3500 m3 of sand excavated from the borrow pit, if the required value of porosity in the compacted fill is 30%? Also, compute the change in degree of saturation.

Soil Mechanics Problems

Problem Statement

Sandy soil in a borrow pit has a unit weight of solids as 26.3 kN/m³, water content equal to 11%, and bulk unit weight equal to 16.4 kN/m³. How many cubic metres of compacted fill could be constructed of 3500 m³ of sand excavated from the borrow pit, if the required value of porosity in the compacted fill is 30%? Also, compute the change in degree of saturation.

Solution

1. Calculate Initial Void Ratio \( e_1 \)

Using the formula:

\( e_1 = \frac{G \cdot \gamma_w}{\gamma_1} – 1 \)

Substituting the values:

\( e_1 = \frac{26.3}{16.4} – 1 = 1.078 \)

2. Calculate Final Void Ratio \( e_2 \)

The final void ratio is related to the porosity \( n \):

\( e_2 = \frac{n}{1 – n} = \frac{0.3}{1 – 0.3} = 0.429 \)

3. Calculate Volume of Compacted Fill \( V_2 \)

The change in volume is calculated using the formula:

\( V_2 = V_1 \cdot \frac{1 + e_2}{1 + e_1} \)

Substituting the values:

\( V_2 = 3500 \cdot \frac{1 + 0.429}{1 + 1.078} = 3500 \cdot \frac{1.429}{2.078} = 2810 \, \text{m}^3 \)

4. Compute Initial Degree of Saturation \( S_1 \)

Using the formula:

\( S_1 = \frac{w \cdot G}{e_1} \)

Substituting the values:

\( S_1 = \frac{0.11 \cdot 26.3}{1.078 \cdot 9.81} = 0.378 \)

5. Compute Final Degree of Saturation \( S_2 \)

Using the same formula:

\( S_2 = \frac{w \cdot G}{e_2} \)

Substituting the values:

\( S_2 = \frac{0.11 \cdot 26.3}{0.429 \cdot 9.81} = 0.687 \)

Results:

Volume of compacted fill: \( V_2 = 2810 \, \text{m}^3 \)
Initial degree of saturation: \( S_1 = 0.378 \)
Final degree of saturation: \( S_2 = 0.687 \)

Explanation

This problem calculates the volume of compacted soil and the change in degree of saturation when sandy soil is excavated and compacted. The void ratio and degree of saturation are critical parameters in geotechnical engineering for assessing soil compaction and water retention characteristics.

Physical Meaning

The reduction in void ratio during compaction increases the degree of saturation, which reflects the soil’s ability to hold water. Understanding this relationship is essential for ensuring the stability and strength of compacted soil structures such as embankments, foundations, and roadbeds.

Problem Statement

Solution

1. Calculate Initial Void Ratio \( e_1 \)

2. Calculate Final Void Ratio \( e_2 \)

3. Calculate Volume of Compacted Fill \( V_2 \)

4. Compute Initial Degree of Saturation \( S_1 \)

5. Compute Final Degree of Saturation \( S_2 \)

Explanation

Physical Meaning

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