An embankment, having a total volume of 5000 m3, has a water content of 16% and a dry density of 1.75 g/cm3. If it was constructed from a borrow pit where the undisturbed soil has a water content of 13% and a voids ratio of 0.6, calculate the quantity of soil which was excavated for the construction of the above embankment. Take the specific gravity of soil solids as 2.68.

Soil Mechanics Problems

Problem Statement

An embankment, having a total volume of 5000 m³, has a water content of 16% and a dry density of 1.75 g/cm³. If it was constructed from a borrow pit where the undisturbed soil has a water content of 13% and a voids ratio of 0.6, calculate the quantity of soil which was excavated for the construction of the above embankment. Take the specific gravity of soil solids as 2.68.

Solution

1. Total Volume of the Embankment

The total volume of the embankment is:

\( V = 5000 \, \text{m}^3 \)

2. Calculate the Dry Mass of Soil

The dry density of the embankment is given as \( \rho_d = 1.75 \, \text{g/cm}^3 = 1.75 \, \text{t/m}^3 \). The total dry mass of soil is:

\( M_d = \rho_d \cdot V = 1.75 \cdot 5000 = 8750 \, \text{t} \)

3. Dry Density of the Borrow Pit Soil

For the soil in the borrow pit, the dry density \( \rho_d \) is calculated using the specific gravity \( G \) and voids ratio \( e \):

\( \rho_d = \frac{G \cdot \gamma_w}{1 + e} = \frac{2.68 \cdot 1}{1 + 0.6} = \frac{2.68}{1.6} = 1.675 \, \text{t/m}^3 \)

4. Volume of Soil Excavated

The volume of soil excavated from the borrow pit is:

\( V_b = \frac{M_d}{\rho_d} = \frac{8750}{1.675} = 5223.8 \, \text{m}^3 \)

Result:

Volume of soil excavated: \( V_b = 5223.8 \, \text{m}^3 \)

Explanation

This problem demonstrates the relationship between soil properties in a borrow pit and the embankment it is used to construct. The calculations involve determining the mass and volume of soil required, considering different dry densities and water contents in the borrow pit and the embankment.

The dry density of the borrow pit soil is lower than that of the embankment soil due to its higher voids ratio. This necessitates a larger volume of borrow pit soil to achieve the required embankment volume.

Physical Meaning

The volume of soil excavated from the borrow pit is larger than the volume of the embankment due to differences in soil properties such as voids ratio and dry density. This concept is essential in earthwork calculations for projects like dams, road embankments, and landfills, where soil properties change between excavation and placement.